Alamouti-coded decode-and-forward protocol with optimum relay selection and power allocation for cooperative communications
© Swasdio et al.; licensee Springer. 2014
Received: 30 November 2012
Accepted: 11 May 2014
Published: 9 July 2014
In this paper, an Alamouti-coded decode-and-forward protocol with optimum relay selection for three-user one destination cooperative communications is investigated. Particularly, we design the new protocol that allows the source node retransmitting the signal to the destination node at the same time as the relay node forwarding the received signal to the destination node with an Alamouti coding scheme. We exploit the cooperative maximum ratio combining technique (C-MRC) at the destination for combining a multiple copy of received signals. Therefore, the proposed scheme achieves the maximum diversity gain and lower probability of error in comparison with the existing decode and forward protocol. We also analyze a symbol error rate (SER) upper bound of the single relay system, and exploit a result of this analysis to select the optimum relay in a multiple-relay cooperation scheme based on the minimum SER selection strategy. Moreover, the optimum power allocation for the proposed protocol is derived, and it is able to provide the optimum transmission power strategy to the source and the relay nodes in order to achieve the minimum probability of error. In the performance analysis, the theoretical error probability is studied and compared with the simulation results. Simulation results indicate that the proposed protocol significantly outperforms the existing protocols, and the theoretical error probability curve is relatively close to the simulated SER curve.
In the future multimedia communications, broadband wireless communications will play a major role in personal voice and data communications that support fixed, nomadic, portable, and mobile accesses. There are many techniques that could be able to enhance the performance of wireless communications, including a multiple-input multiple-output (MIMO) system. However, given the current technology, equipping more antennas to handheld devices is far from practical. Recently, a generalized MIMO system, called cooperative communications , has been proposed for realizing the advantage of the conventional MIMO system, e.g., a diversity gain. By the cooperation of active users equipped with a single antenna in the wireless network, cooperative communications can be established in a distributed fashion.
It is well-known that Alamouti's space-time coding  could enhance the performance of wireless communication systems over flat fading channels by the virtue of the diversity gain obtained from the exploitation of two antennas at the transmitter. Furthermore, the decoding algorithm is also practically feasible with an acceptable complexity. In , a probability of error performance analysis for decode-and-forward cooperation protocol in wireless networks has been proposed, where the comparison between a closed-form symbol error rate (SER) formulation and an upper bound approximation have been investigated. In , the new combining technique, namely a cooperative maximum ratio combining (C-MRC), is proposed to overcome the diversity gain limitation of the conventional decode-and-forward protocol. In , the Hurwitz-Radon space-time code for the wireless relay network has been proposed. The results show that the diversity factor depends on the number of relays, and a 10-dB signal-to-noise ratio (SNR) improvement compared with the single relay system is achieved. In , the authors show the closed-form expression of the average symbol error probability for a distributed Alamouti scheme in wireless relay networks and examine such scheme by using the Monte Carlo simulation. In , the authors investigate a difference between the diversity of multiple relays and the diversity of multiple receivers/transmitters, and show the switching scheme with the space-time modulation that is able to reduce a bit error rate in the wireless relay communications. In , the performance analysis of Alamouti's coded-based cooperative communication has been proposed, where the system uses an amplify-and-forward (AF) strategy over Nakagami's fading. In addition, the system performance is not fully optimized by using this strategy because of the problem of synchronization. The best-relay selection scheme for cooperative networks has been introduced in , and it is called an opportunistic relaying. According to the opportunistic relaying, a single relay among a set of relay nodes is selected, depending on which relay provides the ‘best’ end-to-end path between source and destination nodes. The authors in  show that this scheme yields the same diversity order as the cooperative communication using a space-time coding in both decode-and-forward (DF) and amplify-and-forward protocols. The authors in  investigate the performance of the best-relay selection scheme, where the ‘best’ relay only participates in the relaying phase. Therefore, two channels are only needed in this case (one for the direct link and another one for the best relay link) regardless of the number of relays. The best relay is defined as the relay node that is able to yield the highest signal-to-noise ratio at the destination node. In , a two-hop cooperative multiple-relay communication network is considered. The authors propose the exact outage and capacity performance expression for relay selection over a wide range of SNR regimes. In , the authors propose a new relay selection scheme for cooperative decode-and-forward with multiple antennas that achieve a full diversity order.
