Distributed Estimation in a Wireless Sensor Network Using Hybrid MAC

In this paper, the distributed estimation of a scalar signal by a power-constrained wireless sensor network (WSN) with a fusion center is investigated over a hybrid multiple-access channel (MAC). The proposed hybrid MAC is a composite of conventional orthogonal and coherent MACs and is shown to offer more performance choices than both conventional channels in terms of mean square error (MSE) performance and system outage probability. Both random and deterministic scalar sources are considered for the hybrid MAC WSN in conjunction with linear minimum MSE and maximum-likelihood estimations, respectively. In particular, the optimal and suboptimal schemes are developed to allocate sensor power under the total power constraint, and these power allocation schemes are found to be similar in terms of algorithm and achievable estimation performance for both scalar sources. Moreover, closed-form expressions for sensor power are obtained for suboptimal power allocation, and two-step procedures are proposed to numerically solve the optimal power allocation problems. Furthermore, asymptotic expressions of MSE under various limiting parametric cases and system outage probability are analytically derived for suboptimal power allocation under a uniform sensor grouping strategy. It is analytically shown that, under a uniform sensor grouping strategy, the suboptimal power allocation scheme can asymptotically offer the same MSE performance as the optimal power allocation scheme when the number of sensors that transmit through the same coherent channel increases to infinity. Simulation results also show that the suboptimal power allocation scheme provides nearly optimal MSE performance for arbitrary sensor grouping strategies and that uniform sensor grouping is virtually the best grouping strategy. Moreover, for uniformly grouped hybrid MAC, the system outage probability for suboptimal power allocation is shown to provide a diversity order equal to the number of orthogonal channels when there are sufficiently many orthogonal channels.