Decoding techniques for alternaterelaying BICM cooperative systems
 Hala Mostafa^{1}Email author,
 Mohamed Marey^{2},
 Mohamed H Ahmed^{1} and
 Octavia A Dobre^{1}
https://doi.org/10.1186/168714992013236
© Mostafa et al.; licensee Springer. 2013
Received: 10 May 2013
Accepted: 16 September 2013
Published: 25 September 2013
Abstract
In this paper, we propose the use of bitinterleaved coded modulation in alternaterelaying decodeandforward cooperative communication systems. At the destination, we exploit the interference signal, which results from the simultaneous transmission of data streams through both direct and one of the relay channels to develop an optimal detector. It is shown that the proposed detector can be implemented by parallel concatenating maximum a posteriori (MAP) algorithms and demappers to the decoders. The detector exchanges soft information between the decoders and the MAP algorithms in an iterative way for performance improvement. The proposed optimal detector requires a long delay as the destination has to receive and store the entire frame before performing data detection. To avoid this, a suboptimal detector is also proposed. Unlike the optimal detector, the suboptimal one exploits two consecutive received packets to decode one packet. It turns out that the suboptimal detector has less reduced delay, complexity, memory size, and bandwidth loss with a slight increase of the biterrorrate. Extensive simulation results are presented to demonstrate the effectiveness of the proposed detectors.
Keywords
Cooperative systems MAP principle BICM1 Introduction
Cooperative technology constitutes a breakthrough in the design of wireless communication systems. This is due to its relatively simple implementation and its significant performance gains in terms of link reliability, system capacity, and transmission range [1, 2]. In cooperative communications, multiple terminals in a wireless network cooperate to form a virtual antenna array in a distributed fashion. In this manner, spatial diversity gain can be achieved even when a local antenna array is not available. It is not surprising that cooperative communications have become a strong candidate for many wireless applications, such as cellular networks, wireless local area network, mobile ad hoc networks, and wireless sensor networks [3].
Generally, there are two kinds of relaying modes: full duplex and half duplex. In a fullduplex mode, a relay transmits and receives simultaneously in the same band; however, the transmitted signal interferes at the relay with the received signal. In theory, it is possible for the relay to cancel out the interference because it knows the transmitted signal. However, in practice, a small error in the interference cancellation can be fatal because the transmitted signal is typically 100 to 150 dB stronger than the received signal, as indicated in [2]. This error results from inaccurate knowledge of the device characteristics or from the effects of quantization and finite precision processing. Therefore, the fullduplex mode is not commonly used. In a halfduplex mode, a relay cannot simultaneously transmit and receive. In other words, the source and relay transmissions must be orthogonal in order to eliminate any potential interference. Orthogonality can be in time domain, in frequency domain, or using any set of signals that are orthogonal over the timefrequency plane. A major problem of the halfduplex relaying mode is the reduction in the spectral efficiency [2].
To combat this problem, different cooperative techniques are introduced, such as nonorthogonal, two way, and alternate relaying. In the nonorthogonal cooperative systems (e.g., [4, 5]), the source is active all the time. In the first half of the transmission interval, the source sends data to a relay and destination. However, since the relay is assumed to be half duplex, the relay does not receive what the source transmits in the second half of the transmission interval. This results in a reduction in the diversity order of the system. Furthermore, an additional processing is required at the destination in order to separate the signals received simultaneously in the second half of the transmission interval. In the twoway cooperative systems, two sources exchange data via the aid of a shared relay (e.g., [6, 7]). The two sources send simultaneously during the first time slot, while in the second time slot, the rely broadcasts the mixture of these two signals. Since parts of the transmit signal sent by the relay are known at the destinations, each receiver can extract the data of the other partner. It is obvious that the fullrate transmission can be attained since two time slots are required to transmit the data of the two partners; however, this cooperative transmission requires two partners sending messages to each other simultaneously.
In alternaterelaying transmission protocols (e.g., [8, 9]), the source communicates with the destination via two relays. The basic idea behind these protocols is to use two successively forwarding relays to mimic a fullduplex relay. More specifically, at any time slot, the source sends its information to the destination and one of the relays, while the other relay forwards the information received from the source in the previous time slot to the destination. In this way, the source can continuously transmit data without being halted, and hence, the spectral efficiency loss is recovered.
