Multi-Carrier and Spread Spectrum Systems: From OFDM and MC ...

78 MC-CDMA and MC-DS-CDMAThe channel code rate is defined as the ratioR = L aL b. (2.76)The interleaved coded bit vector ˜b (k) is passed to a symbol mapper, where ˜b (k) is mappedinto a sequence of L d complex-valued data symbols, i.e.d (k) = (d (k)0 ,d(k) 1 ,...,b(k) L d −1 )T . (2.77)A data symbol index κ, κ = 0,...,L d − 1, is introduced to distinguish the different datasymbols d κ(k) assigned to d (k) . Each data symbol is multiplied with the spreading codec (k) according to Equation (2.3) and processed as described in Section 2.1.With single-user detection, the L d soft decided values at the output of the detector aregiven by the vectorv (k) = (v (k)0 ,v(k) 1 ,...,v(k) L d −1 )T . (2.78)The L d complex-valued, soft decided values of v (k) assigned to the data symbols of d (k)aremappedontoL b real-valued, soft decided values represented by ˜w (k) assigned to thecoded bits of ˜b (k) . The output of the symbol de-mapper after de-interleaving is written asthe vectorw (k) = (w (k)0 ,w(k) 1 ,...,w(k) L b −1 )T . (2.79)Based on the vector w (k) , LLRs of the detected coded bits are calculated. The vectorl (k) = (Ɣ (k)0 ,Ɣ(k) 1 ,...,Ɣ(k) L b −1 )T (2.80)of length L b represents the LLRs assigned to the transmitted coded bit vector b (k) . Finally,the sequence l (k) is soft decision-decoded by applying the Viterbi algorithm. At the outputof the channel decoder, the detected source bit vectorâ (k) = (â (k)0 , â(k) 1 ,...,â(k) L a −1 )T (2.81)is obtained.Before presenting the coding gains of different channel coding schemes applied inMC-CDMA systems, the calculation of LLRs in fading channels is given generally formulti-carrier modulated transmission systems. Based on this introduction, the LLRs forMC-CDMA systems are derived. The LLRs for MC-CDMA systems with single-userdetection and with joint detection are in general applicable for the up- and downlink. Inthe uplink, only the user index (k) has to be assigned to the individual channel fadingcoefficients of the corresponding users.