This paper presents a comparison between Eigen value decomposition (EVD) method and Givens rotation (GR) method for the quasi-orthogonal space-time block coded (QO-STBC) wireless communication systems, working under the multipath Rayleigh fading channels, under the condition of imperfect channel state information (CSI) at the receiver side, and also presents the multi-input and multi-output (MIMO) extension of both the QO-STBC methods. The matrix manipulation in both schemes leads to the removal of interference terms in the detection matrix, which in turn results in reduced computational complexity as compared to the conventional linear decoding technique using maximum likelihood criterion. Under realistic conditions the channel estimator cannot provide perfect/ideal channel state information (CSI). In this correspondence, we describe the impact of imperfect channel state information on the diversity gain. The simulation results are presented to demonstrate the adverse effects of imperfect channel state information (CSI) on the bit error rate performance of QO-STBC systems.