Interference rejection by amplitude shading of sonar transducer arrays

Abstract

It is demonstrated that strong coherent interference incident from arbitrary directions can be effectively rejected by amplitude shading or real weighting of channel signals. For a given spatial distribution of interference field, the total interference power received by a transducer array is formulated and superimposed on the power received from an isotropic noise field. The total noise plus interference power is then minimized with respect to the shading coefficients and subject to the constraint that the mainbeam peak be maintained at a fixed level. As an illustrative example, we have calculated the optimum amplitude shading coefficients for a linear array with logarithmically spaced transducer elements to reject an interference field uniformly distributed over a 15°×36° solid angle with an intensity up to 70 dB above the noise field. In each case, the directivity pattern of the array adjusts itself by bunching several null points in the direction of interference incidence to achieve a nearly complete rejection. The merit of a narrow-band processor based on the principle of optimum amplitude shading is then examined by comparing its performance with those of a conventional processor and an optimum processor with both amplitude and phase adaptation. The optimum amplitude shading processor is clearly superior to the ocnventional processor under strong interference, but much simpler to implement than the optimum processor with amplitude and phase adjustment. Furthermore, the very little additional SNR0 due to complex weighting probably cannot be achieved in practice because of the extreme super-gain condition which often results.