short course san fran

Short Course on Array Signal Processing for Sonar


Many applications in acoustics entail the remote sensing and analysis of propagating waves.  Sensing systems are usually formed from multiple spatially separated sensors in order to obtain gains against spatially uncorrelated noise or spatially isolated interferences.  A group of sensors is called an array.  Array signal processing describes the combination of signals received at the sensors into beams primarily containing signals coming from specific angular sectors.  This spatial filtering process is called beamforming and is identical to the focusing accomplished by parabolic dishes.  Beamforming is used in a wide variety of applications in underwater acoustics, including active and passive sonar, marine mammal detection and localization, bottom mapping, oil exploration, and acoustic communications. Additionally, there are applications in many other fields such as radar, telecommunications, biomedical imaging, earthquake detection, and even hearing aid technology.

The course will start by introducing the far-field assumption, plane waves, and conventional beamforming (CBF).  CBF is the most common type of beamforming in use and will command more than half the time in the course.  A variety of topics will be covered (see detailed list below), focusing on a line array of equally spaced sensors but also considering other array configurations such as circular or triplet arrays.  Examples will be drawn from both passive and active sonar applications. 

One limitation of CBF is that it does not account for the spatial structure of the signals impinging on the array.  For example, knowing that an interfering signal occludes a particular bearing, the spatial filter may be modified to produce a null in its direction, thereby improving performance in other directions.  This process is called adaptive beamforming (ABF).  It requires estimation of an array covariance matrix, and, as might be expected, is more computationally intensive than CBF.  Techniques for reducing the computational demands and for making the performance robust against estimation errors will be covered.

The course is suitable for graduate students or professionals.  It is recommended that participants brush up on signal processing, linear algebra, and mathematical statistics before the course.  A recommended but not required text for the course is "Detection, Estimation, and Modulation Theory, Part IV, Optimum Array Processing" by Harry L. Van Trees (John Wiley & Sons, 2002).


The objective of this short course is to introduce the participant to a span of topics in array signal processing starting with the ubiquitous conventional beamformer and progressing to the more arcane adaptive beamformers and their statistical analysis.  This will include exposure to the derivation of fundamental results.


Douglas Abraham obtained B.S., M.S., and Ph.D. degrees in Electrical Engineering and an M.S. degree in Statistics from the University of Connecticut.  He has over twenty years of experience in the sonar field, having held positions at U.S. Navy, NATO, and University laboratories.  His research has primarily been in applying detection and estimation theory to active and passive sonar signal processing problems.  He has both undergraduate and graduate teaching experience at the Electrical and Computer Engineering Department of the University of Connecticut.  He has managed basic and applied research programs at the Office of Naval Research and has been active in professional service through technical-committee membership, conference and workshop organization, and as an associate editor of the IEEE Journal of Oceanic Engineering.


Sunday, 1 December 2013, 1:00 p.m. to 5:00 p.m.

Monday, 2 December 2013, 8:30 a.m. to 12:30 p.m.


●    Introduction and historical notes

      o    Propagating waves

      o    The far-field assumption and plane waves

●    Conventional beamforming

      o    The line array and relationships to spectrum analysis

      o    Time- and frequency-domain implementations

      o    Narrowband and broadband beamforming

      o    Relationship to the detection and estimation problem

      o    Beam patterns, beam responses and bearing-time records

      o    Array gain and the sonar equation

      o    Windowing and how it affects the beampattern

      o    The product formula for beampatterns

      o    Other array apertures (circular, cylindrical, triplet, and vector-sensor arrays)

●    Adaptive beamforming

      o    The sidelobe canceller

      o    Minimum variance distortionless response (MVDR) beamforming

      o    Estimation of the array covariance matrix & SNR loss

      o    Robust adaptive beamforming

      o    Reduced-adaptive-dimension beamforming


The full registration fee is $300 USD ($125 USD for students) and covers attendance, instructional materials and coffee breaks.  The number of attendees will be limited so please register early to avoid disappointment.  Only those who have registered by 31 October will be guaranteed receipt of instruction materials.  There will be a $50 USD discount off the full registration fee (discount does not apply to student fee) for registration made prior to 31 October.  Full refunds will be made for cancellations prior to 1 October.  Any cancellations after 31 October will be charged a $25 USD processing fee.  Register online at or use the downloadable registration form.  If you miss the preregistration deadline and are interested in attending the course, please send an email to