Pilot Optimization and Channel Estimation for Two-way Relaying Network Aided by IRS with Finite Discrete Phase Shifters

TL;DR

This paper proposes an optimized pilot design and channel estimation method for two-way relaying networks aided by IRS with finite discrete phase shifters, demonstrating that low-resolution phase shifters can achieve near-optimal performance.

Contribution

It introduces a novel pilot and phase shift design for IRS-assisted TWRNs, deriving optimal phase matrices and showing low-resolution phase shifters suffice for high accuracy.

Findings

Hadamard matrix achieves optimal MSE with 1-bit phase shifters.

DFT matrix requires at least 3-4 bits for similar performance.

3-4 bits phase shifters are sufficient for negligible MSE loss.

Abstract

In this paper, we investigate the problem of pilot optimization and channel estimation of two-way relaying network (TWRN) aided by an intelligent reflecting surface (IRS) with finite discrete phase shifters. In a TWRN, there exists a challenging problem that the two cascading channels from source-to-IRS-to-Relay and destination-to-IRS-to-relay interfere with each other. Via designing the initial phase shifts of IRS and pilot pattern, the two cascading channels are separated by using simple arithmetic operations like addition and subtraction. Then, the least-squares estimator is adopted to estimate the two cascading channels and two direct channels from source to relay and destination to relay. The corresponding mean square errors (MSE) of channel estimators are derived. By minimizing MSE, the optimal phase shift matrix of IRS is proved. Then, two special matrices Hadamard and discrete Fourier transform (DFT) matrix is shown to be two optimal training matrices for IRS. Furthermore, the IRS with discrete finite phase shifters is taken into account. Using theoretical derivation and numerical simulations, we find that 3-4 bits phase shifters are sufficient for IRS to achieve a negligible MSE performance loss. More importantly, the Hadamard matrix requires only one-bit phase shifters to achieve the optimal MSE performance while the DFT matrix requires at least three or four bits to achieve the same performance. Thus, the Hadamard matrix is a perfect choice for channel estimation using low-resolution phase-shifting IRS.