# Optimal Channel Estimation for Reciprocity-Based Backscattering with a Full-Duplex MIMO Reader

## TL;DR

This paper proposes an optimal channel estimation method for reciprocity-based backscatter communication using a full-duplex MIMO reader, improving communication range and efficiency through joint optimization of pilot design and resource allocation.

## Contribution

It introduces a novel least-squares channel estimator and jointly optimizes pilot number and energy allocation for enhanced backscatter communication performance.

## Key findings

- Improved backscatter SNR with optimized resource allocation.
- Analytical approximation for global optimal design.
- Numerical validation showing gains over benchmarks.

## Abstract

Backscatter communication (BSC) technology can enable ubiquitous deployment of low-cost sustainable wireless devices. In this work we investigate the efficacy of a full-duplex multiple-input-multiple-output (MIMO) reader for enhancing the limited communication range of monostatic BSC systems. As this performance is strongly influenced by the channel estimation (CE) quality, we first derive a novel least-squares estimator for the forward and backward links between the reader and the tag, assuming that reciprocity holds and K orthogonal pilots are transmitted from the first K antennas of an N antenna reader. We also obtain the corresponding linear minimum-mean square-error estimate for the backscattered channel. After defining the transceiver design at the reader using these estimates, we jointly optimize the number of orthogonal pilots and energy allocation for the CE and information decoding phases to maximize the average backscattered signal-to-noise ratio (SNR) for efficiently decoding the tag's messages. The unimodality of this SNR in optimization variables along with a tight analytical approximation for the jointly global optimal design is also discoursed. Lastly, the selected numerical results validate the proposed analysis, present key insights into the optimal resource utilization at reader, and quantify the achievable gains over the benchmark schemes.