Distortion Outage Minimization and Diversity Order Analysis for Coherent Multiaccess

In this paper, we investigate the distortion outage performance of distributed estimation schemes in wireless sensor networks, where a distortion outage is defined as the event that the estimation error or distortion exceeds a predetermined threshold. The sensors transmit their observation signals using the analog amplify and forward scheme through coherent multiaccess channels to the fusion center, which reconstructs a minimum mean squared error (MMSE) estimate of the physical quantity observed. We consider three power allocation schemes: 1) equal power allocation (EPA); 2) short-term optimal power allocation (ST-OPA), where we minimize the distortion subject to a power constraint at each time step; and 3) long-term optimal power allocation (LT-OPA), where we minimize the distortion outage probability subject to a long-term average power constraint. We study their diversity orders of distortion outage in terms of increasing numbers of sensors, and show that under Rayleigh fading EPA and ST-OPA achieve the same diversity order of NlogN, where N is the number of sensors. This suggests that in the case of a large number of sensors, the spatial diversity gain in EPA can overcome fading equally well as in ST-OPA. On the other hand, in LT-OPA, we find that for N >; 1 the outage probability can be driven to zero with a finite amount of total power.