Finite sample size effect on minimum variance beamformers:: Optimum diagonal loading factor for large arrays

被引:157
作者
Mestre, X [1 ]
Lagunás, MA [1 ]
机构
[1] Ctr Tecnol Telecommun Catalunya, ES-08034 Barcelona, Spain
关键词
diagonal loading; G-estimation; minimum variance distortionless beamformer (MVDR); random matrix theory; sample matrix inversion algorithm;
D O I
10.1109/TSP.2005.861052
中图分类号
TM [电工技术]; TN [电子技术、通信技术];
学科分类号
0808 ; 0809 ;
摘要
Minimum variance beamformers are usually complemented with diagonal loading techniques in order to provide robustness against several impairments such as imprecise knowledge of the steering vector or finite sample size effects. This paper concentrates on this last application of diagonal loading techniques, i.e., it is assumed that the steering vector is perfectly known and that diagonal loading is used to alleviate the finite sample size impairments. The analysis herein is asymptotic in the sense that it is assumed that both the number of antennas and the number of samples are high but have the same order of magnitude. Borrowing some results of random matrix theory, the authors first derive a deterministic expression that describes the asymptotic signal-to-noise-plus-interference ratio (SINR) at the output of the diagonally loaded beamformer. Then, making use of the statistical theory of large observations (also known as general statistical analysis or G-analysis), the authors derive an estimator of the optimum loading factor that is consistent when both the number of antennas and the sample size increase without bound at the same rate. Because of that, the estimator has an excellent performance even in situations where the quotient between the number of observations is low relative to the number of elements of the array.
引用
收藏
页码:69 / 82
页数:14
相关论文
共 38 条
[1]  
ABRAMOVICH YI, 1981, RADIOTEKH ELEKTRON+, V26, P2083
[2]   Convergence analysis of linearly constrained SMI and LSMI adaptive algorithms [J].
Abramovich, YI .
IEEE 2000 ADAPTIVE SYSTEMS FOR SIGNAL PROCESSING, COMMUNICATIONS, AND CONTROL SYMPOSIUM - PROCEEDINGS, 2000, :255-259
[3]  
Abramovich Yu. I., 1981, Radio Engineering and Electronic Physics, V26, P67
[4]   SAMPLE-SIZE CONSIDERATIONS FOR ADAPTIVE ARRAYS [J].
BOROSON, DM .
IEEE TRANSACTIONS ON AEROSPACE AND ELECTRONIC SYSTEMS, 1980, 16 (04) :446-451
[5]   HIGH-RESOLUTION FREQUENCY-WAVENUMBER SPECTRUM ANALYSIS [J].
CAPON, J .
PROCEEDINGS OF THE IEEE, 1969, 57 (08) :1408-&
[6]   PROBABILITY DISTRIBUTIONS FOR ESTIMATORS OF FREQUENCY WAVENUMBER SPECTRUM [J].
CAPON, J ;
GOODMAN, NR .
PROCEEDINGS OF THE INSTITUTE OF ELECTRICAL AND ELECTRONICS ENGINEERS, 1970, 58 (10) :1785-&
[8]  
Cheremisin O. P., 1982, Radio Engineering and Electronic Physics, V27, P69
[9]  
CHEREMISIN OP, 1985, RADIOTEKH ELEKTRON+, V30, P2369
[10]   ROBUST ADAPTIVE BEAMFORMING [J].
COX, H ;
ZESKIND, RM ;
OWEN, MM .
IEEE TRANSACTIONS ON ACOUSTICS SPEECH AND SIGNAL PROCESSING, 1987, 35 (10) :1365-1376