Relays can potentially enhance the transmission performance of multi-input multi-output (MIMO) systems. A parallel single-antenna relay network has additional advantages in flexibility, diversity and cost, but also poses significant design problems because the absence of inter-antenna connections over different relays makes the underlying mathematical problems much more difficult to solve. In this study, the authors consider the design of parallel amplify-and-forward relay networks. More specifically, the authors consider the design of relay gains to maximise the system capacity. As no closed-form analytic solution can be found, the authors first develop an iterative algorithm to find a locally optimal solution. Since algorithmic optimisation provides little insight into the analytical properties of the solution, they also attempt analytical solutions for several asymptotic noise conditions. It turns out that the solutions involve some methods to select the optimal subsets of relays for signal forwarding. The authors analyse the resulting capacity outage diversity orders and confirm the analysis with simulation results.