Statistical analysis of the finite sample forward-backward MVDR beamformer

Lei Zhang; Wei Liu; Lei Yu

doi:10.1109/SSP.2011.5967721

Statistical analysis of the finite sample forward-backward MVDR beamformer

Lei Zhang^*
, Wei Liu
, Lei Yu

^*Corresponding author for this work

University of Sheffield

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

2 Scopus citations

Abstract

A statistical analysis is provided for the sample co-variance matrix of the forward-backward (FB) minimum variance distortionless response (MVDR) beamformer. Unlike the forward-only case, its covariance matrix does not follow the complex-valued Wishart distribution. However, we can prove that after a proposed unitary transformation, the new covariance matrix has a real-valued Wishart distribution. Based on this result, a close-form expression of the output SINR (signal-to-interference-plus-noise ratio) for the finite sample FB MVDR beamformer is then derived. Our analysis shows that the error of the output SINR with FB precessing is reduced approximately by half compared with the case without it, as also verified by simulations.

Original language	English
Title of host publication	2011 IEEE Statistical Signal Processing Workshop, SSP 2011
Pages	421-424
Number of pages	4
DOIs	https://doi.org/10.1109/SSP.2011.5967721
State	Published - 2011
Externally published	Yes
Event	2011 IEEE Statistical Signal Processing Workshop, SSP 2011 - Nice, France Duration: 28 Jun 2011 → 30 Jun 2011

Publication series

Name	IEEE Workshop on Statistical Signal Processing Proceedings

Conference

Conference	2011 IEEE Statistical Signal Processing Workshop, SSP 2011
Country/Territory	France
City	Nice
Period	28/06/11 → 30/06/11

Keywords

MVDR beamformer
Wishart distribution
finite sample
forward backward

Access to Document

10.1109/SSP.2011.5967721

Cite this

@inproceedings{7b5c9accefb348f08be89f7b6764d415,

title = "Statistical analysis of the finite sample forward-backward MVDR beamformer",

abstract = "A statistical analysis is provided for the sample co-variance matrix of the forward-backward (FB) minimum variance distortionless response (MVDR) beamformer. Unlike the forward-only case, its covariance matrix does not follow the complex-valued Wishart distribution. However, we can prove that after a proposed unitary transformation, the new covariance matrix has a real-valued Wishart distribution. Based on this result, a close-form expression of the output SINR (signal-to-interference-plus-noise ratio) for the finite sample FB MVDR beamformer is then derived. Our analysis shows that the error of the output SINR with FB precessing is reduced approximately by half compared with the case without it, as also verified by simulations.",

keywords = "MVDR beamformer, Wishart distribution, finite sample, forward backward",

author = "Lei Zhang and Wei Liu and Lei Yu",

year = "2011",

doi = "10.1109/SSP.2011.5967721",

language = "英语",

isbn = "9781457705700",

series = "IEEE Workshop on Statistical Signal Processing Proceedings",

pages = "421--424",

booktitle = "2011 IEEE Statistical Signal Processing Workshop, SSP 2011",

note = "2011 IEEE Statistical Signal Processing Workshop, SSP 2011 ; Conference date: 28-06-2011 Through 30-06-2011",

}

Zhang, L, Liu, W & Yu, L 2011, Statistical analysis of the finite sample forward-backward MVDR beamformer. in 2011 IEEE Statistical Signal Processing Workshop, SSP 2011., 5967721, IEEE Workshop on Statistical Signal Processing Proceedings, pp. 421-424, 2011 IEEE Statistical Signal Processing Workshop, SSP 2011, Nice, France, 28/06/11. https://doi.org/10.1109/SSP.2011.5967721

TY - GEN

T1 - Statistical analysis of the finite sample forward-backward MVDR beamformer

AU - Zhang, Lei

AU - Liu, Wei

AU - Yu, Lei

PY - 2011

Y1 - 2011

N2 - A statistical analysis is provided for the sample co-variance matrix of the forward-backward (FB) minimum variance distortionless response (MVDR) beamformer. Unlike the forward-only case, its covariance matrix does not follow the complex-valued Wishart distribution. However, we can prove that after a proposed unitary transformation, the new covariance matrix has a real-valued Wishart distribution. Based on this result, a close-form expression of the output SINR (signal-to-interference-plus-noise ratio) for the finite sample FB MVDR beamformer is then derived. Our analysis shows that the error of the output SINR with FB precessing is reduced approximately by half compared with the case without it, as also verified by simulations.

AB - A statistical analysis is provided for the sample co-variance matrix of the forward-backward (FB) minimum variance distortionless response (MVDR) beamformer. Unlike the forward-only case, its covariance matrix does not follow the complex-valued Wishart distribution. However, we can prove that after a proposed unitary transformation, the new covariance matrix has a real-valued Wishart distribution. Based on this result, a close-form expression of the output SINR (signal-to-interference-plus-noise ratio) for the finite sample FB MVDR beamformer is then derived. Our analysis shows that the error of the output SINR with FB precessing is reduced approximately by half compared with the case without it, as also verified by simulations.

KW - MVDR beamformer

KW - Wishart distribution

KW - finite sample

KW - forward backward

UR - https://www.scopus.com/pages/publications/80052190235

U2 - 10.1109/SSP.2011.5967721

DO - 10.1109/SSP.2011.5967721

M3 - 会议稿件

AN - SCOPUS:80052190235

SN - 9781457705700

T3 - IEEE Workshop on Statistical Signal Processing Proceedings

SP - 421

EP - 424

BT - 2011 IEEE Statistical Signal Processing Workshop, SSP 2011

T2 - 2011 IEEE Statistical Signal Processing Workshop, SSP 2011

Y2 - 28 June 2011 through 30 June 2011

ER -

Statistical analysis of the finite sample forward-backward MVDR beamformer

Abstract

Publication series

Conference

Keywords

Access to Document

Other files and links

Fingerprint

Cite this