Micromax Mobile How to Increase Market Share Free Essays

Buyer purchasing conduct report Micromax cell phones By Mansi Choksey Roll no. 19 PGDM Marketing Product picked: Micromax Mobile telephones Issue to be tended to: How to expand Market share: Background on the organization: Micromax Mobile needs no presentation today. Only two years back individuals didn't know ofâ the brandâ at everything except today it’s India’s third biggest versatile selling organization by volume after Nokia and Samsung (IDC Report). We will compose a custom article test on Micromax Mobile : How to Increase Market Share or on the other hand any comparative subject just for you Request Now Brand’s achievement can be credited to it’s capacity to comprehend the need of the market ,forceful advertising with a spending plan of Rs. 00 crore and smartâ distribution channelâ management. Its one of the main Indian Telecom Companies with 23 household workplaces the nation over and global workplaces in Hong Kong, USA, Dubai and now in Nepal. With a cutting edge vision and a comprehensive Ramp;D at its rudder, Micromax has effectively created imaginative advances that have changed the telecom consumerspace. According to IDC report Micromax uprooted LG to turn out to be third biggest sellingâ mobile handset companyâ in india with a piece of the overall industry of 6%. Nokia is showcase pioneer with 62% offer and Samsung is on second spot with 8% piece of the overall industry. The organization today sells in excess of a million handsets every month and is currently a Rs. 1600 cr worth brand. The organization has nearness in excess of 500 areas and 90,000â retail outlets. The organization began its Mobile handset business in 2008 and the test was to set up a personality in a market ruled by large MNCs Like Nokia,Samsung,LG and Motorola. Today Micromax has become a brand which individuals relate and turn upward to for understanding their individual gadget inclinations and other out-of-the-crate arrangements. Micromax, is presently producing 1 million telephones per month. Micromax is determined to effectively beat the innovative hindrances and continually cause â€Å"life upgrading solutions†. The company’s vision is to create way breaking advances and productive procedures that brood more current markets, breath life into client yearnings and keep on making Micromax a confided in advertise pioneer among individuals. Micromax originators : Rajesh Agarwal: handles organization funds Sumeet Arora: boss innovation official Vikas jain: handles coalitions with different organizations Rahul Sharma: daring person with the huge thoughts 4 P’s of promoting for Micromax mobiles: 1. Item Micromax has been very powerful in the denoting a distinction with pretty much every item that it propelled. The range that they have secured shifts a serious huge assortment. Directly from the handsets with 30 days battery reinforcement, double SIM, handsets exchanging systems (GSM - CDMA) utilizing gravity sensors, optimistic QWERTY keypad handsets to administrator marked 3G handsets to the most energizing OMH CDMA Handsets, and so on. Each result of Micromax could catch the eye of media as ell as the buyers in a market which is as of now overflowed with cell phone handsets and a dispatch is there in consistently or two. 2. Value Micromax had practical experience in passage level and mid-portion handsets evaluated somewhere in the range of Rs1,800 and Rs2,400 when it began selling the gadgets in 2008, limiting itself to humble communities and provincial territories in the init ial 12-year and a half. Empowered by its prosperity, the firm extended to bigger urban communities and now has an appropriation system of 55,000 retailers, which it intends to scale up to 70,000 before the finish of March as a feature of its technique to raise deals to 1. million handsets per month. 3. Spot Micromax is one of the main Indian Telecom Companies with 23 local workplaces the nation over and global workplaces in Hong Kong, USA, Dubai and now in Nepal. Micromax has contributed Rs100 crore to set up a plant in Baddi in Himachal Pradesh as it feels redistributing fabricating totally welcomes gracefully side vulnerabilities. Creation will be scaled up from an underlying 50,000 every month. â€Å"If everything goes right, by the third stage in March 2011, the Baddi plant will make around 500,000 handsets,† Jain said. On the off chance that the plant isn’t ready to adapt to the numbers, the fallback plan is to get an office in South Korea, Taiwan or China, he included. 4. Advancement Having picked up footing, Micromax is likewise chipping away at a procedure to make mindfulness in the metros, which incorporates tying up with MTV for co-marked telephones. Micromax has additionally tied up with a Bollywood superstar â€Å"AKSHAY KUMAR† as brand minister. Micromax has likewise tied up some quite large brands like Yamaha for upgrading their sound encounters and the X360 accompanies a MTV marking and selective substance. It is using the incorporated market specialized devices like supporting occasions (cricket match and film grants), promoting through hoardings, TV, radio and so on successfully. With a 360 degree promoting and advertising system outlined out, the organization has a hopeful viewpoint for the telecom purchaser space. Right now present in excess of 40,000 stores the nation over, the organization intends to have a forceful market invasion to connect with its clients through 70,000 operational stores in the coming year The accompanying instruments of IMC are being utilized by Micromax: Occasions and encounters For promoting of its items the organization is riding on two suffering Indian obsessionsâ€sports and filmsâ€to construct its image. Lining up on its relationship with the well known Twenty20 cricket Indian Premier League (IPL), Micromax, a brand that is under three years of age, has become the title supporter of practically all competitions and arrangement of which India is a section, including the as of late finished up Asia Cup, the expected India-Sri Lanka Test arrangement and the India-New Zealand-Sri Lanka tri-arrangement in August. The target behind the cricket â€Å"roadblock†, as such conduct is named in promoting, is to drive brand mindfulness and review. The organization accepts that while cricket may support a brand quickly, watchers may at present not recollect the brand after the match or the competition. Regardless of whether customers recollect an arrangement, they may not recall the sponsors. That’s when they thought of a barrier and chose to support all cricketing properties post IPL. Bollywood is likewise a significant stage for the brand, which is focusing on buyers somewhere in the range of 18 and 27 years. Bollywood’s most bankable star Akshay Kumar was marked on as the brand represetative a half year prior. All the more as of late, his significant other Twinkle Khanna was locked in to advance Micromax’s bling telephone that accompanies Swarovski gems and a vanity reflect. To push its relationship with films, the firm likewise supported the IIFA (International Indian Film Academy) Awards held in Sri Lanka, where Micromax as of late propelled its telephones. The brand is currently prepared to enter Bangladesh and West Asia. Publicizing Broadcast media micromax use TV to communicate their commercials. Aside from utilizing cricket, films, superstar micromax likewise promote through news papers. They likewise use accumulating and boards to publicize their items. Prime site as of late commenced a month-long crusade for Micromax cell phones in Delhi, executed for the most part through hoardings. Going further, this advancement will be stretched out to different locales of northern India too. All the Medias utilized by micromax are deliberately chosen as to arrive at its intended interest group and through every medium the creative part of the item is depicted. The three promoting targets of micromax versatile are * To make mindfulness * To build review of their image * To make brand value. Company’s current advertising methodology: 1. Tapping the Indian shoppers by recognizing what they need explicitly: a. Indian setting: When Nokia or Samsung reveal another model they do as such from its worldwide portfolio as opposed to propelling something explicitly for India. Micromax understood the way that there are sure neglected needs still there in the market which isn't being tended to by large brands. Micromax’s methodology ,since their origin has been to distinguish the neglected idle needs of individuals and think of an item which nobody else has and in this way fits well with the shopper need. b. Rustic setting: Micromax at first focused on country advertise and once it built up its essence proceeded to draw urban youth. Micromax’s first advancement †a handset with 30 days of reserve battery life †essential in a nation like India where power disappointments are normal. Additionally in provincial regions it is difficult to charge one’s cell phones in light of the fact that not exclusively are there influence disappointments yet in addition they don’t have cash to pay for power each month and henceforth such a telephone was presented. Likewise One of the significant angles that contribute towards the considerable month to month development of Micromax is its 80% deals in the rustic zones. In the wake of building a solid nearness in the country advertise, where the noticeable quality of the two endorsers and administrators is quickly expanding, Micromax is currently dynamically moving towards setting up its a dependable balance in the serious urban towns also. 2. Incentive for cash amp; Cost viable: The organization didn’t bank on value rivalry just rather it obliged the requirements of individuals unaddressed by MNC brands. Huge brand like Nokia, Samsung had not presented Dual sim telephones before. Be that as it may, with the beginning of such telephones propelled by Micromax, Nokia , Samsung and so on ave intense rivalry and their telephones are only an instance of â€Å"me-too† items. Likewise Micromax has ensured that all their cell phones are an incentive for cash and fill the need and the need of the client. 3. Ramp;D and Innovation : Versatile Product Portfolio: It was the first to present: a) Handsets with 30 days battery reinforcement b) Handset s with Dual SIM/Dual Standby c) Handsets Switching Networks (GSM †CDMA) utilizing gravity sensors d) A

Comparing Edna Pontellier and Adele in Kate Chopins The Awakening :: comparison compare contrast essays

Looking at Enda and Adele in The Awakening   In The Awakening by Kate Chopin, the setting is in the late 1800s on Grand Isle in Louisiana. The principle character of the story is Edna Pontellier who is anything but a Creole. Other significant characters are Adele Ratignolle, Mr. Ratgnolle, Robert Lebrun, and Leonce Pontellier who are all Creole's. In the Creole society the men are predominant. Only here and there do the Creole's acknowledge outcasts to their group of friends, and ladies are required to give all around kept homes and have numerous youngsters. Edna and Adele are companions who are altogether different due to their the manner in which they were raised and they way they treat their spouses. Adele is an unwavering spouse who consistently complies with her significant other's orders. Edna is a lady who strays from her significant other and doesn't comply with her better half's orders. Kate Chopin utilizes Adele to underline the contrasts among her and Edna.   Edna Pontellier is anything but a Creole, so her relationship with her better half is troublesome. In her significant other's eyes she has flopped in her obligations as a spouse and as a mother to her own youngsters. What Enda's significant other anticipates from her is never what she does. Leonce gets back home in the night and converses with Edna while she is resting. At that point he reveals to her that Raoul one of their children is wiped out and advises her to get up and mind him. Edna had never truly wanted to have youngsters yet she did at any rate. She was not a mother-lady since she would prefer to be distant from everyone else now and then; she didn't feel she must be with her youngsters twenty-four hours per day. On the off chance that one Edna's young men ....took a tumble while at play, he would not well-suited surge crying to his mom's arms for comfort; he would almost certain pick himself up(16). Enda never felt that she fit in with Creole society since she ...most coe rcively was their whole nonattendance of prudery(19). The Creoles' would discuss things, for example, labor and would play with others and not mean anything. However Edna could never fantasy about discussing her labor's with anybody or being a tease except if she would not joke about this. Creole ladies dedicated their entire lives to their spouses where Enda was joyful and did however she wanted. She was joyful on the grounds that she would go out onto the sea shore with just a sundress and a little cap on when she was assume to be completely concealed so she would not become sun consumed.

How to Cite a NASA Webpage

How to Cite a NASA Webpage (1) To infinity and beyond! Outer space has captivated our collective attention for years, and there’s no better place for aspiring astronauts to visit than the National Aeronautics and Space Administration (NASA) website. NASA.gov is filled with fascinating facts about our solar system and space exploration. It’s the perfect place to visit for any space-related assignment, whether you’re in elementary school or college. But how does one go about citing information found on a NASA webpage? helps you cite in the most common styles and thousands of others, too, for websites and just about any source type you can think of. There are also free guides for doing MLA in-text citations and an MLA annotated bibliography, too. If you’ve cited a website before, you’ll be happy to know that the process for citing information from NASA is pretty much the same. Even if you’ve never cited a website, it shouldn’t be too trickyâ€"especially with our handy-dandy guide in tow! Below, learn how to cite a NASA webpage in three commonly used citation styles in MLA, APA and Chicago style. We’ll be using this page in the examples. When you’re citing a website, there’s information that you’ll need to gather before you can begin. That information would be: Name of the author or authors Title of the website article Date published and/or modified URL Cite a NASA webpage in MLA format For MLA style citations, the basic format will look like this: Author Last Name, First Initial. “Title of the Article.” Title of the Website, date published, URL.   For the article “Martian Dust Could Help Explain Water Loss, Plus Other Learnings From Global Storm” from NASA’s website, the basic citation would look like this: Shekhtman, L. “Martian Dust Could Help Explain Water Loss, Plus Other Learnings From Global Storm.” NASA, 2 May 2019, www.nasa.gov/feature/goddard/2019/martian-dust-could-help-explain-planet-s-water-loss-plus-other-learnings-from-recent-global.   Cite a NASA webpage in APA format If you’re working in APA style, you’ll take that basic information and the citation will look something like this: Author Last Name, First Initial. (Date). Title of the webpage. Retrieved from //URL.   So for that article on the NASA website, the citation would look like this: Shekhtman, L. (2019, May 2). Martian dust could help explain water loss, plus other learnings from global storm. Retrieved from //www.nasa.gov/feature/goddard/2019/martian-dust-could-help-explain-planet-s-water-loss-plus-other-learnings-from-recent-global Cite a NASA webpage in MLA format For a Chicago style citation, keep the general basic format: Author Last Name, Author First Name. “Title of the Article.” Title of Website, Date Modified. URL. With that NASA article, it would look like this: Shekhtman, Lonnie. “Martian Dust Could Help Explain Water Loss, Plus Other Learnings From Global Storm.” NASA, May 2, 2019. //www.nasa.gov/feature/goddard/2019/martian-dust-could-help-explain-planet-s-water-loss-plus-other-learnings-from-recent-global Before you turn in your next paper, visit EasyBib for a free grammar check. Stuck for a paper idea? Check the EasyBib topic guides and get inspired by interesting history facts!

