A physical-layer network coding (PNC) scheme is developed using serially concatenated continuous phase modulation (SCCPM) with symbol interleavers in a two-way relay channel (TWRC), i.e., SCCPM-PNC. The decoding structure of the relay is designed and the corresponding soft input soft output (SISO) iterative decoding algorithm is discussed. Simulation results show that the proposed SCCPM-PNC scheme performs good performance in bit error rate (BER) and considerable improvements can be achieved by increasing the interleaver size and number of iterations.

In this letter, a physical-layer network coding (PNC) scheme based on continuous phase modulation (CPM) signal using the titled-phase model, i.e., TIP-CPM-PNC, is presented, and the combined titled-phase state trellis for the superimposed CPM signal in TIP-CPM-PNC is discussed. Simulation results show that the proposed scheme with low decoding complexity can achieve the same error performance as CPM-PNC using the traditional-phase model.

We consider a physical-layer network coding (PNC) scheme based on M-ary continuous phase frequency shift keying (M-CPFSK) modulation for a bidirectional relay network. In this scheme, the maximum-likelihood sequence detection (MLSD) algorithm for the relay receiver over Rayleigh fading channels is discussed. Moreover, an upper bound on the minimum Euclidean distance for the superimposed signals is analyzed and the corresponding lower bound for the average symbol error rate (SER) at the relay is derived. Numerical results are also sustained by simulations which corroborate the exactness of the theoretical analysis.

Network coding on the physical-layer has recently been widely discussed as a potentially promising solution to the wireless access problem in a relay network. However, the existing research on physical-layer network coding (PNC), usually assumes that the symbol timing of the nodes is fully synchronized and hardly investigates the unavoidable symbol timing errors. Similar to many telecommunication systems, symbol timing plays a critical role in PNC and precise alignment has to be provided for the encoding. In this work, we propose a novel symbol timing algorithm with a low oversampling factor (samples per symbol) based on the a priori knowledge of the transmitted pulse shape. The proposed algorithm has the dual advantages of the low oversampling rate and high precision. The mean square error (MSE) performance is verified by simulations to be at least one order of magnitude better than that of the conventional optimum phase (OP) algorithm for a signal noise ratio (SNR) greater than 5dB.

In this letter, we combine minimum-shift keying (MSK) with physical-layer network coding (PNC) to form a new scheme, i.e., MSK-PNC, for two-way relay channels (TWRCs). The signal detection of the MSK-PNC scheme is investigated, and two detection methods are proposed. The first one is orthogonal demodulation and mapping (ODM), and the second one is two-state differential detection (TSDD). The error performance of the proposed MSK-PNC scheme is evaluated through simulations.

A joint continuous phase frequency shift keying (CPFSK) modulation and physical-layer network coding (PNC), i.e., CPFSK-PNC, is proposed for two-way relay channels (TWRCs). This letter discusses the signal detection of the CPFSK-PNC scheme with emphasis on the maximum-likelihood sequence detection (MLSD) algorithm for the relay receiver. The end-to-end error performance of the proposed CPFSK-PNC scheme is evaluated through simulations.

Physical-layer network coding with binary turbo coding in a two-way relay channel is considered. A two-user turbo decoding scheme is proposed with a simplified sum trellis. For two-user iterative decoding at a relay, the component decoder with its simplified sum trellis decodes the superimposed signal to the arithmetic sum of two users' messages. The simplified sum trellis is obtained by removing one of the states in a pair of mutual symmetrical states from a sum trellis. This removal reduces the decoding complexity to half of that with the sum trellis, and does not degrade decoding performance over AWGN channel since two output sequences from the pair of mutual symmetrical states are the same.

This letter considers a two-way relaying network where two nodes exchange their information based on the principle of physical layer network coding (PNC). We study the amplify-and-forward (AF) relay filter design with multiple-input multiple-output (MIMO) system. In order to maximize the sum-rate for information exchange, we propose a relay filter for two-way relaying network. Simulation results show that the proposed scheme performs better than the conventional schemes for two-way relay channel.

We propose a two-phase diversity scheme to achieve the end-to-end spatial diversity gain for physical-layer network coding (PNC) based two-way relay with a multiple-antenna relay node. A novel binary PNC-specific maximal-ratio-combining like (MRC-L) scheme is proposed to obtain receive diversity in the multiple-access (MA) phase with linear complexity; the Max-Min criterion based transmit antenna selection (TAS) is adopted to obtain transmit diversity in the broadcast (BC) phase. Both the brief diversity analysis and the Monte Carlo (MC) simulation results demonstrate that the proposed scheme achieves full diversity and outperforms other comparable schemes in terms of end-to-end diversity or power advantage.