Multiple-Relay Selection in Amplify-and-Forward Cooperative Wireless Networks with Multiple-Source Nodes

In this article, we propose multiple-relay selection schemes for multiple source nodes in amplify-and-forward wireless relay networks based on the sum capacity maximization criterion. Both optimal and sub-optimal relay selection criteria are discussed, considering that sub-optimal approaches demonstrate advantages in reduced computational complexity. Using semi-definite programming convex optimization, we present computationally efficient algorithms for multiple-source multiple-relay selection (MSMRS) with both fixed number and varied number of relays. Finally, numerical results are provided to illustrate the comparisons between different relay selection criteria. It is demonstrated that optimal varied number MSMRS outperforms optimal fixed number MSMRS under the same power constraints. Introduction Multihop relaying has emerged as a promising approach to achieve high-rate coverage in wireless communications [1,2]. Several amplify-and-forward (AF) and decode-andforward (DF) relaying techniques have been introduced such as in [2,3]. Following those pioneer works, a number of cooperative diversity schemes have been proposed, including, for example, distributed space-time coding [35], adaptive power control for relay networks or relay beamforming [6-9], and relay selection [10-19]. The objective of relay selection is to achieve higher throughput or lower error probability through choosing one or more relays for transmission according to channel conditions. In comparison to relay beamforming, relay selection is attractive due to its deployment of simpler signaling scheme and energy saving. Most currently available relay selection approaches assume only a single source node [10-12,14-18], and can be classified into two categories: 1. A majority of relay selection rules are restrictive in the sense that they either always use all the available *Correspondence: [email protected]; [email protected] 1Bell Laboratories, Alcatel-Lucent, Shanghai 201206, P.R. China 2Center for Advanced Communications, Villanova University, Villanova, PA 19085, USA Full list of author information is available at the end of the article relays or always use just a single relay, such as in [10-18,20-29]. In [21], four simple relay selection criteria are described: Two criteria are based on the selection of a single relay according to mean channel gains, while the other two select all available relays. Selecting all available relays are the simplest approach with multiple relays, and this approach may not be allowed when the sum power limit is less than the summation of the power values of all available relays. A single-relay node is selected based on average channel state information (CSI), e.g., distance or path loss [20,22,30], and on the instantaneous fading states of the various links such as in [23]. 2. Multiple-relay selection for a single source has attracted attention as well [31-33]. Jing and Jafarkhani proposed sub-optimal two-step optimization approaches for single-source multiple-relay selection in [31,33]: In the first step, phase rotation is performed at each relay, and thus only power allocation is considered due to signal-to-noise ratio (SNR) consisting of a summation of purely real terms. In the second step, several sub-optimal methods were introduced [31,33]: (a) By introducing the idea of relay ordering, several schemes with linear complexity were proposed; © 2012 Wu et al.; licensee Springer. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Wu et al. EURASIP Journal onWireless Communications and Networking 2012, 2012:256 Page 2 of 13 http://jwcn.eurasipjournals.com/content/2012/1/256 (b) Based on recursion, a scheme with quadratic complexity was proposed. Although both singleand multiple-relay selection approaches for a single source node network have been investigated, relay selection approaches for multiple source nodes are rarely addressed in literature. Only the following three existing publications [34-36] have discussed multiple-source relay selection (MSRS) approaches. Elzbieta and Raviraj have proposed MSRS for DF relay networks [34]. Xu et al. have presented MSRS approaches in which only a single source is considered as the desired user over each selected relay per transmission while other sources or users are considered as interferers during the transmission [35]. Guo et al. have analyzed MSRS for opportunistic relays, in other words, only a single source is transmitted over each selected relay per transmission [36]. Further, there have been several recent research works on two-way relay selections [37-40]. In this article, we consider AF relay-based cooperative communication systems for simultaneousmultiple-source transmission over each selected relay, and more than one relay is allowed per multiple-source transmission. Each relay is assumed to satisfy practical individual short-term power constraints, that is, each relay has two power levels: zero and its maximum power. This assumption has been used for single-source multiple-relay selection in, for example, [31,33]. The main contributions of this article can be listed as: 1. Based on the sum capacity criteria, we derive and propose several multiple-relay selection techniques in AF relay networks with multiple source nodes. 2. Using semi-definite programming optimization, we propose computationally efficient algorithms for multiple-source multiple-relay selection (MSMRS) in the presence of both fixed number and varied number of relays. The following notations are used: (·)T denotes matrix transpose, (·)∗ conjugate, (·)H matrix conjugate transpose, Hardmard product operator, [A]a,b the (a, b)th entry (element) of matrix A, tr (·) matrix trace operation, Re (·) real part of the object (matrix or variable), Im (·) imaginary part of the object (matrix or variable), Eα (·) expectation over random variable or random variable set α, diag (a) denotes a square matrix with all-zeros entries except the main diagonal filled with the entries of the vector a, φ denotes empty set, and X 0 denotes that X is a positive semi-definite matrix. Systemmodel and problem formulation Consider a wireless relay network with M source nodes (transmitters), K relay nodes, and one destination node (receiver). Each node is equipped with a single antenna. Assume no direct channel path between the source nodes and the destination node. The source nodes and the relay nodes are assumed to share the same transmission channel. Based on two-phase half-duplex AF relay assumption, we consider a multiple-source AF relay selection approach. The period of one two-phase AF relay procedure is defined as one time channel use. During the tth time channel use, the two-phase AF protocol is performed as follows: 1. In the first phase, the mth source node (transmitter) sends source information symbol x(t) m using power P(S) m to the relay nodes, wherem = 1, . . . ,M, E (∣∣∣x(t) m ∣∣∣2) = 1. the information symbols x(t) m , m = 1, . . . ,M, are selected randomly from M independent codebooks. It is assumed that M source nodes simultaneously send uncorrelated signal streams x(t) m ,m = 1, . . . ,M, and the corresponding channel symbols are received at relay k at the same time. 2. In the second phase, L relays with indices {k1, . . . , kL} are selected according to some criteria, which will be elaborated later. Here, L, 1 ≤ L ≤ K , is an integer, which is referred to as “relay selection order” in this article. Then, the kith relay, i = 1, . . . , L, scales its received signal power to unity, and, using power P(R) ki , amplifies and forwards it to the receiver. Note that, in this two-phase AF protocol, multiple source nodes share the same channels. The transmission and reception among the source nodes, the relay nodes and the destination node are assumed to be perfectly synchronized. In the tth time channel use, the channel from the mth source node (transmitter) to the kth relay is denoted as h(k,t) m and the channel from the kth relay to the receiver is denoted as g(t) k . The channels are modeled as frequency non-selective Rayleigh fading, and are assumed to independently vary over different time channel uses. Denote v(t) k as the noise component at the kth relay, k = 1, . . . ,K , and denote w(t) as the noise component at the destination node, where v(t) k and w (t) are assumed to be independently and identically distributed (i.i.d.) complex Gaussian random variables with zero mean and unit variance. During the tth time channel use, the received signal at the kth relay is