The impairments caused by timing jitter are a signi ficant limiting factor in the performance of very high data rate OFDM systems. In this letter we show that oversampling can reduce the noise caused by timing jitter. Both fractional oversampling achieved by leaving some band-edge OFDM subcarriers unused and integral oversampling are considered. The theoretical results are compared with simulation results for the case of white timing jitter showing very close agreement. Oversampling results in a 3 dB reduction in jitter noise power for every doubling of the sampling rate.
Index Terms—Timing jitter, OFDM, oversampling.
Orthogonal frequency division multiplexing(OFDM) is used in many wireless broadband communication systems because it is a simple and scalable solution to intersymbol interference caused by a multipath channel. Very recently the use of OFDM in optical systems has attracted increasing interest (see and the references therein). Data rates in optical fiber systems are typically much higher than in RF wireless systems. At these very high data rates, timing jitter is emerging as an important limitation to the performance of OFDM systems. A major source of jitter is the sampling clock in the very high speed analog-to-digital converters (ADCs) which are required in these systems. Timing jitter is also emerging as a problem in high frequency bandpass sampling OFDM radio. The effect of timing jitter has been analyzed. These papers focus on the coloured low pass timing jitter which is typical of systems using phase lock loops (PLL). They consider only integral oversampling.
This paper presents a tutorial introduction to OFDM. A typical OFDM transmitter and receiver are described and the roles of the main signal processing blocks explained. The time and frequency domain signals at various points in the system are described. It is shown that if a cyclic prefix is added to each OFDM symbol, any linear distortion introduced by the channel can be equalized by a single tap equalizer. This process is explained by considering the effect of a simple two-path channel on the component of the transmitted signal due to one subcarrier frequency. Throughout the description particular emphasis is given to those aspects of an OFDM system that are often misunderstood.
complex values representing the constellation points are used to modulate up to subcarriers. Timing jitter can be introduced at a number of points in a practical OFDM system but in this letter we consider only jitter introduced at the sampler block of the receiver ADC. Fig. 2 shows how timing jitter is defined. Ideally the received OFDM signal is sampled at uniform intervals of The dashed lines in Fig. 2(a) represent uniform sampling intervals. The solid arrows represent the actual sampling times. The effect of timing jitter is to cause deviation between the actual sampling times and the uniform sampling intervals. Fig. 2(b) shows the discrete timing jitter for this example.
We now analyze the effect of both fractional and integral oversampling in OFDM and show that either or both can be used to reduce the degradation caused by timing jitter. To achieve integral oversampling, the received signal is sampled at a rate of where is an integer. For fractional oversampling some band-edge subcarriers are unused in the transmitted signal. When all subcarriers are modulated, the bandwidth of the baseband OFDM signal is 2 so sampling at intervals of as shown in Fig. 2 is Nyquist rate sampling. If instead, only the subcarriers with indices between − and + are non zero, the bandwidth of the signal is ( + /2 in this case sampling at intervals of is above the Nyquist rate. the degree of oversampling is given by ( + /).
It has been shown both theoretically and by simulation that oversampling can reduce the degradation caused by timing jitter in OFDM systems. Two methods of oversampling were used: fractional oversampling achieved by leaving some of the band-edge subcarriers unused, and integral oversampling implemented by increasing the sampling rate at the receiver. For the case of white timing jitterboth techniques result in a linear reduction in jitter noise power as a function of oversampling rate. Thus oversampling gives a 3 dB reduction in jitter noise power for every doubling of sampling rate. It was also shown that in the presence of timing jitter, high frequency subcarriers cause more ICI than lower frequency subcarriers, but that the resulting ICI is spread equally across all subcarriers.