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Oversampled Perfect Reconstruction Filter Bank Transceivers Oversampled Perfect Reconstruction Filter Bank Transceivers Siavash Rahimi Department of Electrical & Computer Engineering McGill University Montreal, Canada March 2014 A thesis submitted to McGill University in partial fulfillment of the requirements for the degree of Doctor of Philosophy. c 2014 Siavash Rahimi 2014/03/05 i Contents 1 Introduction 1 1.1 Multicarrier Modulation ............................ 1 1.2 Literature Review ................................ 3 1.2.1 Oversampled perfect reconstruction filter bank ............ 5 1.2.2 Synchronization and equalization ................... 6 1.2.3 Extension to multi-user applications .................. 8 1.3 Thesis Objectives and Contributions ..................... 9 1.4 Thesis Organization and Notations ...................... 12 2 Background on Filter Bank Multicarrier Modulation 14 2.1 OFDM ...................................... 15 2.1.1 The Cyclic Prefix ............................ 17 2.1.2 OFDM Challenges ........................... 19 2.2 Multirate Filter Banks ............................. 22 2.2.1 Basic Multirate Operations ...................... 24 2.2.2 Transceiver Transfer Relations and Reconstruction Conditions . 29 2.2.3 Modulated Filter Banks ........................ 32 2.2.4 Oversampled Filter Banks ....................... 37 2.3 A Basic Survey of Different FBMC Types .................. 39 2.3.1 Cosine Modulated Multitone ...................... 39 2.3.2 OFDM/OQAM ............................. 41 2.3.3 FMT ................................... 45 2.3.4 DFT modulated OPRFB ........................ 46 Contents ii 3 OPRFB Transceivers 47 3.1 Background and Problem Formulation .................... 47 3.2 A Factorization of Polyphase Matrix P(z) .................. 51 3.2.1 Preliminary Factorization of P(z)................... 51 3.2.2 Structure of U(z) ........................... 52 3.2.3 Expressing U(z) in terms of Paraunitary Building Blocks ...... 54 3.3 Choice of a Parameterization for Paraunitary Matrix B(z) ......... 57 3.3.1 Order-based method . ....................... 57 3.3.2 CSD-based method ........................... 59 3.3.3 Post-filtering based method ...................... 60 3.4 Prototype Filter Design ............................ 62 3.4.1 Optimization of Prototype Filter ................... 63 3.4.2 Comparison of Prototype Filters .................... 64 3.4.3 Prototype Filter for M = 128 and K =132.............. 65 3.5 Numerical Results ................................ 68 3.5.1 Methodology .............................. 68 3.5.2 Results and Discussion ......................... 69 3.6 Conclusion .................................... 74 4 Joint Channel and Frequency Offset Estimation for OPRFB Systems 79 4.1 Problem Formulation . ............................. 79 4.1.1 OPRFB System Model ......................... 79 4.1.2 Effects of Carrier Frequency Offset .................. 81 4.1.3 Problem Formulation .......................... 83 4.2 Joint Estimation ................................ 83 4.2.1 Data-aided ML estimator ....................... 83 4.2.2 Simplifications of the LLF ....................... 88 4.3 Joint Cramer Rao Bound ............................ 89 4.4 Experimental Results .............................. 92 4.4.1 Methodology and Setup ........................ 92 4.4.2 Results and Discussions ........................ 94 4.5 Conclusion .................................... 99 Contents iii 5 Joint Synchronization and Equalization in the Uplink of MU-OPRFB 104 5.1 Multi-user OPRFB System Model ....................... 104 5.2 Joint Estimation ................................ 109 5.2.1 Iterative Joint Estimation ....................... 113 5.3 Results ...................................... 114 5.4 Conclusion .................................... 117 6 Conclusions and Future Works 121 6.1 Summary and Conclusions ........................... 121 6.2 Future Works .................................. 124 A Factorization of P(z) 126 B Statistical Properties of Data-interference 128 References 130 iv List of Figures 1.1 Generic multicarrier modulation system .................... 2 2.1 OFDM with IDFT/DFT implementation ................... 15 2.2 Addition of CP with length Lcp to the OFDM samples ........... 16 2.3 Magnitude of the frequency response of three adjacent subband filters of OFDM (M = 64, l ∈{15, 16, 17})....................... 20 2.4 Use of AFB followed by SFB for subband processing application ...... 23 2.5 Use of SFB followed by AFB for MCM application ............. 23 2.6 K-fold decimation with anti-aliasing filter .................. 24 2.7 Downsampling by a factor of 2 in the time-domain .............. 25 2.8 Downsampling by a factor of 4 with ideal anti-aliasing complex filter in three steps (top) input signal (middle) filtered signal (bottom) downsampled signal 26 2.9 Upsampling by a factor of 2 in the time-domain ............... 