Referring to the existing Alamouti-based decode-and-forward protocol in , it is obvious that the degree-of-freedom of the system, i.e., a possible opportunity of signal transmission in all available time slots, is not fully used. Furthermore, such system performance could be enhanced by the cooperative maximum ratio combining (C-MRC) technique, and the bandwidth efficiency could also be increased by using the optimum relay selection technique. These facts motivate us to propose the new protocol, and the main contributions of this paper are as follows.
In this paper, we propose the Alamouti-coded decode-and-forward protocol with an optimum relay selection technique for cooperative communications. The system allows the source node transmitting the signal in the second time slot at the same time as the relay node is decoding and forwarding the signal that is received from the source node in the first time slot to the destination using Alamouti's coding scheme. At the destination node, the received signal from both source and relay nodes will be combined by using a cooperative maximum ratio combining technique. In the C-MRC technique, the received signal sent by the relay node at the destination is weighted by the quality of the channel, i.e., a ratio of channel variances, before combining with the received signal sent by the source node resulting in an enhanced error probability and signal-to-noise ratio (SNR). The proposed scheme provides a much lower error probability in comparison with existing cooperative protocols. We also analyze a symbol error rate upper-bound for the Alamouti-coded decode-and-forward protocol with the C-MRC signal combining, and evaluate the analysis results by comparing with the simulation results. Based on this analysis, we can select the optimum relay that provides the lower probability of error for cooperative communications. Finally, we derive the optimum power allocation for the proposed system by minimizing the upper-bound on probability of error, and we are able to provide the optimum power transmission strategy to the source and relay nodes for data transmission. In the performance analysis section, the result shows that the theoretical error probability curve is close to that the simulated one, and the error probability of the optimum relay selection strategy is lower than the fixed relay strategy.
The rest of this paper is organized as follows: In section 2, we describe the system and received signal models. In section 3, we analyze the total SNR of the system and the expressions of MRC and C-MRC signal combining techniques for Alamouti-coded decode-and-forward protocol. In section 4, we analyze the average SER of the proposed system and propose the optimum relay selection technique for the Alamouti-coded decode-and-forward protocol. We also investigate the optimum power allocation for the proposed system in this section. In section 5, the simulation results are shown, and we conclude this paper in section 6.
2 System and received signal models
2.1 System model
where C is the Alamouti's coding matrix, and S1 and S2 are the transmitting symbols in two consecutive time slots.In Figure 2a,b, it is worth noticing that we also exploit the source-to-destination symbols in the broadcasting phases, i.e., phases 1 and 3, as additional received signals for combining with the source-to-destination symbols in the relaying phases, i.e. phases 2 and 4, by using the cooperative maximum ratio combining technique in order to enhance the SNR of the received signal sent by the source node. Therefore, the error probability will be correspondingly reduced. In addition, this benefit is achieved by a full utilization of signal transmission in both broadcasting and relaying phases of cooperative communications. By integrating the proposed cooperative communications with the Alamouti's coding scheme, we could achieve a full diversity gain with the enhanced SNR for the source-to-destination received signal. We divide our communications into four phases as follows.In phase 1 of Figure 2a, the source node broadcasts its modulated signal to the selected relay (based on the optimum relay selection technique described in section 4.2) and the destination nodes through wireless channels. In phase 2 of Figure 2a, the relay node decodes and forwards the received signal, sent by the source node, to the destination node. In this relaying phase, the source node transmits another signal to the destination node based on the Alamouti's coding. Similarly, the signal transmission in phases 3 and 4 in Figure 2b is equivalent to phases 1 and 2, respectively, except the symbol encoding has to obey the Alamouti's coding matrix, as shown in (1). We employ a time-division multiple access (TDMA) scheme for signal transmission, and we consider a half-rate communication with the QPSK modulation so that the bandwidth efficiency equals 1 bit/s/Hz. Essentially, we will lose four times in one communication frame to transmit two symbols so that we employ the QPSK modulation to compensate such bandwidth efficiency loss.
