Research On Algorithms Of Precise Directing Finding And Broadband Beamforming With Systematic Errors

In satellite, signal to interface plus noise ratio (SINR) can be improvedwith the beamformer aiming at a specific direction which the signal comesfrom. Because a broadband signal received by the array has phase differencedependent on frequency, the best performance can not be obtained based onusing a complex weighted method. Meanwhile, in array signal processing,there are systematic array errors resulted from amplitude and phaseuncertainties, mutual coupling, and sensor position, so the actual arrayresponse is different from the ideal one. In this paper, algorithms of precisedirecting finding and robust broadband beamforming are mainly researched.The direction of arrival (DOA) of a broadband signal is independent ofits frequency, so a super resolution direction finding algorithm adapted to thenarrowband signal can be used to a broadband one, such as multiple signalclassification (MUSIC). A joint estimation algorithm is presented with fewercalibration signal sources to overcome the systemic errors of array model,which transforms the estimation of systematic error matrix into the one ofsystematic error coefficients. Moreover, least squares algorithm is applied tojoint estimations of amplitude, phase and mutual coupling error coefficients,and then the MUSIC algorithm is utilized to measure the DOA with theestimated error matrix. As to the broadband beamformer, a modified robustalgorithm is also designed based on Frost structure in this paper, which iscomposed of delay filter and weighting filter. The fractional delay filter isused in the part of delay filter so that the desired signal vectors are effectivelycoherent in order to get the maximum energy of the desired signal. Withregard to the weighting filter, the signal is extracted within the range of DOAerror in order to decrease the effect of the systematic errors; likewise theweighting values are obtained with minimum energy criterion. The constraintof DOA error is added to make the response of the desired signal ripple, so more degrees of freedom can be used to suppress interference and noise tooptimize the weighting value.The detailed mathematical derivation and simulation for the proposedalgorithms are given in the paper. As an universal example, a10elementslinear array is discussed with coupling effect, and the uncertainties foramplitude and phase are also taken into account, which are±2dB and±20degrees, respectively. The accuracy of the proposed directing findingalgorithm with only three calibration sources drop about0.05degreescompared to the ideal array. Furthermore, the proposed broadbandbeamformer algorithm is more robust than the worst-case and other typicalalgorithms, which improves SINR1~3dB relative to the worst-case in thecondition of4degrees of DOA error, and improves about1~2dB relative tothe same one with amplitude uncertainties±2dB and phase uncertainties±20degrees.