Indira Rajagopal Joydeep Acharya Madhavi V Ratnagiri Sumathi Gopal Implementation and Performance Evaluation of an OFDM Modem With Variations in Cyclic Prefix Length and Channel Coding for Different Channels Indira Rajagopal Joydeep Acharya Madhavi V Ratnagiri Sumathi Gopal Course: Communication Theory (ECE 545); Rutgers University Professor: Dr. Predrag Spasojevic

Topics Introduction to OFDM Description of OFDM system simulated Channel Simulation Results Conclusions References 04/23/2003 OFDM Performance

Introduction to OFDM Orthogonal Frequency Division Multiplexing; Part of xDSL, IEEE 802.11a standards Improves Data rates, such as 56Mbps in IEEE 802.11a 04/23/2003 OFDM Performance

Introduction to OFDM Resilience to frequency selective channels In real life we encounter channels which exhibit variation of gain and phase with frequency. A wideband signal is hence likely to get distorted differently at different frequencies. Hence if we split the wideband signal into multiple narrow band signals, the channel can be treated as constant over those individual narrow bands, and the Courtesy : “Multicarrier Primer” Resilience to frequency selective channels 04/23/2003 OFDM Performance

OFDM Transmitter Bits per OFDM symbol = (IFFT_Size/2) * log2(M) S/P Channel Coding Inter Leaving S/P Modulation (M) IFFT Cyclic Prefix Mapping from size N/2 to N Source Data To Modulation, IFFT is the crux of OFDM. The incoming bitsteam is split into separate subchannels, each correesponding to a ortho. Subcarrier. Why IFFT: instead of using multiple analog ortho. Subcarriers, same effect is achieved digitally using IFFT/FFT. Bits per OFDM symbol = (IFFT_Size/2) * log2(M) 04/23/2003 OFDM Performance

Channel Coding BCH Code k=16; t = 3; Convolutional code; Inter Leaving S/P Modulation IFFT P/S Cyclic Prefix Mapping from size N/2 to N Source Data To BCH Code n = 31; k=16; t = 3; Convolutional code; Rate = ½ ; K=7 Courtesy: 802.11a std. 04/23/2003 OFDM Performance

Interleaving Read out b1 b4 b7 b10 b2 b5 b8 b11 Fill in b3 b6 b9 b12 Channel Coding Inter Leaving S/P Modulation IFFT P/S Cyclic Prefix Mapping from size N/2 to N Source Data To Read out b1 b4 b7 b10 b2 b5 b8 b11 Fill in b3 b6 b9 b12 04/23/2003 OFDM Performance

Interleaving b1 b4 b7 b10 Read out b2 b5 b8 b11 Fill in b3 b6 b9 b12 Channel Coding Inter Leaving S/P Modulation IFFT P/S Cyclic Prefix Mapping from size N/2 to N Source Data To b1 b4 b7 b10 Read out b1 b4 b7 b10 b2 b5 b8 b11 b3 b6 b9 b12 b2 b5 b8 b11 Fill in b3 b6 b9 b12 04/23/2003 OFDM Performance

Modulation Schemes Used Channel Coding Inter Leaving S/P Modulation IFFT P/S Cyclic Prefix Mapping from size N/2 to N Source Data To QPSK (4-QAM) 16-QAM 64-QAM We have employed QPSK… in our system higher order mod schemes are used to achieve higher data rtes. 04/23/2003 OFDM Performance

N/2 to N Mapper and IFFT X*n-k = Xk where k : 1,… n/2 IFFT Block Channel Coding Inter Leaving S/P Modulation IFFT P/S Cyclic Prefix Source Data To Mapping from size N/2 to N X*n-k = Xk where k : 1,… n/2 Mapping done so that the input seq to IFFT is conjugsate-symmetric so that we have real valued ifft output. IFFT Block Real Valued samples N N/2 Mapper Re(XN/2) X1 XN/2-1 Im(XN/2) X*N/2-1 X*1 X2 XN/2 04/23/2003 OFDM Performance

Adding cyclic prefix x(n) * h(n) = X(k)H(k) S/P Modulation Mapping from size N/2 to N IFFT P/S Channel Coding Source Data Inter Leaving Modulation Cyclic Prefix To Channel Modulation Modulation x(n) * h(n) = X(k)H(k) Original N Samples Time Added Prefix Cyclic prefix length 04/23/2003 OFDM Performance

Channel Models AWGN: Rayleigh Flat fading: r = s + n Rayleigh Flat fading: r = ρs + n where ρ is Rayleigh distributed Rayleigh Frequency Selective: r = h*s + n where h is channel impulse response 04/23/2003 OFDM Performance

OFDM Receiver De- Coding De- Inter Demod FFT P/S Remove Cyclic Prefix Channel De- Coding De- Inter Leaving Demod FFT P/S Remove Cyclic Prefix Mapping from size N to N/2 From Received Bits Thres- holding S/P 04/23/2003 OFDM Performance

Thresholding S/P FFT Mapping from size N to N/2 Thres- holding P/S Demod Remove Cyclic Prefix From Channel Demod De- Inter Leaving Channel De- Coding Received Bits Demod Demod 04/23/2003 OFDM Performance

Thresholding based on decision regions for 16-QAM 04/23/2003 OFDM Performance

De-Interleaving Read out b1 b2 b3 b4 b5 b6 Fill in b7 b8 b9 b10 b11 S/P Mapping from size N to N/2 FFT Thres- holding P/S Demod From Channel Remove Cyclic Prefix Demod De- Inter Leaving Channel De- Coding Received Bits Demod Demod Read out b1 b2 b3 b1 b2 b3 b4 b5 b6 b7 b8 b9 b10 b11 b12 b4 b5 b6 Fill in b7 b8 b9 b10 b11 b12 04/23/2003 OFDM Performance

Topics Introduction to OFDM Description of OFDM system Channel Models Results Conclusions References 04/23/2003 OFDM Performance

Received Signal Constellation for 16-QAM in Presence of AWGN 04/23/2003 OFDM Performance

Bit Error Rate for AWGN for various IFFT sizes 04/23/2003 OFDM Performance

Bit Error Rate for AWGN for various Modulation Schemes 04/23/2003 OFDM Performance

Bit Error Rate for AWGN with and without Coding 04/23/2003 OFDM Performance

OFDM spectrum 04/23/2003 OFDM Performance

Coded and uncoded BER for flat fading Rayleigh channel 04/23/2003 OFDM Performance

Effect of varying cyclic prefix in a flat fading channel 04/23/2003 OFDM Performance

Conclusions We were able to demonstrate the performance of an OFDM system in AWGN channel and a Rayleigh channel with flat fading 04/23/2003 OFDM Performance

Further work Obtain BER plots of frequency selective channel with and without coding Demonstrate change in BER with change in length of cyclic prefix, for a frequency selective channel Analyze any tradeoffs between coding and length of cyclic prefix 04/23/2003 OFDM Performance

References IEEE 802.11a standard J. M. Cioffi, “A multicarrier primer,” ANSI T1E1.4 Committee Contribution, Nov. 1991. Rappaport, T.S., “Wireless Communications, Principles and Practice”, Second Edition Prentice Hall. Sklar Bernard, “Digital Communications” , Pearson Education Asia, Second Edition, 2001. 04/23/2003 OFDM Performance

It was FUN! Thank You for your patience Acknowledgements WINLAB students and faculty: Predrag, Leo, Praveen, Hithesh, Ahmed, Lang, Rueheng, Jassi, Amith, and many more. Zoran Kostic at Thomson Inc. It was FUN! Thank You for your patience 04/23/2003 OFDM Performance