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This paper presents a novel adaptive equalization algorithm for time-varying, frequency-selective MIMO systems that harnesses the finite alphabet property inherent in digital communication. The algorithm leads to a direct, cost-efficient QR-based recursive updating procedure for the equalizer coefficients that forces adaptation to changing channel characteristics. The proposed method does not require precise channel estimation and uses significantly less pilot symbols than other traditional equalizers, implying a drastic reduction in bandwidth overhead. Simulation results confirm that this approach outperforms the traditional recursive least squares (RLS) adaptive equalizer for this application and rivals the MMSE equalizers with perfect channel knowledge.