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Wireless Access Systems: Exercise 2 – Coded OFDM Modem

Wireless Access Systems: Exercise 2 – Coded OFDM Modem. Schedule:. Coded OFDM Modem. We will simulate a complete coded OFDM (COFDM) modem . . Input bits. Estimated bits. Coded OFDM Modem. We will simulate a complete coded OFDM (COFDM) modem . . Task 2: OFDM. Task 1:

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Wireless Access Systems: Exercise 2 – Coded OFDM Modem

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  1. Wireless Access Systems:Exercise 2 – Coded OFDM Modem

  2. Schedule: Communication Technology Laboratory Wireless Communication Group

  3. Coded OFDM Modem • We will simulate a completecoded OFDM (COFDM) modem. Input bits Estimated bits Communication Technology Laboratory Wireless Communication Group

  4. Coded OFDM Modem • We will simulate a completecoded OFDM (COFDM) modem. Task 2: OFDM Task 1: Channel Coding From Exercise 1 Input bits Estimated bits Communication Technology Laboratory Wireless Communication Group

  5. Coded OFDM Modem • Task 1– Channel Coding: Groups 1, 3 and 5 • Getfamiliarwithchannelcoding: convolutionalcodes, Viterbidecoder and bit-interleaver • Task 2 – OFDM: Groups 2, 4 and 6 • Getacquaintedwithconceptsof OFDM modulation/demodulation, cyclicprefix, frequencyselectivefadingchannel, channelestimation. • Combination Task – COFDM: Group {1,2}, {3,4} and {5,6} Communication Technology Laboratory Wireless Communication Group

  6. Task 1 – Convolutional Coding • Channel codingenablesthecorrectionand/ordetectionofbiterrorsintroducedbytransmissionof a modulatedsignalthrough a wirelesschannel. • Block codesandconvolutionalcodes. • A rate R = k/n convolutionalencoderwithmemorym isnothing but a k-input, n-output linear sequentialcircuitwithmemorym. Communication Technology Laboratory Wireless Communication Group

  7. Task 1 – Convolutional Coding k = 1, n = 2, m= 3 • Implementation: [0 0 1 0 1 1] Modulo 2 Conv g(0) Modulo 2 Conv g(1) [0 0 1 1 1 1] Communication Technology Laboratory Wireless Communication Group

  8. Task 1 – Interleaving • Channel codes are designed for good performance in AWGN channels. • In fading channels, when the channel is in deep fade, the errors usually occur in long bursts. • To improve coding performance in fading channels, interleaving has been introduced. • The basic idea: Spread error bursts due to deep fades over many codewords such that the received codeword exhibits at most a few simultaneous errors. Communication Technology Laboratory Wireless Communication Group

  9. Task 1 – Interleaving Without interleaver: Transmitted: 1 2 3 4 5 6 7 … Burst Error: 1 2 3 x x x 7 … Cannot be corrected Example: Hamming code (7,4) can correct only one error Communication Technology Laboratory Wireless Communication Group

  10. Task 1 – Interleaving read write With interleaver: Example: Hamming code (7,4) can correct only one error Communication Technology Laboratory Wireless Communication Group

  11. Task 1 – Interleaving With interleaver: Transmitted: 1 8 15 22 29 36 43 … Burst Error: 1 8 15 x x x 43 … Example: Hamming code (7,4) can correct only one error Communication Technology Laboratory Wireless Communication Group

  12. Task 1 – Interleaving With interleaver: Transmitted: 1 8 15 22 29 36 43 Burst Error: 1 8 15 x x x 43 Only one error  can be corrected Example: Hamming code (7,4) can correct only one error Communication Technology Laboratory Wireless Communication Group

  13. Task 1 – Viterbi Decoding • The convolutionalencodershave a naturaltrellisstructure. • Maximum likelihooddetectionof a convolutionalcodeentailsfindingthemostlikelysequenceofcodedsymbolsgiventhereceivedsequenceofcodedsymbols. • The Viterbialgorithmreducesthecomplexityofmaximumlikelihooddecodingbysystematicallyremovingpathsfromconsiderationthatcannotachievethehighestpathmetric. Communication Technology Laboratory Wireless Communication Group

  14. Task 2 - ODFM Modem Communication Technology Laboratory Wireless Communication Group

  15. Task 2 - ODFM Modem Circulant Channel Matrix Communication Technology Laboratory Wireless Communication Group

  16. Task 2 - ODFM Modem • Example: 2 taps channel • Remove Cyclic Prefix • Add Cyclic Prefix Circulant Channel Matrix Communication Technology Laboratory Wireless Communication Group

  17. Task 2 - ODFM Modem Diagonal Channel Matrix Communication Technology Laboratory Wireless Communication Group

  18. Task 2 – ODFM Modem • Let the vector of one OFDM symbol be: • The received vector (after CP removal): • Here, is circulant because of the cyclic prefix assumption. • Therefore, can be decomposed as: with a diagonal matrix • Hence, we perform an IDFT at the transmitter and a DFT at the receiver: with Communication Technology Laboratory Wireless Communication Group

  19. Task 2 – OFDM Detection and Estimation • After FFT, weshouldremovetheeffectofthechannelfromthedemodulatedsymbols. • Letbethedetectedk-thsymbolwhichisgivenby • The estimateofthechannelsisneededtobeperformedatthereceiver. • Howtoestimatethechannel? Communication Technology Laboratory Wireless Communication Group

  20. Task 2 – OFDM Detection and Estimation Communication Technology Laboratory Wireless Communication Group

  21. Combination Task – COFDM Same groups cooperate as last time. Combination Task Task 2: OFDM Task 1: Channel Coding Input bits Estimated bits Communication Technology Laboratory Wireless Communication Group

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