Fundamentals of Differential Beamforming

This book provides a systematic study of the fundamental theory and methods of beamforming with differential microphone arrays (DMAs), or differential beamforming in short. It begins with a brief overview of differential beamforming and some popularly used DMA beampatterns such as the dipole, cardioid, hypercardioid, and supercardioid, before providing essential background knowledge on orthogonal functions and orthogonal polynomials, which form the basis of differential beamforming.

 From a physical perspective, a DMA of a given order is defined as an array that measures the differential acoustic pressure field of that order; such an array has a beampattern in the form of a polynomial whose degree is equal to the DMA order. Therefore, the fundamental and core problem of differential beamforming boils down to the design of beampatterns with orthogonal polynomials. But certain constraints also have to be considered so that the resulting beamformer does not seriously amplify the sensors’ self noise and the mismatches among sensors.

 Accordingly, the book subsequently revisits several performance criteria, which can be used to evaluate the performance of the derived differential beamformers. Next, differential beamforming is placed in a framework of optimization and linear system solving, and it is shown how different beampatterns can be designed with the help of this optimization framework. The book then presents several approaches to the design of differential beamformers with the maximum DMA order, with the control of the white noise gain, and with the control of both the frequency invariance of the beampattern and the white noise gain. Lastly, it elucidates a joint optimization method that can be used to derive differential beamformers that not only deliver nearly frequency-invariant beampatterns, but are also robust to sensors’ self noise.

Jacob Benesty received a Master’s degree in microwaves from Pierre & Marie Curie University, France, in 1987, and a Ph.D. degree in control and signal processing from Orsay University, France, in April 1991. During his Ph.D. (from Nov. 1989 to Apr. 1991), he worked on adaptive filters and fast algorithms at the Centre National d’Etudes des Telecommunications (CNET), Paris, France. From January 1994 to July 1995, he worked at Telecom Paris University on multichannel adaptive filters and acoustic echo cancellation. From October 1995 to May 2003, he was first a Consultant and then a Member of the Technical Staff at Bell Laboratories, Murray Hill, NJ, USA. In May 2003, he joined the University of Quebec, INRS-EMT, in Montreal, Quebec, Canada, as a Professor. He is also a Visiting Professor at the Technion, Haifa, in Israel, an Adjunct Professor at Aalborg University, in Denmark, and a Guest Professor at Northwestern Polytechnical University, Xi’an, Shaanxi, in China.

Jingdong Chen received the Ph.D. degree in pattern recognition and intelligence control from the Chinese Academy of Sciences in 1998. From 1998 to 1999, he was with ATR Interpreting Telecommunications Research Laboratories, Kyoto, Japan, where he conducted research on speech synthesis, speech analysis, as well as objective measurements for evaluating speech synthesis. He then joined the Griffith University, Brisbane, Australia, where he engaged in research on robust speech recognition and signal processing. From 2000 to 2001, he worked at ATR Spoken Language Translation Research Laboratories on robust speech recognition and speech enhancement. From 2001 to 2009, he was a Member of Technical Staff at Bell Laboratories, Murray Hill, New Jersey, working on acoustic signal processing for telecommunications. He subsequently joined WeVoice Inc. in New Jersey, serving as the Chief Scientist. He is currently a professor at the Northwestern Polytechnical University in Xi’an, China. His research interests include acoustic signal processing, adaptive signal processing, speech enhancement, adaptive noise/echo control, microphone array signal processing, signal separation, and speech communication.

Chao Pan received the Bachelor degree in electronics and information engineering from the Northwestern Polytechnical University (NPU) in 2011. He is currently a Ph.D. student in information and communication engineering at NPU and also a visiting Ph.D. student at INRS-EMT, University of Quebec. His research interests are in speech enhancement, noise reduction, and microphone array signal processing for hands-free speech communications.