#### Date of Award

9-2003

#### Degree Type

Thesis

#### Degree Name

Doctor of Philosophy (PhD)

#### Department

Electrical and Computer Engineering

#### Supervisor

Dr. James P. Reilly

#### Co-Supervisor

Dr. Thia Kirubarajan

#### Abstract

This thesis focuses on joint model order detection and estimation of the parameters of interest, with applications to narrowband and wideband array signal processing in both off-line and on-line contexts. A novel data model that is capable of handling both narrowband and wideband cases with the use of an interpolation function and signal samples is proposed. In the off-line mode, Markov Chain Monte Carlo methods are applied to obtain a numerical approximation of the joint posterior distribution of the parameters under the condition that they have stationary distribution functions. On the other hand, if the distribution functions are nonstationary, the on-line approach is used. That approach employs a sequential implementation of Monte Carlo methods, applied to probabilistic dynamic systems. Four inter-related problems were addressed in the course of this thesis. 1. A new data structure based on interpolation functions and signal samples to approximate wideband signals was developed. This data model, after appropriate transformation, has similar features found in the conventional narrowband data model. Furthermore, as the novel data model is developed for the wideband scenario, it can also address the narrowband scenario without change of structure or parameters. This novel data model is the basis on which the MCMC and the SMC approaches solve the array signal processing problems developed in the subsequent chapters. 2. The first algorithm presents an advanced approach using sequential MC methods to beamforming for narrowband signals in white noise with unknown variance. Traditionally, beamforming techniques assume that the number of sources is given and the signal of interest (or target) is stationary within an observation period. However, in reality these two assumptions are commonly violated. The former assumption can be dealt with by jointly estimating the number of sources, whereas the latter severely limits the usefulness of conventional beamforming techniques when the target is indeed moving. In the case where the sources are moving, tracking the incident angles of the sources are required, and the accuracy of such tracking significantly affects the performance of signal separation and recovery, which is the objective of beamforming. The proposed method is capable of recursively estimating the time-varying number of sources as well as incident angles of the sources as new data arrive such that the signal amplitudes can be separated and restored in an on-line fashion. 3. The second algorithm presents an application of MCMC methods for the joint detection and estimation problem for the wideband scenario in white noise with unknown variance. In general, compared to the narrowband scenario, it is more difficult and cumbersome to solve this array signal processing problem in the wideband context. Conventional approaches tend to solve this problem in the frequency domain, and as such require a considerable amount of data to sustain accuracy, which imposes a large computational burden for these approaches. Furthermore, these approaches employ separate algorithms like AIC and MDL to estimate the number of sources. In contrast, the proposed method utilizes the reversible jump MCMC technique that simultaneously detects the number of sources and estimates the parameter of interest within the same algorithm. The proposed method is applied to the novel data model mentioned earlier and solves the problem in the time domain, which significantly reduces the requirement for a large number of data samples. 4. The final algorithm is an extension of the off-line approach to wideband array signal processing problem using sequential MC methods. Most conventional array signal processing approaches are developed under the assumption that the sources are stationary in direction of arrival. If this assumption is invalid, the solutions from these approaches become suboptimal and their performance is significantly degraded. When sources are nonstationary, tracking the motions of the sources is needed, but in wideband scenarios the same problem becomes more difficult and cumbersome than in narrowband scenario because the methods for wideband scenarios usually require a considerable amount of data for processing. The proposed algorithm focuses on the sequential implementation of particle filters for probabilistic dynamic systems. This algorithm is applied to the modified novel data structure mentioned earlier in white noise with unknown variance for recursive estimation of the motions of the sources as new data arrive. A systematic statistical testing procedure is used to keep track of the number of sources.

#### Recommended Citation

Ng, William, "Advances in Wideband Array Signal Processing Using Numerical Bayesian Methods" (2003). *Open Access Dissertations and Theses.* Paper 1263.

http://digitalcommons.mcmaster.ca/opendissertations/1263