The vast majority of research in alternaterelaying transmission protocols focuses on informationtheoretic analysis to assess achievable rates, capacity bounds, and diversitymultiplexing tradeoff (e.g., [8–12]). However, the major issue associated with these protocols is how to handle the interference, which is caused by the simultaneous transmission of the source and one of the relays, in a simple way. Basically, the way used to treat the interference at the relays and destination depends on whether the relays employ amplifyandforward (AF) or decodeandforward (DF) relaying strategies.
For the AF alternaterelaying protocols, the authors in [8] propose successive decoding at the destination with partial cancellation of interrelay interference. The authors in [9] introduce interrelay selfinterference cancellation, where the cancellation is performed at one of the relays; however, the detection process at the destination requires high computational complexity. The authors in [10] propose a full interrelay interference algorithm, where the cancellation is performed at the destination in a simple manner; however, the noise accumulation associated with the algorithm limits the overall system performance.
Generally, the deployment of AF relaying strategy in alternaterelaying cooperative systems is challenging, as the interference and noise accumulation which results from the interrelay link degrade the overall performance. Accordingly, the detection process at the destination has to be associated with sophisticated interference cancellation detectors. This increases the computational complexity significantly, as shown in [10]. Due to its symbolbysymbol decision base, DF is an attractive relaying strategy to avoid interference accumulation at the destination for alternaterelaying cooperative systems.
For DF alternaterelaying protocols, it is usually assumed that the interrelay link is either sufficiently weak and then its contribution can be treated as extra noise, or sufficiently strong that it can be canceled through successive interference cancellation at the relay [8, 11]. However, these two extreme scenarios may not always occur in practical systems. In [13, 14], dirty paper coding based on interference presubtraction at the source is proposed to cancel the interrelay interference. However, this requires high computational complexity and full knowledge of the channel state information of all the links at the source, which is not easy to achieve in practice. Beamforming/smart antennas [15] and code division multipleaccess techniques [16] are also proposed to eliminate the interference at the relays and destination. The technique comes at the cost of complexity, where the latter comes at the cost of wasting resources. In [12], the authors propose employing multiple antenna at the relays to cancel out the interrelay interference. However, implementing multiple antennas at the relays is not applicable for some wireless applications due to size, power, and cost constraints. A rotated signal constellation has been proposed to achieve full interference cancellation [17]. The idea is that there are no two symbols in the rotated constellation having the same real or imaginary value. Accordingly, an orthogonal transmission can be achieved between source relays and interrelay links by assigning real parts of the rotated symbols to one link and imaginary parts to the other link. However, the direct link between the source and destination is not available, and there is significant degradation in the BER performance when compared with that of the original constellation.
All the previous works deal with uncoded transmission, which is not usually used in practice. To the best of our knowledge, this is the first work in the literature that applies errorcorrecting coding for alternaterelaying cooperative systems. In this paper, we exploit the interference signal at the destination to develop an optimal detector for alternaterelaying DF cooperative systems in conjunction with a bitinterleaved coded modulation (BICM) signal. Starting from the maximum a posteriori (MAP) principle, it is shown that the proposed detector can be implemented by combining the MAP algorithm with the decoder of BICM. Furthermore, to reduce the delay associated with the optimal detector, a suboptimal one is also introduced. The proposed detectors can work with any receiver as long as this can compute the a posteriori probabilities of the data symbols.
The remainder of the paper is organized as follows. In Section 2, the system model and problem formulation are presented. In Sections 3 and 4, the optimal and suboptimal detectors are proposed at the destination, respectively. Section 5 explains the used detector at the relays. The performance of the proposed detectors is evaluated through computer simulations in Section 6. Finally, the paper is concluded in Section 7.
