This paper investigates coherent detection for physical-layer network coding (PNC) with short packet transmissions in a two-way relay channel (TWRC). PNC turns superimposed EM waves into network-coded messages to improve throughput in a relay system. To achieve this, accurate channel information at the relay is a necessity. Much prior work applies preambles to estimate the channel. For long packets, the preamble overhead is low because of the large data payload. For short packets, that is not the case. To avoid excessive overhead, we consider a set-up in which short packets do not have preambles. A key challenge is how the relay can estimate the channel and detect the network-coded messages jointly based on the received signals from the two end users. We design a coherent detector that makes use of a belief propagation (BP) algorithm to do so. For concreteness, we focus on frequency-shift-keying (FSK) modulation. We show how the BP algorithm can be simplified and made practical with Gaussian-mixture passing. In addition, we demonstrate that prior knowledge on the channel distribution is not needed with our framework. Benchmarked against the detector with prior knowledge of the channel distribution, numerical results show that our detector can have nearly the same performance without such prior knowledge.
The authors of @cite_20 put forth a coherent FSK-PNC detector for power-balanced channels, assuming that the channels are perfectly known at the relay. That is, the detector does not need to do channel estimation and only has to do detection. Although channel estimation can be performed using a preamble in the packet, a preamble would have occupied a large portion of a short packet, causing large overhead. To avoid the overhead, we consider short packets without preambles. In addition, we do not assume power-balanced channel and our detector can work with arbitrary channel distributions.
@cite_20
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This paper investigates the noncoherent detection in a two-way relay channel operated with physical-layer network coding (PNC), assuming FSK modulation and short-packet transmissions. For noncoherent detection, the detector has access to the magnitude but not the phase of the received signal. For conventional communication in which a receiver receives the signal from a transmitter only, the phase does not affect the magnitude, and hence the performance of the noncoherent detector is independent of the phase. PNC, on the other hand, is a multiuser system in which a receiver receives signals from multiple transmitters simultaneously. The relative phase of the signals from different transmitters affects the received signal magnitude through constructive-destructive interference. In particular, for good performance, the noncoherent detector of a multiuser system such as PNC must take into account the influence of the relative phase on the signal magnitude. Building on this observation, this paper delves into the fundamentals of PNC noncoherent detector design. To avoid excessive overhead, we assume a set-up in which the short packets in the PNC system do not have preambles. We show how the relative phase can be deduced directly from the magnitudes of the received data symbols, and that the knowledge of the relative phase thus deduced can in turn be used to enhance performance of noncoherent detection. Our overall detector design consists of two components: 1) a channel gains estimator that estimates channel gains without preambles; and 2) a detector that builds on top of the estimated channel gains to jointly estimate relative phase and detect data using a belief propagation algorithm. Numerical results show that our detector performs nearly as well as a “fictitious” optimal detector that has perfect knowledge of the channel gains and relative phase. Although this paper focuses on PNC with FSK modulation, we believe that the insight of this paper applies generally to noncoherent detection in other multiuser systems with other modulations. Specifically, our insight is that the relative phase of overlapped signals affects the signal magnitude in multiuser systems, but fortunately the relative phase can be deduced from the magnitudes and this knowledge can be used to improve the detection performance. This paper investigates noncoherent detection in a two-way relay channel operated with physical- layer network coding (PNC), assuming FSK modulation and short-packet transmissions. For noncoherent detection, the detector has access to the magnitude but not the phase of the received signal. For conventional communication in which a receiver receives the signal from a transmitter only, the phase does not affect the magnitude, hence the performance of the noncoherent detector is independent of the phase. PNC, on the other hand, is a multiuser system in which a receiver receives signals from multiple transmitters simultaneously. The relative phase of the signals from different transmitters affects the received signal magnitude through constructive-destructive interference. In particular, for good performance, the noncoherent detector of a multiuser system such as PNC must take into account the influence of the relative phase on the signal magnitude. Building on this observation, this paper delves into the fundamentals of PNC noncoherent detector design. To avoid excessive overhead, we assume a set-up in which the short packets in the PNC system do not have preambles. We show how the relative phase can be deduced directly from the magnitudes of the received data symbols, and that the knowledge of the relative phase thus deduced can in turn be used to enhance performance of noncoherent detection. We design a noncoherent detector that jointly estimates relative phase and detects data using a belief propagation algorithm. Numerical results show that our detector performs as well as a “fictitious” optimal detector that has perfect knowledge of the relative phase. Although this paper focuses on PNC with FSK modulation, we believe the insight of this paper applies generally to noncoherent detection in other multiuser systems with other modulations. Specifically, our insight is that the relative phase of overlapped signals affects the signal magnitude in multiuser systems, but fortunately the relative phase can be deduced from the magnitudes and this knowledge can be used to improve detection performance. This paper investigates various subtleties of applying linear physical-layer network coding (PNC) with @math -level pulse amplitude modulation ( @math -PAM) in two-way relay channels. A critical issue is how the PNC system performs when the received powers from the two users at the relay are imbalanced. In particular, how would the PNC system perform under slight power imbalance that is inevitable in practice, even when power control is applied? To answer these questions, this paper presents a comprehensive analysis of @math -PAM PNC. Our contributions are as follows. First, we give a systematic way to obtain the analytical relationship between the minimum distance of the signal constellation induced by the superimposed signals of the two users (a key performance determining factor) and the channel-gain ratio of the two users, for all @math . In particular, we show how the minimum distance changes in a piecewise linear fashion as the channel-gain ratio varies. Second, we show that the performance of @math -PAM PNC is highly sensitive to imbalanced received powers from the two users at the relay, even when the power imbalance is slight (e.g., the residual power imbalance in a power-controlled system). This sensitivity problem is exacerbated as @math increases, calling into question the robustness of high-order modulated PNC. Third, we propose an asynchronized PNC system in which the symbol arrival times of the two users at the relay are deliberately made to be asynchronous. We show that such asynchronized PNC, when operated with a belief propagation decoder, can remove the sensitivity problem, allowing a robust high-order modulated PNC system to be built. Abstract This paper presents the first implementation of a two-way relay network based on the principle of physical-layer network coding (PNC). To date, only a simplified version of PNC, called analog network coding (ANC), has been successfully implemented. The advantage of ANC is that it is simple to implement; the disadvantage, on the other hand, is that the relay amplifies the noise along with the signal before forwarding the signal. PNC systems in which the relay performs XOR or other denoising PNC mappings of the received signal have the potential for significantly better performance. However, the implementation of such PNC systems poses many challenges. For example, the relay in a PNC system must be able to deal with symbol and carrier-phase asynchronies of the simultaneous signals received from multiple nodes, and the relay must perform channel estimation before detecting the signals. We investigate a PNC implementation in the frequency domain, referred to as FPNC, to tackle these challenges. FPNC is based on OFDM. In FPNC, XOR mapping is performed on the OFDM samples in each subcarrier rather than on the samples in the time domain. We implement FPNC on the universal soft radio peripheral (USRP) platform. Our implementation requires only moderate modifications of the packet preamble design of 802.11a g OFDM PHY. With the help of the cyclic prefix (CP) in OFDM, symbol asynchrony and the multi-path fading effects can be dealt with simultaneously in a similar fashion. Our experimental results show that symbol-synchronous and symbol-asynchronous FPNC have essentially the same BER performance, for both channel-coded and non-channel-coded FPNC systems.