Distributed Detection over Fading MACs with Multiple Antennas at the Fusion Center

TL;DR

This paper investigates how multiple antennas at a fusion center improve distributed detection over fading MACs, revealing significant gains without channel info at sensors and limited gains with info, supported by theoretical and numerical analysis.

Contribution

It provides a comprehensive analysis of error exponent gains from multiple antennas under various channel knowledge scenarios, including new scaling laws and practical schemes.

Findings

Large error exponent gains without channel info at sensors with more antennas

Limited error exponent gains (~8/pi) with channel info at sensors regardless of antennas

Scaling laws for simultaneous increase of sensors and antennas

Abstract

A distributed detection problem over fading Gaussian multiple-access channels is considered. Sensors observe a phenomenon and transmit their observations to a fusion center using the amplify and forward scheme. The fusion center has multiple antennas with different channel models considered between the sensors and the fusion center, and different cases of channel state information are assumed at the sensors. The performance is evaluated in terms of the error exponent for each of these cases, where the effect of multiple antennas at the fusion center is studied. It is shown that for zero-mean channels between the sensors and the fusion center when there is no channel information at the sensors, arbitrarily large gains in the error exponent can be obtained with sufficient increase in the number of antennas at the fusion center. In stark contrast, when there is channel information at the sensors, the gain in error exponent due to having multiple antennas at the fusion center is shown to be no more than a factor of (8/pi) for Rayleigh fading channels between the sensors and the fusion center, independent of the number of antennas at the fusion center, or correlation among noise samples across sensors. Scaling laws for such gains are also provided when both sensors and antennas are increased simultaneously. Simple practical schemes and a numerical method using semidefinite relaxation techniques are presented that utilize the limited possible gains available. Simulations are used to establish the accuracy of the results.