2 System model and problem formulation
2.1 Transmission protocol
Transmission schedule of the fullrate cooperative system
Time slot  Source S  Relay R_{1}  Relay R_{2}  Destination D 

1  Send d^{(1)}  Receive/decode d^{(1)}  Silent  Receive d^{(1)} 
2  Send d^{(2)}  Send d^{(1)}  Receive d^{(2)} and d^{(1)},  Receive d^{(2)} and d^{(1)} 
decode d^{(2)}  
3  Send d^{(3)}  Receive d^{(3)} and d^{(2)},  Send d^{(2)}  Receive d^{(3)} and d^{(2)} 
decode d^{(3)}  
4  Send d^{(4)}  Send d^{(3)}  Receive d^{(4)} and d^{(3)},  Receive d^{(4)} and d^{(3)} 
decode d^{(4)}  
⋮  ⋮  ⋮  ⋮  ⋮ 
2.2 Received signals at relays and destination
For each link, the channel is assumed to be frequency nonselective and modeled as a zeromean independent complex Gaussian random variable. In addition, we consider that all the nodes have equal additive white Gaussian noise (AWGN) power spectral density of N_{0}. Finally, we suppose that perfect channel state information is available at the destination and relays.
where ${w}_{{R}_{1}}^{(p+1)}\left(n\right)$ is the AWGN contribution at relay R_{1}, and $\phantom{\rule{0.3em}{0ex}}\phantom{\rule{0.3em}{0ex}}\phantom{\rule{0.3em}{0ex}}\phantom{\rule{0.3em}{0ex}}{\widehat{d}}_{{R}_{2}}^{\phantom{\rule{0.3em}{0ex}}\left(p\right)}\left(n\right)$ is the n th detected symbol for the p th packet at relay R_{2}. Our goal is to develop BICM detectors at relays and destination.
3 Optimal decoding technique at the destination
Each row indicates the branch labels for the transitions from states corresponding to the inputs {α_{1}, α_{2}, α_{3}, α_{4}, α_{5}, α_{6}, α_{7}, α_{8}}, respectively. Accordingly, using this equivalent model, we can apply the MAP criterion to develop an optimal decoding technique.
3.1 MAP algorithms
where $\left[{d}^{\left(p\right)}\left(n\right)\phantom{\rule{2.22144pt}{0ex}}{d}_{{R}_{x}}^{(p1)}\left(n\right)\right]$ represents the output associated with this transition. Note that ${\gamma}_{n}^{\left(p\right)}({s}^{\prime},s)$ represents the probability to transit from the state s’ to the state s for the n th symbol in the p th packet, given the received symbol ${y}_{D}^{\left(p\right)}\left(n\right)$. We employ the BCJR algorithm to implement the optimal demapper of the DF alternaterelaying transmission, which is analogous to a convolutional code with constraint length of two, as the BCJR algorithm is the optimal decoding technique for convolutional codes [19]. The a priori probability P(d^{(p)}(n)) in (5) is unavailable at the first iteration. Therefore, in the initialization phase, it is assumed that all d^{(p)}(n) are equally probable. Equation (5) is used as the input to the demapper, which then generates the bit metrics.
3.2 Demapper
where the subset $\phantom{\rule{1em}{0ex}}\phantom{\rule{1em}{0ex}}\Psi (f,b)=\left\{\mu \left(\phantom{\rule{1em}{0ex}}\left[{v}_{n}^{\left(p\right)}\phantom{\rule{1em}{0ex}}\left(1\right),{v}_{n}^{\left(p\right)}\phantom{\rule{1em}{0ex}}\left(2\right),\cdots \phantom{\rule{0.3em}{0ex}},{v}_{n}^{\left(p\right)}\left(m\right)\right]\mid {v}_{n}^{\left(p\right)}\left(f\right)=b\right)\right\}$. For more details on the bit metric concept, the reader is referred to [20–22].
3.3 Decoder
These a posteriori symbol probabilities are provided to the MAP algorithms as a priori information, as seen in (5). At the last iteration, the final decoded outputs are the hard decisions based on the a posteriori probabilities.
3.4 Implementation aspects
The implementation aspects are as follows:

An additional tail consisting of N_{ d } zero symbols is included to the end of the transmitted frame to force the trellis path to return back to the initial state, from which the decoding process starts.

As commonly assumed in the literature, the relays forward the received packets only when they have been correctly decoded; otherwise, they remain idle. In practice, the relays send acknowledgment signals to the destination, indicating the status of each packet. For illustration, if the destination receives negative acknowledgment for the p th packet, this implies that the relay R_{ x } is unable to decode and forward this packet. In this case, the channel coefficient that corresponds to the R_{ x } packet, ${h}_{{R}_{x}}^{\left(p\right)}$, is set to zeros in (5).

