On Optimal Power Allocation over Time-Varying Rayleigh Fading Channels for Maximum-Ratio Combining in Diversity Systems with Partial CSI

This paper studies the problem of optimal power allocation (OPA) over independent but not necessarily identically distributed time-varying Rayleigh fading channels with maximum-ratio combining to exploit transmit and/or receive diversity. Specifically, the optimal average rate-maximizing and M-ary phase shift keying symbol-error-rate (SER)-minimizing power allocation problems subject to a total transmit power constraint are formulated as stochastic optimization problems. After that, the stochastic problems are reformulated into deterministic ones in terms of the average rate and SER, respectively, which require only partial channel state information (CSI) in the form of channel gains. Novel closed-form expressions are derived for the deterministic OPA for average rate-maximization and SER-minimization, and a linear-complexity water-filling algorithm is then proposed to efficiently determine the OPA based on derived closed-form solutions. Moreover, dynamic OPA (with full CSI knowledge) is analyzed and closed-form solutions for the optimal average rate and SER are obtained. Simulation results are presented to validate the theoretical analysis, and demonstrate that the deterministic OPA algorithm outperforms equal power allocation and yields comparable average rate and SER performances to the dynamic OPA.