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Background on Array Processing 15
2.2.2 The Minimum Variance Distortionless Response Beamformer
The minimum variance distortionless response (MVDR) [2] beamformer is designed by minimizing the output power of the beamformer while constraining the gain to be one in the direction of interest. This problem can be stated as follows:
min E[ y*y] subject to wHa(θ) = W( θ) = 1.
h
The weights of the MVDR [2] are given by
wMVDR = |
|
Rxx− 1a(θ) |
, |
|
H |
− 1 |
a(θ) |
||
|
a |
(θ)Rxx |
|
|
(2.39)
(2.40)
where a(θ) is the steering vector corresponding to the desired signal and w is the vector of complex weights. This beamformer represents a significant improvement over the conventional beamformer because, for a given DOA, it minimizes the power from unwanted directions.
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