SCIENCE CHINA Information Sciences
. RESEARCH PAPER .
February 2013, Vol. 56 022304:1–022304:8 doi: 10.1007/s11432-012-4776-3
Special Issue
Sort-based relay selection algorithm for decode-and-forward relay system XIE Gang1 ∗ , LIU YuanAn2 , GAO JinChun2 & LI XingZheng3 1Beijing
Key Laboratory of Network System Architecture and Convergence, Beijing University of Posts and Telecommunications, Beijing 100876, China; 2School of Electronic Engineering, Beijing University of Posts and Telecommunications, Beijing 100876, China; 3Division of Research, China Mobile Group Design Institute Co.,Ltd, Beijing 100080, China Received July 14, 2012; accepted December 9, 2012
Abstract In this paper, a sort-based relay selection algorithm is proposed for decode-and-forward wireless relay systems. The proposed algorithm can reduce computational complexity and system overhead in the relay selection for practical decode-and-forward wireless relay systems with multiple sources and multiple relays. This would be a very important improvement. Firstly, the sufficient and necessary conditions for a relay to be feasible to a source are derived. By adopting relay transmission via its feasible relay, the source can improve channel capacity compared to direct transmission. Then, a sort-based relay selection algorithm is proposed based on the sufficient and necessary conditions. In the proposed algorithm, each relay makes decision on its feasibility individually, but the final source-relay paring decision is made in a centralized manner. Simulation results show that the proposed algorithm can provide considerable system performance improvement over the existing algorithm. Especially at low signal-to-noise (SNR) region, the performance of the proposed algorithm almost reaches the optimal one. Keywords
relay selection, decode-and-forward relay, cooperative communication, wireless relay system
Citation Xie G, Liu Y A, Gao J C, et al. Sort-based relay selection algorithm for decode-and-forward relay system. Sci China Inf Sci, 2013, 56: 022304(8), doi: 10.1007/s11432-012-4776-3
1
Introduction
Cooperative diversity has been known to provide significant performance gains for wireless systems in the case of fading channel. Relaying is an emerging technology to obtain virtual spatial diversity in wireless communication networks without deploying physical antenna arrays [1]. The basic idea is that relays in wireless system overhear the information transmitted from the source, and then relay what is received to the destination. Since the same information is obtained at the destination from different spatially located nodes, i.e., the source and cooperative relay nodes, the so-called cooperative diversity is achieved. Among the most popular relaying protocols are amplify-and-forward (AF), where the relay amplifies the received signal and forwards it to the destination, and decode-and-forward (DF, also referred to as regenerative), where the relay decode the received signal, re-encodes it and forwards the re-encoded signal ∗ Corresponding
author (email:
[email protected])
c Science China Press and Springer-Verlag Berlin Heidelberg 2013
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to the destination [2–4]. The effectiveness of relay transmission on wireless system performance improvement has been demonstrated in [2,5–8]. However, analytical results also indicate that such performance improvement heavily depends on selecting suitable relay partners. Otherwise, the introduction of relay transmission may not improve the system performance, or may even worsen the performance compared to direct transmission [9,10]. So the selection of relay partners is a key for the success of the overall relay transmission. Some centralized and distributed relay partner selection algorithms have been developed for multiple-source-single-relay and single-source-multiple-relay scenarios [11–15], aiming at optimizing the channel capacity performance of a single two-hop link. The centralized algorithms usually give the optimal relay allocation scheme, while the amount of feedback information results in a heavy feedback overhead from the relays to destination node. On the contrary, the destination node does not require whole feedback information and bases itself on opportunistic cooperation, which induces high system overhead due to contention. Therefore, the centralized and distributed algorithms are