Power allocation for Zero Forcing scheme in Multi-Antenna Multiple Relays Networks

Multi-Antenna Multiple Relays (MAMR) Networks are systems composed of multiple relays, each having multiple antennas. We consider a variation of two-hop AF relaying, dubbed ZF-ZF method, in which each relay performs Zero Forcing(ZF) beamforming and ZF pre-coding, respectively, throughout reception and transmission intervals. Using ZF-ZF method together with applying diagonal weight matrices at the relays, it is shown that the overall channel between the multi-antenna source and affiliated multi-antenna destination can be simplified to M independent parallel paths, where M is the number of source and destination antennas. This enables to incorporate power allocation methods proposed for single antenna multiple relay (SAMR) networks in such channel. Accordingly, using the BER as the performance metric, we have used the optimal power allocation method proposed by Jing et al. for single antenna multiple relay networks, showing our proposed approach along with the aforementioned power allocation method outperforms the common ZF-ZF method addressed in the literature.