Effect of element failure and random errors in amplitude and phase on the sidelobe level attainable with a linear array

Abstract

In experiments with linear arrays at sea, one frequently operates with an array which has not only errors in amplitude and phase between channels but also inoperative elements. Previous calculations have shown that in the presence of random errors in amplitude and phase, the sidelobe level of the mean beam pattern is the sum of that of the error-free pattern plus an angle-independent background level due to the random errors. If the time constant of the random process is much larger than the integration time of the beamformer (as is most often the case), then a more relevant statistic is the mean value of the peak sidelobe due to a single realization of the random process. Our numerical calculations show that this value can be substantially larger (approximately 6 dB) than the peak sidelobe of the mean beam pattern. When the error-related sidelobes are predominant, appreciably greater sidelobe suppression cannot be achieved by using a set of amplitude weights which yield an error-free sidelobe level less than that of the error-related level. Element failure also produces an elevated sidelobe level whose peak value can be estimated and in many cases bounded above by the ratio of the sum of the amplitude weights of the faulty elements to the sum of the amplitude weights of the functioning elements. This ratio is nearly linearly related to the rms amplitude and phase errors in the way in which each affects the peak sidelobe level. This allows one to construct a characteristic curve for the peak sidelobe level in the presence of all these degrading factors, given an array of N elements and a set of amplitude weights. Processing techniques are available which may allow one to regain the sidelobe suppression lost due to inoperative elements. Among such techniques are algorithms for adjusting the amplitude weights, cross-sensor beamforming, subaperture processing and a procedure for estimating the signal at inoperative elements by using those from neighboring elements.