Matrix Computation Based On FPGA And Its Application In OFDM Systems Over Time-Varying Channels

Matrix computations, particularly matrix multiplication and matrix inversion operations are widely used in signal processing for communications. The matrix computations in signal processing for communications are intensive and real-time processing and high accuracy are needed, so the computation of matrix operation are usually performed using high-speed FPGA. It is significant to implement matrix operations based on FPGA with high speed, high precision, and low-cost resources.At first, the characteristics and the principles of matrix operations are introduced, and then the matrix multiplication, cumulative addition module, and the triangular matrix inversion module are designed by Verilog language in the ISE software platform. Secondly, the OFDM system fundamental principle is described briefly, where the orthogonality between subcarriers in OFDM system is destroyed by high mobility of the terminals, which introduces itercarrier interference (ICI) and causes severe performance degradations. To compensate the degrading effects of ICI caused by channel variations, various equalization techniques have been proposed. In a fast-varying OFDM channel, minimum mean square error (MMSE) equalization algorithm is the basis method for the design. Our research group proposed a low-complexity MMSE equalization algorithm, and recursive calculation of matrix inverse is the most important calculation in this algorithm. This low complexity MMSE equalizer for OFDM systems is implemented on FPGA. We introduce how to save FPGA resources and reduce the accumulated errors and so on. In the end, the programmer is downloaded on Virtex-2 FPGA hardware platform to realize the equalizer. The result is transferred to PC by RS-232 and simulated in Matlab to validate its good performance.