Physical Layer Network Coding Mapping Research Articles

Performance Analysis of Physical Layer Network Coding in Massive MIMO Systems With M-QAM Modulations

In this paper, we develop a practical approach for deploying Physical Layer Network Coding (PNC) in multi-user M-Ary Quadrature Amplitude Modulation (M-QAM) Massive Multiple-Input Multiple-Output (MIMO) systems. We formulate a PNC mapping scheme as a function of clusters of estimated summation and difference (SD) of the transmitted symbols from user pairs. Utilizing existing linear detection schemes, such as Zero Forcing (ZF) and Minimum Mean Square Error (MMSE), a cluster of SD symbols are detected using an SD linearly transformed channel matrix. Furthermore, utilizing Maximum a Posteriori (MAP) soft decoding, the SD symbols are mapped to the PNC symbols, leveraging on the PNC symbol that maximizes the likelihood function. For each variant of M-QAM, we derive and simplify a specialization of the generalized PNC mapping function. The error performance results, through simulation, reveal that the proposed PNC scheme achieves twice the spectral efficiency in Massive MIMO, without changing the latter's underlying framework and without any degradation in the bit-error-rate (BER). In fact, our investigation has proved that the BER of the proposed Massive MIMO and PNC is slightly better than that of the conventional Massive MIMO. The feasibility of deploying our proposed PNC scheme in Massive MIMO systems paves way for NC applications to be realized in cellular systems.

Physical Layer Network Coding in Network MIMO: A New Design for 5G and Beyond

Physical layer network coding (PNC) has been studied to serve wireless network MIMO systems with much lower backhaul load than approaches such as Cloud Radio Access Network (Cloud-RAN) and coordinated multipoint (CoMP). In this paper, we present a design guideline of engineering applicable PNC to fulfil the request of high user densities in 5G wireless RAN infrastructure. We show that the proposed design criteria guarantee that: 1) the whole system operates over binary system; 2) the PNC functions utilized at each access point overcome all singular fade states; and 3) the destination can unambiguously recover all source messages, while the overall backhaul load remains at the lowest level. We then develop a two-stage search algorithm to identify the optimum PNC mapping functions which greatly reduces the real-time computational complexity. The impact of estimated channel information and reduced number of singular fade states in different QAM modulation schemes are studied in this paper. Numerical results show that the proposed schemes achieve low outage probability with reduced backhaul load.

Channel quantization-based physical-layer network coding for two-way relay STBC system

Wireless multiple-input multiple-output (MIMO) two-way relay systems have received increasing attention recently. In a simple two-hop relay system, physical-layer network coding (PNC) is an effective scheme for relay to map the transmitted symbols from two terminal nodes into the network coded symbol. This paper considers a two-hop two-way relay system which uses the Alamouti space-time code for signaling between all nodes and channel quantization for PNC mapping at the relay. Specifically, based on the concept of CQ-PNC we derive a PNC mapping rule for two pairs of network coded symbols. An adaptive mapping scheme based on minimum residual interference power is introduced to reduce the effect of quantization error. Finally, a relay selection method based on minimum residual interference power is proposed as a means to increase the system performance.

Complex Linear Physical-Layer Network Coding

This paper presents the results of a comprehensive investigation of complex linear physical-layer network coding (PNC) in two-way relay channels. In this system, two nodes A and B communicate with each other via a relay R. Nodes A and B send complex symbols, $w_{A}$ and $w_{B}$ , simultaneously to relay R. Based on the simultaneously received signals, relay R computes a linear combination of the symbols, $w_{N}=\alpha w_{A}+\beta w_{B}$ , as a network-coded symbol and then broadcasts $w_{N}$ to nodes A and B. Node A then obtains $w_{B}$ from $w_{N}$ and its self-information $w_{A}$ by $w_{B}=\beta ^{-1}(w_{N}-\alpha w_{A})$ . Node B obtains $w_{B}$ in a similar way. A critical question at relay R is as follows: “given channel gain ratio $\eta = h_{A}/h_{B}$ , where $h_{A}$ and $h_{B}$ are the complex channel gains from nodes A and B to relay R, respectively, what is the optimal coefficients $(\alpha ,\beta )$ that minimizes the symbol error rate (SER) of $w_{N}=\alpha w_{A}+\beta w_{B}$ when the relay attempts to detect $w_{N}$ in the presence of noise?” Our contributions with respect to this question are as follows: 1) we put forth a general Gaussian-integer formulation for complex linear PNC in which $\alpha ,\beta ,w_{A}, w_{B}$ , and $w_{N}$ are the elements of a finite field of Gaussian integers, that is, the field of $\mathbb {Z}[i]/q$ , where $q$ is a Gaussian prime. Previous vector formulation, in which $w_{A}$ , $w_{B}$ , and $w_{N}$ were represented by 2-D vectors and $\alpha $ and $\beta $ were represented by $2\times 2$ matrices, corresponds to a subcase of our Gaussian-integer formulation, where $q$ is real prime only. Extension to the Gaussian prime $q$ , where $q$ can be complex, gives us a larger set of signal constellations to achieve different rates at different values of SNR; and 2) we show how to divide the complex plane of $\eta $ into different Voronoi regions, such that the $\eta $ within each Voronoi region shares the same optimal PNC mapping $(\alpha _{\mathrm{ opt}},\beta _{\mathrm{ opt}})$ . We uncover the structure of the Voronoi regions that allows us to compute a minimum-distance metric that characterizes the SER of $w_{N}$ under optimal PNC mapping $(\alpha _{\mathrm{ opt}},\beta _{\mathrm{ opt}})$ . Overall, the contributions in 1) and 2) yield a toolset for a comprehensive understanding of complex linear PNC in $\mathbb {Z}[i]/q$ . We believe investigation of linear PNC beyond $\mathbb {Z}[i]/q$ can follow the same approach.