The optimal detector requires a large memory for storing the entire frame before starting data detection, which in turns increases the required processing time for decoding. This may prohibit the optimal detector from practical implementation, as such we propose a suboptimal one.
4 Suboptimal decoding technique at the destination
After computing the a posteriori probabilities of the data symbols as in (11), (6) can be applied to produce the bit metrics. As for the optimal detector, these bit metrics are then deinterleaved and passed to the SISO detector. The soft information provided by the decoder is fed back to (11) to refine the computation.
After detecting ${\left\{{d}^{\left(p\right)}\left(n\right)\right\}}_{n=1}^{{N}_{d}}$, their contribution can be removed from ${\left\{{y}_{D}^{(p+1)}\left(n\right)\right\}}_{n=1}^{{N}_{d}}$, forming ${z}_{D}^{\left(p\right)}(n+1)={y}_{D}^{(p+1)}\left(n\right){d}^{\left(p\right)}\left(n\right){h}_{{R}_{y}D}^{(p+1)}$. Similarly, from ${\left\{{z}_{D}^{(p+1)}\left(n\right)\right\}}_{n=1}^{{N}_{d}}$ and ${\left\{{y}_{D}^{(p+2)}\left(n\right)\right\}}_{n=1}^{{N}_{d}}$, and by averaging over ${\left\{{d}^{(p+2)}\left(n\right)\right\}}_{n=1}^{{N}_{d}}$, the (p+1)th packet, ${\left\{{d}^{(p+1)}\left(n\right)\right\}}_{n=1}^{{N}_{d}},$ can be detected, and so on. Similar to the optimal detector, if the destination receives a negative acknowledgment from relays about the status of the p th packet, we set ${h}_{{R}_{y}}^{\left(p\right)}=0$ in (13).
A comparison of the optimal and suboptimal detectors
Complexity (flops)  Delay  MS  BW loss  

Optimal  65M^{2}N_{ d }P + Υ  N _{ d } P  N _{ d } P  1/P 
Suboptimal  (34M^{2}  M)N_{ d }P + 8N_{ d }(P  1) + Υ  N _{ d }  N _{ d }  zero 
5 Decoding technique at the relays
In DF alternaterelaying protocols, it is usually assumed that successive interference cancellation, where the strongest signal is detected first, and then its contribution is subtracted from the received signal before detecting the other signal, can be employed at the relays [8, 11]. In order to provide a reliable BER performance, this requires that the interrelay link is either sufficiently weak or sufficiently strong when compared with the sourcerelays links. However, these two extreme scenarios may not always occur in practical systems. In this section, at the relays, we show how the bit metric can be generated to have a better performance in the presence of the interference resulting from the forwarding relay transmission. Note that at the destination, each packet is received twice through the direct and relaying links, if the forwarding relay was able to correctly detect this packet. Otherwise, it is received only through the direct link. At the listening relay, each packet is received through the sourcetolistening relay link, interfered by the data sent from the forwarding relay. As such, the proposed detectors at the destination are inapplicable at the listening relay.
where the subset $\Psi (f,b)=\left\{\mu \left(\left[{v}_{n}^{\left(p\right)}\left(1\right),{v}_{n}^{\left(p\right)}\left(2\right),\cdots \phantom{\rule{0.3em}{0ex}},{v}_{n}^{\left(p\right)}\left(m\right)\right]\mid {v}_{n}^{\left(p\right)}\left(f\right)=b\right)\right\}$. The a priori probability P(a) is unavailable on the first iteration of the demapping. Therefore, in the initialization phase, it is assumed that all a are equally probable. Equation (18) is used as the input to the SISO decoder, which then generates the a posteriori probabilities for the coded bits. On the second iteration, these probabilities are interleaved and fed back as a priori probabilities to the demapper as shown in Figure 3.
