Relay Location Optimization for Differential Amplify-and-Forward Cooperative Relaying

Differential amplify-and-forward (DAF) cooperative relaying appears to be an attractive strategy for wireless networks where channel estimation is not feasible or it is rather avoided. In this work, we intend to determine the optimum relay location in order to minimize the outage probability of the DAF cooperative relaying in case that the system is allowed to deploy the relay. We consider two scenarios. First, we optimize the relay location for the DAF cooperative relaying with any given power assignment at the source and the relay. Second, we further consider relay location optimization with optimum power assignment in which the performance of the DAF relaying is further enhanced with the price of higher complexity. In order to obtain the optimum relay location, we develop a recursive algorithm based on the fix-point theorem and show that the relay location has a unique optimum solution which can be determined recursively from the sequence developed in our theorem. We also study the impact of the path-loss exponent to the optimal relay location and found that the relay should be deployed closer to the source in lossy environment such as near-ground environment than that in the free space environment. Extensive numerical results are provided to validate and illustrate the theoretical development.