Minimum bit-error-rate decision fusion receivers for robust DS spread-spectrum communications

The conventional matched filter (MF) correlation receiver for direct sequence spread spectrum transmissions is reconsidered from the theoretical point of view of robust distributed detection (decision fusion). Separate chip-by-chip decisions on the transmitted information bit of interest are generated. The individual decisions are then optimally fused to produce the final decision on the transmitted bit. It is proven that the majority-vote strategy is the statistically optimal fusion rule for additive white Gaussian noise channels. An exact closed form expression is given for the probability of error induced by the majority-vote receiver. It is shown that the performance is independent of the identity of the active interfering user population, that is signatures and signature cross-correlations, in DS-CDMA environments. This perfect robustness with respect to the identity of the multiuser interference component is coupled by significant resistance toward occasional high-power jamming (equivalently occasional natural severe channel imperfections) or outlier-prone background noise, or both. Some numerical studies illustrate these theoretical findings.