How to Cite a NASA Webpage

How to Cite a NASA Webpage (1) To infinity and beyond! Outer space has captivated our collective attention for years, and there’s no better place for aspiring astronauts to visit than the National Aeronautics and Space Administration (NASA) website. NASA.gov is filled with fascinating facts about our solar system and space exploration. It’s the perfect place to visit for any space-related assignment, whether you’re in elementary school or college. But how does one go about citing information found on a NASA webpage? helps you cite in the most common styles and thousands of others, too, for websites and just about any source type you can think of. There are also free guides for doing MLA in-text citations and an MLA annotated bibliography, too. If you’ve cited a website before, you’ll be happy to know that the process for citing information from NASA is pretty much the same. Even if you’ve never cited a website, it shouldn’t be too trickyâ€"especially with our handy-dandy guide in tow! Below, learn how to cite a NASA webpage in three commonly used citation styles in MLA, APA and Chicago style. We’ll be using this page in the examples. When you’re citing a website, there’s information that you’ll need to gather before you can begin. That information would be: Name of the author or authors Title of the website article Date published and/or modified URL Cite a NASA webpage in MLA format For MLA style citations, the basic format will look like this: Author Last Name, First Initial. “Title of the Article.” Title of the Website, date published, URL.   For the article “Martian Dust Could Help Explain Water Loss, Plus Other Learnings From Global Storm” from NASA’s website, the basic citation would look like this: Shekhtman, L. “Martian Dust Could Help Explain Water Loss, Plus Other Learnings From Global Storm.” NASA, 2 May 2019, www.nasa.gov/feature/goddard/2019/martian-dust-could-help-explain-planet-s-water-loss-plus-other-learnings-from-recent-global.   Cite a NASA webpage in APA format If you’re working in APA style, you’ll take that basic information and the citation will look something like this: Author Last Name, First Initial. (Date). Title of the webpage. Retrieved from //URL.   So for that article on the NASA website, the citation would look like this: Shekhtman, L. (2019, May 2). Martian dust could help explain water loss, plus other learnings from global storm. Retrieved from //www.nasa.gov/feature/goddard/2019/martian-dust-could-help-explain-planet-s-water-loss-plus-other-learnings-from-recent-global Cite a NASA webpage in MLA format For a Chicago style citation, keep the general basic format: Author Last Name, Author First Name. “Title of the Article.” Title of Website, Date Modified. URL. With that NASA article, it would look like this: Shekhtman, Lonnie. “Martian Dust Could Help Explain Water Loss, Plus Other Learnings From Global Storm.” NASA, May 2, 2019. //www.nasa.gov/feature/goddard/2019/martian-dust-could-help-explain-planet-s-water-loss-plus-other-learnings-from-recent-global Before you turn in your next paper, visit EasyBib for a free grammar check. Stuck for a paper idea? Check the EasyBib topic guides and get inspired by interesting history facts!

Memory in Virginia Woolfs Mrs. Dalloway Essay examples

Memory in Virginia Woolfs Mrs. Dalloway Clarissa Dalloway and Peter Walsh are defined by their memories. Virginia Woolf creates their characters through the memories they share, and indeed fabricates their very identities from these mutual experiences. Mrs. Dalloway creates a unique tapestry of time and memory, interweaving past and present, memory and dream. The past is the key to the future, and indeed for these two characters the past creates the future, shaping them into the people they are on the June day described by Woolf. Peter and Clarissa’s memories of the days spent at Bourton have a profound effect on them both and are still very much a part of them. These images of their younger selves are not broad, all-encompassing†¦show more content†¦However, she does not let them overwhelm her with yearnings for the past. She remembers the good times nostalgically and the hard times without bitterness. There is no doubt that the emotional responses invoked by the squeaking of hinges and the flipping of a p ocket-knife are seeded deep inside Clarissa’s being, attached to the very core of her self. â€Å"One must seek out the people who completed them; even the places,† and it was with Sally and Peter at Bourton that Clarissa took shape, forming the seed of the woman she becomes by her fifties. It was at Bourton that Clarissa first tasted love and it left its mark on her in the form of memories. Clarissa’s memories of Peter aren’t of moonlight walks or love letters; rather they are the more personal observations, personality traits that were impressed upon her memory: â€Å"his eyes, his pocket-knife, his smile, his grumpiness and, when millions of things had utterly vanished– how strange it was!– a few sayings . . . about cabbages† (4). Peter Walsh is Clarissa’s complement rather than her opposite; they fill the emptiness within each other and even after years of separation they are still very much a part of one another, creating the foundation for the other’s life, for the memories and the laughs and the tears tha t are the substance of self and the threads of identity.Show MoreRelatedParallels Between Mrs Dalloway and The Hours1059 Words   |  5 PagesThe ongoing relationship between the literary movements of modernism and post-modernism is encompassed by the intertextual relationships between Stephen Daldry’s â€Å"The Hours† and Virginia Woolf’s â€Å"Mrs Dalloway†. These relationships communicate the inadequacy of previous writings to convey trauma, cultural crisis and the deep fragmentation within their respective societies. The immediate context of these social dialogues creates a clear division between each text, however the intertextual similaritiesRead MoreAnalysis Of Virginia Woolf s Gone At The Lighthouse Never Go Return 1706 Words   |  7 PagesElizabeth Conner 9 November 2017 ENGL-4010-001 Professor Westover Virginia Woolf: Gone to the Lighthouse, Never to Return Many authors inject a little bit of their personalities and lives into their writing, making it more relatable to their readers and more marketable to publishers. However, depending on the work, it can sometimes be difficult to determine what is inspired by real life and what is merely fiction. Therefore how important an author’s biography is to a story can also be hard to understandRead MoreAnalysis of Mrs. Dalloway by Ââ€" Virginia Woolf Essay1460 Words   |  6 PagesAnalysis of Mrs. Dalloway by Ââ€" Virginia Woolf Mrs. Dalloway, published in 1925, is a romantic drama with deep psychological approaching in to the world of urban English society in the summer of 1923, five years after the end of World War I. The book begins in the morning with the arrangements for a party Clarissa Dalloway will give and it ends late in the evening when the guests are all leaving. There are many flashbacks to tell us the past of each character, but it does not leave the range ofRead MoreStream of Consciousness in Virginia Woolfs Mrs. Dalloway1354 Words   |  5 PagesConsciousness in Virginia Woolf’s Mrs Dalloway. â€Å"These novels may very well be within a category we can label stream of consciousness, so long as we know what we are talking about. The evidence reveals that we never do – or never have done so.† (5). (Humphrey, 1954). This quote from Robert Humphrey, author of Stream of Consciousness in the Modern Novel, is about the use of the writing technique, stream of consciousness, in novels such as James Joyce’s Ulysses and Virginia Woolf’s Mrs Dalloway; he highlightsRead MoreMrs. Dalloway Paper1209 Words   |  5 PagesMrs. Dalloway Paper Mrs. Dalloway, by Virginia Woolf, was written in 1925, a time filled with many large changes to civilization. The book was written and set right after the biggest war human-kind can remember which killed millions of people, during the peak of industrialization which caused the mass production of items and created thousands of new inventions, while modernist arts and thoughts were growing and, and when national pride was very large for the citizens of the Allied countries in WorldRead MoreThe Hours - Film Analysis12007 Words   |  49 PagesThe Suicide of the Author and his Reincarnation in the Reader: Intertextuality in The Hours by Michael Cunningham Andrea Wild In his novel The Hours, Michael Cunningham weaves a dazzling fabric of intertextual references to Virginia Woolfs works as well as to her biography. In this essay, I shall partly yield to the academic itch to tease out the manifold and sophisticated allusions to the numerous intertexts. My aim, however, is not to point out every single reference to Woolf and her works--suchRead MoreMrs Dalloway1427 Words   |  6 PagesAnalysis of Mrs. Dalloway Ââ€" Virginia Woolf Mrs. Dalloway, published in 1925, is a romantic drama with deep psychological approaching in to the world of urban English society in the summer of 1923, five years after the end of World War I. The book begins in the morning with the arrangements for a party Clarissa Dalloway will give and it ends late in the evening when the guests are all leaving. There are many flashbacks to tell us the past of each character, but it does not leave the range of thoseRead MoreMrs. Dalloway, by Virginia Woolf1696 Words   |  7 PagesIn the novel Mrs. Dalloway, by Virginia Woolf, the author uses narrative techniques of stream of consciousness and interior monologue in order to depict the workings of an â€Å"ordinary† or normal mind in narrative form. She also rejects the conventional structure of ‘chapters’ in order to give an â€Å"ordinary† portrayal of the mind. This essay will firstly contextualise the extract for analysis, namely the opening scene in the novel. This will be followed by defining the narrative techniques that is depictedRead Morethe theme of madness in mrs dalloway1443 Words   |  6 PagesMadness in Mrs Dalloway Madness is a prevalent theme in ‘Mrs Dallway’ and is expressed primarily, and perhaps most obviously through the characters Septimus Warren Smith and Clarissa Dalloway – however the theme is also explored more subtly in more minor characters such as Lucrezia and Mrs Kilman. Virgina Woolf’s own issues inspired her greatly, as she herself suffered her first mental breakdown at the tender age of thirteen and was prescribed ‘rest cure’ – just as Septimus is; Woolf is often describedRead MoreWilliam Woolf s Mrs. Dalloway1730 Words   |  7 Pagesgives the characters, author, and reader the reference point of a shared experience upon which to build a literary work. In the case of Virginia Woolf’s Mrs. Dalloway, this uniting experience was the Great War. The remnants of this conflict can be seen throughout the novel in the lives and experiences of its characters. The integral nature of tragedy in Mrs. Dalloway means that future reim aginings and reframings must also include a uniting tragic event as a means by which to create parallels and show

