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Proposed next-generation radar systems have multiple transmit apertures with complete flexibility in the choice of the signals transmitted at each aperture. Here we propose the use of multiple signals with arbitrary cross-correlation matrix R and show that R can be chosen to achieve or approximate a desired spatial transmit beampattern. This leads to the constrained optimization problem of the finding the value of the R, which causes the true transmit beampattern to be close in some sense to a desired beam-pattern. This is approached using a gradient search in the space of Cholesky factors of R.