Gaussian Signal Detection With Product Arrays

The paper specifies the probability density function (PDF) for the detection statistic for a product processor of colinear arrays. The product processor’s detection PDF is a scaled product of the detection statistic with modified Bessel functions. Using the PDF, this research compares the product processor’s detection performance against a conventional beamforming (CBF) linear array with an equal number of sensors. For the basic detection case of a single known signal in Gaussian noise with a single Gaussian plane wave interferer, receiver operation characteristics curves and mean discriminating information over a range of interferer power illustrate that the product processor’s performance is inferior to the CBF detector with an equal number of sensors over all possible interferer locations. The detection performance of a product processor matches or outperforms the CBF detector only for high power interferers in specific locations.

[1]  P. P. Vaidyanathan,et al.  Sparse Sensing With Co-Prime Samplers and Arrays , 2011, IEEE Transactions on Signal Processing.

[2]  Pieter G. Cath.  Three methods of nonlinear processing for direction finding , 1958 .

[3]  Kaushallya Adhikari,et al.  Design and Statistical Analysis of Tapered Coprime and Nested Arrays for the Min Processor , 2019, IEEE Access.

[4]  V. G. Welsby.  Multiplicative receiving arrays: the angular resolution of targets in a sonar system with electronic scanning , 1961 .

[5]  John R. Buck,et al.  Gaussian Source Detection and Spatial Spectral Estimation Using a Coprime Sensor Array With the Min Processor , 2016, IEEE Transactions on Signal Processing.

[6]  Kaushallya Adhikari,et al.  Symmetry-Imposed Rectangular Coprime and Nested Arrays for Direction of Arrival Estimation With Multiple Signal Classification , 2019, IEEE Access.

[7]  Joseph Lipka,et al.  A Table of Integrals , 2010 .

[8]  P. P. Vaidyanathan,et al.  Nested Arrays: A Novel Approach to Array Processing With Enhanced Degrees of Freedom , 2010, IEEE Transactions on Signal Processing.

[9]  Bernard D. Steinberg,et al.  Principles of aperture and array system design: Including random and adaptive arrays , 1976 .

[10]  Aarnout Brombacher,et al.  Probability... , 2009, Qual. Reliab. Eng. Int..

[11]  P. P. Vaidyanathan,et al.  Nested Arrays in Two Dimensions, Part I: Geometrical Considerations , 2012, IEEE Transactions on Signal Processing.

[12]  C. R. Ward,et al.  Low sidelobe patterns from thinned arrays using multiplicative processing , 1980 .

[13]  John R. Buck,et al.  Super-resolution DOA estimation using a coprime sensor array with the min processor , 2016, 2016 50th Asilomar Conference on Signals, Systems and Computers.

[14]  G. Kefalas.  An aperture distribution technique for product-array antennas , 1968 .

[15]  Vaibhav Chavali,et al.  Multiplicative and min processing of experimental passive sonar data from thinned arrays. , 2018, The Journal of the Acoustical Society of America.

[16]  John R. Buck,et al.  Gaussian signal detection by coprime sensor arrays , 2015, 2015 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP).

[17]  L. Miller,et al.  Signal detection and bearing estimation by square-law and multiplicative array processors , 1973 .

[18]  John R. Buck,et al.  Spatial Spectral Estimation with Product Processing of a Pair of Colinear Arrays , 2017, IEEE Transactions on Signal Processing.

[19]  Albert H. Nuttall,et al.  Accurate Efficient Evaluation of Cumulative or Exceedance Probability Distributions Directly from Characteristic Functions , 1983 .

[20]  John R. Buck,et al.  Detecting Gaussian signals in the presence of interferers using the coprime sensor arrays with the min processor , 2015, 2015 49th Asilomar Conference on Signals, Systems and Computers.

[21]  A. H. Nuttall.  Numerical evaluation of cumulative probability distribution functions directly from characteristic functions , 1969 .

[22]  D. G. Tucker,et al.  Multiplicative receiving arrays , 1959 .

[23]  Kaushallya Adhikari,et al.  Sampling with semi-coprime arrays , 2018, 1806.08419.

[24]  C. Clay,et al.  Theory of Time‐Averaged‐Product Arrays , 1957 .

[25]  Robert N. McDonough,et al.  Detection of signals in noise , 1971 .

[26]  L. Scharf,et al.  Statistical Signal Processing of Complex-Valued Data: The Theory of Improper and Noncircular Signals , 2010 .

[27]  D. C. Fakley.  Comparison between the Performances of a Time‐Averaged Product Array and an Intraclass Correlator , 1959 .

[28]  Kathleen E. Wage,et al.  When Two Wrongs Make a Right : Combining Aliased Arrays to Find Sound Sources Sparse array processing enables detection and localization of acoustic sources with fewer sensors than a more expensive uniform array , 2018 .

[29]  D. G. Tucker.  Signal/noise performance of multiplier (or correlation) and addition (or integrating) types of detector , 1955 .

[30]  Leonard E. Miller,et al.  The probability density function for the output of an analog cross-correlator with correlated bandpass inputs , 1974, IEEE Trans. Inf. Theory.

[31]  John R. Buck,et al.  Extending coprime sensor arrays to achieve the peak side lobe height of a full uniform linear array , 2014, EURASIP J. Adv. Signal Process..

[32]  P. P. Vaidyanathan,et al.  Theory of Sparse Coprime Sensing in Multiple Dimensions , 2011, IEEE Transactions on Signal Processing.

[33]  S. Mitra,et al.  General polynomial factorization-based design of sparse periodic linear arrays , 2010, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control.

[34]  D. G. Tucker.  Multiplicative arrays in radio-astronomy and sonar systems , 1963 .

[35]  M. Simon.  Probability distributions involving Gaussian random variables : a handbook for engineers and scientists , 2002 .

[36]  James J. Faran,et al.  CORRELATORS FOR SIGNAL RECEPTION , 1952 .

[37]  Thomas M. Cover,et al.  Elements of Information Theory , 2005 .

[38]  Yimin Zhang,et al.  Generalized Coprime Array Configurations for Direction-of-Arrival Estimation , 2015, IEEE Transactions on Signal Processing.