Anime And The Anime Of Anime - 1468 Words

Subtitles are captions displayed somewhere on the screen that translate foreign language. Whether or not an anime has subtitles has proven its importance amongst its western fans. Anime is Japanese made so for other countries like the United States to be able to watch it without any prior knowledge of their spoken language it must either have subtitles added in or translate the japanese to the native language of said group by recording also known as dubbing. Many people in the western culture begin by watching dubbed anime as children then eventually transition to watching subbed. With so many who belong to opposing sides this led to disagreements to which is better, anime subbed or English dubbed. This disagreement led to a sub group within the anime community known as the purist, purist are fans that only watch subbed anime. These fans are often known to belittle dubbed viewers on a variety of different points that make dubs inferior. Many of these claims actually manage to carry some weight, such as dubs changing the meanings of entire situations, changing the animation to remove what they consider explicit and removing scenes, that cause choppy character development. Needless to say that the experience between the two groups must be vastly different. The claims made by the the purist audience is true Anime with subtitles is more beneficial to the anime community than English dubbed anime. Dubbed anime are known to make errors in the translation that has the capacityShow MoreRelatedAnime Of Anime And Anime1212 Words   |  5 Pages  Ã‚  Ã‚     Ã‚  Ã‚     Ã‚  Ã‚     Ã‚  Ã‚     Ã‚  Ã‚     Ã‚  Ã‚     Ã‚  Ã‚   Period 1/4   Ã‚  Ã‚     Ã‚  Ã‚     Ã‚  Ã‚     Ã‚  Ã‚     Ã‚  Ã‚   History of Anime Manga and anime are a huge part in American and the Japanese culture. Anime and Manga were once used for war, propaganda, and recruitment, but is now used for entertainment and leisure. Anime was not just created by one man but by many working together. Anime has had a long line of history causing it to become more and more loved throughout the years. It not only caused Japan a great deal of money and working jobs butRead MoreAnime And Manga Of Anime1627 Words   |  7 PagesAnime and Manga According to Stewart (2013), Japanese culture is becoming increasingly popular within Western society†, particularly anime, cosplay and games. In the comic world of Japan, comic books are called manga, and anime means that animation cartoon. Manga is a visual narrative to gratify readers through the capability of its plot and characters, and many animation, movie and computer game stories are from manga. In the academic and art fields, fan culture, the majority of visual imagesRead MoreManga and Anime947 Words   |  4 Pages Manga and anime are popular for many people around the world and has been one of Japan’s most lucrative businesses. Manga and anime are misunderstood by some Americans who are unable to recognize the draw to them. To understand both styles, people need to know where they came from and what makes them a preferred interest of so many others. Japanese scroll paintings called the Animal Scrolls progressed into what today is known as manga and then into anime. Animal Scrolls are from the middle ofRead More Anime Essay1141 Words   |  5 PagesAnime Anime is the Japanese take on the word animation. It represents the Japanese style of animating cartoons. However, not all anime is for children. Majority imported to America is aimed at an adult audience- containing deep storylines, graphic violence, gore, as well as nudity and adult situations. This cinematic genre is a fast growing trend in the west and can now possibly be considered the most popular phenomenon among children, considering the success of the much-in-demand animeRead MoreAnime Addiction3646 Words   |  15 Pagesto watch anime to needing to watch it. Our personal take on anime is we watch what we enjoy. And we truly like anime. But we keep thinking we should stop watching because it is childish. We purchase anime on rare occasions, and watch anime maybe once a week. Recently we have been watched a lot more anime than we should often since we found online site for anime. We’ve guess what we am saying is most of my friends and family dont get the anime thing. Therefore, we end up watching anime on my ownRead MoreHistory of Anime2688 Words   |  11 PagesHISTORY OF ANIME: Osamu Tezuka ________________________________________ (picture) Dr. Osamu Tezuka: Legend. by Brian Cirulnick Walt Disney of Japan, God of Comics, A Legend in his Own Time. Many of these phrases will forever be used to describe Dr. Tezuka, but mere words cannot even begin to describe his work, or how it changed an industry, or even the incredible wealth of material produced by this one man. As I began to research this article, friends sent me copies ofRead MoreANIME ADDICTION2849 Words   |  12 PagesANIME ADDICTION A Term Paper Presented to Instructor. MANGORSI, FARHANNA Department of English Philippine Muslim Teacher,s College Marawi City In Partial Fulfillment of the Requirements for the Course General-Education ( English II) 2014-2015 By KHALID, AMNAH L. January, 2014 Anime Addiction Anime had widely spread in the whole world, its positive and negative effects are continuously being debated. 1. What is the history of Anime? 2. What are the reasons Anime Addiction? 3. What are theRead MoreThe Death Of An Anime1723 Words   |  7 Pageslot of energy, and I found myself focusing on keeping my breath even. Movement was seen, distracting me for a second or two, but it was horribly blurred, and whatever it was, it was wearing a boring shade of green. I felt as if I was watching an anime at horrible quality, and when the green blob spoke, it s voice was loud and garbled to my ears. Wait. Never mind the mysterious beings. Why was I alive? I saw my body being carried off, and the accidents.. Perhaps it was all a dream? But my bodyRead MoreWhat Are Anime and Manga3381 Words   |  14 PagesWhat are Anime and Manga? Thesis Statement: Anime and Manga are getting a lot of attention around the world. But what is the relationship of Anime and Manga? Outline: 1.0 Introduction 2.1 Definition of Anime and Manga 2.2 Brief History of Anime and Manga 2.0 The Father of Manga and Anime 3.0 Relation of Manga to Anime 4.0 Categories of Anime and Manga 5.0 Comparison 6.3 Anime and the American Animation 6.4 Manga and the American Comics 6.0 ConclusionRead MoreAnime and Manga632 Words   |  3 PagesWriting Mode: A research paper is a form of EXPOSITORY writing (informs, explains, clarifies, or defines), anchored to researched, cited information. Scoring Guidelines |6 = Exemplary |3= Developing | |5 = Strong |2 = Emerging | |4 = Proficient |1 = Beginning | Reminder: If a student receives Emerging or Developing in any category the teacher must include

The Hidden Secret of Buy a Paper

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Ramanujan free essay sample

In 1917 he was hospitalized, his doctors fearing for his life. By late 1918 his health had improved; he returned to India in 1919. But his health failed again, and he died the next year. O Five years old – primary school O Jan 1898 – town high school in Kumbakonam O 1904 – he got scholarship O 1906 – he entered in to Pachaiyappa’s college O 14th July 1909 – he married ten year old girl S. Janaki Ammal O 1911 – His first paper published, 17 page works on Bernoulli numbers journal of the Indian Mathematical Society. O Ramanujan was appointed to the post of clerk and began his duties on 1stMarch 1912. O 1914 – he went England O 1916 – Cambridge university granted him a bachelor of science degree O 1919 – he returned India Contributions  · Ramanujam made substantial contributions to the analytical theory of numbers and worked on elliptic functions, continued fractions and infinite 1900 he began to work on his own on mathematics summing geometric and arithmetic series.  · He worked on divergent series. He sent 120 theorems on imply divisibility properties of the partition function.  · He gave a meaning to eulerian second integral for all values of n (negative, positive and fractional). He proved that the integral of xn-1 e-7 = ? s true for all values of gamma. thiyagusurimathematicians. blogspot. in/2012/07/module-4-srinivasa-ramanujan-1887-ad. html (gamma) 1/3 5/27/13 MATHEMATICIANS CONTRIBUTIONS: MODULE 4 SRINIVASA RAMANUJAN (1887 AD 1920 AD)  ·  ·  ·  ·  · Goldbach’s conjecture: Goldbach’s conjecture is one of the important illustrations of ramanujan contribution towards the proof of the conjecture. The statement is every even integer greater that two is the sum of two primes, that is, 6=3+3 : Ramanujan and his associates had shown that every large integer could be written as the sum of at most four (Example: 43=2+5+17+19). Partition of whole numbers: Partition of whole numbers is another similar problem that captured ramanujan attention. Subsequently ramanujan developed a formula for the partition of any number, which can be made to yield the required result by a series of successive approximation. Example 3=3+0=1+2=1+1+1; Numbers: Ramanujan studied the highly composite numbers also which are recognized as the opposite of prime numbers. He studies their structure, distribution and special forms. Fermat Theorem: He also did considerable work on the unresolved Fermat theorem, which states that a prime number of the form 4m+1 is the sum of two squares. Ramanujan number: 1729 is a famous ramanujan number. It is the smaller number which can be expressed as the sum of two cubes in two different ways- 1729 = 13 + 123 = 93 + 103 Cubic Equations and Quadratic Equation: Ramanujam was shown how to solve cubic equations in 1902 and he went on to find his own method to solve the quadratic. The following year, not knowing that the quintic could not be solved by radicals, he tried (and of course failed) to solve the quintic. Euler’s constant : By 1904 Ramanujam had began to undertake deep research. He investigated the series (1/n) and calculated Euler’s constant to 15 decimal places. Hypo geometric series: He worked hypo geometric series, and investigated relations between integrals and series. He was to discover later that he had been studying elliptic functions. Ramanujan’s own works on partial sums and products of hyper-geometric series have led to major development in the topic. Journal of the Indian mathematical society: Ramanujan continued to develop his mathematical ideas and began to pose problems and solve problems in the journal of the Indian mathematical society. He developed relations between elliptic modular equations in 1990. Bernoulli numbers: He published a brilliant research paper on Bernoulli numbers in 1911 in the journal of the Indian mathematical society and gained recognition for his work. Despite his lack of a university education, he was becoming well known in the madras area as a mathematical genius. He began to study the Bernoulli numbers, although this was entirely his own independent discovery. Ramanujan worked out the Riemann series, the elliptic integrals hyper geometric series and functions equations of the zeta functions on the other hand he had only a vague idea of what constitutes a mathematical proof. Despite many brilliant results, some of his theorems on prime numbers were completely wrong. Ramanujan independently discovered results of gauss, Kummar and others 2/3  ·  ·  ·  ·  ·  ·  · thiyagusurimathematicians. blogspot. in/2012/07/module-4-srinivasa-ramanujan-1887-ad. html 5/27/13 MATHEMATICIANS CONTRIBUTIONS: MODULE 4 SRINIVASA RAMANUJAN (1887 AD 1920 AD)  ·  · on hyper-geometric series. Perhaps has most famous work was on the number p(n) for small numbers n, and ramaujan used this numerical data to conjecture some remarkable properties some of which he proved using elliptic functions. thers were only proved after Ramanujan’s death. In a joint paper with hardly, ramanujan gave an asymptotic formulas for p(n). It had the remarkable property that it appeared to give the correct value of p(n), and this was later proved by Rademacher. Ramanujan discovered a number of remarkable identities that imply divisibility properties of the partition function. He a lso produced quite a number of results in definite integrals in the form of general formulate. Besides his published work, ramanujan left behind several notebooks filled with theorems that mathematicians have continued to study. The English Mathematician G. N Watson, from 1918 to 1951, published 14 papers under the general title theorems stated by Ramanujan and in all he published nearly 30 papers which were inspired by ramanjan work. In 1997 ramanujan journal was launched to publish work in areas mathematics influenced by Ramanujan†. thiyagusurimathematicians. blogspot. in/2012/07/module-4-srinivasa-ramanujan-1887-ad. html 3/3

Religion Paper Rusy Riggs essay rough draft Essays - Religion

Rusy Riggs 3/15/18 Religion 101 Buddhism : Chenrezig Deity I attended a Buddhist religious service at the Gampopa Center in Annapolis, Maryland. The service I attended was a Compassion Buddha Practice, based on the teachings of Chenrezig , one of the Buddhist deities. Chenrezig is considered the embodiment of compassion in Tibetian Buddhism, and is one of the most popular Buddhist deities after Buddha himself. I chose Buddhism because I wanted to understand why Buddhist s fo llow the Buddha even though they do not consider him to be a god. I attended a Tibetan Buddhist Temple in Annapolis to get a visual understanding of how Buddhist s practice their religion and what they do in their service . At t he event I attended , we practiced the Chenrezig d eity, the Buddha of Compassion. Chenrezig is considered the patron Bodhisattva in Tibet. In Tibetan Buddhism , the Chenrezig is considered to be the embodiment of the compa ssion of all Buddha's . For this event we used the Chenrezig text, which is a small packet of texts. This is a very common practice in Buddhism that Tibetans use for meditation. In the Chenrezig , everything was and still is written in Pali , which is the original language in Buddhist culture. To understand what happened at the Buddhist Temple one must first understand the Chenrezig deit y, the images used in the worship practice , and the ways in which Buddhism tries to educate its followers . The Gampopa Center is upstairs in a small office building in Annapolis. I arrived there at 7 pm for the Compassion Buddha Practice service, which was an hour and a half long. Th e service was conducted by Karen, who was friendly and happy to have me there as a guest. She explained that they often have students attend services to learn about Buddhism. Karen began by describing some of what we saw around us in the room. There was a sort of altar on which was a statue of Buddha . In front of Buddha was seven bowls of water, called water offerings. Behind Buddha were seven more bowls of water. Going from left to right the bowls are water for washing, water for drinking, water for flowers, water for incense, water for light, water for perfume , and water for music. In the Seven Branch Prayer these vessels of water are verbally offered. The most important object in the templ e is the statue in the center of Siddhartha Gau tama , also known as the Buddha . Siddhartha atta ined enlightenment under a fig t ree at a village in Northern India. He sat for forty nine days w ith demons and devils trying to stop Siddhartha from achieving enlightenment. He taught what is known in Buddhism as the " Middle Way ", a path of moderation between extremes. What I saw was just one of many eminations of the Buddha . Another statue in the room was the Chenrezig statue. Its four arms and h ands represent the f our immeasurables: loving kindness, compassion, joy, and equanimity. Karen explained that the Buddhist ceremony is regimented, much in the same way a Catholic Mass is structured and follows an order. There are specific steps that must be followed for the Chenrezig deity . I sat on a mat and a pillow with the Chenrezig text in front of me. To read the text you must follow b y reading to the bottom, then flipping the page up and read to the bott om again and so on. We began by taking Refuge Bodhisattva , which was repeated three times. Next , we generated a visualization, then we said prayers. We only di d two prayers in the Chenrezig t ext. The two are the Seven Branch Prayer which is the offer ing prayer and Om Mani Padme Hu ng . The prayers were said first in English, then repeated in the native language of Buddhism. Afterwards we had a ten m inute meditation. Meditation in Buddhism is everything. T he reason we meditate with the Chenrezig deity is to be come more compassionate . There is a certain way to meditate to achieve

