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A Generalization of Spherically Invariant Random Vectors (SIRVs) with an Application to Reverberation Reduction in a Correlation Sonar
DOI link for A Generalization of Spherically Invariant Random Vectors (SIRVs) with an Application to Reverberation Reduction in a Correlation Sonar
A Generalization of Spherically Invariant Random Vectors (SIRVs) with an Application to Reverberation Reduction in a Correlation Sonar book
A Generalization of Spherically Invariant Random Vectors (SIRVs) with an Application to Reverberation Reduction in a Correlation Sonar
DOI link for A Generalization of Spherically Invariant Random Vectors (SIRVs) with an Application to Reverberation Reduction in a Correlation Sonar
A Generalization of Spherically Invariant Random Vectors (SIRVs) with an Application to Reverberation Reduction in a Correlation Sonar book
ABSTRACT
Generalized Models ............................................................... 807
14.3. Generalized SIRV Properties............................................................... 810
14.3.1. Linear Transformation ........................................................... 810
14.3.2. The Generalized SIRV “Bootstrap” Theorem ...................... 811
14.3.3. The Monotonicity of h
ða
;…;a
Þ ................................. 812
14.3.4. Spherical Coordinates ............................................................ 812
14.3.5. The Generalized SIRV Bessel Function
Representation........................................................................ 817
14.3.6. Minimum Mean Square Error Estimation............................. 822
14.3.7. The Generalized SIRV Laplace
Transform Representation...................................................... 824
14.4. The Generalized SIRV Density Function ........................................... 826
14.4.1. Direct Evaluation of h
(a
)................................................. 827
14.4.1.1. Case 1 ................................................................... 828
14.4.1.2. Case 2 ................................................................... 841
14.4.2.1. Case 3 ................................................................... 846
14.4.2.2. Case 4 ................................................................... 854
14.5. Generalized SIRV Generation ............................................................. 856
14.5.1. Multivariate Rejection Theorem............................................ 857
14.5.2. Application of the Rejection Theorem.................................. 860
14.5.3. Examples of Random Variable Generation .......................... 861
14.5.3.1. Example 1 ............................................................. 861
14.5.3.2. Example 2 ............................................................. 863
14.6. Generalized SIRV Density Approximation......................................... 863
14.6.1. Univariate Density Approximation ....................................... 865
14.6.2. 2-D Density Approximation .................................................. 867
14.6.3. Multivariate Density Approximation .................................... 868
14.6.4. Real Data Analysis ................................................................ 869
14.7. Correlation Sonar Fundamentals ......................................................... 876
14.7.1. Correlation Sonar Basic Operation........................................ 876
14.7.2. Correlation Sonar Reverberation Model ............................... 880
14.7.2.1. Monostatic and Bistatic Reverberation ................ 881
14.7.2.2. Reverberation as Heard on a Moving
Correlation Sonar Platform .................................. 883
14.7.3. A Sub-Optimal Correlation Sonar Receiver ......................... 890
14.7.4. Performance in Previous Pulse Interference ......................... 895
14.8. M-ary Detection ................................................................................... 896
14.8.1. Optimum M-ary Detection..................................................... 897
14.8.2. Sub-Optimum M-ary Detection ............................................. 901
14.8.3. Generalized SIRV M-ary Detection ...................................... 904
14.9. Conclusion ........................................................................................... 909
14.9.1. Suggestions for Future Research ........................................... 910
An active sonar system operates by transmitting an acoustic pulse into the water
and monitoring a target echo. Besides receiving an echo from a desired target,
the system may also receive an echo from the ocean floor or the surface as
shown in Figure 14.1. In sonar terminology, any nontarget echo arising
explicitly from bottom or surface, is referred to as boundary reverberation.
Typically, boundary reverberation power greatly exceeds that of a target. If it
arrives at the same time as the target echo, this reverberation interferes with
detection of the desired signal.