Investigation on iterative multiuser detection physical layer network coding in two-way relay free-space optical links with turbulences and pointing errors.

Physical layer network coding (PNC) improves the throughput in wireless networks by enabling two nodes to exchange information using a minimum number of time slots. The PNC technique is proposed for two-way relay channel free space optical (TWR-FSO) communications with the aim of maximizing the utilization of network resources. The multipair TWR-FSO is considered in this paper, where a single antenna on each pair seeks to communicate via a common receiver aperture at the relay. Therefore, chip interleaving is adopted as a technique to separate the different transmitted signals at the relay node to perform PNC mapping. Accordingly, this scheme relies on the iterative multiuser technique for detection of users at the receiver. The bit error rate (BER) performance of the proposed system is examined under the combined influences of atmospheric loss, turbulence-induced channel fading, and pointing errors (PEs). By adopting the joint PNC mapping with interleaving and multiuser detection techniques, the BER results show that the proposed scheme can achieve a significant performance improvement against the degrading effects of turbulences and PEs. It is also demonstrated that a larger number of simultaneous users can be supported with this new scheme in establishing a communication link between multiple pairs of nodes in two time slots, thereby improving the channel capacity.

Full diversity reception based on Dempster-Shafer theory for network coding with multiple-antennas relay

In this paper, a two-way relay system which achieves bi-directional communication via a multiple-antenna relay in two time slots is studied. In the multiple access (MA) phase, the novel receive schemes based on Dempster-Shafer (D-S) evidence theory are proposed at the relay node. Instead of traditional linear detection, the first proposed MIMO-DS NC scheme adopts D-S evidence theory to detect the signals of each source node before mapping them into network-coded signal. Moreover, different from traditional physical-layer network coding (PNC) based on virtual MIMO model, the further proposed MIMO-DS PNC comes from the vector space perspective and combines PNC mapping with D-S theory to obtain network-coded signal without estimating each source node signal. D-S theory can appropriately characterize uncertainty and make full use of multiple evidence source information by Dempster's combination rule to obtain reliable decisions. In the broadcast (BC) phase, the space-time coding (STC) and antenna selection (AS) schemes are adopted to achieve transmit diversity. Simulation results reveal that the STC and AS schemes both achieve full transmit diversity in the BC phase and the proposed MIMO-DS NC/PNC schemes obtain better end-to-end BER performance and throughputs compared with traditional schemes with a little complexity increasing and no matter which scheme is adopted in the BC phase, MIMO-DS PNC always achieves full end-to-end diversity gain as MIMO-ML NC but with a lower complexity and its throughput approaches the throughput of MIMO-ML NC in high SNR regime.

Secure Beamforming Design for Physical Layer Network Coding Based MIMO Two-Way Relaying

In this letter, we propose a secure beamforming scheme for physical layer network coding (PNC)-based multiple-input multiple-output (MIMO) two-way relaying system. The relay node performs PNC mapping. An eavesdropper is attempting to intercept the user information. The channel state information (CSI) of the user-to-eavesdropper channel is imperfect at the user nodes. A robust optimization problem is formulated to design beamforming vectors at the user nodes and relay. The problem is non-convex, and an algorithm is proposed to solve that. In the numerical analysis, we discuss the convergence of the proposed algorithm and the impact of the CSI error on the performance.