MIMO wireless communication systems with channel state estimation, in which 2 to 4 transmit-receive antenna pairs are employed, are simulated. The channel estimation is fulfilled by the orthogonal pilot signal approach, where the Walsh Hadamard-ordered sequences are commonly used for piloting. The signal is modulated by applying the quaternary phase shift keying method. Maximum 250 000 packets are transmitted through flat-fading Rayleigh channels, to which white Gaussian noise is added. Based on simulating 10 subcases of the frame length and number of pilot symbols per frame, it is ascertained that pilot symbol orthogonal sequences in 2×2 to 4×4 MIMO systems can be improved by substituting Walsh functions with partially unsymmetrical binary functions constituting the eight known orthogonal bases. The benefit is that the bit-error rate is substantially decreased, especially for 2×2 MIMO systems. Considering three cases of the pilot signal de-orthogonalization caused by two indefinite and definite pilot sequence symbol errors, the relative decrement varies from 0.123 % to 14.7 %. However, the decrement becomes less significant as the number of transmit-receive antenna pairs is increased.