When multiple relays exist in the network, several strategies which utilize multiple re-lays are developed to achieve some desired goals. Those strategies including power al-location [3] [10], distributed beamforming [6] [7], distributed space time coding [5] and
relay selection (RS) [8] [9] are widely studied in the literature. Some challenges will be encountered when all relays participate in relaying. One of the problems is the interfer-ence. Most of the works assume that the relays transmit on orthogonal channels such that the interference can be avoided. However, this assumption reduces the capacity of the network. Relaxing the orthogonality constraint can increase the capacity while the implement complexity is raised as well. On the other hand, ideal frequency or time syn-chronization across the relays should be taken into consideration if all relays are used in the network. RS has been proposed and recognized as an effective method to over-come these difficulties. Because of its ability to facilitate the system design and achieve full diversity with less synchronization requirement and overhead, RS has attracted much attention. Some works which relate to RS are introduced in the following paragraphs.
RS has been studied extensively for a one-way relay network consisting of a source, a destination, and multiple relays. One most commonly used RS strategy is to select a sin-gle best relay based on different objectives. In [16], a selective relaying scheme based on signal-to-noise-ratio (SNR) to minimize the end-to-end bit error rate (BER) in cooperative digital relaying systems using BPSK modulation was studied. In the SNR-based selective relaying, the relay either retransmitted or remained quiet depending on the SNRs of all links in the network. Among all relays whose received SNRs were larger than a thresh-old would participate in relaying. In addition, approximations for the optimal threshthresh-old values that minimized the end-to-end BER and the resulting performance were derived.
Also, the authors found that the optimal threshold was independent of the average source-relay SNR. Bletsas et al. developed and analyzed a distributed method to select the best relay on local channel measurements of the instantaneous channel conditions [17]. Two different selective policies were considered and represented as follows:
• Policy I
hi = min {|asi|2, |aid|2} (2.4)
• Policy II
hi = 2|asi|2|aid|2
|asi|2+ |aid|2 (2.5)
where asi and aid described the quality of the path between source-relay-destination for each relay i. The relay i that maximized function hiwas the one with the best end-to-end path quality and would be selected. Furthermore, it indicated that there was no loss in performance if only the best relay participated in cooperation in orthogonal cooperative diversity protocols. Moreover, Bletsas et al. showed that no mater what kind of strategy was applied, the single RS can achieve full spatial diversity order as if all relays were used.
As in the one-way relay networks, RS can be applied to the two-way relay networks when there exist multiple relays. Since the concept of two-way relay networks was pro-posed recently, the amount of works is small compared with that in one-way relay net-works. Relay selection for bidirectional relaying was first introduced in [9]. Oechtering et al. considered a system using superposition encoding at relay nodes. The RS criterion was to maximize the weighted sum rate for any bidirectional rate pair on the boundary of the achievable rate region. Oechtering et al. showed that in the case of independent and identical distribution (i.i.d) Rayleigh fading, RS could achieve the same diversity order as distributed beamforming. In [14], RS with ANC and TDBC in AF-based bidirectional relay networks was studied. The RS was based on a max-min criterion to minimize the outage probabilities and could be expressed as
ˆl= arg max
l=1,...,Lmin£
I1,l, I2,l¤
(2.6) where L was the number of relays, I1,l and I2,l denoted the mutual information of two opposite traffic flows for the l-th relay-path from source S1 via relay l to source S2 and from S2 via relay l to S1, respectively. That is, a relay which maximized min£
I1,l, I2,l¤ over all the relays would be selected.
Chapter 3
Relay Selection in Multiuser Two-Way Cooperative Relaying Systems
3.1 Problem Setup
Relay communication has received a great amount of attention because it is recognized as an effective technique to mitigate channel impairments. A typical multi-relay two-way network consisting of two sources and multiple relays is depicted in Fig. 3.1. Two sources S1 and S2 can exchange information with the help of relays. Recently, some studies have taken the issue of multi-source into account. In [18], the authors considered a network consisting of m pairs (i.e., m two-way relay channels) and n relay nodes. How to assign the relay node to each pair in conjunction with network coding was the main problem addressed in [18]. In [10], a two-way multi-relay multi-user network with amplify-and-forward relaying strategy was considered. The authors showed the algorithms to deal with the power allocation problem by maximizing the instantaneous sum rate and mini-mizing the symbol error rate when the multi-user interference can be ignored by a channel assignment algorithm. In our work, the system model is similar to [11]. A network con-sisting of multiple sources, multiple relays and a single destination is presented in both works. However, the considered scenarios and problems are different. First, the infor-mation flow is unidirectional in [11] but bidirectional in our work. Second, in [11], the authors proposed a joint selection scheme that selected the best source-relay pair to access
Figure 3.1: A multi-relay two-way network: sources S1 and S2 communicate with each other with the help of relays.
the channel in the network. However, it is not the case in our work. The issues that we are interested in are how to deal with the multi-user interference and select the best relay based on some criteria to achieve the best performance in terms of SINR for the network.
To the best of our knowledge, most of the research activies related to relay communica-tion were interference-free. These studies ignored the effect of interference by assuming channel orthogonality. Only a few of works took multi-user interference into considera-tion [19], [20]. In [19], the authors considered a simple ad-hoc configuraconsidera-tion consisting of two neighboring clusters and the target was to analyze the inter-cluster interference.
The results showed that the interference changed the statistical description of the conven-tional amplify-and-forward protocol and limited the diversity gain of the system. In [20], a multiuser two-way relay network employing Code Division Multiple Access (CDMA) was considered. The authors proposed a jointly demodulate-and-XOR forward relaying scheme. In phase one, all users transmitted their symbols to the relay simultaneously.
The relay broadcasted an estimate of XORed symbol for each user pair in phase two. The decision rules and the corresponding bit error rate at the relay and each user node were derived. And the authors dealt with the power control problem and receiver optimization
problem for each phase. Except for different scenarios and relaying strategies applied, the main difference between [20] and our work is that the most important problem in our work is to do relay selection (RS) while there is no RS in [20] because of only a single relay node therein. To sum up, a multi-source multi-relay bidirectional relay network employing CDMA is considered in our research. The problems we try to solve are to mitigate interference and perform relay selection such that the best performance in terms of SINR can be achieved.
Notations
We use uppercase and lower case boldface letters to represent matrices and vectors, re-spectively. Complex conjugate, transpose, and Hermitian transpose are represented by (·)∗, (·)T and (·)H, respectively. We use E{·} to denote statistical expectation. We denote the identity matrix by I and 0 to represent all-zero vectors or matrices.