Least square based piecewise parabolic interpolation for timing synchronization

Fractional delay interpolators play a key role in timing synchronization of digital communication modems[1],[2]. Piecewise polynomial interpolators are widely used for such purposes in many practical receivers [2]. Since the order of such polynomial based interpolators has a bearing on computational complexity, smaller degree interpolation kernels are often called for. A piecewise cubic polynomial interpolator is known to provide performance-complexity tradeoff. Further reduction in complexity is possible by good approximations of cubic polynomials by quadratic functions. Such piecewise parabolic interpolators are proposed in the literature and are commonly used. However, these schemes are not the best fit in terms of the minimizing the squared error. In this paper, we present a set of piecewise parabolic interpolators optimized in terms of minimum squared error, when compared to the piecewise cubic polynomial schemes. The derived structures can be efficiently implemented using the Farrow structure [3]. The performance of the new class of interpolators are compared.