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Multiple-input-multiple-output (MIMO) radar is an emerging technology that has significant potential for advancing the state-of-the-art of modern radar. When orthogonal waveforms are transmitted, with M+N (N transmit and M receive) antennas, an MN-element filled virtual array can be obtained. To successfully utilize such an array for high-resolution MIMO radar imaging, constant-modulus transmit signal synthesis and optimal receive filter design play critical roles. We present in this paper a computationally attractive cyclic optimization algorithm for the synthesis of constant-modulus transmit signals with good auto- and cross-correlation properties. Then we go on to discuss the use of an instrumental variables approach to design receive filters that can be used to minimize the impact of scatterers in nearby range bins on the received signals from the range bin of interest (the so-called range compression problem). Finally, we present a number of numerical examples to demonstrate the effectiveness of the proposed approaches.