Method for optimal microphone array design under uniform acoustic coupling constraints
A method of designing a beamformer, and a beamformer made in accordance with this method, characterized by a uniform speakerphone response condition, resulting in optimal beamforming directivity under a uniform coupling constraint. According to the present invention, a finite number of individual beamformers are constrained to have the same response to a loudspeaker signal (as well as the same gain in their respective look directions) without specifying the exact value of their response to this signal. This results in beamformer weights that are optimal in the minimum variance sense and satisfy the uniform coupling constraint. The minimum variance condition combines all beamformer weights at once, and the uniform coupling constraint is expressed as a finite number of linear constraints on the weights of the individual beamformers, without specifying an arbitrary, a priori value for the actual value of the uniform response.
1. In an audio conferencing system having a loudspeaker for outputting and a plurality of M microphones for inputting their respective signals, a combined beamformer comprising a plurality of J individual beamformers for modifying the gain of each of said signals by respective beamformer weight vectors of length M, Wj(v),where j=1 to J, to simultaneously create respective beams each pointing in a different look direction, said combined beamformer having a common response to said loudspeaker signal without having to specify an exact value of said (a) response and being characterized by a minimum variance condition that combines all of said beamformer weight vectors simultaneously as
Min
W
(
W
H
(
v
)
R
(
v
)
W
(
v
)
)
subject to the constraint W H (v)C(v)=G(v)
where W j (v) is the vector of length M×J formed of concatenated vectors Wj(v), W H (v) denotes the Hermitian transpose of W(v), R(v) is a concatenated noise correlation matrix of size M×J by M×J, C(v) is a uniform coupling constraint matrix expressed as a number involving more than one beamformer of linear constraints on the components of the concatenated weights vector, W(v) and G(v) is a constraint response vector, a unique solution to said minimum variance condition being given by
W ( v )= R −1 ( v ) C ( v )[ C H ( v ) R −1 ( v ) C ( v )] −1 G H ( v )
such that individual ones of said beamformers satisfy said uniform coupling constraint and is expressed as a linear function of the combined weight vectors of said beamformers and are optimal in terms of said minimum variance condition.
2. A method of making a combined beamformer for use in an audio conferencing system having a loudspeaker for outputting and a plurality of M microphones for inputting their respective signals, said combined beamformer having a common response to said loudspeaker signal without having to specify an exact value of said (a) response, said method comprising providing a plurality of J individual beamformers for modifying the gain of each of said signals by respective beamformer weight vectors of length M, Wj(v), where j=1 to J, to simultaneously create respective beams each pointing in a different look direction and having the same (a similar) gain, subjecting said combined beamformer to a minimum variance condition that combines all of said beamformer weight vectors simultaneously as
Min
W
(
W
H
(
v
)
R
(
v
)
W
(
v
)
)
subject to the constraint W H (v)C(v)=G(v)
where W(v) is the vector of length M×J formed of concatenated vectors Wj(v), W H (v) denotes the Hermitian transpose of W(v), R(v) is a concatenated noise correlation matrix of size M×J by M×J, C(v) is a uniform coupling constraint matrix expressed as a number involving more than one beamformer of linear constraints on the components of the concatenated weights vector W(v) and G(v) is a constraint response vector, and providing a unique solution to said minimum variance condition, said solution being
W ( v )= R −1 ( v )C( v )[C H ( v ) R −1 ( v ) C ( v )] −1 G H ( v )
such that individual ones of said beamformers satisfy said uniform coupling constraint and is expressed as a linear function of the combined weight vectors of said beamformers and are optimal in terms of said minimum variance condition.