The estimation of the frequency‐wavenumber spectrum of the ambient noise field from data collected by a totally random array is considered. The standard estimator [J. Acoust. Soc. Am.71, 97–99 (1982)], which is a normalized beampower pattern, is shown to be biased for sparse arrays. A modified estimator which removes this bias is introduced and its performance is studied. In particular, precise asymptotic expressions for the bias, variance, and covariance of the estimator are established. The density of the number of sensors per unit volume is allowed to be arbitrary and thus the results hold for sparse arrays as well. An application to a representative planar array is given.