Array Processing

Kronecker Product Beamforming

  • Jacob Benesty
  • Israel Cohen
  • Jingdong Chen

Part of the Springer Topics in Signal Processing book series (STSP, volume 18)

Table of contents

  1. Front Matter
    Pages i-xi
  2. Jacob Benesty, Israel Cohen, Jingdong Chen
    Pages 1-7
  3. Jacob Benesty, Israel Cohen, Jingdong Chen
    Pages 9-17
  4. Jacob Benesty, Israel Cohen, Jingdong Chen
    Pages 19-81
  5. Jacob Benesty, Israel Cohen, Jingdong Chen
    Pages 83-112
  6. Jacob Benesty, Israel Cohen, Jingdong Chen
    Pages 113-145
  7. Jacob Benesty, Israel Cohen, Jingdong Chen
    Pages 147-167
  8. Jacob Benesty, Israel Cohen, Jingdong Chen
    Pages 169-186
  9. Back Matter
    Pages 187-189

About this book


The focus of this book is on array processing and beamforming with Kronecker products. It considers a large family of sensor arrays that allow the steering vector to be decomposed as a Kronecker product of two steering vectors of smaller virtual arrays. Instead of directly designing a global beamformer for the original array, once the steering vector has been decomposed, smaller virtual beamformers are designed and separately optimized for each virtual array. This means the matrices that need to be inverted are smaller, which increases the robustness of the beamformers, and reduces the size of the observations.

The book explains how to perform beamforming with Kronecker product filters using an unconventional approach. It shows how the Kronecker product formulation can be used to derive fixed, adaptive, and differential beamformers with remarkable flexibility. Furthermore, it demonstrates how fixed and adaptive beamformers can be intelligently combined, optimally exploiting the advantages of both. The problem of spatiotemporal signal enhancement is also addressed, and readers will learn how to perform Kronecker product filtering in this context.


Microphone Arrays Uniform Linear Arrays Nonuniform Linear Arrays Rectangular Arrays Fixed Beamforming Adaptive Beamforming Differential Beamforming Kronecker Product Filter

Authors and affiliations

  • Jacob Benesty
    • 1
  • Israel Cohen
    • 2
  • Jingdong Chen
    • 3
  1. 1.INRS-EMT, Suite 6900University of QuebecMontrealCanada
  2. 2.Department of Electrical EngineeringTechnion—Israel Institute of TechnologyHaifaIsrael
  3. 3.School of Marine Science and TechnologyNorthwestern Polytechnical UniversityXi'anChina

Bibliographic information

  • DOI
  • Copyright Information Springer Nature Switzerland AG 2019
  • Publisher Name Springer, Cham
  • eBook Packages Engineering Engineering (R0)
  • Print ISBN 978-3-030-15599-5
  • Online ISBN 978-3-030-15600-8
  • Series Print ISSN 1866-2609
  • Series Online ISSN 1866-2617
  • Buy this book on publisher's site