Catherine of Aragon - Early Life and First Marriage

Catherine of Aragon - Early Life and First Marriage Catherine of Aragon, whose parents united Castile and Aragon with their marriage, was promised in marriage to the son of Henry VII of England, in order to promote the alliance between the Spanish and English rulers. Dates: December 16, 1485 - January 7, 1536Also Known as: Katharine of Aragon, Catherine of Aragon, CatalinaSee: more Catherine of Aragon Facts Catherine of Aragon Biography Catherine of Aragons role in history was, first, as a marriage partner to strengthen the alliance of England and Spain (Castile and Aragon), and later, as the center of Henry VIIIs struggle for an annulment that would permit him to remarry and try for a male heir to the English throne for the Tudor dynasty. She was not simply a pawn in the latter, but her stubbornness in fighting for her marriage and her daughters right to inherit were key in how that struggle ended, with Henry VIII separating the Church of England from the Church of Romes authority. Catherine of Aragon Family Background Catherine of Aragon was the fifth child of Isabella I of Castile and Ferdinand of Aragon. She was born in Alcal de Henares. Catherine was likely named for her mothers grandmother, Katherine of Lancaster, the daughter of Constance of Castile who was second wife of John of Gaunt, himself son of Englands Edward III. Constance and Johns daughter, Catherine of Lancaster, married Henry III of Castile and was the mother of John II of Castile, Isabellas father. Constance of Castile was the daughter of Peter (Pedro) of Castile, known as Peter the Cruel, who was overthrown by his brother Henry (Enrique) II. John of Gaunt tried to claim the throne of Castile on the basis of his wife Constances descent from Peter. Catherines father Ferdinand was the great-grandson of Philippa of Lancaster, the daughter of John of Gaunt and his first wife, Blanche of Lancaster. Philippas brother was Henry IV of England. Thus, Catherine of Aragon had considerable English royal heritage herself. Her parents were also both part of the House of Trastmara, a dynasty that ruled kingdoms in the Iberian peninsula from 1369 to 1516, descended from King Henry (Enrique) II of Castile who overthrew his brother, Peter, in 1369, part of the War of the Spanish Succession the same Peter who was the father of Isabellas grandmother Constance of Castile, and the same Henry John of Gaunt tried to overthrow. Catherine of Aragon Childhood and Education: In her early years, Catherine traveled extensively within Spain with her parents as they fought their war to remove the Muslims from Granada. Because Isabella regretted the lack of her own educational preparation when she became a ruling queen, she educated her daughters well, preparing them for their likely roles as queens. So Catherine had an extensive education, with many European humanists as her teachers. Among the tutors who educated Isabella, and then her daughters, was Beatriz Galindo. Catherine spoke Spanish, Latin, French and English, and was well-read in philosophy and theology. Alliance with England Through Marriage Catherine was born in 1485, the same year Henry VII seized the crown of England as the first Tudor monarch. Arguably, Catherines own royal descent was more legitimate than Henrys, who was descended from their common ancestor John of Gaunt through the children of Katherine Swynford, his third wife, who were born before their marriage and later legitimized but declared ineligible for the throne. In 1486, Henrys first son, Arthur was born. Henry VII sought powerful connections for his children through marriage; so did Isabella and Ferdinand. Ferdinand and Isabella first sent diplomats to England to negotiate Catherines marriage to Arthur in 1487. The next year, Henry VII agreed to the marriage, and a formal agreement including dowry specifications was drwan up. Ferdinand and Isabella were to pay the dowry in two parts, one when Catherine arrived in England (traveling at her parents expense), and the other after the wedding ceremony. Even at this point, there were some differences between the two families over the terms of the contract, each wanting the other to pay more than that other family wanted to pay. Henrys early recognition of the unification of Castile and Aragon in the Treaty of Medina del Campo in 1489 was important to Isabella and Ferdinand; this treaty also aligned the Spanish with England rather than France. In this treaty, the marriage of Arthur and Catherine was further defined. Catherine and Arthur were far too young to actually marry at that time. Challenge to Tudor Legitimacy Between 1491 and 1499, Henry VII also had to contend with a challenge to his legitimacy when a man asserted himself to be Richard, duke of York, son of Edward IV (and brother of Henry VIIs wife Elizabeth of York). Richard and his older brother had been confined to the Tower of London when their uncle, Richard III, seized the crown from their father, Edward IV, and they were not seen again. Its generally agreed that either Richard III or Henry IV had them killed. If one had been alive, hed have a greater legitimate claim to the English throne than Henry VII did. Margaret of York (Margaret of Burgundy) another of the children of Edward IV had opposed Henry VII as a usurper, and she was drawn into supporting this man who claimed to be her nephew, Richard. Ferdinand and Isabella supported Henry VII and their future son-in-laws inheritance by helping to expose the pretenders Flemish origins. The pretender, whom the Tudor supporters called Perkin Warbeck, was finally seized and executed by Henry VII in 1499. More Treaties and Conflict Over the Marriage Ferdinand and Isabella began secretly exploring marrying Catherine to James IV of Scotland. In 1497, the marriage agreement between the Spanish and English was amended and treaties of marriage were signed in England. Catherine was to be sent to England only when Arthur turned fourteen. In 1499, the first proxy wedding of Arthur and Catherine was held in Worcestershire. The marriage required a papal dispensation because Arthur was younger than the age of consent. The next year, there was new conflict over the terms and especially over payment of the dowry and Catherines arrival date in England. It was in Henrys interest for her to arrive earlier rather than later, as payment of the first half of the dowry was contingent on her arrival. Another proxy wedding was held in 1500 in Ludlow, England. Catherine and Arthur Marry Finally, Catherine embarked for England, and arrived in Plymouth on October 5, 1501. Her arrival took the English by surprise, apparently, as Henrys steward did not receive Catherine until October 7. Catherine and her large accompanying party began their progress towards London. On November 4, Henry VII and Arthur met the Spanish entourage, Henry famously insisting on seeing his future daughter-in-law even if in her bed. Catherine and household arrived in London on November 12, and Arthur and Catherine were married at St. Pauls on November 14. A week of feasts and other celebrations followed. Catherine was given the titles of Princess of Wales, Duchess of Cornwall and Countess of Chester. As prince of Wales, Arthur was being sent to Ludlow with his own separate royal household. The Spanish advisors and diplomats argued whether Catherine should accompany him and whether she was old enough for marital relations yet; the ambassador wanted her to delay going to Ludlow, and her priest disagreed. Henry VIIs wish that she accompany Arthur prevailed, and they both left for Ludlow on December 21. There, they both became ill with the sweating sickness. Arthur died on April 2, 1502; Catherine recovered from her serious bout with the illness to find herself a widow. Next: Catherine of Aragon: Marriage to Henry VIII About Catherine of Aragon: Catherine of Aragon Facts | Early Life and First Marriage | Marriage to Henry VIII | The Kings Great Matter | Catherine of Aragon Books | Mary I | Anne Boleyn | Women in the Tudor Dynasty

M_Q_2 Essay Example | Topics and Well Written Essays - 1250 words

M_Q_2 - Essay Example The culture of an organization shows the way the employees deal and interact with each other while performing their job related tasks. I believe that the culture of an organization develops with time when the employees, managers, and all governing bodies of an organization work with full commitment shaping a positive organizational culture. In my view, the culture of an organization really improves the performance and productivity of an organization. A strong organizational culture unites the employees and motivates them to work efficiently and professionally towards their goals. Organizational culture includes such elements, which play a vital role in making a company reach desired sets of goals and objectives in an effective way. Some of the most influencing tasks, which organizational culture performs, include determining the organization’s effectiveness and capacity, putting energy and momentum in the employees in order to ensure organization’s success, injecting se nse of responsibility in the employees, and making the employees work efficiently towards achievement of desired goals and objectives. These were some of those roles, which culture plays in making an organization achieve desired goals and objective effectively and efficiently. Answer: No: 2 Culture of an organization is one of the main drivers of organizational performance and it can definitely be used to increase performance. Daniels A. and Daniels J. found that managers need to evaluate performances of the employees and the organizations in order to implement positive changes. It depends on the managers of an organization to motivate and encourage employees to work with full dedication and commitment. The dedication and commitment shown by the employees of a company towards their job responsibilities shape the culture of the company. If the employees carry out their job related tasks efficiently, it creates an enthusiastic and motivated culture of the organization, which positivel y affects the new employees who come and join the company. From here, the transition process starts where impact of employees’ performance on the culture of an organization shifts towards impact of organizational culture on the performance of new employees. Once the employees succeed in shaping a work-oriented culture in an organization, it plays a considerable role in motivating new employees to work hard for the company. A new employee is not very much aware of the culture of the company where he/she gets a job. When that employee starts working for the company, he/she observes the overall workplace culture of the company and shapes his/her job behavior according to that culture. If a company will have work-oriented culture enriched with the elements of motivation, innovation, and workplace ethics, it will make a positive impact on the new employees and will make them work hard to achieve the company’s goals and objectives. Therefore, we can say that strong culture o f an organization not only increases employees’ productivity but also increases the overall organizational performance. Answer: No: 3 As a senior leader, I will like to change the culture of the organization by integrating the elements of hard work, commitment, dedication, and enthusiasm in the existing culture of the organization. I believe that when employees feel like owning the company, they work with more commitment in order to make their company reach heights of success in any specific market. If a company injects the sense of

McDonald's Essay Example | Topics and Well Written Essays - 1500 words

McDonald's - Essay Example In case of McDonalds’ regular operation General Manager is controlling assistant and staffs who are mainly focusing on selling different products and offering services to customers. In case of McDonalds’ decision makings are done in a decentralized manner. McDonalds’ has divided its organization structure into three geographic locations. Those are 1) USA, 2) Europe and 3) Asia pacific, Middle East and Africa. Chief operating officers of those three regions directly reports to the CEO for all company related operations. Company’s geographical organization structure has three main hierarchies for operating globally. This organization structure is very simple and well designed. The main products of the McDonalds’ are hamburgers, chicken sandwiches of different types, French fries, breakfast items, desserts and soft drinks. In some markets McDonalds’ also sales vegetarian dishes and salads. It also sales some seasonal foods like McRib. Company is also offering soup in Asian market. It has given lots of importance to the local food. Company has done great localization of their menu. They also maintained local food taboos in different countries like India and Indonesia. McDonalds’ also sells beer in Germany and in various Western parts of Europe. McDonalds’ also provides different services to its customers like free Wi- Fi. Customers can access the Internet facilities by using their mobile phones and laptops without any charges. More than 11,000 restaurants have this super service around the world. The McDonalds’ is having a prepaid card service. It is named as Arch Card. This card helps customers for quick and convenient way of payment at McDonalds’. Customers can buy from any McDonalds’ restaurant with the help of this card (Molch, 2009, p. 182). Company is providing services in terms of giving space for child parties. These services are provided in limited locations. McDonalds’ is World’s largest

