Improved Nyquist filter characteristics using spline interpolation

Abstract

This paper presents and investigates a novel approach for constructing a family of intersymbol interference (ISI)-free pulses that shows comparable or better ISI performance in the presence of sampling errors, compared with some recently proposed pulses. We propose and discuss a new parametric method for the design of Nyquist filter characteristics using constraints in frequency characteristics construction. The method for constructing the filter characteristics uses a piecewise polynomial approximation of an ideal optimized staircase characteristic by spline functions. The spline polynomials are used to approximate a function that must pass through specified points. The performances of new ISIfree pulses are studied with respect to the ISI error probability. This family provides flexibility in designing an appropriate pulse even after the roll-off factor has been chosen. The results for error probability outperform the fourth-degree polynomial pulse [4].

A New Family of Nyquist Pulses With Improved Performance

“…1 The polynomial functions s j (x) can be expressed as ( 4), shown at the bottom page 9, where A ij , B ij , C ij and D ij are constant real parameters. 1 As it will become evident later on, the proposed design approach is different to the approach proposed in [25]. Specifically, in [25], the so-called staircase characteristic has been adopted, using rectangles of equal width.…”

“…1 As it will become evident later on, the proposed design approach is different to the approach proposed in [25]. Specifically, in [25], the so-called staircase characteristic has been adopted, using rectangles of equal width. The height of the rectangles has been determined by employing trial and error techniques that minimize the resulting error probability.…”

“…Next, we compare the propose pulse designs with ones employing multiple parameters, namely those proposed in [25] and [22]. In Table 8, the BER performance of the standard and the improved fourth pulses is compared with that of the spline (Spline 3) and staircase pulses (X 3 (f ) and X 4 (f )), proposed in [25]. In the same table, results for the polynomial pulse (Poly), proposed in [22], are also presented.…”

“…A different pulse design approach has been adopted in [19], [20], [21], [22], [23], [24], [25], and [26]. In these works, additional design parameters have been included, whose values has been obtained using optimization techniques.…”

“…In [23], an ISI-free pulse has been proposed, whose roll-off characteristic is tunable with one power parameter. In [25], improved Nyquist pulses with transfer function that approximates a staircase frequency characteristic using spline functions have been proposed. In [26], an ISI-free pulse with piece-wise exponential frequency characteristic has been presented.…”