Maximum Likelihood Time Delay Estimation Based on Monte Carlo Importance Sampling in Multipath Environment

Bin Ba,Daming Wang,Jianhui Wang,Weijia Cui

doi:10.1155/2017/4215293

Abstract

In multipath environment, the computation complexity of single snapshot maximum likelihood for time delay estimation is huge. In particular, the computational complexity of grid search method increases exponentially with the increase of dimension. For this reason, this paper presents a maximum likelihood estimation algorithm based on Monte Carlo importance sampling technique. Firstly, the algorithm takes advantage of the channel frequency response in order to build the likelihood function of time delay in multipath environment. The pseudoprobability density function is constructed by using exponential likelihood function. Then, it is crucial to choose the importance function. According to the characteristic of the Vandermonde matrix in likelihood function, the product of the conjugate transpose Vandermonde matrix and itself is approximated by the product of a constant and an identity matrix. The pseudoprobability density function can be decomposed into product of many probability density functions of single path time delay. The importance function is constructed. Finally, according to probability density function of multipath time delay decomposed by importance function, the time delay of the multipath is sampled by Monte Carlo method. The time delay is estimated via calculating weighted mean of sample. Simulation results show that the performance of proposed algorithm approaches the Cramér-Rao bound with reduced complexity.

Highlights

The time delay estimation problem has always been a hot topic in wireless communications and is widely applied in radar [1], sonar [2], wireless communication system [3], and other fields
The effective bandwidth becomes narrow, which will lead to the result that mean square error (MSE) of the time delay estimation cannot be close to the Cramer-Rao bound (CRB)
According to (4) and noise related assumptions, the likelihood function of a single snapshot for time delay estimation can be expressed as p

Summary

Introduction

The time delay estimation problem has always been a hot topic in wireless communications and is widely applied in radar [1], sonar [2], wireless communication system [3], and other fields. The iterative algorithm will converge to local maxima of the likelihood function. The iterative algorithm converges to the global maxima at the cost of high computational complexity. For this reason, literature [9] adopted Monte Carlo (MC) importance sampling to determine the ML estimation of time delay under the condition of no data assistance. Literature [9] adopted Monte Carlo (MC) importance sampling to determine the ML estimation of time delay under the condition of no data assistance This algorithm does not need iterative calculation, but it can only be applied to the single path scenario. The symbols and the operators used in the paper are as follows: [⋅]Τ denotes a transpose; [⋅]∗ represents a conjugated matrix; [⋅]H represents a conjugate transpose; E[⋅] means an expectation

Signal Model

Time Delay Estimation Algorithm Based on Importance Sampling

Cramér-Rao Bound

Simulation Result and Performance Analysis

Conclusions