Development of Improved Nyquist Filters with piecewise linear frequency characteristics

Abstract

In this paper we present a design concept for a new family of Improved Nyquist Filters (INFs). The filters performance, in terms of error probability, depends on the presence of symbol timing errors for the same values of the excess bandwidth, timing jitter, signal to noise ratio and number of interfering pulses. The characteristic property of the new family of inter-symbol interference (ISI) free pulses generated by the proposed filters is the asymptotic decay rate of t -1 and t -2 . The proposed design concept to construct Nyquist filters is based on a piece-wise frequency characteristic, composed of two or three linear pieces in the transition region with different slopes. Analytical and simulation results are presented to show that improvements can be achieved as compared to previously reported pulses taken as references.

Devising a method for increasing the noise immunity of systems with orthogonal frequency division multiplexing under the conditions of inter-channel interference

“…The results on improving the interference resistance of the OFDM system using forming pulses with a selective spectrum indicate that the pulse with piecewise linear approximation, proposed in [11,17], has the lowest probability of a bit error in comparison with such pulses as a trapezoidal pulse [6] and the "Raised cosine" impulse [3]. So, with a signal-to-noise ratio of 15 dB, BPSK modulation and a normalized frequency shift of 0.2, the probability of a bit error for a given pulse is 3•10 -4 ; for QPSK modulation and a normalized frequency shift of 0.1, 10 -6 ; for QAM-16 modulation and a normalized frequency shift of 0.03, 2•10 -4 .…”

“…A piecewise linear and polynomial approximation of the transition region of the Nyquist pulse is proposed in [10]. A piecewise linear approximation of the transition region of the Nyquist pulse is proposed in [11]. However, both studies do not focus on the application of Nyquist pulse data for OFDM technology.…”

“…Fig. 7 shows pulses with a selective spectrum (2) to (11) in the time (Fig. 7, a) and frequency (Fig.…”