Sum-rate optimal network beamforming and power allocation for single-carrier asynchronous bidirectional relay network

Abstract

We study the problem of sum-rate maximization, under a total transmit power budget, for an asynchronous single-carrier bidirectional (two-way) network. The network consists of two single-antenna transceivers which wish to exchange information with the help of multiple single-antenna amplify-and-forward (AF) relays. We assume that the network is asynchronous meaning that different transceiver-relay links cause significantly different propagation delays in the signal they convey. As a result, the end-to-end channel is not amenable to a frequency flat model, rather a multi-path channel model with multiple taps appears to be more appropriate. Such a multi-path model for the end-to-end channel raises the issue of inter-symbol-interference (ISI) at the two transceivers. In a block transmission/ reception scheme, ISI leads to inter-block interference (IBI), which could result in loss in the sum-rate of the network, if it is not considered in the design of the system. Considering a block transmission/reception scheme and assuming a total transmit power budget, we maximize the sum-rate of this ISI end-to-end channel over the relay complex weights and transceivers’ transmit powers. We rigorously prove that such a sum-rate maximization problem leads to a relay selection scheme, where only those relays which contribute to one tap of the end-to-end channel impulse response are turned on and the rest of the relays are switched off. Indeed, we prove that at the optimum, the end-to-end channel impulse response (CIR) has only one non-zero tap, rendering the end-to-end channel frequency flat. We present the optimal value of the vector of the weights of the active relays and the optimal values of the transceivers’ transmit powers in a semi-closed form.