We analyze the outage probability of the multiuser two-way relay network (TWRN) where the N-th best mobile user (MU) out of M MUs and the base station (BS) exchange messages with the aid of an amplify-and-forward relay. In the analysis, we focus on the practical unbalanced Nakagami-m fading between the MUs-relay link and the relay-BS link. We also consider both perfect and outdated channel state information (CSI) between the MUs and the relay. We first derive tight closed-form lower bounds on the outage probability. We then derive compact expressions for the asymptotic outage probability to explicitly characterize the network performance in the high signal-to-noise ratio regime. Based on our asymptotic results, we demonstrate that the diversity order is determined by both Nakagami-m fading parameters, M, and N when perfect CSI is available. When outdated CSI is available, the diversity order is determined by Nakagami-m fading parameters only. In addition, we quantify the contributions of M, N, and the outdated CSI to the outage probability via the array gain.

This paper studies an underlay-based cognitive two-way relay network which consists of a primary network (PN) and a secondary network (SN). Two secondary users (SUs) exchange information with the aid of multiple single-antenna amplify-and-forward relays while a primary transmitter communicates with a primary receiver in the same spectrum. Unlike the existing contributions, the transmit powers of the SUs and the distributed beamforming weights of the relays are jointly optimized to minimize the sum interference power from the SN to the PN under the quality-of-service (QoS) constraints of the SUs determined by their output signal-to-interference-plus-noise ratio (SINR) and the transmit power constraints of the SUs and relays. This approach leads to a non-convex optimization problem which is computationally intractable in general. We first investigate two necessary conditions that optimal solutions should satisfy. Then, the non-convex minimization problem is solved analytically based on the obtained conditions for single-relay scenarios. For multi-relay scenarios, an iterative numerical algorithm is proposed to find suboptimal solutions with low computational complexity. It is shown that starting with an arbitrarily initial feasible point, the limit point of the solution sequence derived from the iterative algorithm satisfies the two necessary conditions. To apply this algorithm, two approaches are developed to find an initial feasible point. Finally, simulation results show that on average, the proposed low-complexity solution considerably outperforms the scheme without source power control and performs close to the optimal solution obtained by a grid search technique which has prohibitively high computational complexity.