Beamforming Using Exact Evaluation of Leakage and Ergodic Capacity of MU-MIMO System.

Ahmad Kamal Hassan,Muhammad Moinuddin

doi:10.3390/s21206792

Abstract

Closed-form evaluation of key performance indicators (KPIs) of telecommunication networks help perform mathematical analysis under several network configurations. This paper deals with a recent mathematical approach of indefinite quadratic forms to propose simple albeit exact closed-form expressions of the expectation of two significant logarithmic functions. These functions formulate KPIs which include the ergodic capacity and leakage rate of multi-user multiple-input multiple-output (MU-MIMO) systems in Rayleigh fading channels. Our closed-form expressions are generic in nature and they characterize several network configurations under statistical channel state information availability. As a demonstrative example of the proposed characterization, the derived expressions are used in the statistical transmit beamformer design in a broadcast MU-MIMO system to portray promising diversity gains using standalone or joint maximization techniques of the ergodic capacity and leakage rate. The results presented are validated by Monte Carlo simulations.

Highlights

Sensors 2021, 21, 6792. https://Quadratic forms find applications in multifarious fields of engineering
An indefinite quadratic forms approach [7] is used to obtain an exact solution of the outage probability expression of a covariance shaping channel model in [22], only approximate solutions of ergodic capacity are reported under this approach
Exact closed-form expressions of the ergodic capacity and leakage are presented for a generic model which includes co-channel interference, distinct correlation matrices, Hermitian indefinite weight matrices of correlated channels, and any deterministic beamformers

Summary

Introduction

Quadratic forms find applications in multifarious fields of engineering. In telecommunication systems, quadratic forms in Gaussian random variables are of particular interest [1,2,3,4,5,6]. Metrics dealing with the expectation of logarithmic functions such as ergodic capacity and leakage rate were not characterized therein These metrics are central to any telecommunication network, and the availability of closed-form analytical formulas can lead to effective beamforming techniques. An indefinite quadratic forms approach [7] is used to obtain an exact solution of the outage probability expression of a covariance shaping channel model in [22], only approximate solutions of ergodic capacity are reported under this approach. There is a need for a unified approach that provides exact closed-form expression of ergodic capacity by relaxing the above-mentioned assumptions on the transmit beamformers, antenna diversity, correlated channel gains, and indefinite weight matrices involved in SINR and SLNR expressions.

The Main Results

Application Example and Discussion

Validation of the Closed-Form Expressions

Beamforming Using the Closed-Form Expressions

Conclusions