Approach to Optimum Performance in Random Spreading CDMA by Linear-Complex LAS Detectors

In this paper, we first present a BER upper bound for the family of LAS detectors. Then the upper bound is applied to analyze the performance of local maximum likelihood (LML) detectors in large random spreading CDMA (LRS-CDMA) channels where user number A´ and spreading gain N tend to infinity and KIN keeps a constant. The LRS-CDMA channels are shown to possess the LML characteristic. In the regime of K/N < 1/2 - 1/(4ln2) and Nsigma² equal to a constant where sigma² is the noise power, an LML point is almost surely a global maximum likelihood (GML) point and the asymptotic multiuser efficiency of all the LML detectors converges almost surely to one. Given a practical CDMA system with fixed finite K and N, we then propose to construct a quasi-LRS-CDMA channel where bits are extended by a factor of B and spread by unit-length BN-chip sequences and each user transmits B extended bits. Simulation results show that in the regime of BK > 1000, K/N < 1.0 and SNR ges 4 dB, while their average per-bit complexity is less than 0.79BK, the LAS detectors can achieve the BER indistinguishable from the large-system limit BER of the GML detector.