Iterative Decoding with M-ary Orthogonal Walsh Modulation in ...

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Iterative Decoding with M-ary Orthogonal Walsh Modulation in ...

c 0dChannelencoderb tbS/Plog 2( M)Walsh-Mod.MN pN pc N-1 pc N M -N pc N M -1 fN MOFDMMod.w mw ms mOFDM-CDMA-transmitterFigure 1: SCCS and OFDM-CDMA transmitterleaving ( t ) in time domain the encoded bits are serial/parallelconverted to groups of log 2 (M) bits each. The Walsh modulationmaps the log 2 (M) encoded bits to one correspondingWalsh symbol (vector) w m = [w m 0 wm 1 ::: wm M;1 ]T ,m 2 f0::: M ; 1g including M Walsh chipsw m 2 f1g =0::: M;1. Each of the M parallel Walshchips has a duration of T =log 2 (M) T b .In contrast to the application of the Walsh modulation in DS-CDMA based systems [6, 9], be aware that for the consideredOFDM-CDMA system each Walsh symbol is arranged in frequencydirection. Furthermore, the Walsh modulation can alsobe interpreted as a systematic block code (Walsh-Hadamardblock code) of rate log 2 (M)=M and Hamming-distance M=2[5]. Each Walsh symbol (Walsh-Hadamard codeword) containslog 2 (M) systematic bits b at positionssys() = 12 M =0::: log +1 2 (M) ; 1 (1)with Walsh chips (Walsh-Hadamard code symbols)w m sys() =(;1)b b 2f0 1g: (2)In order to obtain the symbols to be transmitted, the WH codesymbols are replicated into N p copies. Each branch of theparallel stream is then multiplied with one chip of the userspecific PN-code c i 2 f1= p N M g i =0::: N M ; 1, andN M indicates the number of used subcarriers.For the j-th user, we obtain the vector s mjs mj =[s mj0::: s mjN M ;1] T s mji = ~w i mj c j i (3)with ~w mji = wmj8 = bi=N pc mj. The interleaver( f ) scrambles s mj and passes it onto the OFDM modulator.Finally, OFDM modulation includes the IDFT and inserts theguard interval between adjacent OFDM symbols.Note that for the proposed transmission, log 2(M) systematicbits b are always mapped to one corresponding OFDM symbol.In this context, N M = M N p , i.e. the number of subcarriersN M will be increased if the product M N p will beraised. Moreover, for an unchanged entire bandwidth, this proposedmapping on an OFDM symbol will result in reducedmismatching if M is raised.Due to the insertion of the guard interval, each subcarrier isaffected by only one channel transfer coefficient [2]. For anuplink transmission scenario, the i-th coefficient for each userj is given by Hi j , where Hj i is complex valued Gaussian distributed.For the remainder of the paper, we assume coherentreception with perfectly known channel coefficients Hi 0 for allsubcarriers i of user j =0. The other active users are receivedasynchronously 2 .III. COHERENT OFDM-CDMA RECEPTION WITHITERATIVE DECODINGThe receiver with iterative decoding is shown in fig. 2. TheOFDM-CDMA receiver (shadowed block) includes the OFDMdemodulation, deinterleaving ( ;1f ), multiplication with theuser specific code, one tap equalization, and correlation of N psubcarriers [2]. Finally, since the Walsh-Hadamard code symbolsare real-valued, we take the real part.Reception for the user j =0is assumed. With (3) the componentsof vector v can be expressed byX8

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