27 2.10 K-fold interpolation with anti-imaging filter ................. 27 2.11 Upsampling by a factor of 4 with interpolation filter in three steps (top) input signal (middle) upsampled signal (bottom) filtered signal ....... 29 2.12 First Noble identity ............................... 30 2.13 Second Noble identity ............................. 30 2.14 Cosine modulated filter bank with odd stacked subbands .......... 33 2.15 Cosine modulated filter bank with even stacked subbands .......... 34 2.16 DFT modulated filter bank .......................... 36 2.17 Spectral characteristics of an oversampled FBMC system .......... 38 2.18 OFDM/OQAM transceiver chain with OQAM pre-processing and post-processing blocks...................................... 41 List of Figures v 3.1 Oversampled FB transceiver .......................... 48 3.2 Oversampled DFTM FB transceiver in polyphase representation ...... 50 3.3 Comparison of the first few sidelobes of magnitude responses for prototype filter of different design approaches with M = 64 subbands ......... 66 3.4 Magnitude responses of prototype filters for M = 128 and K =132.... 67 3.5 BER versus Eb/N0 for different MCM systems with M = 64 subbands over AWGN channel ................................. 71 3.6 BER versus Eb/N0 for different MCM systems with M = 64 subbands over 5-tap Rayleigh fading channel ......................... 72 3.7 BER versus Eb/I (NBI) for different MCM systems with M = 64 subbands over AWGN channel with SNR=7dB ..................... 73 3.8 BER versus Eb/I (NBI) for different MCM systems with M = 64 subbands over 5-tap Rayleigh fading channel with SNR=7dB ............. 74 3.9 BER versus Eb/N0 for different MCM systems with M = 64 subbands over AWGN channel with carrier frequency offset Δf =2%............ 75 3.10 BER versus Eb/N0 for different MCM systems with M = 64 subbands over AWGN channel with carrier frequency offset Δf =5% ........... 76 3.11 BER versus Eb/N0 for different MCM systems with M = 64 subbands over 5-tap Rayleigh fading channel with carrier frequency offset Δf =2%.... 77 3.12 BER versus Eb/N0 for different MCM systems with M = 64 subbands over 5-tap Rayleigh fading channel with carrier frequency offset Δf =5% ... 78 4.1 DFT-modulated OPRFB transceiver with CFO and CIR estimation .... 80 4.2 Distribution of pilots over frequency (Scheme A and Scheme B with S =4 pilot-subbands in M = 16 subbands) and time (G =1, 2 and 3 groups for T = 6 pilot-frames in N = 30 frames) ..................... 85 | n,p | 4.3 Interference level Γi,j (μ) from pth input sample of jth subband on the nth output sample of ith subband (p ∈{0, 1,...,10}, j ∈{0, 1,...,63}, n =4, i = 16, μo =5%)................................ 94 4.4 Sample LLF versus CFO μ (μo = 5%, SNR= 40dB, S = 64, T = 6 and G =1) ..................................... 95 4.5 RMSE of CFO estimation versus SNR (μo = 5%, S = 64, T = 6 and G =1) 96 4.6 RMSE of CIR estimation versus SNR (μo = 5%, S = 64, T = 6 and G =1) 97 List of Figures vi 4.7 BER versus SNR (μo = 5%, S = 64, T = 6 and G =1)........... 98 4.8 RMSE of CFO estimation versus number of pilot-frames (μo = 5%, S = 64, G = 1 and SNR= 20dB) ............................ 99 4.9 RMSE of CIR estimation versus number of pilot-frames (μo = 5%, S = 64, G = 1 and SNR= 20dB) ............................ 100 4.10 RMSE of CFO estimation versus SNR for various pilot distributions in fre- quency (μo = 5%, NP = 192, G =1)..................... 101 4.11 RMSE of CIR estimation versus SNR for various pilot distributions in fre- quency (μo = 5%, NP = 192, G =1)..................... 101 4.12 RMSE of CFO estimation versus SNR for various pilot distributions in time (μo = 5%, S = 64, T =12)........................... 102 4.13 RMSE of CIR estimation versus SNR for various pilot distributions in time (μo = 5%, S = 64, T =12)........................... 102 4.14 RMSE of CFO estimation versus Doppler Frequency (μo = 5%, T = 12 and SNR= 20dB) .................................. 103 4.15 RMSE of CIR estimation versus Doppler Frequency (μo = 5%, T = 12 and SNR= 20dB) .................................. 103 5.1 Uplink transmission in MU-OPRFB system ................. 105 5.2 Allocation schemes with U = 3 users over M = 12 subbands ........ 106 5.3 Transceiver chain of the uth user in a MU-OPRFB system with CFO and channel estimation ............................... 107 5.4 RMSE of CFO (solid lines) and Equalizer (dashed lines) estimation versus SNR (μ = 5%, Tu = 6 and G =1)....................... 115 5.5 BER versus SNR (μ = 5%, Tu = 6 and G =1)................ 116 5.6 RMSE of CFO (solid lines) and Equalizer (dashed lines) iterative estimation versus SNR (μ = 5%, Tu = 6 and G =1)................... 117 5.7
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