High Performance Wireless Telecommunications Modulation

High Performance Wireless Telecommunications Modulation Introduction The primary goal of the project is to analyze of OFDM system and to assess the suitability of OFDM as a modulation technique for wireless communications. In the part of project is covered two leading successfully implementation of OFDM based technologies are Digital Video Broadcasting (DVB-T and DVB-H) and Long Term Evolution (LTE advanced for 4G). Wireless communications is an emerging field, which has seen enormous growth in the last several years. The huge uptake rate of mobile phone technology, Wireless Local Area Networks (WLAN) and the exponential growth of the Internet have resulted in an increased demand for new methods of obtaining high capacity wireless networks. For cellular mobile applications, we will see in the near future a complete convergence of mobile phone technology, computing, Internet access, and potentially many multimedia applications such as video and high quality audio. In fact, some may argue that this convergence has already largely occurred, with the advent of being able to send and receive data using a notebook computer and a mobile phone. The goal of third and fourth generation mobile networks is to provide users with a high data rate, and to provide a wider range of services, such as voice communications, videophones, and high speed Internet access. The higher data rate of future mobile networks will be achieved by increasing the amount of spectrum allocated to the service and by improvements in the spectral efficiency. OFDM is a potential candidate for the physical layer of fourth generation mobile systems. Basic Principles of OFDM OFDM overview The Orthogonal Frequency Division Multiplexing (OFDM) is a modulation technique where multiple low data rate carriers are combined by a transmitter to form a composite high data rate transmission. The first commercial use of OFDM in the communication field was in the 1980s, and it was later widely used in the broadcast audio and video field in the 1990s in such areas as, ADSL, VHDSL, ETSI standard digital audio broadcast (DAB), digital video broadcast (DVB), and high-definition digital TV (HDTV). Digital signal processing makes OFDM possible. To implement the multiple carrier scheme using a bank of parallel modulators would not be very efficient in analog hardware. However, in the digital domain, multi-carrier modulation can be done efficiently with currently available DSP hardware and software. Not only can it be done, but it can also be made very flexible and programmable. This allows OFDM to make maximum use of available bandwidth and to be able to adapt to changing system requirements. Figure 1 is illustrated, Instead of separate modulators; the outgoing waveform is created by executing a high-speed inverse DFT on a set of time-samples of the transmitted data (post modulation). The output of the DFT can be directly modulated onto the outgoing carrier, without requiring any other components. Each carrier in an OFDM system is a sinusoid with a frequency that is an integer multiple of a base or fundamental sinusoid frequency. Therefore, each carrier is like a Fourier series component of the composite signal. In fact, it will be shown later that an OFDM signal is created in the frequency domain, and then transformed into the time domain via the Discrete Fourier Transform (DFT). Two periodic signals are orthogonal when the integral of their product, over one period, is equal to zero. This is true of certain sinusoids as illustrated in Equation 1. Definition of Orthogonal The carriers of an OFDM system are sinusoids that meet this requirement because each one is a multiple of a fundamental frequency. Each one has an integer number of cycles in the fundamental period. [2, 145-153; 6] The importantance of being orthogonal The main concept in OFDM is orthogonality of the sub-carriers.Since the carriers are all sine/cosine wave, we know that area under one period of a sine or a cosine wave is zero. Lets take a sine wave of frequency m and multiply it by a sinusoid (sine or a cosine) of a frequency n, where both m and n are integers. The integral or the area under this product is given by These two components are each a sinusoid, so the integral is equal to zero over one period. When we multiply a sinusoid of frequency n by a sinusoid of frequency m/n the area under the product is zero. In general for all integers n and m , sin(mx), cos(mx), cos(nx) , sin(nx) are all orthogonal to each other. These frequencies are called harmonics. Making the subcarriers mathematically orthogonal was a breakthrough for OFDM because it enables OFDM receivers to separate the subcarriers via an FFT and eliminate the guard bands. As figure 3 shows, OFDM subcarriers can overlap to make full use of the spectrum, but at the peak of each subcarrier spectrum, the power in all the other subcarriers is zero. OFDM therefore offers higher data capacity in a given spectrum while allowing a simpler system design. Creating orthogonal subcarriers in the transmitter is easy using an inverse FFT. To ensure that this orthogonality is maintained at the receiver (so that the subcarriers are not misaligned), the system must keep the transmitter and receiver clocks closely synchronizedwithin 2 parts per million in 802.11a systems. The 802.11a standard therefore dedicates four of its 52 subcarriers as pilots that enable phase-lock loops in the receiver to track the phase and frequency of the incoming signal. The 802.11a standard therefore dedicates four of its 52 subcarriers as pilots that enable phase-lock loops in the receiver to track the phase and frequency of the incoming signal. This method also eliminates low-frequency phase noise.Separating the subcarriers via an FFT require about an order of magnitude fewer multiply-accumulate operations than individually filtering each carrier. In general, an FFT implementation is much simpler than the RAKE receivers used for CDMA and the decision-feedback equalizers for TDMA.This idea are key to understanding OFDM. The orthogonality allows simultaneously transmission on a lot of sub- carriers in a tight frequency space without interference form each other. In essence this is similar to CDMA, where codes are used to make data sequences independent (also orthogonal) which allows many independent users to transmitin same space successfully.[2, 153-154; 6 ; 7] OFDM Operation Preliminary Concepts When the DFT (Discrete Fourier Transform) of a time signal is taken, the frequency domain results are a function of the time sampling period and the number of samples as shown in Figure 4. The fundamental frequency of the DFT is equal to 1/NT (1/total sample time). Each frequency represented in the DFT is an integer multiple of the fundamental frequency. Parameter Mapping from Time to Frequency for the DFT The maximum frequency that can be represented by a time signal sampled at rate 1/T is fmax = 1/2T as given by the Nyquist sampling theorem. This frequency is located in the center of the DFT points. All frequencies beyond that point are images of the representative frequencies. The maximum frequency bin of the DFT is equal to the sampling frequency (1/T) minus one fundamental (1/NT).The IDFT (Inverse Discrete Fourier Transform) performs the opposite operation to the DFT. It takes a signal defined by frequency components and converts them to a time signal. The parameter mapping is the same as for the DFT. The time duration of the IDFT time signal is equal to the number of DFT bins (N) times the sampling period (T).It is perfectly valid to generate a signal in the frequency domain, and convert it to a time domain equivalent for practical use (The frequency domain is a mathematical tool used for analysis. Anything usable by the real world must be converted into a real, time domain signal). This is how modulation is applied in OFDM. In practice the Fast Fourier Transform (FFT) and IFFT are used in place of the DFT and IDFT, so all further references will be to FFT and IFFT.[1 ,118 ; 4] Definition of Carriers The maximum number of carriers used by OFDM is limited by the size of the IFFT. This is determined as follows in Equation 2. OFDM Carrier Count In order to generate a real-valued time signal, OFDM (frequency) carriers must be defined in complex conjugate pairs, which are symmetric about the Nyquist frequency (fmax). This puts the number of potential carriers equal to the IFFT size/2. The Nyquist frequency is the symmetry point, so it cannot be part of a complex conjugate pair. The DC component also has no complex conjugate. These two points cannot be used as carriers so they are subtracted from the total available. If the carriers are not defined in conjugate pairs, then the IFFT will result in a time domain signal that has imaginary components. This must be a viable option as there are OFDM systems defined with carrier counts that exceed the limit for real-valued time signals given in Equation 2.In general, a system with IFFT size 256 and carrier count 216. This design must result in a complex time waveform. Further processing would require some sort of quadrature technique (use of parallel sine and cosine processing paths). In this report, only real-value time signals will be treated, but in order to obtain maximum bandwidth efficiency from OFDM, the complex time signal may be preferred (possibly an analogous situation to QPSK vs. BPSK). Equation 2, for the complex time waveform, has all IFFT bins available as carriers except the DC bin. Both IFFT size and assignment (selection) of carriers can be dynamic. The transmitter and receiver just have to use the same parameters. This is one of the advantages of OFDM. Its bandwidth usage (and bit rate) can be varied according to varying user requirements. A simple control message from a base station can change a mobile units IFFT size and carrier selection.[2,199-206; 4] Modulation Binary data from a memory device or from a digital processing stream is used as the modulating (baseband) signal. The following steps may be carried out in order to apply modulation to the carriers in OFDM: combine the binary data into symbols according to the number of bits/symbol selected convert the serial symbol stream into parallel segments according to the number of carriers, and form carrier symbol sequences apply differential coding to each carrier symbol sequence convert each symbol into a complex phase representation assign each carrier sequence to the appropriate IFFT bin, including the complex conjugates take the IFFT of the result OFDM modulation is applied in the frequency domain. Figure 5 and Figure 6 give an example of modulated OFDM carriers for one symbol period, prior to IFFT. OFDM Carrier Magnitude prior to IFFT For this example, there are 4 carriers, the IFFT bin size is 64, and there is only 1 bit per symbol. The magnitude of each carrier is 1, but it could be scaled to any value. The phase for each carrier is either 0 or 180 degrees, according to the symbol being sent. The phase determines the value of the symbol (binary in this case, either a 1 or a 0). In the example, the first 3 bits (the first 3 carriers) are 0, and the 4th bit (4th carrier) is a 1. OFDM Carrier Phase prior to IFFT Note that the modulated OFDM signal is nothing more than a group of delta (impulse) functions, each with a phase determined by the modulating symbol. In addition, note that the frequency separation between each delta is proportional to 1/N where N is the number of IFFT bins. The frequency domain representation of the OFDM is described in Equation 3. OFDM Frequency Domain Representation (one symbol period) After the modulation is applied, an IFFT is performed to generate one symbol period in the time domain. The IFFT result is shown in 7. It is clear that the OFDM signal has varying amplitude. It is very important that the amplitude variations be kept intact as they define the content of the signal. If the amplitude is clipped or modified, then an FFT of the signal would no longer result in the original frequency characteristics, and the modulation may be lost. This is one of the drawbacks of OFDM, the fact that it requires linear amplification. In addition, very large amplitude peaks may occur depending on how the sinusoids line up, so the peak-to-average power ratio is high. This means that the linear amplifier has to have a large dynamic range to avoid distorting the peaks. The result is a linear amplifier with a constant, high bias current resulting in very poor power efficiency. OFDM Signal, 1 Symbol Period Figure 8 is provided to illustrate the time components of the OFDM signal. The IFFT transforms each complex conjugate pair of delta functions (each carrier) into a real-valued, pure sinusoid. Figure 8 shows the separate sinusoids that make up the composite OFDM waveform given in Figure 7. The one sinusoid with 180 phase shift is clearly visible as is the frequency difference between each of the 4 sinusoids. Transmission The key to the uniqueness and desirability of OFDM is the relationship between the carrier frequencies and the symbol rate. Each carrier frequency is separated by a multiple of 1/NT (Hz). The symbol rate (R) for each carrier is 1/NT (symbols/sec). The effect of the symbol rate on each OFDM carrier is to add a sin(x)/x shape to each carriers spectrum. The nulls of the sin(x)/x (for each carrier) are at integer multiples of 1/NT. The peak (for each carrier) is at the carrier frequency k/NT. Therefore, each carrier frequency is located at the nulls for all the other carriers. This means that none of the carriers will interfere with each other during transmission, although their spectrums overlap. The ability to space carriers so closely together is very bandwidth efficient. OFDM Time Waveform Figure 9 shows the OFDM time waveform for the same signal. There are 100 symbol periods in the signal. Each symbol period is 64 samples long (100 x 64 = 6400 total samples). Each symbol period contains 4 carriers each of which carries 1 symbol. Each symbol carries 1 bit. Note that Figure 9 again illustrates the large dynamic range of the OFDM waveform envelope. OFDM Spectrum Figure 10 shows the spectrum for of an OFDM signal with the following characteristics: 1 bit / symbol 100 symbols / carrier (i.e. a sequence of 100 symbol periods) 4 carriers 64 IFFT bins spectrum averaged for every 20 symbols (100/20 = 5 averages) Red diamonds mark all of the available carrier frequencies. Note that the nulls of the spectrums line up with the unused frequencies. The four active carriers each have peaks at carrier frequencies. It is clear that the active carriers have nulls in their spectrums at each of the unused frequencies (otherwise, the nulls would not exist). Although it cannot be seen in the figure, the active frequencies also have spectral nulls at the adjacent active frequencies. It is not currently practical to generate the OFDM signal directly at RF rates, so it must be up converted for transmission. To remain in the discrete domain, the OFDM could be upsampled and added to a discrete carrier frequency. This carrier could be an intermediate frequency whose sample rate is handled by current technology. It could then be converted to analog and increased to the final transmit frequency using analog frequency conversion methods. Alternatively, the OFDM modulation could be immediately converted to analog and directly increased to the desired RF transmits frequency. Either way, the selected technique would have to involve some form of