Design and verification of a frequency domain equalizer

In this work we provide a methodology for the design and verification of a frequency domain equalizer. The performance analysis of the equalizer is conducted using two methods: simulation based verification in Simulink and System Generator and theorem proving techniques in Higher Order Logic. We conduct both floating-point and fixed-point error estimations for the design in Simulink and System Generator, respectively. Then, we use formal error analysis based on the theorem proving to verify an implementation of the frequency domain equalizer based on the Fast LMS algorithm. The formal error analysis and simulation based error estimation of the algorithm intend to show that, when converting from one number domain to another, the algorithm produces the same values with an accepted error margin caused by the round-off error accumulation. This work shows the efficiency of combining simulation and formal verification based methods in verifying complex systems such as the frequency domain equalizer.