Optimization for Pragmatic Half-Duplex Relay Network

In relay networks, we may not possess the ability to tune all system parameters in order to achieve the maximum achievable rate promised by theoretical analysis. This paper investigates the pragmatic issue of sub-optimal relay networks, where we can only optimize either on the time allocation, or on the power allocation. Our study concludes that optimizing on the power allocation, or on the time allocation, can achieve more than 95% of the relaying gain relative to the optimization of both time and power simultaneously. To produce the result, we derive the closed-form expression of the optimum power allocation for the source and relay that obtains the achievable rate of the half-duplex relay channel with fixed (equal) time allocation. We also derive the closed-form expression of the optimum time allocation between the source and relay transmission that obtains the achievable rate of the half-duplex relay channel with fixed power allocation. We demonstrate that for small SNR, where relaying is most advantageous, almost all relaying gain can be achieved by only optimizing the power allocation. Conversely, optimizing the time allocation alone is sufficient to achieve most of the relaying gain when the system´s SNR is large. This result is important for pragmatic designs of emerging relay communication systems.