In this paper, a mathematical model for generating AWGN and Rayleigh fading is presented and argued based around the generation of Gaussian distributed numbers. This paper is focused on a multiple input multiple output (MIMO) channel model for the design and implementation of space-time coded MIMO modem systems such that the complexity of the design is as much as possible pushed into the digital domain and that the architecture is computationally efficient, driving the emphasis and complexity of implementation into software. We present an FPGA architecture to yield a Rayleigh fading and AWGN model for MIMO systems requiring up to four transmit and two receive antennas while requiring only a slight increase in logic resource over a single input single output model. The design entry was in VHDL and the target FPGA was the Xilinx Spartan 3 XC3S4000.