Analysis of the maximum likelihood channel estimator for OFDM systems in the presence of unknown interference

Azzouz Dermoune,Eric Pierre Simon

doi:10.1186/s13634-017-0504-x

Abstract

This paper is a theoretical analysis of the maximum likelihood (ML) channel estimator for orthogonal frequency-division multiplexing (OFDM) systems in the presence of unknown interference. The following theoretical results are presented. Firstly, the uniqueness of the ML solution for practical applications, i.e., when thermal noise is present, is analytically demonstrated when the number of transmitted OFDM symbols is strictly greater than one. The ML solution is then derived from the iterative conditional ML (CML) algorithm. Secondly, it is shown that the channel estimate can be described as an algebraic function whose inputs are the initial value and the means and variances of the received samples. Thirdly, it is theoretically demonstrated that the channel estimator is not biased. The second and the third results are obtained by employing oblique projection theory. Furthermore, these results are confirmed by numerical results.

Highlights

Narrow band interference (NBI) arises in orthogonal frequency-division multiplexing (OFDM) systems in a number of transmission scenarios, such as Wi-Fi communications [1, 2] or cognitive radio, where different types of wireless services can use the same frequency band
8 Conclusions This article has addressed the problem of maximum likelihood channel estimation for OFDM systems in the presence of unknown interference
It was proved that the solution is without ambiguities as long as the number of transmitted OFDM symbols is strictly greater than one

Summary

Introduction

Narrow band interference (NBI) arises in orthogonal frequency-division multiplexing (OFDM) systems in a number of transmission scenarios, such as Wi-Fi communications [1, 2] or cognitive radio, where different types of wireless services can use the same frequency band. Due to the nature of NBI, neither the number of affected subcarriers nor their location in the spectrum is known This brings about the need to estimate the noise variance for each subcarrier, yielding a vector estimation, denoted σ 2, rather than a scalar. After formulating the maximum likelihood (ML) algorithm for the joint estimation of h, σ 2 , it is shown in [11] that the solution is nonunique when the channel order (denoted by L) is greater than the number of transmitted OFDM symbols (denoted by K), leading to ambiguous channel estimates This is a severe limitation since K ≤ L is a common scenario in practice.

System model

Conditional ML

The mean of the CML estimator

Complexity of the CML algorithm

Simulation results

Conclusions