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This paper investigates the problem of progressive transceiver design for integrated multi-input multioutput (MIMO) systems with automatic repeat request (ARQ) capability. We consider a generic MIMO transceiver architecture that utilizes a linear transmission precoder and a linear decoder followed by decision feedback interference cancellation at the receiver. To be consistent with ARQ, our goal is to progressively design the optimal transmission precoder and receiver feedback system to jointly minimize the mean square error (MSE) under the assumption of perfect feedback. We consider both zero-forcing and minimum MSE (MMSE) decoder as joint ARQ receivers. Unlike in single transmission design, joint ARQ receivers cannot change previous precoders. Here, we propose an approach to design the precoder and receiver which improves the system performance successively over each retransmission to achieve MSE performance close to the known lower bound.