Performance analysis of partial transmission cooperative strategy with unreliable relays

Cooperative communications, as an emerging concept for wireless networks [1, 2], have received the significant attention recently. As a distributed transmission, the cooperative communications enable the neighboring nodes to share the resources to participate in the information transmission, through which the relays provide the spatial diversity as well as multiplexing gain for the destinations. Therefore, cooperative communications improve system performance and robustness of wireless networks, especially in some severe attenuation environments.

The idea of cooperative communications can be traced back to 1979 [1]. In recent years, various cooperative relaying protocols such as amplify-and-forward (AF) relaying strategy [2], decode-and-forward (DF) relaying strategy [3, 4], and their successors are proposed for wireless networks. Most of them adopt either maximal ratio combining or equal gain combining at the destination. Some work of them utilizes optimum power and time allocation [5], soft information [6], or global information [7] to get the performance improvements. The concept of relaying has been integrated into the fifth generation (5G) communication [8] and cellular structure [9], which has been written in the World interoperability for Microwave Access (WiMAX) standard [10] and Wireless World Initiative New Radio (WINNER) standard [11, 12]. The relay selection techniques have also been studied extensively, and several selection criteria that select the “reliable” relays have been proposed [2, 8, 13, 14]. Moreover, cooperation techniques have also been considered in some latest communication standards such as IEEE 802.11s standard [6], IEEE 802.16j standard [10], and 3GPP’s Long Term Evolution (LTE)-Advanced standard [15].

The relay’s ability to reliably forward the message determines the performance of cooperative communications. In relay’s AF strategy, the relays amplify the signal and then forward the message originally [16]. The message as well as the noise is sent together with the amplified signal strength; hence, the SNR at the destination is not improved. While in relay’s conventional DF strategy, the relays need to decode the messages before they forward the messages, where the SNR at receiver can be improved [17]. Then, the selective decode-and-forward (SDF) strategy [2] is proposed. The SDF falls back to direct transmission if the relay cannot decode, where the energy can be saved compared to DF. Moreover, the concept of lossy forward (LF) is proposed, where the relays always forward the message with its soft information on each bit, even though it may contain errors [6, 18]. With the LF scheme, the destination always receives the most useful information.

In this paper, we consider the situation where the relays have a high probability of failing in decoding the message due to the severe attenuation in channel or low SNR of the source. In AF, DF, and LF, the wrong message transmitted results in unwanted resource assumption. And in SDF, the solution to this problem is to let the relay make the decision whether its output is correct or not and discard it if it turns out to be erroneous. However, this may result in losing useful information that may help the destination’s decoding, because the discarded information sequences have high probability to be decoded partly correct.

In this paper, we analyze the partial transmission (PT) cooperative strategy, which can overcome the shortcomings aforementioned. Compared to LF, PT allows relays to discard the bits with low soft information according to the channel state, which in fact allows the relays to make the decision for the destination. Moreover, the saved power helps to increase the transmit SNR for the useful information. Assuming that the power assumption to send every bit is identical, we implement the optimal block process, where the transmitted information from source is divided into a certain amount of information blocks in relay. The relays obtain the reliability information of the transmitted information bits by implementing the soft-input soft-output (SISO) decoders. With the channel state information (CSI) at receivers, the relays are able to calculate the optimal number of the correctly decoded information blocks. Consequently, the relays only forward the information blocks with low error probability. Correspondingly, the destination employs block combining to jointly decode the message. We derive the end-to-end outage probability of the proposed strategy as a function of the transmission rate and SNR with M-relaying. In addition, the numerical simulations are carried out in both one-relaying system and two-relaying system. Continuous changing channels show the advantage of the proposed strategy. The results show that the proposed strategy can get more diversity gain from the relay-to-destination channel and provide a significant improvement over the conventional strategies, particularly when the relay cannot reliably decode the message. We note that the more information transmission rate and channel gain from relay to destination are, the greater improvement PT can get.

The remainder of the paper is organized as follows. Section 2 describes the system model. Section 3 presents the outage probabilities of the proposed strategy. Section 4 gives numerical results and discussions. Section 5 concludes the paper.

In this framework, the communication is considered to be cluster-crossed. Sources are either base station, head nodes, or gateway nodes of other clusters. Relays are head nodes and gateway nodes in the same cluster of the destination [19, 20], shown as Fig. 1.

