The Detectionperformance Analysis Of Krylov Subspace Multi-channeladaptive Signal Detection Method

The multi-channel signal detection system can identify the space-time characteristics of signal under clutter or interference background. Now it has been widely applied in the field of radar, sonar, medical detection. For classical linear multi-channel signal detection methods, the matched filter has the best detection performance, but it is not applicable in practice due to the unknown disturbance covariance matrix. Besides, Generalized Likelihood Ratio Test(GLRT) and Adaptive Matched Filter(AMF) have great computational cost in detection and great demand in training samples. As a kind of effective iteration method, Krylov subspace methods can be used to solve the weight vectors of the AMF detector, it is called KAMF detector. KAMF detector has the advantages of low computation cost and less training samples demand in the background of strong clutter or strong interference.Firstly, the basic theory and methods of the Krylov subspace are introduced in this paper. The definition of the Krylov subspace is shown by the Cayley-Hamilton theorem, and several common Krylov subspace methods are summarized in this part, such as Arnoldi algorithm, Lanczos algorithm, Conjugate gradient algorithm, generalized minimal residualalgorithm. The principle, adapted conditions, advantages and disadvantages of these algorithms are analyzed. It founds the important theoretical foundation to accomplish the Krylov subspace application in the field of signal processing.Then, the classic theories about signal detection are introduced. A data model based on binary assumption is established, and the performance index of the signal detection, such as the probability of false alarm, the probability of detection and the output signalto interferenceplus noise ratio is given. Moreover, several existing classical methods about signal detection, like the MF detection, GLRT detection, AMF detection and matched filter detection based on conjugate gradient algorithm are introduced mainly; Finally,The different detection performance between each detector are shown by making simulation and theory analysis.On the basis of the above discussion, The following issues are carried out in this paper:Firstly, The detection performance of Krylov subspace adaptive matched filter is studied. The covariance matrix has a low-rank correction structure when the strength of the clutter and interference is far stronger than the noise power. The false-alarm probability of KAMF detector is obtained by the weight vectors first-order approximation of the KAMF detectors. At the same time, KAMF detectors are a series of approximate CFAR detectors are proved with first-order approximation; Besides, the detection probability of KAMF detector is deduced by the properties of Wishart distribution; Finally, The CFAR behavior and the detection probability of KAMF detector are verified by using the computer generated data.Secondly, theoutput SINR statistical properties of Krylovsubspaceadaptivematched filter is discussed in this paper. CGalgorithm can be used to solvethe weight vectors of AMF detectors. The output SINR of KAMF detector can be obtained bythe tridiagonalizing nature ofalgorithmcombined with the CG algorithm. The approximate form of the output SINR is shown when the covariance matrixis a low rankcorrectionmatrix. Further, The approximate PDF of the SINR is deduced by the matrix block and the basic nature of the Wishart distribution. Finally, the numercial analysis has revealed that the approximate PDF is accuracy.The classical linear adaptive detector has a great computational cost due to the solution of matrix inversion. KAMF detector can reduce the computation cost, and has a favorable detection performance. It’s an effective detective method, and is worthy of to be study deeply.