linear AM (possibly implemented with a mixer). [1, 122-125; 6] Reception and Demodulation The received OFDM signal is down converted (in frequency) and taken from analog to digital. Demodulation is done in the frequency domain (just as modulation was). The following steps may be taken to demodulate the OFDM: partition the input stream into vectors representing each symbol period take the FFT of each symbol period vector extract the carrier FFT bins and calculate the phase of each calculate the phase difference, from one symbol period to the next, for each carrier decode each phase into binary data sort the data into the appropriate order OFDM Carrier Magnitude following FFT Figure 11 and Figure 12 show the magnitude and spectrum of the FFT for one received OFDM symbol period. For this example, there are 4 carriers, the IFFT bin size is 64, there is 1 bit per symbol, and the signal was sent through a channel with AWGN having an SNR of 8 dB. The figures show that, under these conditions, the modulated symbols are very easy to recover. OFDM Carrier Phase following FFT In Figure 12 that the unused frequency bins contain widely varying phase values. These bins are not decoded, so it does not matter, but the result is of interest. Even if the noise is removed from the channel, these phase variations still occur. It must be a result of the IFFT/FFT operations generating very small complex values (very close to 0) for the unused carriers. The phases are a result of these values. [1, 125 -128; 3] OFDM transceiver OFDM signals are typically generated digitally due to the difficulty in creating large banks of phase lock oscillators and receivers in the analog domain. Figure 13 shows the block diagram of a typical OFDM transceiver. The transmitter section converts digital data to be transmitted, into a mapping of subcarrier amplitude and phase. It then transforms this spectral representation of the data into the time domain using an Inverse Discrete Fourier Transform (IDFT). The Inverse Fast Fourier Transform (IFFT) performs the same operations as an IDFT, except that it is much more computationally efficiency, and so is used in all practical systems. In order to transmit the OFDM signal the calculated time domain signal is then mixed up to the required frequency. Block diagram showing a basic OFDM transceiver [3] The receiver performs the reverse operation of the transmitter, mixing the RF signal to base band for processing, then using a Fast Fourier Transform (FFT) to analyze the signal in the frequency domain. The amplitude and phase of the subcarriers is then picked out and converted back to digital data. The IFFT and the FFT are complementary function and the most appropriate term depends on whether the signal is being received or generated. In cases where the Signal is independent of this distinction then the term FFT and IFFT is used interchangeably. [1, 125 -128, 3] Analysis of OFDM characteristics Guard Period OFDM demodulation must be synchronized with the start and end of the transmitted symbol period. If it is not, then ISI will occur (since information will be decoded and combined for 2 adjacent symbol periods). ICI will also occur because orthogonality will be lost (integrals of the carrier products will no longer be zero over the integration period), To help solve this problem, a guard interval is added to each OFDM symbol period. The first thought of how to do this might be to simply make the symbol period longer, so that the demodulator does not have to be so precise in picking the period beginning and end, and decoding is always done inside a single period. This would fix the ISI problem, but not the ICI problem. If a complete period is not integrated (via FFT), orthogonality will be lost. The effect of ISI on an OFDM signal can be further improved by the addition of a guard period to the start of each symbol. This guard period is a cyclic copy that extends the length of the symbol waveform. Each subcarrier, in the data section of the symbol, (i.e. the OFDM symbol with no guard period added, which is equal to the length of the IFFT size used to generate the signal) has an integer number of cycles. Because of this, placing copies of the symbol end-to-end results in a continuous signal, with no discontinuities at the joins. Thus by copying the end of a symbol and appending this to the start results in a longer symbol time. Addition of a guard period to an OFDM signal [3] In Figure 14, The total length of the symbol is Ts=TG + TFFT, where Ts is the total length of the symbol in samples, TG is the length of the guard period in samples, and TFFT is the size of the IFFT used to generate the OFDM signal. In addition to protecting the OFDM from ISI, the guard period also provides protection against time-offset errors in the receiver. For an OFDM system that has the same sample rate for both the transmitter and receiver, it must use the same FFT size at both the receiver and transmitted signal in order to maintain subcarrier orthogonality. Each received symbol has TG + TFFT samples due to the added guard period. The receiver only needs TFFT samples of the received symbol to decode the signal. The remaining TG samples are redundant and are not needed. For an ideal channel with no delay spread the receiver can pick any time offset, up to the length of the guard period, and still get the correct number of samples, without crossing a symbol boundary. Function of the guard period for protecting against ISI [3] Figure 15 shows this effect. Adding a guard period allows time for the transient part of the signal to decay, so that the FFT is taken from a steady state portion of the symbol. This eliminates the effect of ISI provided that the guard period is longer than the delay spread of the radio channel. The remaining effects caused by the multipath, such as amplitude scaling and phase rotation are corrected for by channel equalization. In order to avoid ISI and ICI, the guard period must be formed by a cyclic extension of the symbol period. This is done by taking symbol period samples from the end of the period and appending them to the front of the period. The concept of being able to do this, and what it means, comes from the nature of the IFFT/FFT process. When the IFFT is taken for a symbol period (during OFDM modulation), the resulting time sample sequence is technically periodic. This is because the IFFT/FFT is an extension of the Fourier Transform which is an extension of the Fourier Series for periodic waveforms. All of these transforms operate on signals with either real or manufactured periodicity. For the IFFT/FFT, the period is the number of samples used. Guard Period via Cyclic Extension With the cyclic extension, the symbol period is longer, but it represents the exact same frequency spectrum. As long as the correct number of samples are taken for the decode, they may be taken anywhere within the extended symbol. Since a complete period is integrated, orthogonality is maintained. Therefore, both ISI and ICI are eliminated. Note that some bandwidth efficiency is lost with the addition of the guard period (symbol period is increased and symbol rate is decreased) [2,154-160, 3] Windowing The OFDM signal is made up of a series of IFFTs that are concatenated to each other. At each symbol period boundary, there is a signal discontinuity due to the differences between the end of one period and the start of the next. These discontinuities can cause high frequency spectral noise to be generated (because they look like very fast transitions of the time waveform). To avoid this, a window function (Hamming, Hanning, Blackman, ) may be applied to each symbol period. The window function would attenuate the time waveform at the start and the end of each period, so that the discontinuities are smaller, and the high frequency noise is reduced. However, this attenuation distorts the signal and some of the desired frequency content is lost.[1, 121;2 154] Multipath Characteristics OFDM avoids frequency selective fading and ISI by providing relatively long symbol periods for a given data rate. This is illustrated in Figure 17. For a given transmission channel and a given source data rate, OFDM can provide better multipath characteristics than a single carrier. OFDM vs. Single Carrier, Multipath Characteristic Comparison However, since the OFDM carriers are spread over a frequency range, there still may be some frequency selective attenuation on a time-varying basis. A deep fade on a particular frequency may cause the loss of data on that frequency for a given time, but the use of Forward Error Coding can fix it. If a single carrier experienced a deep fade, too many consecutive symbols may be lost and correction coding may be ineffective. [8] Bandwidth A comparison of RF transmits bandwidth between OFDM and a single carrier is shown in Figure 18 (using the same example parameters as in Figure 17). OFDM Bandwidth Efficiency In Figure 18, the calculations show that OFDM is more bandwidth efficient than a single carrier. Note that another efficient aspect of OFDM is that a single transmitters bandwidth can be increased incrementally by addition of more adjacent carriers. In addition, no bandwidth buffers are needed between transmit bandwidths of separate transmitters as long as orthogonality can be maintained between all the carriers.[2, 161-163; 8; 9] Physical Implementation Since OFDM is carried out in the digital domain, there are many ways it can be implemented. Some options are provided in the following list. Each of these options should be viable given current technology: ASIC (Application Specific Integrated Circuit) ASICs are the fastest, smallest, and lowest power way to implement OFDM Cannot change the ASIC after it is built without designing a new chip General-purpose Microprocessor or MicroController PowerPC 7400 or other processor capable of fast vector operations Highly programmable Needs memory and other peripheral chips Uses the most power and space, and would be the slowest Field-Programmable Gate Array (FPGA) An FPGA combines the speed, power, and density attributes of an ASIC with the programmability of a general purpose processor. An FPGA could be reprogrammed for new functions by a base station to meet future (currently unknown requirements).This should be the best choice.[9] OFDM uses in DVB (Digital Video Broadcasting) DVB (Digital Video Broadcast) is a set of standards for the digital transmission of video and audio streams, and also data transmission. The DVB standards are maintained by the DVB Project, which is an industry-led consortium of over 260 broadcasters, manufacturers, network operators, software developers, regulatory bodies and others in over 35 countries. DVB has been implemented over satellite (DVB-S, DVB-S2), cable (DVB-C), terrestrial broadcasting (DVB-T), and handheld terminals (DVB-H). the DVB standard following the logical progression of signal processing steps, as well as source and channel coding, COFDM modulation, MPEG compression and multiplexing methods, conditional access and set-top box Technology. In this project is presented an investigation of two OFDM based DVB standards, DVB-T and DVB-H. DVB-T (Digital Video Broadcasting Terrestrial) The first Terrestrial Digital Video Broadcasting pilot transmissions were started in the late 90s, and the first commercial system was established in Great Britain. In the next few years the digital broadcasting system has been set up in many countries, and the boom of the digital terrestrial transmission is estimated in the next few years, while the analogue transmission will be cancelled within about 15 years. The greatest advantage of the digital system is the effective use of the frequency spectrum and its lower radiated power in comparison with the analogue transmission, while the covered area remains the same. Another key feature is the possibility of designing a so-called Single Frequency Network (SFN), which means that the neighboring broadcast stations use the same frequency and the adjacent signals dont get interfered. The digital system transmits a data stream, which means that not only television signals but data communication (e.g. Internet service) may be used according to the demands. The data stream consists of an MPEG-2 bit stream, which means a compression is used, enabling the transfer of even 4 or 5 television via the standard 8 MHz wide TV channel. For the viewer, the main advantages are the perfect, noise-free picture, CD quality sound, and easier handling, as well as services like Super Teletext, Electronic Programme Guide, interactivity and mobility.[11, 251-253] Modulation technique in DVB-T The DVB-T Orthogonal Frequency Division Multiplexing (OFDM) modulation system uses multi-carrier transmission. There are 2 modes, the so-called 2k and 8k modes, using 1705 and 6817 carriers respectively, with each carrier modulated separately and transmitted in the 8 MHz TV channel. The common modulation for the carriers is typically QPSK, 16-QAM or 64-QAM. Each signal can be divided into two, so-called „In Phase (I) and „Quadrature Phase components, being a 90Â ° phase shift between them. The constellation diagram and the bit allocation is shown in bellow 16-QAM constellation diagram and bit allocation [6] This modulation can be demonstrated in the constellation diagram, where the 2 axes represent the 2 components (I and Q). In case of using 16-QAM modulation, the number of states is 16, so 1 symbol represents 4 bits. [11, 255; 6; 14] Bir errors If we simulate all the carriers in the constellation diagram we get not just 1 discrete point, but many points, forming a „cloud and representing each state. In case of additive noise the „cloud gets bigger and the receiver may decide incorrectly, resulting in bit errors. Figure 2 shows the measured constellation diagram without and with additive noise. Measured 16-QAM constellation diagram a) without additive noise b) with additive noise [6] To ensure perfect picture quality, the DVB-T system uses a 2 level error correction (Reed-Solomon and Viterbi). This corrects the bad bits at an even 10-4 Bit Error Rate (BER) and enables error-free data transmission. [13, 32-36] The multi-carrier structure The structure of carriers can be illustrated also in the function of time (Figure 20). The horizontal axis is the frequency and the vertical axis is the time. The 8 MHz channel consists of many carriers, placed 4462 Hz or 1116 Hz far from each other according to the modulation mode (2k or 8k). Structure of OFDM carriers [13] There are some reserved, so-called Transmission Parameter Signalling (TPS) carriers that do not transfer payload, just provide transmission mode information for the receiver, so the total number of useful carriers is 1512 and 6048 respectively in the two transmission modes, and the resultant bit rate is between 4,97 and 31,66 Mbit/s, depending on the modulation (QPSK, 16-QAM or 64-QAM), the transmission mode (2k or 8k), the Code Rate (CR) used for error correction and the selected Guard Interval (GI). This guard interval means that there is a small time gap between each symbol, so the transmission is not continuous. This guarding time enables perfect reception by eliminating the errors caused by multipath propagation.