not suitable for practical systems. In [9], the authors propose a semi-distributed relay selection algorithm in which each relay node can make decision on its feasibility individually, and one of relay nodes is randomly selected from its feasible set without channel gain information. The semi-distributed one means that each relay can individually decide its feasibility for a certain source while the final relay partner selection decision is still carried out in a centralized manner. Since there is no requirement on exchanging channel state information, the proposed algorithm is simple for implementation and suitable for practical wireless communication network, which can effectively reduce system overhead. In this paper, we propose a sorted-based relay selection algorithm in which DF relays are used. Under uniform power allocation between sources and relays, conditions are derived for determining the feasibility of the relay nodes in this paper. For a certain source, only applying relay transmission through its feasible relay can provide better capacity than direct transmission. After getting the channel information in relay node, each relay node generates its sorted feasible sources set and sends the final sorting source indices to the destination. This is different from the algorithm in [9], in which each relay sends the unsorted source indices to the destination, and thus the destination has no alternative but randomly selects the relay from its feasible set due to lack of channel gain information. The destination in our proposed algorithm can select the appropriate relay based on the feedback of feasible source information. In the process of this algorithm, the system gets more cooperative diversity than the algorithm in [9]. The simulation results prove it. The reminder of this paper is organized as follows. In Section 2, we will introduce the system model and derive the necessary and sufficient conditions of the feasibility of the relay nodes. The sort-based relay selection algorithm will be proposed in Section 3 and when the relay resource are scarce or the transmit SNR is low, the performance of the proposed algorithm is close to the optimal one as shown in Section 4. Finally, we draw conclusions in Section 5.
2
System model
We consider a wireless communication system consists of multiple sources, multiple half-duplex relays and a single destination. For each source, except for the direct link to the destination, one of the relay nodes can be chosen to construct a relay link. It is assumed that the direct link and the relay link use the same frequency resource, and inter-source interference is omitted by adopting orthogonal frequency division multiple access (OFDMA). The number of relay nodes can be selected for each source is limited to no more than one; on the other hand, each relay can only serve one source and operate under DF mode. The signal transmission from each source to the destination is on a frame-by-frame basis, and each frame consists of two consecutive time slots. The first time slot is used for the transmission of the sources and the second one is used for either relays or sources depending on whether relay transmission is applied. Specifically, consider a single relay-assisted sub-system which consists of a source-relay pair and the destination D as shown in Figure 1. Denote the equipment IDs of the source and relay as s and r respectively. Let a frame begin at time slot n. Then the received signal at relay r and the destination
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Source Relay D Destination D
D r
r
s
s slot n
slot n+1 Figure 1
System model.
D at this time slot can be respectively expressed as ys,D [n] = gs,D Ps xs [n] + ZD [n], ys,r [n] = gs,r Ps xs [n] + Zr [n],
(1) (2)
