Matched filter bounds for low spreading factor DS-CDMA with random spreading sequences

We evaluate the matched filter bound (MFB) for QPSK symbols with random QPSK spreading sequences at low spreading factors in discrete-multipath, Rayleigh fading channels. We recognize the importance of the effect of the autocorrelation of the symbol waveform (spreading sequence) in the form of inter-path interference (IPI) on the performance of the matched filter receiver. With the decision statistic as a quadratic form of complex Gaussian variables dependent on the aperiodic code autocorrelation, we perform eigenvalue and characteristic function analysis to arrive at a probability of bit error or bit error rate (BER). For a 3GPP Case 3 dispersive channel and a spreading factor of SF=4, we note a spread of the MFBs of the individual codes of 1.4 dB in E_b/N₀ at BER=1%. Examining the MFB averaged over codes, we note a 0.5 dB difference at BER=1% between this and the MFB with no consideration of IPI. For a 3GPP typical urban channel, we note a spread of 1.1 dB at BER=1%, and for average MFB, there is a 0.4 dB difference from the MFB with no consideration of IPI. Thus we see that, at low spreading factors, the inclusion of the autocorrelation of the random spreading sequence, or the IPI, is an important consideration in obtaining accurate results for the MFB. The paper further extends the analysis to multiple receiver branches, and evaluates the MFB for other dispersive channels and additional spreading factors.