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The multiple-input-multiple-output (MIMO) communication systems using an adaptive beamformer processor (BFP) in a receive antenna array and a fixed (non- adaptive) BFP in a transmit antenna array are considered. The transmitter does not have channel knowledge in such systems. Different variants of the adaptive BFP are proposed. The maximum likelihood (ML) detector and the simplified algorithms of the independent symbol detection are investigated. In the case of the Rayleigh fading environment the simulation results for the bit error rate (BER) are given.