Lowcomplexity quantizeandforward cooperative communication using twoway relaying
 Iancu Avram^{1}Email author,
 Nico Aerts^{1} and
 Marc Moeneclaey^{1}
https://doi.org/10.1186/168714992014194
© Avram et al.; licensee Springer. 2014
Received: 1 August 2014
Accepted: 7 November 2014
Published: 21 November 2014
Abstract
Cooperative communication is used as an effective measure against fading in wireless communication systems. In a classical oneway cooperative system, the relay needs as many orthogonal channels as the number of terminal it assists, yielding a poor spectral efficiency. Efficiency is improved in twoway relaying systems, where a relay simultaneously assists two terminals using only one timeslot. In the current contribution, a twoway quantizeandforward (QF) protocol is presented. Because of the coarse quantization, the proposed protocol has a low complexity at the relay and can be used with halfduplex devices, making it very suitable for lowcomplexity applications like sensor networks. Additionally, channel parameter estimation is discussed. By estimating all channel parameters at the destination terminals, relay complexity is kept low. Using Monte Carlo simulations, it is shown that the proposed QF protocol achieves a good frame error rate (FER) performance as compared to twoway amplifyandforward (AF) and oneway relaying systems. It is further shown that, using the proposed estimation algorithm, the FER degradation arising from the channel parameter estimation is negligible when compared to an (unrealistic) system in which all parameters are assumed to be known.
Keywords
Cooperative communication Twoway relaying Estimation Sensor networks Diversity1 Introduction
Cooperative telecommunication systems can effectively be used to combat fading by exploiting the broadcast nature of the wireless medium [1–6]. In a classical cooperative communication system, only unilateral communication is considered: one transmitting terminal communicates to one receiving terminal with the help of a relaying terminal. Many practical applications however require bilateral communication, in which two terminals both send and receive information to/from each other. Using a classical (oneway) cooperative system in this situation would yield a poor spectral efficiency, as this would require four orthogonal channels, i.e., the two transmitting terminals need one channel each, and the relay transmits over two channels that the data received from the first and second terminal, respectively. The spectral efficiency can be improved using a twoway relaying system, in which the relay uses a single channel to simultaneously assist in the information transfer from the first to the second terminal and from the second to the first terminal.
As for oneway cooperative systems, a variety of forwarding protocols have been developed for twoway systems, including, but not limited to, network coding [7, 8], amplifyandforward (AF) [9], decodeandforward (DF) [9, 10], and compressandforward (CF) [11]. While many of these protocols achieve satisfactory results regarding outage probability and frame error rate (FER), they also impose a (large) burden upon the relay in terms of computational complexity and/or storage space requirements. The DF strategy requires the relay to decode the received data. In the AF protocol, the relay needs to store the analog signals awaiting retransmission, requiring a highprecision analogtodigital conversion (i.e., many quantization bits per sample) and, therefore, a large memory to store the samples.
Twoway quantizeandforward (QF) protocols have been studied in [12] and [13]. In [13], the capacity of a twoway relaying channel is maximized using an information theoretical approach. Channel symmetry is assumed, i.e. both users’ channel qualities need to be the same, both in the uplink and downlink. In [12], a twoway QF relaying scheme using spacetime block coding (STBC) is proposed. The two transmitting nodes use STBC to simultaneously transmit their signals to the relay, where they are estimated by using minimum mean square errorordered successive interference cancellation (MMSEOSIC). The main drawback of the proposed system is the MMSEOSIC algorithm that needs to be executed at the relay, inevitably raising its complexity. Furthermore, the relay is required to have multiple antenna’s, also raising its hardware cost. Both [12] and [13] also assume that there is no direct link between the two user terminals, making it impossible to exploit cooperative diversity.
