# Sum-MSE performance gain of DFT-based channel estimator over frequency-domain LS one in full-duplex OFDM systems with colored interference

## TL;DR

This paper analyzes the performance improvement of DFT-based LS channel estimation over frequency-domain LS in full-duplex OFDM systems with colored interference, providing a closed-form expression and bounds for the sum-MSE gain.

## Contribution

It derives a closed-form expression and bounds for the sum-MSE gain, revealing how interference correlation affects the estimator's performance in full-duplex OFDM systems.

## Key findings

- Sum-MSE gain approaches N/L as interference correlation decreases.
- Maximum gain of N/L occurs with independent interference.
- No gain (1) when interference is fully correlated.

## Abstract

In this paper, we make an investigation on the sum-mean-square-error (sum-MSE) performance gain achieved by DFT-based least-square (LS) channel estimator over frequency-domain LS one in full-duplex OFDM system in the presence of colored interference and noise. The closed-form expression of the sum-MSE performance gain is given. Its simple upper and lower bounds are derived by using inequalities of matrix eigen-values. By simulation and analysis, the upper lower bound is shown to be close to the exact value of MSE gain as the ratio of the number N of total subcarriers to the cyclic prefix length L grows and the correlation factor of colored interference increases. More importantly, we also find that the MSE gain varies from one to N/L as the correlation among colored interferences decreases gradually. According to theoretical analysis, we also find the MSE gain has very simple forms in two extreme scenarios. In the first extreme case that the colored interferences over all subchannels are fully correlated, i.e., their covariance matrix is a matrix of all-ones, the sum-MSE gain reduces to 1. In other words, there is no performance gain. In the second extreme case that the colored-interference covariance matrix is an identity matrix, i.e, they are mutually independent, the achievable sum-MSE performance gain is N/L. A large ratio N/L will achieve a significant sum-MSE gain.