In this paper, the strategies are analyzed in the system with the identical power consumption for fairness. We consider the narrowband transmissions in the wireless network in which the channels between any two nodes are subject to the effects of slow-flat Nakagami-m fading with Nakagami factor m_i and additive white Gaussian noise (AWGN). Nodes in the network work in a half-duplex mode where they cannot transmit and receive simultaneously in the same time slot. We assume that CSI is only known at the receivers and all the transmitters are assigned with an averaging time slot. After the destination receives several copies of the information sequences, it implements a novel spatial reception scheme, block combining, to jointly decode the message.

Similar to [5‐8, 16], we consider a cooperative wireless network that consists of one source node S, one destination node D, and M relay nodes. The simplified system model is shown as Fig. 2. The squared envelope of the channel gains associated with source-destination, source-relay, and relay-destination links are denoted by γ_sd, \( {\gamma}_{\mathrm{s}{\mathrm{r}}_{\mathrm{i}}} \), and \( {\gamma}_{{\mathrm{r}}_{\mathrm{i}}\mathrm{d}} \), respectively. These squared envelope of the channel gains are independent exponentially distributed random variables (RVs) with mean values \( {\overline{\gamma}}_{\mathrm{sd}} \), \( {\overline{\gamma}}_{\mathrm{s}{\mathrm{r}}_{\mathrm{i}}} \), and \( {\overline{\gamma}}_{{\mathrm{r}}_{\mathrm{i}}\mathrm{d}} \). The amplitudes of the channel gains of source-destination links, source-relay links, and relay-destination links follow independent Nakagami-m distribution. The cooperative strategy is described as two phases. In phase I, the source transmits information signal to the destination in the first time slot, and the signal is also received by the relays as well. In phase II, the relays help transmitting the received message in M equal time slots respectively.

More specifically, we assume b bit information every time transmitted from the source are divided into N information blocks, and each block contains L bit information. The information is modulated by BPSK.

In phase I, the source broadcasts its information signal x to the destination and all the relays. The received signals y_sd and \( {y}_{\mathrm{s}{\mathrm{r}}_{\mathrm{i}}} \) at the destination and the relays can be written as:where \( {P}_{\mathrm{s}\mathrm{d}}={P}_{\mathrm{s}{\mathrm{r}}_{\mathrm{i}}}=\frac{P}{M+1} \), which is the transmission power in phase I. In (1) and (2), n_sd and \( {n}_{\mathrm{s}{\mathrm{r}}_{\mathrm{i}}} \) are the corresponding received AWGN at the destination and the relays with mean zero and variance N₀. h_sd and \( {h}_{\mathrm{s}{\mathrm{r}}_{\mathrm{i}}} \) are the channel coefficients from the source to the destination and the i-th relay, respectively. The fraction \( \frac{1}{M+1} \) is the fact that the power P of each transmission is averaged by one source and M relays. The bandwidth of the whole cooperation system is normalized. In the whole process, each node needs some certain amount of time slots, which is \( \frac{1}{M+1} \). The received SNR,\( {\mathrm{SNR}}_{\mathrm{s}{\mathrm{r}}_{\mathrm{i}}} \) and SNR_sd at the relay and the destination, can be expressed as:and \( \rho =\frac{P}{M+1}/{N}_0 \), which is the transmission SNR of the source node.

In phase II, the relays transmit the message to the destination with the signal \( {\widehat{\mathrm{x}}}_{\mathrm{i}} \), and the transmission power of the relay is \( {P}_{{\mathrm{r}}_{\mathrm{i}}} \). The received signal \( {y}_{{\mathrm{r}}_{\mathrm{i}}\mathrm{d}} \) at the destination can be written aswhere \( {n}_{{\mathrm{r}}_{\mathrm{i}}\mathrm{d}} \) is the corresponding received noise at destination, and \( {h}_{{\mathrm{r}}_{\mathrm{i}}\mathrm{d}} \) is the channel coefficients from the relays to the destination.

In this section, we evaluate the end-to-end outage probabilities of the proposed strategy based on multiple relays.

In this section, we analyze and compare four strategies, PT, SDF, AF, and direct transmission (DT), on the situation with one-relaying system and two-relaying system, i.e., M = 1 and M = 2 in the above analyses. For these four strategies, we do simulation works of the information outage probability with and without direct link respectively. We assume the number of information bits b = 100,000 and the transmission rate of information R_t = 0.5 (b/s/Hz).

