A prerequisite for the implementation of the adaptive focusing detection scheme [A. J. Claus and F. M. Labianca, abstract F2, this session] is a temporally stable signal field distribution across the array aperture. Stability is characterized by a low‐rank signal covariance matrix. The case of absolute stability, that is, unity rank, occurs rarely in practice, but is of interest because its theoretical treatment can be carried out in closed form and lends insight to the choice of practical test statistics in less stable cases. The model is constructed under the assumption that linear filtering of the acoustic array data produces a vector time series in p‐dimensional unitary space U, where p is significantly smaller than the array dimension. Under H0 (noise only) the process in U is centered isotropic Gaussian, white of unit power. Under H1 (noise plus signal) the signal has constant but unknown ray direction in U, and the amplitude process along this ray is white (complex) Gaussian of specified power. The joint likelihood ratio for L observations in U is found in closed form, suitable for numerical calculation; it is a function of the eigenvalues of the p × p sample covariance matrix. The results of Monte Carlo simulation of the model, including cumulative distributions, ROC curves and performance curves are presented with emphasis on application to cases which might occur in practice. [This work has been supported in part by the Independent Research and Development Program of the Department of Defense and in part by the Naval Electronics Systems Command, Code ELEX‐320.]