A simple optimal solution for relay assignment in cooperative systems based on the max-min criterion

This paper deals with relay assignment in cooperative networks based on the max-min criterion. A simple algorithm is proposed in order to find the optimum relay assignment permutation to avoid brute-force prohibitive search method. It is assumed that there are N source-destination pairs and M relays in the network. The problem is how to assign each relay to a source-destination pair in order to achieve the highest diversity order. The proposed algorithm achieves the maximum spatial diversity for all of the nodes and leads us to simplify the analysis and simulation of the optimal answer. It is shown that the Probability Density Function (PDF) of the end-to-end signal-to-noise ratio (SNR) after relay assignment can be expressed as a weighted sum of the order statistics of the PDF of individual end-to-end links. Since the analytical calculation of the weighting coefficients in the mentioned weighting sum becomes difficult, we propose an approximation in order to calculate the mentioned weighting coefficients. The validity of this fit is shown through some simulations.