Filter-and-forward beamforming with adaptive decoding delays in asynchronous multi-user relay networks

• We address the critical and challenging issue of timing synchronization in a multi-user relay network.
• We propose to employ individual adaptive decoding delays at the destination nodes to address the synchronization issue.
• We consider the joint optimization of the filter coefficients at the relays and the decoding delays at the destinations.
• We propose a customized branch-and-cut method offering a lower bound as a benchmark.
• We propose a low-complexity iterative deflation method yielding an approximate solution.

We consider distributed relay beamforming in frequency selective fading channels where the relays employ the filter-and-forward (FF) protocol to mitigate inter-symbol interference (ISI). Recently, the FF scheme has been expanded by incorporating an adaptive decoding delay at the destination to facilitate ISI suppression in single-user (SU) relay networks. In this paper, we propose a non-trivial generalization of the FF approach with adaptive decoding delays for multi-user peer-to-peer (MUP2P) systems in which flexible decoding delays are of crucial importance: Unlike in SU relay networks, perfect timing synchronization is generally impossible in realistic MUP2P relay networks. The problem of jointly optimizing the filter coefficients at the relays and the individual decoding delays at the destinations is a nonconvex mixed integer (MI) programming problem which is generally hard to solve optimally. We propose an efficient deflation algorithm providing an approximate solution and a branch-and-cut (BnC) method yielding a lower bound as a benchmark. Our simulation results demonstrate that the approximate solution obtained using the proposed scheme is close to optimal and outperforms the solutions obtained by state-of-the-art schemes which do not make use of adaptive decoding delays.