On diversity orders of distortion outage for coherent multi-access channels

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 pre-determined threshold. The sensors transmit their observation signals using analog amplify and forward through coherent multi-access 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), and 3) long-term optimal power allocation (LT-OPA). 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 N logN, where N is the number of sensors. 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.