Symbol error rate analysis for M-QAM modulated physical-layer network coding with phase errors

Recent theoretical studies of physical-layer network coding (PNC) show much interest on high-level modulation, such as M-ary quadrature amplitude modulation (M-QAM), and most related works are based on the assumption of phase synchrony. The possible presence of synchronization error and channel estimation error highlight the demand of analyzing the symbol error rate (SER) performance of PNC under different phase errors. Assuming synchronization and a general constellation mapping method, which maps the superposed signal into a set of M coded symbols, in this paper, we analytically derive the SER for M-QAM modulated PNC under different phase errors. We obtain an approximation of SER for general M-QAM modulations, as well as exact SER for quadrature phase-shift keying (QPSK), i.e. 4-QAM. Afterwards, theoretical results are verified by Monte Carlo simulations. The results in this paper can be used as benchmarks for designing practical systems supporting PNC. © 2012 IEEE

Distributed MAC Protocol Supporting Physical-Layer Network Coding

Physical-layer network coding (PNC) is a promising approach for wireless networks. It allows nodes to transmit simultaneously. Due to the difficulties of scheduling simultaneous transmissions, existing works on PNC are based on simplified medium access control (MAC) protocols, which are not applicable to general multi-hop wireless networks, to the best of our knowledge. In this paper, we propose a distributed MAC protocol that supports PNC in multi-hop wireless networks. The proposed MAC protocol is based on the carrier sense multiple access (CSMA) strategy and can be regarded as an extension to the IEEE 802.11 MAC protocol. In the proposed protocol, each node collects information on the queue status of its neighboring nodes. When a node finds that there is an opportunity for some of its neighbors to perform PNC, it notifies its corresponding neighboring nodes and initiates the process of packet exchange using PNC, with the node itself as a relay. During the packet exchange process, the relay also works as a coordinator which coordinates the transmission of source nodes. Meanwhile, the proposed protocol is compatible with conventional network coding and conventional transmission schemes. Simulation results show that the proposed protocol is advantageous in various scenarios of wireless applications.Comment: Final versio

Improvement in Performance of Wireless Relay Nodes Using Physical Layer Network Coding

Recent advancements in high data rate networks have led to a growing interest in improving performance of wireless relay networks through the use of Physical Layer Network Coding (PLNC) technique. In the PLNC technique, the relay node exploits the network coding operation that occurs naturally when the two electromagnetic (EM) waves are superimposed on one another to directly decode the modulo-2 sum of the transmitted symbols. In this thesis, we will present an optimal power control algorithm for performance improvement in wireless relay nodes implementing physical layer network coding. We shall also present a sub-optimal power control algorithm and compare its performance with the optimal power control algorithm. Our approach will first derive the probability of error for the amplitude-controlled system using Maximum Likelihood detection and then minimize the probability of error using amplitude control functions as variables to derive the optimal power control functions. We shall start by considering the thresholds of the system to be the maximum of the independent received amplitudes to derive the probability of error equations and then extend it to a variable threshold system, where the threshold is a function of independent received amplitudes. We then derive an optimal power control algorithm for a single channel Rayleigh system and implement this power control algorithm independently on the terminals to achieve a sub-optimal power control algorithm. Our results show that the proposed optimal power control algorithm boosts the performance of the PLNC system significantly compared to the no power control system. We also show that there are no significant differences between the performances of optimal power control and the sub-optimal power control algorithms. We further show that the performance of the system is not degraded much when the amplitudes of the terminals deviate from the optimal amplitudes

Differential Distributed Space-Time Coding with Imperfect Synchronization in Frequency-Selective Channels

Differential distributed space-time coding (D-DSTC) is a cooperative transmission technique that can improve diversity in wireless relay networks in the absence of channel information. Conventionally, it is assumed that channels are flat-fading and relays are perfectly synchronized at the symbol level. However, due to the delay spread in broadband systems and the distributed nature of relay networks, these assumptions may be violated. Hence, inter-symbol interference (ISI) may appear. This paper proposes a new differential encoding and decoding process for D-DSTC systems with multiple relays over slow frequency-selective fading channels with imperfect synchronization. The proposed method overcomes the ISI caused by frequency-selectivity and is robust against synchronization errors while not requiring any channel information at the relays and destination. Moreover, the maximum possible diversity with a decoding complexity similar to that of the conventional D-DSTC is attained. Simulation results are provided to show the performance of the proposed method in various scenarios.Comment: to appear in IEEE Transaction on Wireless Communications, 201

Asynchronous Physical-layer Network Coding

A key issue in physical-layer network coding (PNC) is how to deal with the asynchrony between signals transmitted by multiple transmitters. That is, symbols transmitted by different transmitters could arrive at the receiver with symbol misalignment as well as relative carrier-phase offset. A second important issue is how to integrate channel coding with PNC to achieve reliable communication. This paper investigates these two issues and makes the following contributions: 1) We propose and investigate a general framework for decoding at the receiver based on belief propagation (BP). The framework can effectively deal with symbol and phase asynchronies while incorporating channel coding at the same time. 2) For unchannel-coded PNC, we show that for BPSK and QPSK modulations, our BP method can significantly reduce the asynchrony penalties compared with prior methods. 3) For unchannel-coded PNC, with half symbol offset between the transmitters, our BP method can drastically reduce the performance penalty due to phase asynchrony, from more than 6 dB to no more than 1 dB. 4) For channel-coded PNC, with our BP method, both symbol and phase asynchronies actually improve the system performance compared with the perfectly synchronous case. Furthermore, the performance spread due to different combinations of symbol and phase offsets between the transmitters in channel-coded PNC is only around 1 dB. The implication of 3) is that if we could control the symbol arrival times at the receiver, it would be advantageous to deliberately introduce a half symbol offset in unchannel-coded PNC. The implication of 4) is that when channel coding is used, symbol and phase asynchronies are not major performance concerns in PNC.Comment: Full length version of APN

Iterative decoding combined with physical-layer network coding on impulsive noise channels

PhD ThesisThis thesis investigates the performance of a two-way wireless relay channel (TWRC) employing physical layer network coding (PNC) combined with binary and non-binary error-correcting codes on additive impulsive noise channels. This is a research topic that has received little attention in the research community, but promises to offer very interesting results as well as improved performance over other schemes. The binary channel coding schemes include convolutional codes, turbo codes and trellis bitinterleaved coded modulation with iterative decoding (BICM-ID). Convolutional codes and turbo codes defined in finite fields are also covered due to non-binary channel coding schemes, which is a sparse research area. The impulsive noise channel is based on the well-known Gaussian Mixture Model, which has a mixture constant denoted by α. The performance of PNC combined with the different coding schemes are evaluated with simulation results and verified through the derivation of union bounds for the theoretical bit-error rate (BER). The analyses of the binary iterative codes are presented in the form of extrinsic information transfer (ExIT) charts, which show the behaviour of the iterative decoding algorithms at the relay of a TWRC employing PNC and also the signal-to-noise ratios (SNRs) when the performance converges. It is observed that the non-binary coding schemes outperform the binary coding schemes at low SNRs and then converge at higher SNRs. The coding gain at low SNRs become more significant as the level of impulsiveness increases. It is also observed that the error floor due to the impulsive noise is consistently lower for non-binary codes. There is still great scope for further research into non-binary codes and PNC on different channels, but the results in this thesis have shown that these codes can achieve significant coding gains over binary codes for wireless networks employing PNC, particularly when the channels are harsh