In this paper, we analyze by theoretical calculation of the proposed scheme for collision detection in wireless local area networks (WLANs). The proposed scheme utilizes the medium access control (MAC) procedure of multiple input multiple output (MIMO) transmission technology, which is used to achieve high-speed transmission in WLANs in recent years; however, the transmission efficiency degrades at the MAC layer level, although a high transmission link rate is achieved at the physical (PHY) layer. The proposed scheme were performed high transmission efficiency of approximately 90% by the computer simulation in our previous work. In this paper, the results of our theoretical calculations correspond with the computer simulation results, indicating that the proposed scheme is indeed efficient and reliable.