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The five noted methods, namely, complex acoustic intensity measurement (CAIM) method, weighted complex acoustic intensity measurement (WCAIM) method, conventional beamforming (CBF) method, minimum variance distortionless response (MVDR) beamforming method, and multiple signal characteristic (MUSIC) method, are investigated in this paper.
The above equation is known as MVDR. The optimal solution of (5) can be easily found, [w.sub.opt] = [beta][[??].sup.-1][a.sub.s], where [beta] = ([a.sup.H.sub.s][[??].sup.-1][a.sub.s]) 1 is a constant and it has no influence on the SINR.
One of the beamforming algorithm used in smart antenna is MVDR beamforming, which can calculate the weight vector to determine the desired signal from the interference.
Bayesian beamformer  is the sum of the MVDR beamformers (Equation (6)) along the interval of uncertainty weighted by the a posteriori pdf.
Yang and K.K.Chan, A neural network approach to MVDR beamforming problem, IEEE Trans.
The beamforming algorithms are classified mainly into three types: (1) estimating the Angle Of Arrival (AOA) algorithms like MUSIC and ESPRIT [9,11-13], (2) non-blind algorithms where the transmitter and the receiver agree to certain code to detect the location of the transmitter to steer the main beam like Maximum Likelihood (ML), and Minimum Variance Distortionless Response (MVDR) , (3) blind beamforming algorithm.
In section 3, the problem formulation using the MVDR method is outlined.
Adaptive beamforming and high resolution direction-of-arrival (DOA) estimation algorithms have received much attention in the past a few decades, and among which, the minimum variance distortionless response (MVDR)  and multiple signal classification (MUSIC) algorithm  are the most popular two techniques.
MLE Maximum Likelihood Estimator IMP Iterative Multiple Parameter EM Estimate Maximize AP Alternate Projection MAP Maximum a posteriori ASPECT Adaptive Signal Parameter Estimation & Classification Technique MODE Method of DOA Estimate AAR Adaptive Angular Response TNA Thermal Noise Algorithm MVDR Minimum Variance Distortionless Response MEM Maximum Entropy Method MUSIC Multiple Signal Classification NSP MUSIC Noise Space Projection MUSIC Root MUSIC Polynomial Rooting MUSIC Cyclic MUSIC Cyclostationary MUSIC WSF Weighted Subspace Fitting MNM Minimum Norm Method ESPRIT Estimation of Signal Parameters via Rotational Invariance TLS-ESPRIT Total Least Squares ESPRIT PRO-ESPRIT Procrustes ESPRIT DPT Discrete Polynomial Transform CM Constant Modulus
One of the most commonly used adaptive beamformers is the minimum variance distortionless response (MVDR) algorithm.
MVDR (Minimum Variance Distortionless Response) is a typical beamforming (beamformer) algorithm, which was proposed by Capon in 1967 .
The beam-forming algorithms such as MVDR  and MEM 4] obtain a nonparametric spatial spectrum by optimizing the filter weights.
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