Distributed Statistical Inference using Type Based Random Access over Multi-access Fading Channels

The problem of distributed detection and estimation in a sensor network over a multiaccess fading channel is considered. A communication scheme known as the type-based random access (TBRA) is employed and its performance is characterized with respect to the mean transmission rate and the channel coherence index. For extreme values of channel coherence index i.e., 0 and infin, we give an optimal TBRA scheme which is essentially a sensor activation strategy that achieves the optimal allocation of transmission energy to spatial and temporal domains. For channels with zero coherence index, it is shown that there exists a finite optimal mean transmission rate maximizing performance. This optimal rate can be calculated numerically or estimated using the Gaussian approximation. On the other hand, for channels with infinite coherence index (i.e., no fading) the optimal strategy is to allocate all the energy to the spatial domain. Numerical examples and simulations confirm our theory.