Constellation Mapping for Physical-Layer Network Coding with M-QAM Modulation

The denoise-and-forward (DNF) method of physical-layer network coding (PNC) is a promising approach for wireless relaying networks. In this paper, we consider DNF-based PNC with M-ary quadrature amplitude modulation (M-QAM) and propose a mapping scheme that maps the superposed M-QAM signal to coded symbols. The mapping scheme supports both square and non-square M-QAM modulations, with various original constellation mappings (e.g. binary-coded or Gray-coded). Subsequently, we evaluate the symbol error rate and bit error rate (BER) of M-QAM modulated PNC that uses the proposed mapping scheme. Afterwards, as an application, a rate adaptation scheme for the DNF method of PNC is proposed. Simulation results show that the rate-adaptive PNC is advantageous in various scenarios.Comment: Final version at IEEE GLOBECOM 201

Physical Layer Network Coding for Two-Way Relaying with QAM

The design of modulation schemes for the physical layer network-coded two way relaying scenario was studied in [1], [3], [4] and [5]. In [7] it was shown that every network coding map that satisfies the exclusive law is representable by a Latin Square and conversely, and this relationship can be used to get the network coding maps satisfying the exclusive law. But, only the scenario in which the end nodes use $M$-PSK signal sets is addressed in [7] and [8]. In this paper, we address the case in which the end nodes use $M$-QAM signal sets. In a fading scenario, for certain channel conditions $\gamma e^{j \theta}$, termed singular fade states, the MA phase performance is greatly reduced. By formulating a procedure for finding the exact number of singular fade states for QAM, we show that square QAM signal sets give lesser number of singular fade states compared to PSK signal sets. This results in superior performance of $M$-QAM over $M$-PSK. It is shown that the criterion for partitioning the complex plane, for the purpose of using a particular network code for a particular fade state, is different from that used for $M$-PSK. Using a modified criterion, we describe a procedure to analytically partition the complex plane representing the channel condition. We show that when $M$-QAM ($M >4$) signal set is used, the conventional XOR network mapping fails to remove the ill effects of $\gamma e^{j \theta}=1$, which is a singular fade state for all signal sets of arbitrary size. We show that a doubly block circulant Latin Square removes this singular fade state for $M$-QAM.Comment: 13 pages, 14 figures, submitted to IEEE Trans. Wireless Communications. arXiv admin note: substantial text overlap with arXiv:1203.326

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

Maximum Euclidean distance network coded modulation for asymmetric decode-and-forward two-way relaying

Network coding (NC) compresses two traffic flows with the aid of low-complexity algebraic operations, hence holds the potential of significantly improving both the efficiency of wireless two-way relaying, where each receiver is collocated with a transmitter and hence has prior knowledge of the message intended for the distant receiver. In this contribution, network coded modulation (NCM) is proposed for jointly performing NC and modulation. As in classic coded modulation, the Euclidean distance between the symbols is maximised, hence the symbol error probability is minimised. Specifically, the authors first propose set-partitioning-based NCM as an universal concept which can be combined with arbitrary constellations. Then the authors conceive practical phase-shift keying/quadrature amplitude modulation (PSK/QAM) NCM schemes, referred to as network coded PSK/QAM, based on modulo addition of the normalised phase/amplitude. To achieve a spatial diversity gain at a low complexity, a NC oriented maximum ratio combining scheme is proposed for combining the network coded signal and the original signal of the source. An adaptive NCM is also proposed to maximise the throughput while guaranteeing a target bit error probability (BEP). Both theoretical performance analysis and simulations demonstrate that the proposed NCM can achieve at least 3 dB signal-to-noise ratio gain and two times diversity gain

Network coded modulation for two-way relaying

Network coding compresses multiple traffic flows with the aid low-complexity algebraic operations, hence holds the potential of significantly improving both the power and bandwidth efficiency of wireless networks. In this contribution, the novel concept of Network Coded Modulation (NCM) is proposed for jointly performing network coding and modulation in bi-directional/duplex relaying. Each receiver is colocated with a transmitter and hence has prior knowledge of the message intended for the distant receiver. As in classic coded modulation, the Euclidian distance between the symbols is maximized, hence the Symbol Error Ratio (SER) is minimized. Specifically, we conceive NCM methods for PSK, PAM and QAM based on modulo addition of the normalized phase or amplitude. Furthermore, we propose low complexity decoding algorithms based on the corresponding conditional minimum distance criteria. Our performance analysis and simulations demonstrate that NCM relying on PSK is capable of achieving a SER at both receivers of the NCM scheme as if the relay transmitted exclusively to a single receiver only. By contrast, when our NCM concept is combined with PAM/QAM, an SNR loss (<1.25dB) is imposed at one of the receivers, usually at the one having a lower data rate in a realistic different rate scenario. Finally, we will demonstrate that the proposed NCM is compatible with existing physical layer designs

Space-Time Coded Spatial Modulated Physical Layer Network Coding for Two-Way Relaying

Using the spatial modulation approach, where only one transmit antenna is active at a time, we propose two transmission schemes for two-way relay channel using physical layer network coding with space time coding using Coordinate Interleaved Orthogonal Designs (CIOD's). It is shown that using two uncorrelated transmit antennas at the nodes, but using only one RF transmit chain and space-time coding across these antennas can give a better performance without using any extra resources and without increasing the hardware implementation cost and complexity. In the first transmission scheme, two antennas are used only at the relay, Adaptive Network Coding (ANC) is employed at the relay and the relay transmits a CIOD Space Time Block Code (STBC). This gives a better performance compared to an existing ANC scheme for two-way relay channel which uses one antenna each at all the three nodes. It is shown that for this scheme at high SNR the average end-to-end symbol error probability (SEP) is upper bounded by twice the SEP of a point-to-point fading channel. In the second transmission scheme, two transmit antennas are used at all the three nodes, CIOD STBC's are transmitted in multiple access and broadcast phases. This scheme provides a diversity order of two for the average end-to-end SEP with an increased decoding complexity of $\mathcal{O}(M^3)$ for an arbitrary signal set and $\mathcal{O}(M^2\sqrt{M})$ for square QAM signal set.Comment: 9 pages, 7 figure

A Cooperative Network Coding Strategy for the Interference Relay Channel.

In this paper, we study an interference relay network with a satellite as relay. We propose a cooperative strategy based on physical layer network coding and superposition modulation decoding for uni-directional communications among users. The performance of our solution in terms of throughput is evaluated through capacity analysis and simulations that include practical constraints such as the lack of synchronization in time and frequency.We obtain a significant throughput gain compared to the classical time sharing case