Lifetime Maximization for Greedy Selective Relay Strategies S. A. Mousavifar Electrical & Computer Engineering University of British Columbia Vancouver, BC V6T 1Z4 seyedm@ece.ubc.ca C. Leung Electrical & Computer Engineering University of British Columbia Vancouver, BC V6T 1Z4 cleung@ece.ubc.ca T. Khattab Electrical Engineering Qatar University Doha, Qatar PO Box 2713 tkhattab@qu.edu.qa Abstract—In this paper we propose a new algorithm for selective relay strategies with Amplify-and-Forward (AF) relays which improves the relay network lifetime. The lifetime of the relay network is defined as the maximum number of messages which can be received with the desired SNR at the destination while the system Probability of Outage (P-outage) requirement is satisfied. The improvement in lifetime increases with the number of relays. When the number of relays is small, the method improves the lifetime under the condition of high initial relay energy levels. The proposed algorithm can be implemented in conjunction with previously proposed energy greedy relay selection strategies such as Minimum Power Transmission (MPT), Maximum Residual Energy (MRE), Minimum Energy Index (MEI), and Maximum Outage Probability (MOP). I. INTRODUCTION Cooperative relay networking is an emerging technology which can be used to reduce the transmit power and increase the performance of telecommunication systems. Many aspects of wireless relay networks such as power allocation [1] [2], capacity [3]- [6], and outage probability for regenerative and non-regenerative relays network [7] [8], and lifetime [9] [10] have been studied extensively. The initial energy levels and power consumptions of the intermediate relays in homogenous and heterogenous wireless relay networks are limited due to battery size restrictions and thus lifetime is a major concern. Depending on the system model and requirements, there are several definitions for lifetime. For the system model in [9] (in which the source message must use one AF relay to reach the destination), the lifetime is defined as the maximum number of successfully received messages satisfying a desired SNR at the destination under probability of outage constraints. Assuming Channel State Information (CSI ) and Residual Energy Information (REI ) are available at all relays, the lifetimes for several relay selection strategies were studied using simulations. However, the strategies in [9] only satisfy the lifetime definition requirements (only satisfy the P-outage requirements) but they do not utilize those requirements efficiently. In the proposed method, we impose transmission power restriction on the relays based on the lifetime definition requirements. In another word, our method exploits the gap between the instantaneous P-outage requirements and the actual instantaneous P-outage. We show that our method can greatly improve the system lifetime for the selective relay strategies in [9] when the number of relays is greater than three. When the number of relays is less than three, the proposed method still increases the lifetime for high initial relay energy levels. In Sections II, III, IV, and V, we describe the system model, the current strategies, the proposed method, and the simulation results respectively. II. SYSTEM MODEL Consider N cooperative relays which can forward a message to the destination using enough power to achieve the desired SNR at the destination while satisfying a P-outage requirement for each transmission (instantaneous outage). At any time slot, only one relay is selected to forward the message received from the source. some relay selection strategies only need CSI whereas others also require REI of the relays. A. Channel and Noise The channel gains are assumed to be independent circularly symmetric complex Gaussian with unit variance and zero mean, i.e. CN (0, 1). We denote the channel gain from the source to the kth relay by h Sk and gain from the kth relay to the destination by h kD , as shown in Fig. 1. Additive White Gaussian Noise (AWGN) with unit variance is present at relay and destination. We denote the noise at the kth relay by w k and the noise at the destination by w D .The signal received at the relay and at the destination in the two phases of the transmitting protocol are as in [9]: r k =  P S h Sk m + w k (1) and y =  P k P S |h Sk | 2 +1  P S h Sk h kD m+  P k P S |h Sk | 2 +1 h kD w k +w D (2)