This book presents a general overview on the concept of MIMO OFDM for communication systems. Moreover, the different detection schemes for such systems are portrayed with special emphasis on the LS, ZF & LMMSE detector. The core of a LMMSE detector requires matrix inversion, which is usually regarded as a computationally intensive task. Hence, the CORDIC and SGR algorithms that can be used to decrease the complexity of matrix inversion are explored in depth and their software and hardware implementation issues are analyzed. The goal of this thesis is to realize an implementation of the LMMSE detector on an FPGA, since results from hardware simulations are faster and more valuable to designers compared to software based simulations.