where gs,D and gs,r denote the channel gains from source node s to destination node D and relay node r, respectively. xs [n] denotes the signal transmitted from the source at time slot n and Ps denotes the transmit power of the source. Zr [n] and ZD [n] denote the background noise at relay node r and destination node D respectively, both of which are independent and identically distributed complex Gaussian random variables with a common variance σ 2 . At time slot n + 1, the relay decodes the received signal and forwards the re-encoded signal to the destination. At the end of this slot, the received signal at the D is (3) yr,D [n + 1] = gr,D Pr xr [n + 1] + ZD [n + 1], where gr,D denotes the channel gain from relay node r to destination node D and xr [n + 1] is the transmitted message from the relay, and Pr denotes the transmit power of relay node. For simplicity, we assume uniform power allocation between relay and source in this sub-system, and then define Ps = Pr = P . The destination combines the signals received from source s and relay r using maximumratio combination (MRC) [16]. Then the maximum average mutual information between source s and destination D is [4] Ps Ps 1 1 Pr r log 1 + 2 βs,r , log 1 + 2 βs,D + 2 βr,D , (4) IDF = min 2 σ 2 σ σ where βs,r = |gs,r |2 , βs,D = |gs,D |2 and βr,D = |gr,D |2 . In Eq. (4), the pre-log factor 1/2 is caused by the half-duplex property of the relay node. If no relaying is applied, both time slots in one frame should be allocated to the source’s direct transmission; under the same transmit power constraint, the achievable maximum average mutual information between the source and destination can be expressed as P (5) ID = log 1 + βs,D 2 . σ A relay is feasible to a source if the source can use relay transmission to provide capacity gain compared with the direct transmission. As a result, if relay r is feasible to source s, the following inequation should be satisfied r > ID IDF ⎧1 1 2 ⎪ ⎨ log(1 + SNRβs,r ) > log (1 + βs,D SNR) 2 2 ⇔ ⎪ 1 2 ⎩ 1 log(1 + SNR(β log (1 + βs,D SNR) s,D + βr,D )) > 2 2
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2 = Cns , βs,r > 2βs,D + SNRβs,D 2 s = Cm , βr,D > βs,D + SNRβs,D
(6)
where SNR = P/σ 2 denoting the transmit signal-to-noise ratio at the relay and source. So the condition that the relay r is feasible to source s is βs,r > Cns , (7) s . βr,D > Cm
3
Relay selection algorithm
3.1
Single-source and multi-relay scenario
For a wireless system with multiple relays and single source s, define Ωs as the set of feasible relays for source s. From Eq. (7), we have the following lemma. Lemma 1. The necessary condition that a relay node r belongs to the feasible set Ωs is s , ∀r ∈ R, βs,r > Cns and βr,D > Cm
(8)
where R is the set which contains all the relay nodes in the system. With Lemma 1, some important observations could be obtained as follows. 1. Only the relay which satisfies the condition in Lemma 1 can be used for source s to achieve better performance in terms of capacity over direct transmission, so that if Ωs is null, the best choice for s is to apply direct transmission for both time slots in a frame. s are both increasing function of βs,D . As a result, if the channel gain 2. The threshold Cns and Cm between the source and destination is good enough, using relay transmission cannot provide performance improvement. s are both increasing function of SNR, so that using relay transmission 3. The threshold Cns and Cm can not offer capacity gain in the system having no power limitation. 4. According to Eq. (4), the optimal relay for source s is the one that satisfies i = arg max{min{βs,j , βs,D + βj,D }}. j∈Ωs
(9)
Because there is only one source in the system, we can use centralized relay selection algorithm to find the optimal relay for source s and the algorithm complexity is affordable. 3.2
Multi-source-multi-relay scenarios
For the system with multiple sources and multiple relays, due to the inherent competition among the sources, it is usually difficult to find the optimal relay selection algorithm. As an alternative, we can reduce the problem to the finding of a relay selection algorithm which can make good use of the relay resource. So in this subsection, we apply the necessary and sufficient conditions derived in the previous section to design a sort-based relay selection algorithm for a more general relay network, which consists of M (M > 1) source and N (N > 1) relays. It is assumed that the source ID is numbered from 1 to M and the relay ID is numbered from 1 to N . 3.2.1
Feasible sources determination for each relay
Assume that the set of sources that relay r can provide service Γr . Then each source in Γr is the feasible source of relay r, 1 r N . The feasible source of relay r means that, through adopting relay transmission via the relay r, the maximum average mutual information between the source and destination can be obtained through comparison with the direct transmission. According to the sufficient and necessary conditions in Eq. (7), we have the following lemma.
