Nyquist Filters with Alternative Balance between Time- and Frequency-Domain Parameters

Abstract

Designing matched pulse shaping filters with their cascade satisfying the Nyquist condition for minimum intersymbol interference constitutes an important task for almost all digital data radio transceivers processing an incoming data signal on the sampleby-sample basis. Despite their practical importance, there are only few sets of Nyquist filter definitions and design techniques to devise digital filter coefficients available for a designer. In this paper we propose a set of Nyquist filters that balance the time-and frequency-domain parameters in favor of a filter stop-band attenuation and residual intersymbol interference compared with the already existing Nyquist filter sets. Using a number of filter examples, this paper shows that the proposed Nyquist filters can be a good option for applications that need to fulfill strict limits of adjacent and alternate channel power attenuation while providing a low level of residual intersymbol interference and group delay of the digital filter.

IEEE 802.15.3d-Compliant Waveforms for Terahertz Wireless Communications

“…Alternatively, the ISI performance of s L (t) can be evaluated based on the relaxed Nyquist condition as follows [33]:…”

Nyquist filter design

“…both filters are the same. The g(t) is the NF and h(t) is the RNF [5,9,15,24]. Considering a sinc function with an infinite interval as a filter, its spectrum is the ideal low-pass filter that suppresses OOBE totally, but, practically, generating a pulse with the infinite interval is not possible.…”

“…Designing a pair of matched filters whose combination (cascade) is a Nyquist pulse shape is a classical problem [5][6][7], and, recently, it was suggested as a candidate pulse-shaping method for 5G [2]. Free inter-symbol interference (ISI), which is addressed by a Nyquist filter (NF) [8], is required in pulse shapes to combat channel distortion [5,9]. The studies in the literature report that the following are the considerations for filter design [5,6,9,10] (i) A low-level and rapidly decaying tail of the filter impulse response (IR) to provide immunity against timing jitter, minimise the ISI [6,9,11], and improve the error performance [10].…”

“…(iv) Amplitude frequency response with fast roll-off and highly attenuated stopband to overcome the sensitivity to frequency offset and mitigate the intercarrier interference [5,9,10].…”

A Family of Square-Root Nyquist Filter With Low Group Delay and High Stopband Attenuation

“…In order to improve the SB A of the truncated Nyquist pulses, FarhangBoroujeny has proposed in [7] an iterative algorithm that could be configured to optimize the SB A. In [8], a squareroot Nyquist δ-filter is designed in order to provide low Gd and good SB A. Ashrafi has proposed a convex optimization procedure to design a filter which minimizes the inter-symbol interference (ISI) satisfying a predefined spectrum mask in [9], but also a filter design relaxing the zero ISI criterion in order to lower the SB A energy in [10]. The design of square-root Nyquist filters with low Gd, high SB A and (almost) zero ISI has been proposed in [11], but the work is limited to a roll-off factor α = 1.…”