These hardware requirements can limit the usefulness of existing twoway relaying strategies in applications requiring a low relay complexity, such as sensor networks and battery powered devices. Therefore, in the current contribution, a lowcomplexity twoway relaying strategy is presented, based on the QF protocol. The main goal is to keep the relay complexity to a minimum by shifting as much operations as possible to the user terminals, where typically there is more processing power available. While QF protocols with a low relayside complexity have been developed for oneway relaying systems [14, 15], the adaptation of these protocols to twoway relaying systems is not straightforward. In the current paper, a novel twoway QF protocol is introduced and its performance is analyzed. The proposed protocol exploits cooperative diversity, by assuming there is a direct path between the user terminals. Furthermore, a practical estimation scheme is proposed for the estimation of all the unknown channel parameters. In order to limit the relay complexity to a minimum, all estimation is performed at the destination terminals, with no additional calculations needed at the relay.
The remainder of this paper is organized as follows: The channel model is outlined in Section 2, whereafter the proposed quantization scheme is presented in Section 3. In Section 4, the receiver structure is obtained and in Section 5, the estimation algorithm is discussed. The FER performance of the proposed algorithms is analyzed using Monte Carlo (MC) simulations in Section 6. Finally, conclusions are drawn in Section 7.
Notations
Bold lower and uppercase letters are used to denote vectors and matrices, respectively. The absolute value and phase of the complex number x are denoted as x and arg(x)∈(0, 2π), respectively. The Hermitian transpose of x is denoted x^{ H } and the suffix mod M is used to denote the moduloM reduction to the interval [ 0, M). The notation p(xy;z) refers to the probability density function (pdf) of the random variable x, conditioned on the random variable y, with z denoting a known deterministic parameter of the considered pdf.
2 Channel model
where r_{0}, r_{1}, and r_{2} denote the signals received by T_{1} (first slot), R (first slot), and T_{1} (third slot), respectively. Similar expressions hold for the reciprocal signals. Assuming the normalization condition c_{0}^{2}=c_{1}^{2}=c_{ r }^{2}=K, the quantities E_{0}, E_{1}, and E_{ r } denote the transmitted energy per symbol at T_{0}, T_{1}, and R, respectively. All channel coefficients are considered to be constant during a frame and have a zeromean circular symmetric complex Gaussian (ZMCSCG) distribution with variances ${N}_{{h}_{x}}=1/{{d}_{x}}^{{n}_{\mathit{\text{loss}}}},x\in \{0,1,2\}$. The quantity d_{ x } represents the distance between the two considered terminals, while n_{ loss } denotes the path loss exponent. The components of the noise vectors n_{ x } are also ZMCSCG distributed with variances N_{ x },x∈{0,1,2}.
3 Twoway relaying
In the following subsections, the operation performed at the relay is discussed, assuming that the symbols transmitted by T_{0} and T_{1} belong to a M_{1}PSK constellation, with M_{1} as the constellation size. This operation results in the symbol vector c_{ r } transmitted by the relay in the third slot. An AF twoway relaying strategy, to be used for benchmarking the performance of the proposed QF system, is briefly discussed first.
3.1 Amplifyandforward
Note that the relay in a twoway AF system needs to know the squared channel magnitudes h_{1}^{2} and h_{2}^{2}.
3.2 Quantizeandforward
A straightforward implementation of a twoway QF relaying system that is similar to the AF relaying system would involve the coarse quantization of the sum of the signals received in the first and second slot from T_{0} and T_{1}, respectively, and the broadcasting of these quantized samples in the third slot. While the initial purpose of quantization is to avoid the storage of analog samples, this approach however would require the relay to store the analog samples received from T_{0} in the first slot, until the data from T_{1} is received in the second slot and the two can be added and quantized. Instead, a quantization scheme that does not necessitate the storage of analog values is proposed, where the relay separately quantizes the signals received in the first and second slot and then properly combines the quantized values. This involves the following operations, which do not require any channel knowledge at the relay.