2.2 Received signal model
Alamouti-coded decoded-and-forward protocol with relay selection for cooperative communication
Phase 1 (Direct)
S: Broadcast S1 to R and D
R: Receive S1 from S
D: Receive S1 from S
Phase 2 (Alamouti)
S: Transmit S2 to D
D: Receive S1 from R, and S2 from S with Alamouti’s coding
R: Retransmit S1 to D
D: Receive − S2* from S
Phase 3 (Direct)
S: Broadcast − S2* to R and D
R: Receive − S2* from S
Phase 4 (Alamouti)
S: Transmit S1* to D
D: Receive − S2*from R, and S1* from S with Alamouti's coding
R: Retransmit − S2* to D
where yd 1 and yr 1 are the received signals at the destination and the relay nodes in phase 1, respectively, in which S1 denotes a transmitted symbol of the source node, yd 2 is the received signal at the destination node in phase 2, in which the source node transmits a symbol S2 and the relay node decodes and forwards the decoded symbol Ŝ1; P1 and P2 are the transmit power of the source and the relay nodes, respectively; Hd 1, Hr 1, Hd 2, and Hr 2 are the channel impulse responses of the source-to-destination link in phase 1, the source-to-relay link in phase 1, the source-to-destination link in phase 2, and the relay-to-destination link in phase 2, respectively. In addition, we introduce a weighting factor w in phase 2 based on a concept of C-MRC signal combining, yd 1 in which w = γeq/γrd, where γeq = min (γsr, γrd), and γsr and γrd are the instantaneous SNR between the source-to-relay link and the relay-to-destination link, respectively. Furthermore, nd 1, nr 1, and nd2 are zero-mean complex additive white Gaussian noise (AWGN) with variance N0 at the destination in phase 1, at the relay in phase 2, and at the destination nodes in phase 2, respectively. Basically, the Alamouti's coding scheme uses two time slots to transmit two symbols. Hence, the received signals of phases 3 and 4 can be described as follows:
where yd 3 and yr 3 are the received signals at the destination and the relay nodes in phase 3, respectively, yd 4 is the received signal at the destination node in phase 4, in which the source node transmits a symbol S1* and the relay node decodes and forwards the decoded symbol − S2*. In addition, nd 3, nr 3, and nd4 are zero-mean complex additive white Gaussian noise (AWGN) with variance N0 at the destination in phase 3, at the relay in phase 4, and at the destination nodes in phase 4, respectively. We now assume that all channels are modeled as quasi-static Rayleigh flat-fading channels, i.e., Hd 1 = Hd 2 = Hd 3 = Hd 4, H r1 = Hr 3 and H r2 = Hr 4, within one transmission frame according to a typical assumption for the Alamouti's coding scheme .
3 Signal combining technique
where γtotal is the total SNR, γdirect is the SNR of a symbol in phase 1 or 3, and γAlamouti is the SNR of a symbol in phase 2 or 4.
3.1 Maximum ratio combining (MRC) technique
where γS 1 is the total SNR of a symbol S1 and γs 2 is the total SNR of a symbol S2.
It is worth noticing that the MRC combining yields the maximum SNR to (15) and (16), given that the estimated signals Ŝ1 and Ŝ2 at the relay node are correctly decoded. Specifically, in practical applications, the correctness of symbols Ŝ1 and Ŝ2 solely depends on the quality of the channel link from the source to relay link. Hence, the MRC combining cannot guarantee the maximum SNR as mentioned in .