6 Results
In this section, we validate the proposed detectors through Monte Carlo computer simulations. We consider an alternaterelaying DF cooperative communication system, using a convolutional code with constraint length 5, rate 1/2, and polynomial generators (23)_{8} and (35)_{8}. The BCJR algorithm [19] is used for decoding. A framebased transmission is assumed; each has 20 packets. A packet length of N_{ b }=150 information bits is chosen, leading to N_{ c }=300 coded bits. The coded bits are set, partition mapped on an 8PSK constellation, resulting in N_{ d }=100 symbols. For each link, the channel is assumed to be frequency nonselective and modeled as a zeromean independent complex Gaussian random variable. To capture the effect of the path loss on the performance, we consider E[h_{ AB }^{2}] = (d_{ SD } / d_{ AB })^{ ε }[2], where h_{ AB }, d_{ SD }, and d_{ AB } are the channel coefficient, the distance between source and destination, and the distance between the nodes A and B, respectively; ε is the path loss exponent, and E[.] is the statistical average operator. Unless mentioned otherwise, the distance between the source and the two relays equals 0.4, while the distance between the two relays is 0.2. All these distances are normalized to the sourcetodestination distance, and ε is set to be 2.
Here we assume, without loss of generality, that $\mathrm{E}\left[{\left{d}^{\left(p\right)}\left(n\right)\right}^{2}\right]=1,\mathrm{E}\left[{\left{h}_{\mathit{\text{SD}}}^{\left(p\right)}\right}^{2}\right]={\sigma}_{\mathit{\text{SD}}}^{2}=1$, and the transmit pulse shaping satisfies the Nyquist criterion. Since two relays are used in the alternaterelaying cooperative systems, the BER performance of the halfrate one relay and best relay from a set of two relays is also shown. For a fair comparison between the halfrate and fullrate (alternaterelaying) systems, we keep the same data rate and transmitted power for both systems. Hence, we use 64PSK modulation for the halfrate systems and 8PSK for the fullrate systems. As one can observe, for the fullrate cooperative systems, iterative processing achieves a significant performance improvement for the proposed optimal and suboptimal detectors. Furthermore, it is seen that the performance of the proposed fullrate cooperative systems outperforms that of the halfrate cooperative systems.
For the sake of comparison, we show the performance when the interference signal can be treated as additional noise, and this is referred to as detector 1. In addition, we show the BER performance of the successive interference cancellation detector proposed in [8, 11], which is based on detecting the strongest signal first, then subtracting its contributions from the received interfered signal before detecting the other signal. In the sequel, this is referred to as detector 2. As one can observe, both detector 1 and detector 2 lead to an unacceptable performance. We also notice that the used detector achieves a strong improvement of the performance after only two iterations. In addition, there is no significant improvement in the performance after three iterations for any E_{ b }/N_{0} values.
7 Conclusions
The receiver design was studied at destination for alternaterelaying decodeandforward cooperative communication systems with BICM signals. The interference signal, which results from the simultaneous transmission of data streams through both direct and one of the relay channels, was exploited as a beneficial resource to develop an optimal detector. We showed that the optimal detector was implemented by parallel concatenating MAP algorithms and demappers to the decoders. In order to avoid the delay problem associated with the optimal detector, a suboptimal detector was also developed. The suboptimal detector achieved a close performance when compared with the optimal one. Both of the optimal and suboptimal detectors exchanged soft information between decoders and MAP algorithms in an iterative fashion for performance improvement.
Declarations
Acknowledgements
H Mostafa gratefully acknowledges the financial support of the Egyptian government.
