The large dynamic range exhibited by the frequency‐wavenumber spectrum of a turbulent boundary layer (TBL) poses a serious problem for estimating the low‐wavenumber region of that spectrum. From the standpoint of sidelobe leakage in beamforming procedures, the convective and sonic regions of the TBL are strong sources of interference which bias the estimate at low wavenumbers. By increasing the number of sensors in the measurement array, the sidelobe‐leakage problem can be minimized. However, this solution is difficult to implement experimentally and to justify theoretically in view of the globally nonhomogeneous nature of the TBL. As an alternative, certain data adaptive procedures can be used which do not have similar problems with sidelobe leakage when the number of sensors is small, but do require that the frequency‐wavenumber spectrum fall within a specified class of spectra. The performance of one such procedure, the maximum likelihood method (MLM), was evaluated under two criteria: spectral fidelity and sensitivity to sampling error. In general, the MLM was superior to the array beamformer in estimating the frequency‐wavenumber spectrum based on simulated observations from a linear array of sensors. [Sponsored by the Office of Naval Research Selected Research Opportunity in Hydroacoustics.]