Analysis of Mean-Square-Error (MSE) for fixed-point FFT units

Range and precision analysis are important steps in assigning suitable integer and fractional bit-widths to the fixed-point variables in a design such that no overflow occurs and a given error bound on maximum mismatch and (or) Mean-Square-Error (MSE) is satisfied. Although, range and maximum mismatch analysis of linear arithmetic circuits has been studied before [8], regarding analysis of MSE, the previous works [9,10,12] cannot analyze the error, when it is defined as the difference between the fixed-point circuit and the reference model, e.g., floating-point format. This paper presents an efficient analysis of MSE for linear arithmetic circuits narrowing on Fast Fourier Transform (FFT) units. Furthermore, an optimization algorithm is introduced to set the bit-widths in an FFT unit while satisfying a given maximum bound on MSE. Experimental results prove the robustness of our MSE analysis and the efficiency of the optimization algorithm compared to [12] for an 8K FFT unit.