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In this paper the design and the implementation of a linear, non-uniform antenna array for a 77-GHz MIMO FMCW system that allows for the estimation of both the distance and the angular position of a target are presented. The goal is to achieve a good trade-off between the main beam width and the side lobe level. The non-uniform spacing in addition with the MIMO principle offers a superior performance compared to a classical uniform half-wavelength antenna array with an equal number of elements. However the design becomes more complicated and can not be tackled using analytical methods. Starting with elementary array factor considerations the design is approached using brute force, stepwise brute force, and particle swarm optimization. The particle swarm optimized array was also implemented. Simulation results and measurements are presented and discussed.