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The problem of narrowband CFAR (constant false alarm rate) detection of an acoustic source at an unknown location in a range-independent shallow ocean is considered. If a target is present, the received signal vector at an array of N sensors belongs to an M-dimensional subspace if N exceeds the number of propagating modes M in the ocean. A subspace detection method which utilises the knowledge of the signal subspace to enhance the detector performance is presented in this paper. It is shown that, for a given number of sensors N, the performance of a detector using a vector sensor array is significantly better than that using a scalar sensor array. If a target is detected, the detector using a vector sensor array also provides a concurrent coarse estimate of the bearing of the target.