Asymptotic Performance of DS-CDMA with Linear MMSE Receiver and Limited Feedback

Signature quantization for reverse-link direct sequence (DS)-code division multiple access (CDMA) is considered. A receiver assumed to have perfect estimates of channel and interference covariance, selects the signature that maximizes signal-to-interference plus noise ratio (SINR) for a desired user from a signature codebook. The codebook index corresponding to the optimal signature is relayed to the user with finite number of bits via a feedback channel. Previously, it was shown that a random vector quantization (RVQ) codebook, which contains independent isotropically distributed vectors, is optimal (i.e., maximizes SINR) in a large system limit in which number of interfering users, processing gain, and feedback bits tend to infinity with fixed ratios. Here we derive exact expressions for a large system SINR for the user whose signature is selected from RVQ codebook. We assume that the receiver is linear minimum mean squared error (MMSE) and consider both ideal and multipath fading channels.