3.2 Cooperative maximum ratio combining technique
In this paper, we employ the C-MRC signal combining technique at the destination node because it could provide a full diversity gain, and it is superior to the MRC signal combining. Once the signal combining, i.e. (23) and (24), has been done at the destination node, the destination node’s receiver will perform the symbol detection, i.e. S1 and S2, by using a maximum-likelihood (ML) receiver.
4 Performance analysis
4.1 Probability of error analysis
It is worth noticing that (28) has been derived by using the assumption that Hsd, Hsr, Hrd, and w are statistically independent; therefore, the result in (28) serves as the upper bound on conditional SER. In fact, Hsr, Hrd, and w are jointly dependent.
where A = bpskP1δsd2 and C = bpskP2δrd2.
where A = bpskP1δsd2 and C = bpskP2δrd2.
4.2 The proposed optimum relay selection technique
4.3 The optimum power allocation
In the cooperative communication system, the source node transmits the data to the destination node with the transmission power P1, and the relay helps the source node to re-transmit the data with transmission power P2. Thus, the total transmission power is equal to P = P1 + P2, and the transmission power ratio is equal to Pr, where Pr = P1/P2.
In this section, the optimum power allocation is investigated, in which the transmission power P1 and P2 could be optimally allocated. The transmission power ratio can be increased or decreased depending on the channel quality of the system. The optimum power allocation strategy can be obtained by minimizing the upper bound on the average SER, i.e. (29), as follows:
It could be observed that the optimum power allocation expressions in (38) and (39) at high SNR regimes mainly depend on the value of noise variances. However, in the low SNR regimes, the transmission power ratio will depend on the channel quality of the source-to-destination and the relay-to-destination links. It could also be observed that if the channel quality of the source-to-destination link is better than the relay-to-destination link, the transmission power ratio (Pr) will be greater than one. However, if the channel quality of the source-to-destination link is less than the relay-to-destination link, the Pr will be less than one. In the system which has the same channel quality between the source-to-destination link and the relay-to-destination link, the transmission power P1 will be equal to P2, i.e., Pr = 1. In addition, the constraint that P1 > 0 and P2 > 0 must be held because the source and relay nodes must be co-existed in order to form the Alamouti-coded cooperative communications.
Therefore, some amount of power must be allocated to both source and relay nodes; as a result, the constraint P1 > 0, P2 > 0, if and only if P > 0, will be valid. In other words, if P1 = 0, it is equivalent to the case that there is no source node, and, hence the relay node cannot form the Alamouti-coded cooperative communications with any other node. This is not the considered case in the paper. It is also worth noticing that the power allocation does not depend on the source-to-relay link because the effect of this link has been averaged in the upper bound on the average SER expression in (32), and it results in a multiplicative factor, i.e., δrd2/δsr2 + δrd2, which is independent of P1 and P2.
5 Simulation result
In this paper, we have proposed the Alamouti-coded decode-and-forward protocol with optimum relay selection for three-user cooperative communications. The optimum relay selection protocol in the scenario of a high channel link, i.e., a channel variance of the source-to-destination link, the source-to-relay link, and the relay-to-destination link are equal to 5, significantly outperforms the existing decode-and-forward (DF) protocol, where the SNR improvement over 5 dB at SER lower than 10−3 is observed. Furthermore, the proposed Alamouti's coding scheme performs better than existing DF protocol of about 1 dB at all SER regimes. In the performance analysis, the derived probability of error shows a close result to the simulated one. In addition, the derived upper bound on an average SER could be used to determine the optimum transmission power for the source node and the relay node. It is worth noticing that the optimum power allocation could enhance the error probability of the system effectively, especially in the low SNR regimes. Furthermore, in the case of no information about the channel variances, the equal power allocation could be fairly used instead as confirmed by the simulation results in high SNR regimes. Furthermore, the proposed protocol achieves a full diversity gain by the virtue of increasing a number of signal transmissions in the relaying phases.
and F R (1) = 1.
where , , , and .
This work is financially supported by the Thailand Research Fund (TRF) and the Office of the Higher Education Commission (OHEC) under the grant number MRG5080388.
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