Capacity of CDMA with random spreading and multiuser detection

Information theoretic aspects of code division multiple access (CDMA) random direct-sequence spread-spectrum (DSSS) are investigated. The CDMA-DSSS channel with randomly and independently chosen spreading sequences accurately models the situation where pseudo-noise sequences span many symbol periods. Its information theoretic analysis provides a comparison baseline for CDMA channels with carefully designed signature waveforms that span one bit period on one hand and optimal multiple-user coded systems on the other. We analyze the spectral efficiency (total capacity per chip) as a function of the number of users, spreading gain and signal-to-noise ratio, and we quantify the loss in efficiency relative to an optimally chosen set of signature sequences and to an optimal multiaccess system without spreading. White Gaussian background noise and equal-power synchronous users are assumed. The analysis comprises the following receivers: (a) optimal joint processing, (b) single-user matched filtering; (c) decorrelation and (d) minimum mean square error linear processing. Some implications due to fading are also addressed.