On Scaling Laws of Diversity Schemes in Decentralized Estimation

TL;DR

This paper analyzes the asymptotic performance of diversity schemes in decentralized Gaussian source estimation, highlighting their slower decay rate of expected distortion compared to multi-access and orthogonal schemes, and explores optimal power allocation.

Contribution

It derives asymptotic expressions for expected distortion in diversity schemes and compares them with other access schemes, also optimizing power allocation and transmission probability.

Findings

Expected distortion decays as 1/ln(M) for diversity schemes.

Coherent and orthogonal schemes achieve a 1/M decay rate.

Tradeoff identified between simplicity of diversity schemes and synchronization/bandwidth requirements.

Abstract

This paper is concerned with decentralized estimation of a Gaussian source using multiple sensors. We consider a diversity scheme where only the sensor with the best channel sends their measurements over a fading channel to a fusion center, using the analog amplify and forwarding technique. The fusion centre reconstructs an MMSE estimate of the source based on the received measurements. A distributed version of the diversity scheme where sensors decide whether to transmit based only on their local channel information is also considered. We derive asymptotic expressions for the expected distortion (of the MMSE estimate at the fusion centre) of these schemes as the number of sensors becomes large. For comparison, asymptotic expressions for the expected distortion for a coherent multi-access scheme and an orthogonal access scheme are derived. We also study for the diversity schemes, the optimal power allocation for minimizing the expected distortion subject to average total power constraints. The effect of optimizing the probability of transmission on the expected distortion in the distributed scenario is also studied. It is seen that as opposed to the coherent multi-access scheme and the orthogonal scheme (where the expected distortion decays as 1/M, M being the number of sensors), the expected distortion decays only as 1/ln(M) for the diversity schemes. This reduction of the decay rate can be seen as a tradeoff between the simplicity of the diversity schemes and the strict synchronization and large bandwidth requirements for the coherent multi-access and the orthogonal schemes, respectively.