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This paper proposes a reduced-rank minimum description length (MDL) method to enumerate the incident waves impinging on a uniform linear array (ULA). First, a new observation data and a reference signal are formed from sensor data by means of the shift-invariance property of the ULA. A cross-correlation between them is calculated, which is able to capture signal information and efficiently suppress additive noise. Second, the normalized cross-correlation is used as initial information for a recursion procedure to quickly partition the observation data into two orthogonal components in a signal subspace and a reduced-rank noise subspace. The components in the noise subspace are employed to calculate the total code length that is required to encode the observation data. Finally, the model with the shortest code length, namely the minimum description length, is chosen as the best model. Unlike the traditional MDL methods, this method partitions the observation data into the cleaner signal and noise subspace components by means of the recursion procedure, avoiding the estimation of a covariance matrix and its eigendecomposition. Thus, the method has the advantage of computational simplicity. Its performance is demonstrated via numerical results.