The effects of a signal coherence which decreases exponentially with sensor separation are examined for a number of line array processors. For the conventional beamformer the limiting gain as the array is made infinitely long is simply (1 + ρ)/(l − ρ), where ρ is the signal coherence between adjacent sensors. The gain of the optimum processor is presented. A simple suboptimum processor which incoherently combines the outputs of a number of subarrays is found to provide near optimum performance. The performance of the split‐beam multiplicative processor is shown to degrade rapidly as signal coherence decreases. [This work was done at the University of California, San Diego, Marine Physical Laboratory of the Scripps Institution of Oceanography, San Diego, California 92132.]