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.

I. Introduction

¹

Approved for Public Release; distribution unlimited: 88ABW-2015-1509.

Cooperative communication has drawn significant attention in recent years as an effective approach to combat severe fading and enhance reliability in wireless communication systems (e.g. see [1], [2], and the references therein). To avoid the burden of channel estimation and reduce implementation complexity, differential cooperative relaying concept, where information can be differentially modulated/demodulated, is particularly attractive in some wireless networks to provide a good balance between overall system performance and complexity [3]–[7]. In [3], [4], differential amplify-and-forward (DAF) relaying were proposed where signal from the source is simply amplified by the relay and be forwarded to the destination. Comparing to coherent decode-and-forward scheme, the implementation of the DAF relaying is much simpler since there is no decoding deployed at relays. Bit error rate (BER) performance and symbol error rate (SER) performance of the DAF scheme with single/multiple relays using differential phase shift keying (DPSK) were analyzed in [3] and [4] respectively. The work [5] extended the BER performance analysis and optimization for the DAF relaying protocol with multiple relay nodes. In [6], the outage probability performance was investigated for the DAF relaying where the expression of the outage probability of the DAF relaying was presented in terms of a triple integral. In [7], we analyzed the outage probability of the DAF relaying and obtained a new expression that involves only a single integral, and to get further insight understanding of the DAF relaying, we developed a close-form approximation for the outage probability which is asymptotically tight at high SNR.