[4, 79-90; 13] Frequency spectrum In 2k mode, 1705 carriers are modulated in the 8 MHz TV channel, so each carrier is 4462 Hz far from its neighbor, while in 8k mode this distance is 1116 Hz. In digital broadcasting, there are no vision and sound carriers, so the power for each carrier is the same. This mean High Performance Wireless Telecommunications Modulation High Performance Wireless Telecommunications Modulation Introduction The primary goal of the project is to analyze of OFDM system and to assess the suitability of OFDM as a modulation technique for wireless communications. In the part of project is covered two leading successfully implementation of OFDM based technologies are Digital Video Broadcasting (DVB-T and DVB-H) and Long Term Evolution (LTE advanced for 4G). Wireless communications is an emerging field, which has seen enormous growth in the last several years. The huge uptake rate of mobile phone technology, Wireless Local Area Networks (WLAN) and the exponential growth of the Internet have resulted in an increased demand for new methods of obtaining high capacity wireless networks. For cellular mobile applications, we will see in the near future a complete convergence of mobile phone technology, computing, Internet access, and potentially many multimedia applications such as video and high quality audio. In fact, some may argue that this convergence has already largely occurred, with the advent of being able to send and receive data using a notebook computer and a mobile phone. The goal of third and fourth generation mobile networks is to provide users with a high data rate, and to provide a wider range of services, such as voice communications, videophones, and high speed Internet access. The higher data rate of future mobile networks will be achieved by increasing the amount of spectrum allocated to the service and by improvements in the spectral efficiency. OFDM is a potential candidate for the physical layer of fourth generation mobile systems. Basic Principles of OFDM OFDM overview The Orthogonal Frequency Division Multiplexing (OFDM) is a modulation technique where multiple low data rate carriers are combined by a transmitter to form a composite high data rate transmission. The first commercial use of OFDM in the communication field was in the 1980s, and it was later widely used in the broadcast audio and video field in the 1990s in such areas as, ADSL, VHDSL, ETSI standard digital audio broadcast (DAB), digital video broadcast (DVB), and high-definition digital TV (HDTV). Digital signal processing makes OFDM possible. To implement the multiple carrier scheme using a bank of parallel modulators would not be very efficient in analog hardware. However, in the digital domain, multi-carrier modulation can be done efficiently with currently available DSP hardware and software. Not only can it be done, but it can also be made very flexible and programmable. This allows OFDM to make maximum use of available bandwidth and to be able to adapt to changing system requirements. Figure 1 is illustrated, Instead of separate modulators; the outgoing waveform is created by executing a high-speed inverse DFT on a set of time-samples of the transmitted data (post modulation). The output of the DFT can be directly modulated onto the outgoing carrier, without requiring any other components. Each carrier in an OFDM system is a sinusoid with a frequency that is an integer multiple of a base or fundamental sinusoid frequency. Therefore, each carrier is like a Fourier series component of the composite signal. In fact, it will be shown later that an OFDM signal is created in the frequency domain, and then transformed into the time domain via the Discrete Fourier Transform (DFT). Two periodic signals are orthogonal when the integral of their product, over one period, is equal to zero. This is true of certain sinusoids as illustrated in Equation 1. Definition of Orthogonal The carriers of an OFDM system are sinusoids that meet this requirement because each one is a multiple of a fundamental frequency. Each one has an integer number of cycles in the fundamental period. [2, 145-153; 6] The importantance of being orthogonal The main concept in OFDM is orthogonality of the sub-carriers.Since the carriers are all sine/cosine wave, we know that area under one period of a sine or a cosine wave is zero. Lets take a sine wave of frequency m and multiply it by a sinusoid (sine or a cosine) of a frequency n, where both m and n are integers. The integral or the area under this product is given by These two components are each a sinusoid, so the integral is equal to zero over one period. When we multiply a sinusoid of frequency n by a sinusoid of frequency m/n the area under the product is zero. In general for all integers n and m , sin(mx), cos(mx), cos(nx) , sin(nx) are all orthogonal to each other. These frequencies are called harmonics. Making the subcarriers mathematically orthogonal was a breakthrough for OFDM because it enables OFDM receivers to separate the subcarriers via an FFT and eliminate the guard bands. As figure 3 shows, OFDM subcarriers can overlap to make full use of the spectrum, but at the peak of each subcarrier spectrum, the power in all the other subcarriers is zero. OFDM therefore offers higher data capacity in a given spectrum while allowing a simpler system design. Creating orthogonal subcarriers in the transmitter is easy using an inverse FFT. To ensure that this orthogonality is maintained at the receiver (so that the subcarriers are not misaligned), the system must keep the transmitter and receiver clocks closely synchronizedwithin 2 parts per million in 802.11a systems. The 802.11a standard therefore dedicates four of its 52 subcarriers as pilots that enable phase-lock loops in the receiver to track the phase and frequency of the incoming signal. The 802.11a standard therefore dedicates four of its 52 subcarriers as pilots that enable phase-lock loops in the receiver to track the phase and frequency of the incoming signal. This method also eliminates low-frequency phase noise.Separating the subcarriers via an FFT require about an order of magnitude fewer multiply-accumulate operations than individually filtering each carrier. In general, an FFT implementation is much simpler than the RAKE receivers used for CDMA and the decision-feedback equalizers for TDMA.This idea are key to understanding OFDM. The orthogonality allows simultaneously transmission on a lot of sub- carriers in a tight frequency space without interference form each other. In essence this is similar to CDMA, where codes are used to make data sequences independent (also orthogonal) which allows many independent users to transmitin same space successfully.[2, 153-154; 6 ; 7] OFDM Operation Preliminary Concepts When the DFT (Discrete Fourier Transform) of a time signal is taken, the frequency domain results are a function of the time sampling period and the number of samples as shown in Figure 4. The fundamental frequency of the DFT is equal to 1/NT (1/total sample time). Each frequency represented in the DFT is an integer multiple of the fundamental frequency. Parameter Mapping from Time to Frequency for the DFT The maximum frequency that can be represented by a time signal sampled at rate 1/T is fmax = 1/2T as given by the Nyquist sampling theorem. This frequency is located in the center of the DFT points. All frequencies beyond that point are images of the representative frequencies. The maximum frequency bin of the DFT is equal to the sampling frequency (1/T) minus one fundamental (1/NT).The IDFT (Inverse Discrete Fourier Transform) performs the opposite operation to the DFT. It takes a signal defined by frequency components and converts them to a time signal. The parameter mapping is the same as for the DFT. The time duration of the IDFT time signal is equal to the number of DFT bins (N) times the sampling period (T).It is perfectly valid to generate a signal in the frequency domain, and convert it to a time domain equivalent for practical use (The frequency domain is a mathematical tool used for analysis. Anything usable by the real world must be converted into a real, time domain signal). This is how modulation is applied in OFDM. In practice the Fast Fourier Transform (FFT) and IFFT are used in place of the DFT and IDFT, so all further references will be to FFT and IFFT.[1 ,118 ; 4] Definition of Carriers The maximum number of carriers used by OFDM is limited by the size of the IFFT. This is determined as follows in Equation 2. OFDM Carrier Count In order to generate a real-valued time signal, OFDM (frequency) carriers must be defined in complex conjugate pairs, which are symmetric about the Nyquist frequency (fmax). This puts the number of potential carriers equal to the IFFT size/2. The Nyquist frequency is the symmetry point, so it cannot be part of a complex conjugate pair. The DC component also has no complex conjugate. These two points cannot be used as carriers so they are subtracted from the total available. If the carriers are not defined in conjugate pairs, then the IFFT will result in a time domain signal that has imaginary components. This must be a viable option as there are OFDM systems defined with carrier counts that exceed the limit for real-valued time signals given in Equation 2.In general, a system with IFFT size 256 and carrier count 216. This design must result in a complex time waveform. Further processing would require some sort of quadrature technique (use of parallel sine and cosine processing paths). In this report, only real-value time signals will be treated, but in order to obtain maximum bandwidth efficiency from OFDM, the complex time signal may be preferred (possibly an analogous situation to QPSK vs. BPSK). Equation 2, for the complex time waveform, has all IFFT bins available as carriers except the DC bin. Both IFFT size and assignment (selection) of carriers can be dynamic. The transmitter and receiver just have to use the same parameters. This is one of the advantages of OFDM. Its bandwidth usage (and bit rate) can be varied according to varying user requirements. A simple control message from a base station can change a mobile units IFFT size and carrier selection.[2,199-206; 4] Modulation Binary data from a memory device or from a digital processing stream is used as the modulating (baseband) signal. The following steps may be carried out in order to apply modulation to the carriers in OFDM: combine the binary data into symbols according to the number of bits/symbol selected convert the serial symbol stream into parallel segments according to the number of carriers, and form carrier symbol sequences apply differential coding to each carrier symbol sequence convert each symbol into a complex phase representation assign each carrier sequence to the appropriate IFFT bin, including the complex conjugates take the IFFT of the result OFDM modulation is applied in the frequency domain. Figure 5 and Figure 6 give an example of modulated OFDM carriers for one symbol period, prior to IFFT. OFDM Carrier Magnitude prior to IFFT For this example, there are 4 carriers, the IFFT bin size is 64, and there is only 1 bit per symbol. The magnitude of each carrier is 1, but it could be scaled to any value. The phase for each carrier is either 0 or 180 degrees, according to the symbol being sent. The phase determines the value of the symbol (binary in this case, either a 1 or a 0). In the example, the first 3 bits (the first 3 carriers) are 0, and the 4th bit (4th carrier) is a 1. OFDM Carrier Phase prior to IFFT Note that the modulated OFDM signal is nothing more than a group of delta (impulse) functions, each with a phase determined by the modulating symbol. In addition, note that the frequency separation between each delta is proportional to 1/N where N is the number of IFFT bins. The frequency domain representation of the OFDM is described in Equation 3. OFDM Frequency Domain Representation (one symbol period) After the modulation is applied, an IFFT is performed to generate one symbol period in the time domain. The IFFT result is shown in 7. It is clear that the OFDM signal has varying amplitude. It is very important that the amplitude variations be kept intact as they define the content of the signal. If the amplitude is clipped or modified, then an FFT of the signal would no longer result in the original frequency characteristics, and the modulation may be lost. This is one of the drawbacks of OFDM, the fact that it requires linear amplification. In addition, very large amplitude peaks may occur depending on how the sinusoids line up, so the peak-to-average power ratio is high. This means that the linear amplifier has to have a large dynamic range to avoid distorting the peaks. The result is a linear amplifier with a constant, high bias current resulting in very poor power efficiency. OFDM Signal, 1 Symbol Period Figure 8 is provided to illustrate the time components of the OFDM signal. The IFFT transforms each complex conjugate pair of delta functions (each carrier) into a real-valued, pure sinusoid. Figure 8 shows the separate sinusoids that make up the composite OFDM waveform given in Figure 7. The one sinusoid with 180 phase shift is clearly visible as is the frequency difference between each of the 4 sinusoids. Transmission The key to the uniqueness and desirability of OFDM is the relationship between the carrier frequencies and the symbol rate. Each carrier frequency is separated by a multiple of 1/NT (Hz). The symbol rate (R) for each carrier is 1/NT (symbols/sec). The effect of the symbol rate on each OFDM carrier is to add a sin(x)/x shape to each carriers spectrum. The nulls of the sin(x)/x (for each carrier) are at integer multiples of 1/NT. The peak (for each carrier) is at the carrier frequency k/NT. Therefore, each carrier frequency is located at the nulls for all the other carriers. This means that none of the carriers will interfere with each other during transmission, although their spectrums overlap. The ability to space carriers so closely together is very bandwidth efficient. OFDM Time Waveform Figure 9 shows the OFDM time waveform for the same signal. There are 100 symbol periods in the signal. Each symbol period is 64 samples long (100 x 64 = 6400 total samples). Each symbol period contains 4 carriers each of which carries 1 symbol. Each symbol carries 1 bit. Note that Figure 9 again illustrates the large dynamic range of the OFDM waveform envelope. OFDM Spectrum Figure 10 shows the spectrum for of an OFDM signal with the following characteristics: 1 bit / symbol 100 symbols / carrier (i.e. a sequence of 100 symbol periods) 4 carriers 64 IFFT bins spectrum averaged for every 20 symbols (100/20 = 5 averages) Red diamonds mark all of the available carrier frequencies. Note that the nulls of the spectrums line up with the unused frequencies. The four active carriers each have peaks at carrier frequencies. It is clear that the active carriers have nulls in their spectrums at each of the unused frequencies (otherwise, the nulls would not exist). Although it cannot be seen in the figure, the active frequencies also have spectral nulls at the adjacent active frequencies. It is not currently practical to generate the OFDM signal directly at RF rates, so it must be up converted for transmission. To remain in the discrete domain, the OFDM could be upsampled and added to a discrete carrier frequency. This carrier could be an intermediate frequency whose sample rate is handled by current technology. It could then be converted to analog and increased to the final transmit frequency using analog frequency conversion methods. Alternatively, the OFDM modulation could be immediately converted to analog and directly increased to the desired RF transmits frequency. Either way, the selected technique would have to involve some form of