The Multiple Input Multiple Output (MIMO) technique is motivating the world-wide researchers to realize the next generation wireless LANs with the higher channel capacity and higher signal quality. This paper proposes and analyzes the Space Division Multiplexing Single Carrier OFDM (SDM-SCOFDM) system with adaptive modulation (AM) method over MIMO channels. The salient features of the proposed method are to enable the significant reduction of the number of required feedback adaptive modulation information (AMI) bits and the improvement of the PAPR (peak to average power ratio) performance at a cost of little degradation of channel capacity as comparing with the AM aided SDM-OFDM system. We also propose the Carrier-to-Noise Power Ratio (CNR) estimation method for SDM-SCOFDM signals over multi-path fading channels, which can be used for the assignment of the optimal modulation scheme in each transmit antenna. This paper presents the various computer simulation results to verify the proposed method under a typical wireless LAN environment.