Two- and four-relay selection schemes for application in interference limited legacy networks
© Chen et al.; licensee Springer. 2012
Received: 7 June 2012
Accepted: 1 November 2012
Published: 21 November 2012
The limiting effect of multi-user interference from an adjacent cell upon the relays used for cooperative transmission is considered in the context of legacy networks which adopt max(min(·,·)) type relay selection policies. We extend previous work which considered single relay selection to the selection of two or four such relays, as is required in distributed space–time coding. We obtain new analytical expressions for outage probability over Rayleigh frequency flat fading channels for two signal-to-noise ratio regimes. We confirm by simulation that such a relay selection scheme has robustness to relay selection feedback error and outperforms a single relay selection scheme.
Cooperative relaying can be considered as an effective method to combat fading by exploiting spatial diversity , and as a way for two users with no or weak direct connection to attain a robust link. One or more relay nodes are generally used in such relaying to forward signals transmitted from the source node to the destination node. In a cooperative communication system, there are two main cooperative methods: decode-and-forward (DF) (regenerative relaying protocol) and amplify-and-forward (AF) (transparent relaying protocol) methods . In the DF method, relay nodes decode the source information and then re-encode and re-transmit it to the destination. In the AF method, relay nodes only amplify and retransmit their received signals, including noise, to the destination. Therefore, compared with DF, AF-type schemes have the advantage of simple implementation and low complexity in practical scenarios. In addition to complexity benefits, it has been shown in  that an AF scheme asymptotically, in terms of appropriate power control, approaches a DF one with respect to diversity.
AF has extensively been studied in the literature, but generally in the context of ideal configurations without interference during the cooperation process [4, 5]. However, more practical systems have been studied in [6–8], which consider the presence of interference effects. The effect of cochannel interference on the performance of multihop wireless networks with AF relaying is analyzed in . The performance of a two-hop channel state information-assisted AF system, with co-channel interference at the relay, is analyzed in .
In a cooperative relay network, moveover, when many relays can help the source to transmit to the destination, sometimes some relays provide a poor channel quality which can affect the end-to-end transmission quality . Therefore, the use of a relay selection scheme is attracting considerable attention to overcome this problem and preserve the potential diversity gains [10–12], while mitigating the problem in synchronizing a large number of cooperative nodes.
In , exact outage and diversity performance expressions for a single relay selection scheme are provided for a wide range of signal-to-noise ratio (SNR) regimes in the context of an AF transmission protocol. The work in  relies on using instantaneous end-to-end wireless channel conditions to obtain the best single relay for cooperative diversity. This study was extended in  to obtain outage-optimal opportunistic relaying in the context of selecting a single relay from a set of N available relays. They show that cooperative diversity gain is achieved even when certain relays remain inactive. However, these relay selection criteria lack the flexibility to deal with the presence or absence of interference effects. In order to improve the practicality, in  the effects of multi-user interference are considered for relay nodes and a single relay selection scheme is used to overcome the effects of the interference, in the context of legacy networks. However, using a single best relay is not always sufficient to satisfy the required outage probability at a destination node. Moreover, these works have not considered feedback error for relay selection, which means sometimes the best relay cannot be chosen because the wrong enable feedback information is received from the destination node. We highlight that this is different from recent work which has considered the effect of only delay in the feedback path .
Therefore, in this article, in order to overcome these shortcomings, first, the basic AF protocol  is considered when external out-of-cell structural/unmanaged interference affects the cooperation process. We also consider maximum ratio combining (MRC) at the destination node and distributed space–time coding (DSTC) to mitigate the associated bandwidth overhead. Furthermore, to facilitate analysis, we just consider interference at the relays and ignore the effect of interference at the destination node, which matches the approach in . Moreover, this study is targeted at legacy systems where max(min(·,·)) type policies are used for relay selection. Second, we focus upon two selection schemes to select two or four relays from a single group of relays. We derive new outage probability expressions for two or four relay selection and compare them with the results for conventional best single relay selection. Finally, we examine by simulation the bit error rate (BER) performance of the best single relay selection scheme and the best two-relay selection scheme, in the presence of errors in the feedback of relay selection information. In practice, this could be as simple as a single permission to transmit bit.
The remainder of this article is organized as follows. The system model and a statistical expression for interference-based AF are described in Section 2. In Section 3., the relay selection criteria for interference-limited systems and asymptotic outage probability analysis are presented. Simulation results for outage probability analysis and impact of relay selection feedback errors are provided in Section 4. And conclusions are drawn in Section 5.
