Performance Analysis and Design of Maximum Ratio Combining in Channel-Aware MIMO Decision Fusion

TL;DR

This paper provides a comprehensive theoretical analysis of maximum ratio combining in channel-aware MIMO decision fusion, deriving closed-form expressions for system probabilities and performance metrics, validated by simulations.

Contribution

It offers new closed-form formulas for performance analysis and sensor threshold design in MIMO decision fusion with MRC, including channel-averaged metrics.

Findings

Closed-form expressions for false alarm and detection probabilities.

Performance evaluation using ROC and area under the curve.

Validation of theoretical results through Monte Carlo simulations.

Abstract

In this paper we present a theoretical performance analysis of the maximum ratio combining (MRC) rule for channel-aware decision fusion over multiple-input multiple-output (MIMO) channels for (conditionally) dependent and independent local decisions. The system probabilities of false alarm and detection conditioned on the channel realization are derived in closed form and an approximated threshold choice is given. Furthermore, the channel-averaged (CA) performances are evaluated in terms of the CA system probabilities of false alarm and detection and the area under the receiver operating characteristic (ROC) through the closed form of the conditional moment generating function (MGF) of the MRC statistic, along with Gauss-Chebyshev (GC) quadrature rules. Furthermore, we derive the deflection coefficients in closed form, which are used for sensor threshold design. Finally, all the results are confirmed through Monte Carlo simulations.