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An efficient spectral domain moment method is presented to analyze the radiation from large finite aperture-coupled microstrip patch arrays. Based on the combination of the equivalence principle and the reciprocity method, the resulting system of integral equations is discretized using subdomain expansion functions in a Galerkin approach. The integrals are represented in the spectral domain and evaluated using special techniques. For typical array dimensions this leads to a large system of linear equations which is solved by the BCG-FFT method. Due to the incorporated simultaneous electric and magnetic surface current densities the BCG algorithm shows usually a slow convergence behaviour, a technique is derived which avoids compound surface current densities of different types in the iterative process. Results for arrays up to 256 elements demonstrate the flexibility of the method, comparisons with available measurements verify its accuracy.