In a shallow water environment, wavenumbers can be estimated by computing time and spatial Fourier transforms of horizontal array measurements. The frequency-wavenumber representation allows wide band estimation but a sufficient number of hydrophones are required for accurate wavenumber resolution. This paper presents the application of an autoregressive (AR) model to compute the high resolution wavenumber spectrum. The smallest number of required sensors for the AR model is found using a stabilization diagram. The method is validated on simulated and experimental data. The wavenumbers are accurately estimated over a wide frequency band using fewer sensors than are needed for the spatial Fourier Transform.