Figures 5 and 6 show the end-to-end outage probability versus the transmission SNR ρ at the source and information transmission rate R_t with direct link, respectively. For simplicity, the channel states of two relays are set as the same, which are expressed by channel gain variance as follows: \( {\overline{\gamma}}_{\mathrm{sr}1}={\overline{\gamma}}_{\mathrm{sr}2}=0.1 \), \( {\overline{\gamma}}_{\mathrm{sd}}=0.1 \), and \( {\overline{\gamma}}_{\mathrm{rd}1}={\overline{\gamma}}_{\mathrm{rd}2}=0.1 \). The Nakagami parameters are set as: m_sd = m_i = 1. The above condition responds to the scenarios in all poor channels, where the relays are considered to be unreliable. We analyze the relationship between the outage probability and channel state of relay-to-destination links in Figs. 7 and 8, in the situation with and without direct link respectively. We then discuss the relaying performances without direct link in Fig. 9, to compare them comprehensively.

In Figs. 5 and 6, the channel states from S to R, R to D, and S to D are the same. Figure 5 shows that the outage probability of PT performs almost the same to that of SDF when M = 1.However, with the R-D channel gets better, PT gets better than SDF, which can be seen in Fig. 7. In the poor channels, the relay can hardly help the decoding at destination. After ρ = 24dB, PT gets the lower outage probability compared with SDF. Because as SNR increases, the relay can transmit more information block in PT, while SDF still has high probability failing to decode at the relay. When M = 2, PT gets better performance over the conventional strategies, two relays can get double spatial diversity than that of the situation with M = 1. As SNR increases, the improvement of PT gets bigger. It is also noted that at low SNR, more relays cost more power and bandwidth, but they are unable to help the destination in such a low channel gain of S-R links.

In Fig. 6, the transmission SNR ρ = 20 dB. It can be seen that the outage probability gets higher as the information transmission rate increases. For the case of M = 2 at low R_t, the PT performs worse than SDF and AF. Because the relays at low rate have high probability to decode the message or help the decoding at destination, so they are reliable relays, while the relays in PT cannot transmit all the information sequence. As R_t gets higher, the relays become unreliable, where the partial transmission shows the great advantage. However, if R_t rises to some certain threshold, all the relays are useless, so that the two-relaying system performs worse than the one-relaying system and even worse than the direct transmission. However, PT can postpone this threshold.

Figures 7 and 8 show the outage probability versus the channel gain between the relay and the destination in one-relaying system and two-relaying system, respectively.

Figure 7 shows that PT gets the better performance than the conventional strategies, as the R-D channel gain gets better than 0.1 with direct link and 0.128 without direct link. It is also shown that SDF and AF are not able to obtain the spatial diversity gain from the R-D channel, because they are limited by the poor channel ahead of the relay. For SDF, the state of the S-D channel determines the decoding ability of the relay. For PT, although R node fails to decode all the information correctly, the benefit of R-D channel still obtains diversity gain for the destination.

In Fig. 8, in order to facilitate the analysis, we assume that the two R-D channels follow the same distribution. PT gets better than SDF after about \( {\overline{\gamma}}_{\mathrm{rd}}=0.05 \) and \( {\overline{\gamma}}_{\mathrm{rd}}=0.35 \), in the situations with and without direct link respectively. As the channel gain between relays and destination increases, the gain value that PT gets better than SDF is nearly half of it in one-relaying system, where the certain amount of location information of PT degrades some performance with and without direct link. Generally speaking, when the R-D channel is better than the severely attenuated S-D channel, i.e., the relays are considered to be unreliable, the performance of PT is better than that of the conventional strategies.

Figure 9 shows the outage probability performances in the situation without direct link. Based on the discussion above, we set \( {\overline{\gamma}}_{\mathrm{rd}}=0.2 \) in Fig. 9, and other parameters remain the same. Certainly, the existence of the direct link helps to gain more spatial diversity gain, which can be seen when compared to Fig. 5. At low SNR, Fig. 9 shows none of the mentioned strategies is reliable. As SNR increases, the improvements of PT are more obvious without direct link.

In this paper, we analyzed the partial transmission cooperative strategy that allows the relays to divide the information into small blocks and only forward the correct blocks. We designed the block processing at relay and block combining at destination to solve the problem of unreliable relays. Relaying processing and block processing compose the system of PT, which is in fact a distributed system allowing the relays to make decisions for destination. We derived the approximate expression of the end-to-end outage probability as a function of SNR, the information transmission rate, S-R channel gain, and the number of relays. Simulations are made in one-relaying system and two-relaying system, which are also carried out in continuous change of the S-R channel. We found that the performance of PT gets overwhelming in unreliable-relaying system. Sequentially, we noted that PT can better benefit from the R-D channel, and the higher the information transmission rate is, the better performance PT can get. Extensive numerical and simulation studies illustrate our theoretical developments and show that the proposed strategy provides a significant improvement over the conventional cooperative strategies on unreliable relays.