3.2.1 Quantization
so that f_{ Q }(x)=q when $\frac{2\pi}{{M}_{2}}\phantom{\rule{0.3em}{0ex}}\left(q\frac{1}{2}\right)\le \text{arg}\left(x\right)<\frac{2\pi}{{M}_{2}}\phantom{\rule{0.3em}{0ex}}\left(q+\frac{1}{2}\right)$ for q=1, 2, …, M_{2}1, and f_{ Q }(x)=0 when $0\le \text{arg}\left(x\right)<\frac{\pi}{{M}_{2}}$ or $2\pi \frac{\pi}{{M}_{2}}\le \text{arg}\left(x\right)<2\pi $. In order to be able to exploit circular symmetry at the relay, we impose that M_{2} is a multiple of M_{1}.
3.2.2 Addition
3.2.3 Relay complexity
In the proposed quantization scheme, the storage and processing requirements at the relay are kept low. For each frame, only the vectors q_{1} and ${\mathit{q}}_{2}^{\prime}$ need to be stored at the relay; the memory requirements are low, because the components of q_{1} and ${\mathit{q}}_{2}^{\prime}$ are represented by only log2M_{2} bits. The memory usage can further be lowered in a practical implementation by storing the elements of q_{1} obtained in the first slot, performing the modulo M_{2} addition elementwise in the second slot as the values of ${\mathit{q}}_{2}^{\prime}$ become available by quantizing the incoming signal ${\mathit{r}}_{2}^{\prime}$, and storing the result of the addition back in q_{1}. The latter is then mapped on M_{2}PSK symbols using Equation 2 and broadcast in the third slot.
The number of computations that the relay needs to perform is also limited. The quantization operation has a low complexity, as only the phase of the incoming signals is quantized, neglecting the amplitude. This complexity is further lowered by only considering uniform quantization. The modulo M_{2} addition of the resulting quantization intervals involves the addition of two integers with a limited range and is thus easily implemented in hardware. Channel parameter estimation does not add to the computational burden of the relay, because all channel parameters are estimated at the destination terminals.
4 Likelihood calculation
which completes the calculation of the symbol likelihoods.
5 Estimation
The likelihoods calculated in the previous section depend on the specific realization of the channel coefficients h_{0}, h_{1}, h_{2}, and ${h}_{2}^{\prime}$ (for the likelihoods calculated at T_{0}) and ${h}_{0}^{\prime}$, ${h}_{1}^{\prime}$, ${h}_{2}^{\prime}$, and h_{1} (for the likelihoods at T_{1}). As these parameters change between frames and are not a priori known, they need to be estimated before the data decoding can be performed. In the remainder of this section, we will focus on the channel estimation at T_{1} in order to decode the data sent by T_{0}. Similar expressions are obtained for the channel estimation at T_{0}.
The channel coefficients that need to be estimated can be divided into two groups: the ones that are directly observed by T_{1} (these are h_{0} and h_{2}) and the ones that are not (these are h_{1} and ${h}_{2}^{\prime}$). The main difficulty is estimating the parameters that are not directly observed. In order to keep the complexity at the relay terminal low, we deliberately choose not to perform any relayside estimation. However, due to the quantization performed at the relay, it is quite difficult to estimate the channel coefficients h_{1} and ${h}_{2}^{\prime}$ at T_{1}. Fortunately, this problem can be circumvented by directly estimating the transition probabilities used in Equation 4, so that we no longer need to know the specific values of h_{1} and ${h}_{2}^{\prime}$. Indeed, in [16], it was shown that the sourcerelay transition probabilities can be estimated at the destination in a oneway quantizeandforward system. Accurate results were obtained by first estimating the transition probabilities using pilot symbols transmitted by the source and then iteratively refining these pilotbased estimates by also using the a posteriori probabilities of the unknown data symbols in the estimation process.
which indicates that, for the given m and n, the elements {T(q,m,n), q=0,1,…,M_{2}1} are obtained as a cyclic shift of the vector $\stackrel{\u0304}{t}=\stackrel{\u0304}{(t}\left(0\right),\dots ,\stackrel{\u0304}{t}({M}_{2}1))$ over $(m+n)\frac{{M}_{2}}{{M}_{1}}$ positions.