Authors’ Affiliations
References
 Nosratinia A, Hunter T, Hedayat A: Cooperative communication in wireless networks. IEEE Commun. Mag 2004, 42(10):7480. 10.1109/MCOM.2004.1341264View ArticleGoogle Scholar
 Laneman N, Tse D, Wornell G: Cooperative diversity in wireless networks: efficient protocols and outage behavior. IEEE Trans. Inf. Theory 2004, 50(12):30623080. 10.1109/TIT.2004.838089MathSciNetView ArticleMATHGoogle Scholar
 Stankovic V, HostMadsen A, Xiong Z: Cooperative diversity for wireless ad hoc networks. IEEE Signal Process. Mag 2006, 23(5):3749.View ArticleGoogle Scholar
 Ding Z, Krikidis I, Rong B, Thompson J, Wang C, Yang S: On combating the halfduplex constraint in modern cooperative networks: protocols and techniques. IEEE Trans. Wireless Commun 2012, 19(6):2027.View ArticleGoogle Scholar
 Rodriguez L, Tran N, LeNgoc T: Multiple frame precoding for NAF relaying over Rayleigh fading channels. IEEE Trans. Veh. Technol 2012, 61(1):398404.View ArticleGoogle Scholar
 Han Y, Ting S, Ho C, Chin W: Performance bounds for twoway amplifyandforward relaying. IEEE Trans. Wireless Commun 2009, 8(1):432439.View ArticleGoogle Scholar
 Louie R, Li Y, Vucetic B: Practical physical layer network coding for twoway relay channels: performance analysis and comparison. IEEE Trans. Wireless Commun 2010, 9(2):764777.View ArticleGoogle Scholar
 Rankov B, Wittneben A: Spectral efficient protocols for half duplex fading relay channels. IEEE J. Sel. Areas Commun 2007, 25(2):379389.View ArticleGoogle Scholar
 Wicaksana H, Ting S, Ho C, Chin W, Guan Y: AF twopath half duplex relaying with interrelay self interference cancellation: diversity analysis and its improvement. IEEE Trans. Wireless Commun 2009, 8(9):47204729.View ArticleGoogle Scholar
 Luo C, Gong Y, Zheng F: Full interference cancellation for twopath relay cooperative networks. IEEE Trans. Veh. Technol 2011, 60(1):343347.View ArticleGoogle Scholar
 Fan Y, Wang C, Thompson J, Poor H: Recovering multiplexing loss through successive relaying using repetition coding. IEEE Trans. Wireless Commun 2007, 10(12):44844493.View ArticleGoogle Scholar
 Wang C, Fan Y, Thompson J, Skoglund M, Poor H: Approaching the optimal diversitymultiplexing tradeoff in a fournode cooperative network. IEEE Trans. Wireless Commun 2010, 12(9):36903700.View ArticleGoogle Scholar
 Chang W, Chung S, Lee Y: Capacity bounds for alternating twopath relay channels. In Paper presented at the Allerton conference on communications, control and computing. Monticello, IL; 26–28 September 2007.Google Scholar
 Zhang R: Characterizing achievable rates for twopath digital relaying. In Paper presented at the IEEE international conference on communications. Beijing; 19–23 May 2008.Google Scholar
 Rost P, Fettweis G: A cooperative relaying scheme without the need for modulation with increased spectral efficiency. In Paper presented at the IEEE 64th vehicular technology conference. Montreal, Quebec; 25–28 September 2006.Google Scholar
 Ribeiro A, Cai X, Giannakis G: Opportunistic multipath for bandwidth efficient cooperative multiple access. IEEE Trans. Inf. Theory 2006, 5(9):23212327.Google Scholar
 Sun L, Zhang T, Niu H: Interrelay interference in twopath digital relaying systems: detrimental or beneficial? IEEE Trans. Wireless Commun 2011, 10(8):24682473.View ArticleGoogle Scholar
 Zehavi E: 8PSK trellis codes for a Rayleigh fading channels. IEEE Trans. Commun 1992, 40(5):873883. 10.1109/26.141453View ArticleMATHGoogle Scholar
 Bahl L, Cocke J, Jelinek F, Raviv J: Optimal decoding of linear codes for minimizing symbol error rate. IEEE Trans. Inf. Theory 1974, 20(2):284287.MathSciNetView ArticleMATHGoogle Scholar
 Caire G, Taricco G, Biglieri E: Bitinterleaved coded modulation. IEEE Trans. Inf. Theory 1998, 44(3):927946. 10.1109/18.669123MathSciNetView ArticleMATHGoogle Scholar
 Li X, Ritcey J: Trelliscoded modulation with bit interleaving and iterative decoding. IEEE J. Sel. Areas Commun 1999, 17(4):715724. 10.1109/49.761047View ArticleGoogle Scholar
 Li X, Chindapol A, Ritcey J: Bitinterleaved coded modulation with iterative decoding and 8PSK signaling. IEEE Trans. Commun 2002, 50(8):12501257. 10.1109/TCOMM.2002.801524View ArticleGoogle Scholar
 Watkins DS: Fundamentals of Matrix Computations. New York: Wiley; 2002.View ArticleMATHGoogle Scholar
Copyright
This article is published under license to BioMed Central Ltd. 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.