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Lemma 2. The condition for a source node s to belong to the feasible set Γr should be satisfied s , ∀s ∈ Γr . βs,r > Cns and βr,D > Cm
(10)
In the wireless system, each relay can determine its feasible sources according to Lemma 2. Before a source node initiates its message transmission to the destination, some hand-shaking signals have to be exchanged, such as request to send (RTS) and clear to send (CTS) in ad-hoc systems. In the following, we borrow the names RTS and CTS to represent the hand-shaking signals before data transmission. s in Lemma 2 and then Upon hearing these signals, relay r can obtain the parameters βs,r , βr,D , Cns , Cm determine its feasible sources through the following procedure. Step 1. When a source s has information to be transmitted, it will send an RTS signal first. So relay r and destination D can estimate the channel gain βs,r and the channel gain βs,D through the received RTS. Step 2. The destination should feed back a CTS signal as an acknowledgement, which should also contain the channel gain βs,D . s according to βs,D in the received CTS signals Step 3. Relay r calculates the threshold Cns and Cm from the destination and estimates the channel gain βrD at the same time. s , respectively. Step 4. Relay r compares the channel gains βs,r and βr,D to the thresholds Cns and Cm By Lemma 2, relay r can determine whether source s belongs to Γr . By doing the above process for all the sources, relay r can generate its feasible sources set Γr . ∀s1 , s2 ∈ Γr , by Eq. (4), if min{βs1 r , βrD + βs1 D } > min{βs2 r , βrD + βs2 D }, relay r can be more effectively used by source s1 than by source s2. So in the next step, relay r sorts all the elements of Γr in a descending order according to the value of min{βsr , βrD + βsD }, ∀s ∈ Γr , and then sends the final sorting indices to the destination. Note that in the above process, each relay does not hold the information about the channel gains associated with other relays. Such a decision-making procedure is distributed and no extra information exchange is required. After all, all the relays will send their feasible sources sorting information to the destination. 3.2.2
A criterion to guarantee fairness among sources
For networks with multiple sources, a source with bad channel gain to the destination experiences lower mutual information than those with good channel conditions. Therefore, to provide some fairness among the sources, higher priority should be given to sources with bad channel condition to select a relay. So the destination should sort the sources in an ascending order according to source-destination channel gain which can be obtained through the RTS signals. Then the relay selection algorithm is carried out for the sources one by one according to the ordering result. 3.2.3
Relay selection algorithm for each source
After obtaining the feasible sources sorting results from all the relays, the destination can generate a two-dimensional matrix CM×N = [cp,q ] where 1 p M and 1 q N . In matrix C, the column index corresponding to the relay ID and the element cp,q represents the source that has the pth priority to use relay q. The value of cp,q should be equal to zero when p is larger than the cardinality of Γq . The actions taken by the destination are expressed as follows: Step 1. For a given source ID s, the destination searches for the matrix C to generate the set Ωs according to cp,q ∈ Ωs , if cp,q = s. Step 2. If Ωs is null, then the best choice is that the source s transmits its signal directly to the destination. If there is only one element in Ωs , then the corresponding relay of this element will be allocated to the source. If there are several elements in Ωs , i.e. several relays can serve source s, then the element in Ωs with minimum row index is chosen, and the corresponding relay of this element is allocated to the source in order to efficiently use the relay. But if more than one element in Ωs shares the same minimum row
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Figure 2 System throughput versus the number of sources with 20 relays.
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Figure 3 System throughput versus the number of sources with 50 relays.
index, in order to make good use of the relays, we choose the relay that can serve less sources in the relays corresponding to these elements. If several relays satisfy the above criterion, one of them will be chosen randomly. Step 3. If relay r is paired for source s, relay r can not be used by other source. Thus the destination will clear the values (set to zeros) in the rth column, and the element in matrix C equals to s is set to zero, too. Step 4. Repeat steps 1–3 until all the elements in C are equal to zero. Then the destination broadcasts the final source-relay pairing results. In this algorithm, each relay node determines its feasible sources set individually and it is not necessary for the destination node to collect the information of all the channel gains, thus significantly reducing the system overhead resulting from the information exchange, since it is semi-distibuted, where the final decision is made by the destination node.
