The Compressed Sensing (CS) framework is heavily utilized to reduce data rate in hardware restricted scenarios by exploiting the intrinsic sparsity of the transmitted data. Considering multiple sensors at the same time, one variation of the Multi Channel (MC) framework takes several measurements at one time instant and then uses CS in the spatial domain to compress the data. This paper provides a theoretical analysis of the proposed system by computing the coherence and the Restricted Isometry Constant (RIC) of the corresponding MC sensing matrix. Additionally, we provide simulation results to further show the applicability and advantages of this system.