Investigation of the mechanism of improvement in improved Nyquist filters

Abstract

In this study, the authors have investigated the mechanism that determines improved Nyquist filters (INFs) to perform better in the presence of timing errors. The authors have explored the role of low- and high-frequency regions in the range [B(1 − α), B], where B is the bandwidth corresponding to T = 1/2B in producing a smaller error probability in the presence of symbol timing error. The authors first have analysed the performance of the POWER pulse and evidenced the role of the slope of the frequency characteristic in the vicinity of B(1 − α), determined the optimal values of the exponent β and derived a formula that links β and the slope value at B(1 − α + α/100) to the normalised time offset. Then, the authors have proposed five new INFs with piece-wise polynomial frequency characteristic, and investigated the influence of component frequency bands and shapes on the error probability, when the impulse response is sampled with a time offset. The authors consider that the slope of the frequency characteristic in the transition band in the vicinity of B(1 − α) has a direct effect on the error probability. Finally, the authors have presented the performance evaluation and practical engineering challenges brought in by the use of the new pulses in an N-subcarrier orthogonal frequency-division multiplexing (OFDM) systems in order to reduce inter-carrier interference power.