Two-way cooperative communications with statistical channel knowledge

• We study the problem of two-way linear relaying with imperfect channel state information for a network of two transceivers and multiple relays.
• We minimize the total transmit power subject to quality of service constraints measured by the signal-to-noise-ratios averaged over random CSI.
• We show that this problem has a closed-form solution which is indeed a relays election scheme.

We consider the problem of distributed beamforming for a two-way relay network which consists of two transceivers and multiple relay nodes. The main assumption in this work, which differentiates it from previously reported results, is that one of the transceivers is assumed to have only statistical information about channels between the other transceiver and the relay nodes. This assumption imposes less stringent restrictions on the bandwidth required to obtain channel state information via training. Based on this statistical modeling, we propose to use a chance-constrained programming approach to design a distributed beamforming algorithm. In this approach, we aim to minimize the total transmit power (consumed in the entire network) as perceived by one of the transceivers, subject to two probabilistic constraints. These constraints guarantee that the outage probability of the transceivers' received SNRs, as perceived by the master transceiver, is not less than certain given thresholds. We prove rigorously that such an approach leads to a relay selection algorithm where the relay with the strongest channel coefficient to the master transceiver participates in relaying and the remaining relays are shut off. As such, the optimal distributed beamforming algorithm is simplified to a power control solution. Closed-form solution to this problem is obtained and its performance is evaluated through numerical examples.