We consider the power allocation and relay selection for rate maximization in a two-path amplify-and-forward (AF) relay network with inter-relay interference (IRI) consideration. We first investigate the power allocation with only a pair of relays under both the individual and global power constraints. To find the global optimum solution to this nonconvex problem, we develop a three-step approach using the rate-profiling technique together with a reformulation of the sum-rate maximization problem as a set of power-minimization geometric programming problems (GPPs). For reduced complexity, we further convert the optimization problem into a set of GPPs in a single-step by using a high signal-to-interference-plus-noise ratio approximation.
Next, we consider the relay pair selection and propose an algorithm in which the achievable rate of each pair of relays with the proposed power allocation is compared. This selection criterion outperforms the conventional selection scheme in terms of the achievable rate. We further propose two low-complexity selection criteria for low and moderate IRI. For moderate IRI, the ratio of the source-relay and relay-destination channel power product to the square of inter-relay channel power can be used for relay selection to achieve a performance close to that of the selection based on the proposed power allocation.