In the ocean environment, where multipath propagation of sound is common, the acoustic signals incident on a passive sonar array are often coherent. Cox has demonstrated that the capability of minimum energy adaptive beamforming to resolve the source bearings of incoherent signals is superior to that of classical beamforming. Seligson observed that when the signal wavefronts deviate from their assumed shape, the adaptive beamformer can be inferior to the classical beamformer in this regard. We study the effect of coherent signals on the capability of classical, adaptive, and linear predictive array processing algorithms to resolve source bearings. For a linear array of equally spaced sensors, we demonstrate the superior resolution capability of the linear predictive algorithm, and the significant effect of signal coherence on all three processing algorithms. We demonstrate the value of utilizing prediction elements in the center of the array to resolve closely-spaced signal bearings. Finally, we investigate the sensitivity of the processing algorithms to imperfections introduced into the correlation matrix by finite averaging, and establish the trade-off that exists between this sensitivity and the capability to resolve closely-spaced signal bearings.