Power-optimal network beamforming in single-carrier asynchronous two-way relay networks
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In this thesis, we consider a single-carrier asynchronous two-way relay network, where the relays employ amplify-and-forward (AF) signaling in a multiple access broadcast channel (MABC) protocol to enable a bi-directional communication link between two transceivers. The network we consider is asynchronous, meaning that each relaying path (which originates from one transceiver, goes through one of the relays, and ends at the other transceiver) causes a delay which is significantly different from the delays caused by other relaying paths. Such a two-way relay channel can be viewed as a multi-path link which can produce inter-symbol-interference at the two transceivers. Assuming a block transmission scheme, we resort to cyclic prefix insertion to eliminate inter-block-interference. We aim to obtain the relay complex beamforming weights and the transceivers’ transmit powers such that the total power consumed in the whole network is minimized subject to two constraints on the transceivers’ data rates. We rigorously prove that at the optimum, only a subset of the relays has to be turned on and the rest of the relays have to be switched off. More specifically, we prove that at the optimum, the end-to-end channel impulse response (CIR) will have only one non-zero tap, and hence, only those relays which contribute to that non-zero tap have to be turned on. We devise a simple search algorithm to optimally determine which tap of the end-to-end CIR has to be non-zero. Finally, we present a semi-closed-form solution for the optimal values of the design parameters, namely the relays’ beamforming weights and the transceivers’ transmit powers. Our simulations results show that our proposed method significantly outperforms an equal power allocation scheme (i.e., when all the nodes in the network consume the same amount of power) which satisfies the same constraints on transceivers’ data rates.