The effects of sequence selection on DS spread spectrum with selective fading and Rake reception

Error probabilities are evaluated for direct-sequence spread-spectrum communications and Rake reception over channels with doubly selective fading. The error probability for such a system depends on the spreading sequence, the autocorrelation function of the fading process, the received signal-to-noise ratio, and the number of taps in the Rake receiver. The focus of the paper is on the effect of the spreading sequence on the performance of each of two systems. One system employs noncoherent detection of differentially-encoded binary direct-sequence spread-spectrum signals and a post-detection diversity-combining Rake receiver which uses equal-gain combining. The other system employs coherent detection of binary direct-sequence spread-spectrum signals and a post-detection diversity-combining Rake receiver with perfect gain estimates for the channel. A simple sequence selection criterion is introduced, and the sensitivity of the performance of the system to the choice of the spreading sequence is examined. It is shown that significant performance differences result from different choices of the spreading sequence. It is also shown that, given a moderate range of delay spreads, sequences can be found that yield low bit error probabilities over that range. These are found to be robust with respect to the delay spectrum for the channel, the number of taps in the Rake receiver, the Doppler spread, and the signal-to-noise ratio.