Water-filling for full-duplex multiple-hop MIMO relay system

A water-filling (WF) method is one of the techniques to improve a performance of multiple-input multiple-output (MIMO) systems. However, the application of the WF method to multiple-hop MIMO relay systems (MMRSs) has not been discussed, especially in amplify-and-forward (AF) schemes. In this paper, the WF method for MMRSs with AF scheme is proposed and evaluated in both perfect and imperfect channel state information (CSI). The effect of imperfect CSI on optimization of transmit power at all transmitters and on co-channel interference is taken into account. Compared to the average transmit power, the end-to-end channel capacity of the WF method is higher in the perfect CSI; however, it is subject to the effect of imperfect CSI. Additionally, half-duplex and full-duplex transmission methods are also discussed in this paper. The end-to-end channel capacity of full duplex is higher and more robust than that of the half duplex due to a double of allocation time and a half of delay time.