In order to assist the estimation of $\mathbf{h}=({h}_{0},{h}_{2},\stackrel{\u0304}{t})$, both T_{0} and T_{1} transmit pilot symbols which are known to both terminals. These pilot symbols are quantized at the relay using the same quantization method as was used for the data symbols. Hence, the relay operation does not need to distinguish between data symbols and pilot symbols. Using the pilot symbols, an initial estimate of h is be obtained at T_{1}. This pilotbased estimate of h is then iteratively refined using codeaided estimation that exploits also the presence of the unknown data symbols contained in r_{0} and r_{2}. The reader is referred to Appendix A and [16] for more details regarding this estimation procedure, which makes use of the expectationmaximization (EM) algorithm.
6 Performance results
The frame error rate (FER) performance of the proposed protocol is investigated using Monte Carlo simulations. We consider frames of 1,024 information bits, encoded by means of an (1,13/15)_{8} RSCC turbo code [17] that is punctured to a rate of 2/3, yielding a total of 1,536 coded bits which are then mapped on binary phaseshift keying (BPSK) symbols (M_{1}=2). At the relay, 2bit quantization of the phase of the received samples is used, yielding transmitted relay symbols belonging to a quadrature phaseshift keying (QPSK) constellation (M_{2}=4). The path loss exponent equals 4 and the distance between T_{0} and T_{1} are considered unity. All symbol energies are considered to be equal (E_{0}=E_{1}=E_{ r }) and all noise variances are also assumed to be equal (${N}_{0}={N}_{0}^{\prime}={N}_{1}={N}_{1}^{\prime}={N}_{2}={N}_{2}^{\prime}$). In the remainder of this section, performance metrics related to the information transfer from T_{0} to T_{1} are considered. Results for the communication in the opposite direction are obtained by simply interchanging the positions of T_{0} and T_{1}.
6.1 Channels and transition probabilities known
In this subsection, the FER performance of the proposed twoway relaying system is analyzed under the assumption that the relevant channels and transition probabilities are known at the receiving terminal. This FER performance is compared to that of a noncooperative system and a classical oneway relaying system. For a fair comparison, we require the three systems to operate at the same spectral efficiency R_{ b }/R_{ s }, with R_{ b } and R_{ s } denoting the average information bitrate and the symbol rate, respectively. This is achieved by dimensioning the systems as indicated in Figure 2:

In the twoway relay system, we use three slots to send 1,024 information bits in each direction (2,048 information bits in total), yielding a total transmission time of 2,048/ R_{ b } and a duration of 2,048/ (3R_{ b }) per slot. As stated in the introduction, the turbo code is punctured to a rate of 2/3, yielding 1,536 coded bits (1,536 BPSK symbols) in the first slot and in the second slot and 1,536 QPSK symbols in the third slot (i.e., 3 × 1536 = 4,608 symbols in total). The resulting spectral efficiency is R_{ b }/R_{ s }= 4/9 information bits per channel use.

In the noncooperative system, there are only two slots as no relay is involved in the communication process. Each slot has a duration of 1,024/ R_{ b }, which is 3/2 times the slot duration of the twoway relay system. The spectral efficiency of R_{ b }/R_{ s }= 4/9 is obtained by puncturing the turbo code to a rate of 4/9 (instead of 6/9 for the twoway relaying systems), yielding 2,304 coded bits (2,304 BPSK symbols) per slot (i.e., 2 × 2,304 = 4,608 symbols in total).

In the oneway relay system, the relay uses two slots, to forward the information from T_{0} to T_{1} and from T_{1} to T_{0}, requiring a total of four slots, each of duration 512/ R_{ b }. The turbo code is punctured to a rate of 8/9 (instead of 6/9 for the twoway relaying systems), yielding 1,152 coded bits (1,152 BPSK symbols) in the first and the third slot and 1,152 QPSK symbols in the second and in the fourth slot (i.e., 4 × 1,152 = 4,608 symbols in total), again resulting in a spectral efficiency of R_{ b }/R_{ s }= 4/9.