4
Simulation results
Consider a common wireless communication cell, which covers a circle area with a radius of 500 m. The BS is located at the center of the cell, and the relays are uniformly distributed in the covered areas. The UEs are located at the edge of the cell and the distance between each source and destination is randomly chosen within a range of [450 500] m. The channel gain between any two nodes introduces path loss and fading, and the path loss exponent is set to 2. So the channel gain between node i and j is given by 2 |hi,j |2 = d−2 i,j |ζi,j | , where di,j is the distance between node i and node j, and fading ζi,j is an independent identically distributed Rayleigh random variable with unit variance. Figures 2 and 3 show the system throughput improvement of different relay selection algorithms over direct transmission with respect to different number of sources and different number of relays, and the transmit SNR is set to 60 dB. It is worth mentioning that all the algorithms in the simulation are based on the fairness criterion mentioned in this paper; that is, the source with poor channel condition to the destination will be paired first. In the simulation, the optimal pairing results are obtained through exhaustive searching. In fact, the optimal relay selection algorithm is a centralized algorithm, in which the destination gets the detailed channel information of every relay nodes through the feedback. Although it gets the best performance by exhaustive searching, high system overhead is not suitable for the practical system. The performance of the relay selection algorithm in [9] is the worst, as the destination in the algorithm randomly chooses one of the feasible relays paired to a source. The random relay selection algorithm does not take full advantage of cooperative diversity. The performance of the relay selection algorithm in [9] is the worst, as the destination in the algorithm randomly choose one of the feasible relays paired to a source. The random relay selection algorithm does not take full advantage of cooperative diversity.
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Exclusive searching The relay selection algorithm in [9] The proposed algorithm 0 35 40 45 50 55 60 65 75 70 SNR (dB) Figure 5 System throughput versus SNR with 50 relays.
It is observed that the proposed algorithm is superior to the relay selection algorithm in [9], since the proposed algorithm makes better use of cooperative diversity and the complexity of the proposed algorithm is the same as the one in [9]. The computation complexity of sorting is O(n log n), which is negligible compared to the decode computation of DF system. And the decision-making procedure is distributed and no extra information exchange is required. After all, all the relays will send their feasible sources sorting information to the destination. The system throughput of our proposed algorithm becomes larger when the number of the sources goes larger. This is mainly because the proposed algorithm can efficiently use the relay resource. So when the number of sources goes larger, more sources will compete for a relay resource; as a result, the advantage of the proposed algorithm becomes obvious. Figures 4 and 5 show the capacity performance improvement of different relay selection algorithms over the direct transmission with respect to different values of transmit SNR, and the number of sources is 50. When the transmit SNR is low, the performance of the proposed relay selection algorithm is near to that of the optimal paring algorithm. The reason is that when SNR is small, the number of sources that each relay can serve is large, so the relay becomes a scarce resource. Fortunately, the proposed algorithm are mainly focused on efficiently using the relay resource. Because cell-edge sources always have low SNR, the proposed relay selection algorithm can be used to efficiently improve the performance of cell-edge sources. But when SNR is high, the performance improvement decreases mainly because more sources choose to transmit directly.
5
Conclusions
It is usually difficult to solve the relay selection problem of systems with multiple sources and multiple relays, due to the inherent competitive nature among the sources. In this paper, we first derive the necessary and sufficient conditions under which a DF relay is feasible for a source. Subsequently, based on the necessary and sufficient conditions, a sort-based relay selection algorithm is proposed to solve the relay selection problem of the relaying systems which have multiple sources and multiple DF relays. It is worth mentioning that the proposed algorithm can make better use of the relay resource than the existing algorithm, so when relay resource are scarce, the algorithm can provide outstanding performance. Furthermore, our algorithm is also a semi-distributed algorithm, and can significantly reduce computational complexity compared with the centralized algorithm which requires global channel gain information.
Acknowledgements This work was supported in part by Sino-Swedish IMT-Advanced Cooperation Project (Grant No. 2008DFA11780), Canada-China Scientific and Technological Cooperation Projects (Grant No. 2010DFA11320), National Natural Science Foundation of China (Grants Nos. 60973111, 61170275), and Important National Science and Technology Specific Projects (Grant No. 2012ZX03003001-004).
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