Optimal Bayesian data fusion and low-complexity approximations for distributed DS-CDMA wireless sensor networks in Rayleigh fading

In this paper we propose non-orthogonal communication between sensors and a data fusion center via direct-sequence code-division multiple-access (DS-CDMA) and investigate the fusion performance in the presence of channel errors due to both multiple-access interference (MAI) and noise. We derive the optimal Bayesian data fusion receiver for such a coherent DS-CDMA based distributed wireless sensor network having a parallel architecture in the presence of Rayleigh fading. It is shown that the complexity of the optimal rule is exponential in the number of local sensors. To provide a low-complexity solution, a class of conceptually simple data fusion receivers that partitions the multi-sensor detection and data fusion into two separate stages are proposed. Several well-known detector structures (joint maximum likelihood (JML), conventional, decorrelator and linear minimum-mean squared error (MMSE)) are considered for the multi-sensor detector at the first stage. The second stage of these receivers perform Bayesian data fusion based on the estimated symbols from the first stage. The performance results indicate that while the conventional detector first stage based receiver performs remarkably close to the optimal fusion receiver in an AWGN noise channel, its performance severely degrades in the presence of Rayleigh fading. In terms of the complexity and performance trade-off, the MMSE first stage based receiver seems to be a good design choice over a wide-range of parameters. It is also observed that the fusion performance is not limited by the channel signal-to-noise ratio (SNR) as long as it is not too small. On the other hand, for large channel SNR values the optimal fusion performance is limited by the quality of local sensor decisions (or, equivalently, the local SNR).