On parameter estimation in wireless communications, sensor array processing and spectral analysis

by Kristensson, Martin

In this thesis, model based parameter estimation in telecommunications, sensor array processing and spectral analysis is considered. The investigated areas have a wide range of applications, e.g., wireless communications and sensor array signal processing. A common theme is the multi dimensional structure of certain appropriate vector valued models for the investigated topics. Tools originally developed in linear algebra are used extensively to estimate the model parameters. The rst investigated topic, direction estimation using sensor arrays, has been subject to extensive research. Starting with a well known estimator, Iterative Quadratic Maximum Likelihood (IQML), a modi ed and improved algorithm, Modi ed IQML (MIQML), is developed. A statistical analysis of MIQML shows that it is possible to improve its performance. The improvement is accomplished by proper weighting of the MIQML criterion function. The so obtained statistically e cient algorithm (WSF-E) shares many of the appealing properties of the popular subspace based estimators and is also numerically attractive. The attention in the thesis is then turned to the estimation of sinusoidal frequencies in a time series. This is de nitely a well investigated area. Herein, a method which yields optimal parameter estimates within the class of subspace based algorithms is studied. The method was originally proposed by Eriksson et. al., but in their analysis of the estimator several questions were left open. Here, some of the gaps in their analysis are lled in and the subspace based method is also related to the Approximate Maximum Likelihood method (AML) proposed by Stoica et. al.. The last part of the thesis is devoted to so called blind channel estimation in telecommunications. The algorithms considered herein assume that multiple communication channels from the transmitter to the iv receiver are available. This is the case in, for example, wireless communication systems where the base stations are equipped with antenna arrays. A subspace based method is thoroughly investigated and a statistically optimal version of it is proposed. When identifying a communication channel using a blind approach, it is crucial to exploit as much as possible of the structure in the input signal. It is shown that with certain digital communication schemes, some attractive properties of the communication signal can be incorporated in a subspace based estimator. This facilitates the use of e cient second order based algorithms even when multiple channels between the transmitter and receiver are not present. Finally, acovariance matching estimator for channel identication is proposed. Since the covariance matching estimator possesses certain optimality properties, it can be used as a benchmark for blind channel algorithms based only on the second order statistics.