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In some radar operating environments multipath clutter is the dominant source of interference. Since the multipath clutter may hide the desired target returns, an effective method of clutter suppression is required. MIMO radar systems can discriminate multipath returns from target returns by estimating the directions of departure and arrival. Multipath clutter suppression using the conventional beamformer is not effective when the multipath returns are much stronger than the target returns. However, effective multipath clutter suppression can be achieved by using an adaptive transmit beamformer in conjunction with an adaptive receive beamformer while still illuminating the entire scene. This work explores the simulated performance of a MIMO radar system with two adaptive filtering algorithms: Iterative Adaptive Approach and Sparse Learning via Iterative Minimization. Simulation results show that these algorithms effectively suppress multipath returns at the cost of increased computational complexity.