Realistic simulations with spatially coherent noise have been run in order to compare the performance of adaptive beamforming (ABF), inverse beamforming (IBF), and conventional beamforming (CBF) for the case of finite-averaging times, where the actual spatial coherence of the acoustic field, or covariance matrix, is not known a priori, but must be estimated. These estimation errors cause large errors in the ABF estimate of the directionality of the acoustic field, partly because ABF is a highly nonlinear algorithm. In addition, it is shown that ABF is fundamentally limited in its suppression capability at very low frequency (VLF), based on the sidelobe level of the conventional beampattern in the direction of the noise interferer [G. L. Mohnkern, "Effects of Errors and Limitations on Interference Suppression," NOSC Technical Document 1478, Naval Ocean Systems Center (1989)]. The simulations include a low-level plane wave signal of interest, a stronger noise plane wave interferer, and spatially random background noise. Both IBF and ABF performed significantly better than CBF, and IBF's performance was slightly better than ABF's performance. The performances of IBF and the ABF algorithm, the minimum variance distortionless response (MVDR) [A. H. Nuttall and D. W. Hyde, "Unified Approach to Optimum and Suboptimum Processing for Arrays," USL Report Number 992, Naval Underwater Systems Center, New London, CT (22 April 1969)] were recently compared independently [J. S. D. Solomon, A. J. Knight, and M. V. Greening, "Sonar Array Signal Processing for Sparse Linear Arrays," Defense Science and Technology Organization (DSTO) Technical Report (June 1999)] using measured data, with the result that IBF outperformed MVDR. This result is significant because MVDR requires orders of magnitude more processing power than IBF or CBF.