Notations: The following notations are used in the article. ε(·) represents the statistical expectation operator. A complex zero mean additive white Gaussian noise n∼CN(0,N0), where N0 is the noise variance; and Pr(A) is the probability of A. Γ(n) is the Gamma function, and denotes the real value.
2 System model
In our model, the source powers at the target and the neighboring cluster are assumed to be the same. This model is representative of an ad-hoc network environment where there is no power control between adjacent clusters.
which is the sum of the ratios between the SNR of the first hop and the INR of the interference, because when SNR→∞, then . In this case, the statistical description of the system is independent of the second hop.
where f(·) and F(·) denote the PDF and the CDF, respectively. The parameter . Note that the parameter L controls the level of interference in the target and neighboring clusters.
Furthermore, considering interference at both the relays and the destination nodes is beyond the scope of this study and is left for analysis in future work. Our two- or four-relay selection scheme assuming interference only at the relays will be implemented as presented in the following sections.
3 Two- or four-relay selection with outage probability analysis
In order to introduce our proposed two- or four-relay selection schemes, we need to introduce first the conventional relay selection scheme.
3.1 Conventional relay selection
where N represents the set of indices of all available relays.
The conventional relay selection policy offers the relay with the “best” end-to-end path between source and destination and provides diversity gain on the order of the number of the relays . However, this relay selection criterion is only considered for environments without interference, and the best relay selection is not always sufficient to achieve the required outage probability at a destination node. Finally, when feedback error is present in the relay selection, the performance of the single relay selection scheme is significantly degraded, further discussion of which will be given in the simulation section. Therefore, to overcome these problems two- and four-relay selection schemes are proposed for use in interference configurations for legacy networks which are restricted to adopt a max(min(·,·)) type policy.
3.2 Asymptotic two- and four-relay selection criterion
where Γ(n)=(n−1)! is the Gamma function.
The outage probability of the best two-relay selection can be expressed by using the CDF expression (14).
Then, exploiting (21) as in (15), the outage probability can be evaluated, for example for the results in Section 4. we employ the Mathematica software package .
In this study, we focus on a two- or four-relay selection approach as it is immediately applicable within a cooperative network, which exploits DSTC  to improve the end-to-end performance, such as an Alamouti or Quasi-Orthogonal code, according to the number of selected relays. Furthermore, for our relay selection policy, it requires only the SNR of the links from source to relay nodes and the INR of the interference links which can be obtained by the relay nodes during the early stage of transmission. In terms of the relay selection policy, moreover, the information describing the links between the relay and destination is not required at the destination node, therefore, this policy has a lower complexity than that of  and may save feedback set-up time.
3.3 Semi-conventional two- and four-relay selection
where b=(i,i ′ ), i.e., the best pair of relay indices, where i denotes the index of the relay with the best link in N, and i ′ is that of the best relay among the remaining N−1. Here, we need to consider the outage behavior of the ratio according to the semi-conventional scheme. In order to simplify the approximation of the corresponding outage bound as in , two cases will be considered.
where and are denoted by (14) and (25), respectively. And the outage probability can be obtained by using (26).
where and are given by (21) and (29), respectively. And the outage probability can be evaluated by using (15) and (30), for example with the Mathematica software package .
4 Simulation results for outage probability analysis and impact of relay selection feedback errors
In this section, in order to verify the results obtained from the above mathematical expressions, we assumed the target source node and the neighboring source node use the same unity transmission power, and there is no direct link between the source and the destination as path loss or shadowing render it unusable. We show outage probability performance of the two- and four-relay selection schemes.
Next, we compare the BER performance of the best two-relay selection from a group of N available relays, N=4, with distributed Alamouti code with the best single relay selection in the presence of relay selection feedback errors, when quadrature phase-shift keying symbols are used in transmission.
We have examined two different selection schemes which are asymptotical and semi-conventional policies to select the best two and four relays from a group of available relays in the same cluster by using local measurements of the instantaneous channel conditions in the context of legacy systems which adopt max(min(·,·)) type policies. New analytical expressions for the PDF, and CDF of end-to-end SNR were derived together with closed form expressions for outage probability over Rayleigh fading channels. Numerical results were provided to show the advantage of the outage probability performance of the best two- and four-relay selection in a cooperative communication system. Moreover, through simulation study, we confirmed the robustness of the best two-relay selection scheme in the presence of moderate to severe relay selection feedback errors.
The authors would like to thank the anonymous reviewers and the editor for improving the clarity of this article.
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