Also note that, while the above three communication systems yield the same spectral efficiency, the relay in a oneway relaying system needs to transmit more symbols (and thus consume more energy) as compared to the relay in a twoway relaying system. Indeed, in a oneway relaying system, the relay is active during two slots, transmitting a total of 2,034 symbols. In a twoway relaying system, the relay is only active during one slot, transmitting a total of 1,536 symbols. This favors the twoway relaying system in applications where low relay energy consumption is required, such as batterypowered sensor networks and onbody relaying networks.
In Figure 4, the position of the relay is varied on a line connecting T_{0} and T_{1}, while the E_{ b }/N_{0} ratio is kept fixed at 9 dB. The resulting FER values are shown as a function of the normalized distance between T_{0} and the relay. In order to better understand the FER behavior of the twoway protocols shown in Figure 4, the FER performance of a twoway AF and QF system in which the relay ignores the signal from T_{1} is also shown. These configurations will be referred to as noninterfering AF and noninterfering QF, respectively. Because the relay ignores the contribution from T_{1}, the sole contribution in the signal transmitted by the relay stems from T_{0}. In the noninterfering QF (AF) system, the first and third slot support a oneway QF (AF) protocol between T_{0} and T_{1} in which the relay only assists T_{0}, while the second slot supports a singlediversity information transfer from T_{1} to T_{0}. The following observations can be made from the aforementioned figure:

In the oneway AF protocol, the FER curve is symmetrical with regard to the relay position. Assuming that E_{0}h_{1}^{2}≫N_{1} and taking into account the operation of the AF relay, it can easily be verified that signal received from the relay is characterized by an instantaneous SNR given by$\text{SNR}={\left(\frac{{N}_{1}}{{E}_{0}{h}_{1}{}^{2}}+\frac{{N}_{2}}{{E}_{r}{h}_{2}{}^{2}}\right)}^{1}.$(10)

Because N_{1}/E_{0}=N_{2}/E_{ r }, as specified in the beginning of this section, Equation 10 is symmetrical with respect to h_{1}^{2} and h_{2}^{2}, implying the symmetry of the FER curve.

Due to the coarse quantization at the relay, the oneway QF protocol is outperformed by oneway AF. The degradation of the former with regard to the latter is negligible when the relay is located close to T_{0}, but increases when their distance gets larger, because of the decreasing SNR on the h_{1} channel.

In the twoway AF protocol, the relay transmits a scaled version of the sum of the signals received from T_{0} and T_{1}, such that the sum signal has a given energy per symbol interval. As the resulting contribution from T_{0} to the transmitted relay symbols is smaller than in the case of noninterfering AF (in which the contribution from T_{0} is the sole contribution), twoway AF is outperformed by noninterfering AF. The degradation of the twoway AF system with regard to the noninterfering AF system decreases when the relay moves in the direction of T_{0}, because in the former system the weight of the signal from T_{0} to the transmitted relay signal increases. When the relay is very close to T_{0}, the signal from T_{1} has a negligible contribution to the relay symbols, so the FER performance of the twoway AF system approaches that of the noninterfering AF system.

In the twoway QF protocol, the symbols transmitted by the relay depend on the phases of the noisy signals received from T_{0} and T_{1} but not on their amplitudes. As the transmitted relay symbols are function of the noise on both the h_{1} and ${h}_{2}^{\prime}$ channels, they are less reliable than in the noninterfering QF system; therefore, noninterfering QF outperforms twoway QF. The degradation of the twoway QF system with regard to the noninterfering QF system decreases when the relay gets closer to T_{1}, because of the increasing SNR on the ${h}_{2}^{\prime}$ channel. When the distance between the relay and T_{1} is very small, the noise on the ${h}_{2}^{\prime}$ channel can be ignored, yielding the same situation, and thus the same FER performance, as the noninterfering QF system.
