Nyquist Pulses in OFDM System

Abstract

Orthogonal frequency division multiplexing or OFDM technology allows converting a single high-speed data stream into parallel low-speed streams, where each stream is transmitted in a channel with its own subcarrier frequency. Unlike FDM, where there is a protective band gap between channels, channels in an OFDM system overlap, what requires orthogonal properties between base pulses of transmitter and receiver to avoid intersymbol (ISI) and inter-channel (ICI) interference. In traditional OFDM, a rectangular pulse is used as envelope of base pulses of the transmitter and receiver. Choice of the rectangular envelope is due to simplicity of its shape and additionally allows implementing the process of receiving OFDM signal using fast Fourier transform technology (FFT). Disadvantage in this case is the increased level of out-of-band emission in frequency domain, as well as increased sensitivity of system to the Doppler effect. Main feature of spectrum of radio pulse with rectangular envelope is the maximum spectral density at the carrier frequency and many zeros located at equal frequency intervals, what means that spectrum is selective. The paper shows that this feature of spectrum for OFDM is not accidental. In turn, Nyquist pulses are a type of pulses that have one maximum and many zeros located at equal time intervals. That is, the spectrum of radio pulse with rectangular envelope can be considered as a Nyquist pulse if time and frequency are replaced. The paper considers general criteria for shape of continuous base pulses of the transmitter and receiver. Requirements are set for shape of receiver base pulses if transmitter base pulses have selective spectrum. Usage features of fast Fourier transform technology for transmitter base pulses with selective spectrum have been investigated.