A case study of the stochastic modeling approach for range estimation

The floating-point to fixed-point conversion is an important part of the hardware design in order to obtain efficient implementations. When trying to optimize the integer word-length under performance constraints, the dynamic variations of the variables during execution must be determined. Traditional range estimation methods based on simulations are data dependent and time consuming whereas analytical methods like interval and affine arithmetic give pessimistic results as they lack of a statistical background. Recently, a novel approach, based on the Karhunen-Loève expansion (KLE) was presented for linear time-invariant (LTI) systems offering a solid stochastic foundation. Our paper presents an implementation of this theory and shows its efficiency for an OFDM modulator test case study. We also present a review of the uncertainty quantifications problem and the different phases of the range estimation methodology.