The FER plots from Figure 4 show that, depending on the position of the relay with respect to T_{0} and T_{1}, twoway QF clearly outperforms twoway AF and vice versa. When sufficient relay resources are available to support a twoway AF protocol, the results from Figure 4 can be used to determine which protocol is best suited to yield the lowest FER (on average) for the information transfer from T_{0} to T_{1} for a given relay position. Of course, for the same relay position, the selected protocol may not be optimal for the information transfer from T_{1} to T_{0}, so tradeoffs will have to be made. When we have the freedom to select the position of the relay, we achieve maximum fairness (information transfer from T_{1} to T_{0} and from T_{0} to T_{1} yield the same FER) when the relay is located halfway between T_{0} and T_{1}; for this relay position, the twoway QF system slightly outperforms the twoway AF system when E_{ b }/N_{0} = 9 dB.
6.2 Channels and transition probabilities estimated
We observe that pilotbased estimation yields a significant degradation with respect to the reference system in which all channel parameters are assumed to be known. This degradation is however almost completely mitigated using the codeaided approach, yielding essentially the same FER performance as the reference system. These results prove that the proposed twoway relaying QF system is suitable to be used in reallife systems, because efficient estimation of the unknown channel parameters can be achieved.
7 Conclusions
In this contribution, an implementation has been proposed for a twoway QF relaying system. The computational complexity at the relay has been kept low, in order to make the proposed algorithm suitable for relaying networks with hardware constraints at the relay, such as sensor networks. After presenting a closedform expression for the symbol likelihoods at the receivers, the estimation of the unknown channel parameters was discussed. In order to keep the relay complexity low, all parameters are estimated at the destination, requiring no additional operations from the relay. The performance of the proposed algorithms for a relay position that is uniformly distributed between the transmitting and receiving terminal was subsequently evaluated using Monte Carlo simulations. It was shown that the considered twoway QF system clearly outperforms both oneway systems and noncooperative ones. It was further shown that the FER degradation with respect to a twoway AF system, which has a much higher relayside complexity, is very low through the full SNR range. In order to gain more insight into the proposed algorithm, the effect of the relay position was also investigated and the results were explained. Finally, it was shown that the proposed estimation algorithms yield only a negligible degradation in FER as compared to an (unrealistic) system in which all channel parameters are assumed to be known, making the presented QF protocol and estimation algorithms suitable to be used in reallife networks that require a low relayside complexity.
Appendix A
At T_{1}, the channel coefficients h_{0} and h_{2} and the transition probabilities $\stackrel{\u0304}{t}$ need to be estimated. In [16], channel parameter estimation using the EM algorithm was discussed for a oneway QF system. These results will now be extended to a twoway QF system. The EM algorithm is an iterative algorithm that, besides using the known pilot symbols, also uses the unknown data symbols in the estimation process. These unknown variables are referred to as nuisance parameters. In the case at hand, data symbols transmitted by T_{0} and the symbols transmitted by the relay are considered to be nuisance parameters.
where the value of ${\widehat{\mathit{h}}}^{\left(0\right)}$ is initialized using the pilotbased estimates.
These a posteriori probabilities are provided by the channel decoder at T_{1}.
where m_{0p}(k) and n_{0p}(k) are the integers that satisfy the relation ${c}_{0p}\left(k\right)={\chi}_{{M}_{1}}\left({m}_{0p}\right(k\left)\right)$ and ${c}_{1p}\left(k\right)={\chi}_{{M}_{1}}\left({n}_{0p}\right(k\left)\right)$, respectively. The initial conditions for the pilotbased EM algorithm are set to ${h}_{2p}^{\left(0\right)}=1$ and ${\Gamma}_{p}^{\left(0\right)}\left(q\right)=1/{M}_{2},\phantom{\rule{2.22144pt}{0ex}}\forall q$.
Declarations
Acknowledgements
The authors wish to acknowledge the Agency for Innovation by Science and Technology Flanders (IWT) that motivated this work. This research has been funded by the Interuniversity Attraction Poles Programme initiated by the Belgian Science Policy Office.
Authors’ Affiliations
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