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 transmitterleav**in**g ( t ) **in** time doma**in** 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 correspond**in**g**Walsh** symbol (vector) w m = [w m 0 wm 1 ::: wm M;1 ]T ,m 2 f0::: M ; 1g **in**clud**in**g M **Walsh** chipsw m 2 f1g =0::: M;1. Each of the M parallel **Walsh**chips 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 **in**terpreted as a systematic block code (**Walsh**-Hadamardblock code) of rate log 2 (M)=M and Hamm**in**g-distance M=2[5]. Each **Walsh** symbol (**Walsh**-Hadamard codeword) conta**in**slog 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 obta**in** the symbols to be transmitted, the WH codesymbols are replicated **in**to 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 **in**dicates the number of used subcarriers.For the j-th user, we obta**in** 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 **in**terleaver( f ) scrambles s mj and passes it onto the OFDM modulator.F**in**ally, OFDM modulation **in**cludes the IDFT and **in**serts theguard **in**terval between adjacent OFDM symbols.Note that for the proposed transmission, log 2(M) systematicbits b are always mapped to one correspond**in**g OFDM symbol.In this context, N M = M N p , i.e. the number of subcarriersN M will be **in**creased if the product M N p will beraised. Moreover, for an unchanged entire bandwidth, this proposedmapp**in**g on an OFDM symbol will result **in** reducedmismatch**in**g if M is raised.Due to the **in**sertion of the guard **in**terval, each subcarrier isaffected by only one channel transfer coefficient [2]. For anupl**in**k transmission scenario, the i-th coefficient for each userj is given by Hi j , where Hj i is complex valued Gaussian distributed.For the rema**in**der 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 decod**in**g is shown **in** fig. 2. TheOFDM-CDMA receiver (shadowed block) **in**cludes the OFDMdemodulation, de**in**terleav**in**g ( ;1f ), multiplication **with** theuser specific code, one tap equalization, and correlation of N psubcarriers [2]. F**in**ally, s**in**ce 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