The statistical properties of estimators for plane‐wave parameters are discussed. A thick large‐aperture array is assumed to be detecting a signal emanating from an unknown continuous wave source. The signal is assumed to be a plane wave embedded in a spatially incoherent Gaussian noise field. Maximum‐likelihood estimators of velocities and directions are derived and their root‐mean‐square errors are obtained, for single and multiple arrivals for linear arrays and square arrays with a large number of sensors. The rms errors of the propagation parameter estimators are proportional toK−1for a square‐lattice array ofKsensors and toK−3/2for a linear array ofKsensors. The rms error of the waveform estimator, however, is proportional toK−1/2in each case. Thus, for the propagation parameters, the figure of merit for rms signal‐to‐noise gain of the array isKfor a square array ofKsensors andK3/2for a linear array ofKsensors.