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A novel method for estimating the power angle spectrum (PAS) is presented that decomposes the true PAS into a small set of basis functions. The basis coefficients for this sparse representation are found by enforcing equality to the covariance or Bartlett PAS subject to a minimum lscr1-norm constraint. The method, referred to as sparse PAS estimation (SPASE), can be implemented conveniently using existing linear-programming (LP) solvers. Further, because only a few clusters are required in the representation, the method enables reduced-complexity stochastic models for the channel and possibly allows reduced overhead in channel feedback schemes. Application of the method to simulated channels and multiple-input multiple-output (MIMO) propagation data demonstrates the utility of the method.