This article examines how the QSM-MBM-SIMO system's performance is affected by Gaussian imperfect channel estimation (IChE). An analytical expression and a closed-form expression for the generic QSM system's pair-wise error probability (PEP) are utilized while calculating a precise Lower bound for the Average Bit Error Probability (ABEP) over Rayleigh fading. Quantifying the impact of channel estimation errors (ChEE) on system performance yields analytical results. The accuracy of the lower bound-based analysis of the scheme proposed is demonstrated by the Monte Carlo simulation (MCS) results. The MCS results of the proposed scheme demonstrate signal-to-noise ratio (SNR) gain of approximately 1.5dB at a BER of when compared to the SIMO-MBM scheme with perfect channel estimation. Furthermore, when compared to perfect channel estimation (PChE), we discovered a 2dB loss in coding gains caused by ChEE.