Nyquist filter design

Abstract

Designing a new pulse-shaping filter that satisfies the Nyquist condition to mitigate inter-symbol interference and achieve better stopband attenuation is a new step towards the development of next-generation mobile communication systems. In this study, the authors propose a novel Nyquist filter based on the convolution of a rectangular and a truncated sinc pulses. Introducing two-time parameters in the filter function provides more degrees of freedom and high flexibility to shape different Nyquist pulses. Four Nyquist pulse shapes are introduced, examined in terms of time and frequency characteristics, and compared with those of the two most popular pulses in the literature: Root-raised cosine (RRC) and PHYDYAS. The results demonstrate an improvement in the eye pattern, impulse response, and spectrum behaviours. The error rates are evaluated over a noisy channel, and the new pulses offered better performance than PHYDYAS and RRC. The intrinsic interference was examined by determining the autocorrelation and cross-correlation coefficients of the prototype filters in the frequency-time grid. The results for the proposed filters portray good interference confinement either in time or frequency axis. The reduction in the out-of-band emission makes the proposed filter an efficient candidate for future filter bank multicarrier scheme.