Abstract : The theory of optimum arrays became widely known in the underwater acoustics community through the work of Bryn and Mermoz. The relationship of their work to other detection and estimation problems has been discussed. Optimum array processing structures use detailed information about the signal and noise fields. Since this information is not known precisely in advance, one is led naturally to adaptive beamformers which continually adjust their parameters based upon on-line measurements of some kind. Since adaptive processors are continually adjusting, it is natural to question how sensitive performance is to small variations of the signal field, noise field and system parameters from their assumed or estimated values. The question of sensitivities has been examined tin the past in conjunction with 'super-directive' arrays. An attempt will be made to point out the relationship of the results of this paper to those earlier results. The emphasis in this paper is on receiving arrays. In Section II an introduction to the problem is provided using an intuitive approach. The performance measures of array gain and output power are used. Section III presents the principal sensitivity results. The approach is to take partial derivatives of the gain and output signal power with respect to the size of signal, noise and steering perturbations. Section IV discusses the problem of signal suppression which arises in passive adaptive processors when measurements of signal-plus-noise are used when noise only measurements are desired. Interference rejection is also discussed. A number of optimization problems are discussed in Section V.
[1]
P. Schultheiss,et al.
Optimum and Conventional Detection Using a Linear Array
,
1971
.
[2]
R. McDonough.
Degraded Performance of Nonlinear Array Processors in the Presence of Data Modeling Errors
,
1972
.
[3]
P. Schultheiss.
Passive Sonar Detection in the Presence of Interference
,
1968
.
[4]
T. Taylor.
Design of line-source antennas for narrow beamwidth and low side lobes
,
1955
.
[5]
S. Shor.
Adaptive Technique to Discriminate against Coherent Noise in a Narrow‐Band System
,
1966
.
[6]
J. Capon.
High-resolution frequency-wavenumber spectrum analysis
,
1969
.
[7]
D. Cheng,et al.
Optimum spatial processing in a noisy environment for arbitrary antenna arrays subject to random errors
,
1968
.
[8]
V. Anderson.
DICANNE, a Realizable Adaptive Process
,
1969
.
[9]
E. Gilbert,et al.
Optimum design of directive antenna arrays subject to random variations
,
1955
.
[10]
M. Schwartz,et al.
Adaptive Nonlinear Optimization of the Signal‐to‐Noise Ratio of an Array Subject to a Constraint
,
1972
.
[11]
P. Rudnick,et al.
Rejection of a Coherent Arrival at an Array
,
1969
.
[12]
F. Tuteur,et al.
A New Class of Adaptive Array Processors
,
1971
.
[13]
F. Bryn.
Optimum Signal Processing of Three‐Dimensional Arrays Operating on Gaussian Signals and Noise
,
1962
.