The performance of a linear array of 2Mtransducers in determining the bearing of a plane‐wave random signal in a background of isotropic random noise is considered. The processing the array is arranged by means of wide‐band phase‐shifting filters and infinite clippers to produce a null response when the array is “on target.” Expressions for the angular uncertainty of the null response are derived, and the filter parameters that minimize this bearing uncertainty are determined. An expression for the minimum bearing uncertainty is also derived for arbitrary signal and noise spectra and also for a case employing well‐known models for signal and noise spectra. The bearing uncertainty of a system with simple filter characteristics determined and compared with the minimum bearing uncertainty.