We consider multiple-input multiple-output (MIMO) communication systems with adaptive antenna arrays at both ends of the link in which the data transmission is performed via parallel eigenchannels matched to the random spatial channel. The effectiveness of the projection method of space-division multiple access is studied. The method does not require estimation of the arrival directions of signals and is based on orthogonalization of all eigenchannels. Exact analytical expressions are obtained for the bit-error probability during the data transmission via the channel with uncorrelated Rayleigh fading of signals in an MIMO system with an arbitrary number of users and antennas.