# Wireless Bidirectional Relaying using Physical Layer Network Coding with Heterogeneous PSK Modulation

## TL;DR

This paper analytically derives network coding maps for bidirectional relaying with heterogeneous symmetric PSK modulations, improving understanding and performance in physical layer network coding scenarios.

## Contribution

It provides an analytical method to determine network coding maps for heterogeneous PSK modulations, avoiding computationally intensive algorithms used previously.

## Key findings

- Analytical expressions for network coding maps are derived.
- Performance evaluated in terms of Relay Error Rate and Bit Error Rate.
- Results demonstrate improved efficiency over previous methods.

## Abstract

In bidirectional relaying using Physical Layer Network Coding (PLNC), it is generally assumed that users employ same modulation schemes in the Multiple Access phase. However, as observed by Zhang et al., it may not be desirable for the users to always use the same modulation schemes, particularly when user-relay channels are not equally strong. Such a scheme is called Heterogeneous PLNC. However, the approach in [1] uses the computationally intensive Closest Neighbour Clustering (CNC) algorithm to find the network coding maps to be applied at the relay. Also, the treatment is specific to certain cases of heterogeneous modulations. In this paper, we show that, when users employ heterogeneous but symmetric PSK modulations, the network coding maps and the mapping regions in the fade state plane can be obtained analytically. Performance results are provided in terms of Relay Error Rate (RER) and Bit Error Rate (BER).

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Source: https://tomesphere.com/paper/1703.04141