linear AM (possibly implemented with a mixer). [1, 122-125; 6] Reception and Demodulation The received OFDM signal is down converted (in frequency) and taken from analog to digital. Demodulation is done in the frequency domain (just as modulation was). The following steps may be taken to demodulate the OFDM: partition the input stream into vectors representing each symbol period take the FFT of each symbol period vector extract the carrier FFT bins and calculate the phase of each calculate the phase difference, from one symbol period to the next, for each carrier decode each phase into binary data sort the data into the appropriate order OFDM Carrier Magnitude following FFT Figure 11 and Figure 12 show the magnitude and spectrum of the FFT for one received OFDM symbol period. For this example, there are 4 carriers, the IFFT bin size is 64, there is 1 bit per symbol, and the signal was sent through a channel with AWGN having an SNR of 8 dB. The figures show that, under these conditions, the modulated symbols are very easy to recover. OFDM Carrier Phase following FFT In Figure 12 that the unused frequency bins contain widely varying phase values. These bins are not decoded, so it does not matter, but the result is of interest. Even if the noise is removed from the channel, these phase variations still occur. It must be a result of the IFFT/FFT operations generating very small complex values (very close to 0) for the unused carriers. The phases are a result of these values. [1, 125 -128; 3] OFDM transceiver OFDM signals are typically generated digitally due to the difficulty in creating large banks of phase lock oscillators and receivers in the analog domain. Figure 13 shows the block diagram of a typical OFDM transceiver. The transmitter section converts digital data to be transmitted, into a mapping of subcarrier amplitude and phase. It then transforms this spectral representation of the data into the time domain using an Inverse Discrete Fourier Transform (IDFT). The Inverse Fast Fourier Transform (IFFT) performs the same operations as an IDFT, except that it is much more computationally efficiency, and so is used in all practical systems. In order to transmit the OFDM signal the calculated time domain signal is then mixed up to the required frequency. Block diagram showing a basic OFDM transceiver [3] The receiver performs the reverse operation of the transmitter, mixing the RF signal to base band for processing, then using a Fast Fourier Transform (FFT) to analyze the signal in the frequency domain. The amplitude and phase of the subcarriers is then picked out and converted back to digital data. The IFFT and the FFT are complementary function and the most appropriate term depends on whether the signal is being received or generated. In cases where the Signal is independent of this distinction then the term FFT and IFFT is used interchangeably. [1, 125 -128, 3] Analysis of OFDM characteristics Guard Period OFDM demodulation must be synchronized with the start and end of the transmitted symbol period. If it is not, then ISI will occur (since information will be decoded and combined for 2 adjacent symbol periods). ICI will also occur because orthogonality will be lost (integrals of the carrier products will no longer be zero over the integration period), To help solve this problem, a guard interval is added to each OFDM symbol period. The first thought of how to do this might be to simply make the symbol period longer, so that the demodulator does not have to be so precise in picking the period beginning and end, and decoding is always done inside a single period. This would fix the ISI problem, but not the ICI problem. If a complete period is not integrated (via FFT), orthogonality will be lost. The effect of ISI on an OFDM signal can be further improved by the addition of a guard period to the start of each symbol. This guard period is a cyclic copy that extends the length of the symbol waveform. Each subcarrier, in the data section of the symbol, (i.e. the OFDM symbol with no guard period added, which is equal to the length of the IFFT size used to generate the signal) has an integer number of cycles. Because of this, placing copies of the symbol end-to-end results in a continuous signal, with no discontinuities at the joins. Thus by copying the end of a symbol and appending this to the start results in a longer symbol time. Addition of a guard period to an OFDM signal [3] In Figure 14, The total length of the symbol is Ts=TG + TFFT, where Ts is the total length of the symbol in samples, TG is the length of the guard period in samples, and TFFT is the size of the IFFT used to generate the OFDM signal. In addition to protecting the OFDM from ISI, the guard period also provides protection against time-offset errors in the receiver. For an OFDM system that has the same sample rate for both the transmitter and receiver, it must use the same FFT size at both the receiver and transmitted signal in order to maintain subcarrier orthogonality. Each received symbol has TG + TFFT samples due to the added guard period. The receiver only needs TFFT samples of the received symbol to decode the signal. The remaining TG samples are redundant and are not needed. For an ideal channel with no delay spread the receiver can pick any time offset, up to the length of the guard period, and still get the correct number of samples, without crossing a symbol boundary. Function of the guard period for protecting against ISI [3] Figure 15 shows this effect. Adding a guard period allows time for the transient part of the signal to decay, so that the FFT is taken from a steady state portion of the symbol. This eliminates the effect of ISI provided that the guard period is longer than the delay spread of the radio channel. The remaining effects caused by the multipath, such as amplitude scaling and phase rotation are corrected for by channel equalization. In order to avoid ISI and ICI, the guard period must be formed by a cyclic extension of the symbol period. This is done by taking symbol period samples from the end of the period and appending them to the front of the period. The concept of being able to do this, and what it means, comes from the nature of the IFFT/FFT process. When the IFFT is taken for a symbol period (during OFDM modulation), the resulting time sample sequence is technically periodic. This is because the IFFT/FFT is an extension of the Fourier Transform which is an extension of the Fourier Series for periodic waveforms. All of these transforms operate on signals with either real or manufactured periodicity. For the IFFT/FFT, the period is the number of samples used. Guard Period via Cyclic Extension With the cyclic extension, the symbol period is longer, but it represents the exact same frequency spectrum. As long as the correct number of samples are taken for the decode, they may be taken anywhere within the extended symbol. Since a complete period is integrated, orthogonality is maintained. Therefore, both ISI and ICI are eliminated. Note that some bandwidth efficiency is lost with the addition of the guard period (symbol period is increased and symbol rate is decreased) [2,154-160, 3] Windowing The OFDM signal is made up of a series of IFFTs that are concatenated to each other. At each symbol period boundary, there is a signal discontinuity due to the differences between the end of one period and the start of the next. These discontinuities can cause high frequency spectral noise to be generated (because they look like very fast transitions of the time waveform). To avoid this, a window function (Hamming, Hanning, Blackman, ) may be applied to each symbol period. The window function would attenuate the time waveform at the start and the end of each period, so that the discontinuities are smaller, and the high frequency noise is reduced. However, this attenuation distorts the signal and some of the desired frequency content is lost.[1, 121;2 154] Multipath Characteristics OFDM avoids frequency selective fading and ISI by providing relatively long symbol periods for a given data rate. This is illustrated in Figure 17. For a given transmission channel and a given source data rate, OFDM can provide better multipath characteristics than a single carrier. OFDM vs. Single Carrier, Multipath Characteristic Comparison However, since the OFDM carriers are spread over a frequency range, there still may be some frequency selective attenuation on a time-varying basis. A deep fade on a particular frequency may cause the loss of data on that frequency for a given time, but the use of Forward Error Coding can fix it. If a single carrier experienced a deep fade, too many consecutive symbols may be lost and correction coding may be ineffective. [8] Bandwidth A comparison of RF transmits bandwidth between OFDM and a single carrier is shown in Figure 18 (using the same example parameters as in Figure 17). OFDM Bandwidth Efficiency In Figure 18, the calculations show that OFDM is more bandwidth efficient than a single carrier. Note that another efficient aspect of OFDM is that a single transmitters bandwidth can be increased incrementally by addition of more adjacent carriers. In addition, no bandwidth buffers are needed between transmit bandwidths of separate transmitters as long as orthogonality can be maintained between all the carriers.[2, 161-163; 8; 9] Physical Implementation Since OFDM is carried out in the digital domain, there are many ways it can be implemented. Some options are provided in the following list. Each of these options should be viable given current technology: ASIC (Application Specific Integrated Circuit) ASICs are the fastest, smallest, and lowest power way to implement OFDM Cannot change the ASIC after it is built without designing a new chip General-purpose Microprocessor or MicroController PowerPC 7400 or other processor capable of fast vector operations Highly programmable Needs memory and other peripheral chips Uses the most power and space, and would be the slowest Field-Programmable Gate Array (FPGA) An FPGA combines the speed, power, and density attributes of an ASIC with the programmability of a general purpose processor. An FPGA could be reprogrammed for new functions by a base station to meet future (currently unknown requirements).This should be the best choice.[9] OFDM uses in DVB (Digital Video Broadcasting) DVB (Digital Video Broadcast) is a set of standards for the digital transmission of video and audio streams, and also data transmission. The DVB standards are maintained by the DVB Project, which is an industry-led consortium of over 260 broadcasters, manufacturers, network operators, software developers, regulatory bodies and others in over 35 countries. DVB has been implemented over satellite (DVB-S, DVB-S2), cable (DVB-C), terrestrial broadcasting (DVB-T), and handheld terminals (DVB-H). the DVB standard following the logical progression of signal processing steps, as well as source and channel coding, COFDM modulation, MPEG compression and multiplexing methods, conditional access and set-top box Technology. In this project is presented an investigation of two OFDM based DVB standards, DVB-T and DVB-H. DVB-T (Digital Video Broadcasting Terrestrial) The first Terrestrial Digital Video Broadcasting pilot transmissions were started in the late 90s, and the first commercial system was established in Great Britain. In the next few years the digital broadcasting system has been set up in many countries, and the boom of the digital terrestrial transmission is estimated in the next few years, while the analogue transmission will be cancelled within about 15 years. The greatest advantage of the digital system is the effective use of the frequency spectrum and its lower radiated power in comparison with the analogue transmission, while the covered area remains the same. Another key feature is the possibility of designing a so-called Single Frequency Network (SFN), which means that the neighboring broadcast stations use the same frequency and the adjacent signals dont get interfered. The digital system transmits a data stream, which means that not only television signals but data communication (e.g. Internet service) may be used according to the demands. The data stream consists of an MPEG-2 bit stream, which means a compression is used, enabling the transfer of even 4 or 5 television via the standard 8 MHz wide TV channel. For the viewer, the main advantages are the perfect, noise-free picture, CD quality sound, and easier handling, as well as services like Super Teletext, Electronic Programme Guide, interactivity and mobility.[11, 251-253] Modulation technique in DVB-T The DVB-T Orthogonal Frequency Division Multiplexing (OFDM) modulation system uses multi-carrier transmission. There are 2 modes, the so-called 2k and 8k modes, using 1705 and 6817 carriers respectively, with each carrier modulated separately and transmitted in the 8 MHz TV channel. The common modulation for the carriers is typically QPSK, 16-QAM or 64-QAM. Each signal can be divided into two, so-called „In Phase (I) and „Quadrature Phase components, being a 90Â ° phase shift between them. The constellation diagram and the bit allocation is shown in bellow 16-QAM constellation diagram and bit allocation [6] This modulation can be demonstrated in the constellation diagram, where the 2 axes represent the 2 components (I and Q). In case of using 16-QAM modulation, the number of states is 16, so 1 symbol represents 4 bits. [11, 255; 6; 14] Bir errors If we simulate all the carriers in the constellation diagram we get not just 1 discrete point, but many points, forming a „cloud and representing each state. In case of additive noise the „cloud gets bigger and the receiver may decide incorrectly, resulting in bit errors. Figure 2 shows the measured constellation diagram without and with additive noise. Measured 16-QAM constellation diagram a) without additive noise b) with additive noise [6] To ensure perfect picture quality, the DVB-T system uses a 2 level error correction (Reed-Solomon and Viterbi). This corrects the bad bits at an even 10-4 Bit Error Rate (BER) and enables error-free data transmission. [13, 32-36] The multi-carrier structure The structure of carriers can be illustrated also in the function of time (Figure 20). The horizontal axis is the frequency and the vertical axis is the time. The 8 MHz channel consists of many carriers, placed 4462 Hz or 1116 Hz far from each other according to the modulation mode (2k or 8k). Structure of OFDM carriers [13] There are some reserved, so-called Transmission Parameter Signalling (TPS) carriers that do not transfer payload, just provide transmission mode information for the receiver, so the total number of useful carriers is 1512 and 6048 respectively in the two transmission modes, and the resultant bit rate is between 4,97 and 31,66 Mbit/s, depending on the modulation (QPSK, 16-QAM or 64-QAM), the transmission mode (2k or 8k), the Code Rate (CR) used for error correction and the selected Guard Interval (GI). This guard interval means that there is a small time gap between each symbol, so the transmission is not continuous. This guarding time enables perfect reception by eliminating the errors caused by multipath propagation.[4, 79-90; 13] Frequency spectrum In 2k mode, 1705 carriers are modulated in the 8 MHz TV channel, so each carrier is 4462 Hz far from its neighbor, while in 8k mode this distance is 1116 Hz. In digital broadcasting, there are no vision and sound carriers, so the power for each carrier is the same. This mean