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A sub-optimal precoding scheme for distributed antenna systems in a spatially correlated Rayleigh channel is developed by asymptotical analysis at low and high SNRs. A Newton's method based practical iterative algorithm is presented to find the power allocation coefficients in this scheme. Compared to the existing optimal scheme which requires multidimensional roots finding, the scheme developed in this reported work only needs one-dimensional root finding, and thus it has lower calculation complexity. Moreover, it can converge to the solution quickly, and obtain a performance close to a optimal scheme. Simulation results corroborate the effectiveness of the developed scheme.