Distributed consensus-based demodulation: algorithms and error analysis

This paper deals with distributed demodulation of space-time transmissions of a common message from a multi-antenna access point (AP) to a wireless sensor network. Based on local message exchanges with single-hop neighboring sensors, two algorithms are developed for distributed demodulation. In the first algorithm, sensors consent on the estimated symbols. By relaxing the finite-alphabet constraints on the symbols, the demodulation task is formulated as a distributed convex optimization problem that is solved iteratively using the method of multipliers. Distributed versions of the centralized zero-forcing (ZF) and minimum mean-square error (MMSE) demodulators follow as special cases. In the second algorithm, sensors iteratively reach consensus on the average (cross-) covariances of locally available per-sensor data vectors with the corresponding AP-to-sensor channel matrices, which constitute sufficient statistics for maximum likelihood demodulation. Distributed versions of the sphere decoding algorithm and the ZF/MMSE demodulators are also developed. These algorithms offer distinct merits in terms of error performance and resilience to non-ideal inter-sensor links. In both cases, the per-iteration error performance is analyzed, and the approximate number of iterations needed to attain a prescribed error rate are quantified. Simulated tests verify the analytical claims. Interestingly, only a few consensus iterations (roughly as many as the number of sensors), suffice for the distributed demodulators to approach the performance of their centralized counterparts.