Beamforming and Array Processing
Subject code: SIP 7025
Lecturers
Prof. Doug Gray
University of Adelaide
Mode of delivery
Mixed mode: on-line and short course/weekly lectures.
Assumed knowledge
A knowledge of Linear Systems (discrete and continuous), Linear Algebra (matrices),
Probability Theory, Fourier and Z Transforms and MATLAB.
Aims/Learning Objectives
This subject is both mathematically and experimentally (computer pracs) based.
It's principal aim is to teach students the fundamental mathematical principles
underlying the subject and to enable them to understand and apply these
principles to real data through problem based learning using simulated data.
The subject is specifically structured around these aims.
On successful completion of the course students will
- have sufficient grasp of the principles of conventional,
optimum and adaptive beamforming, to act as a basis for
understanding current research literature on this subject.
- be able to design optimum and adaptive beamformers for
application to noisy multichannel time series data from arrays
of receivers.
- be able to implement algorithms in MATLAB and to
understand and interpret results obtained.
Content
Introductory Material: Concepts, key issues and motivating array examples;
Simple propagating field models.
Deterministic Signals: Conventional beamforming concepts: narrowband
beamforming; Beam patterns: beamwidth, sidelobes and grating lobes, Array shading
real weights, Array factor theorems; Multiple simultaneous beams; Wavevectors
and frequency wavenumber beamforming; Time delay and sum beamforming.
Random Signals: Probability and random processes for arrays; Cross-spectral
matrices.
Frequency Domain Beamforming: Frequency domain Approach single and multiple
beams; Array Gain; Frequency wavenumber; Array shading and null steering.
Optimum Beamforming in Frequency Domain: Optimisation criteria constrained
minimum mean square and Conventional and Optimum Comparisons; Constraints: minbeam
and nulls; Sample Matrix Inverse and statistical considerations.
Adaptive Beamforming in Frequency Domain: Sample Matrix Inverse update,
Gradient descent and optimisation surfaces with constraints; Convergence requirements;
Stochastic Descent Methods: Least Mean Square; Convergence in the mean
and mean square convergence.
Optimum and Adaptive Beamforming in Time Domain: Multichannel tapped
delay line approach; Optimum solution; Adaptive solution with passband constraints.
Assessment
Assessment will generally be 50% assignments (5), 25% examinations, 25% quizes,
however these percentages are indicative only and may be varied at the lecturer's
discretion. Details of the actual assessment used in a given year can be found
in the study guide provided at the start of the semester.
Resources
The lecture
material is presented within a rigorous mathematical framework although the
notational details have been kept to a minimum as much as possible. Students
are expected to be able to master but not remember such proofs. Many of the
assignments and tutorials are focussed on the application of the theory covered
in lectures to data and the course standard of Matlab has been chosen for this.
Students will be provided with a copy of a comprehensive array processing
Matlab toolbox and will find that this toolbox is referred to in many of the
exercises that are linked to the electronic version of the notes. To be able to
run this toolbox Matlab 5.3 or higher wil be needed.
All this material is available on the web or on the course CD. Additional
material will be emailed to students during the course.