EVALUATION OF FREQUENCY OFFSET AND DOPPLER EFFECT IN TERRESTRIAL RF AND IN UNDERWATER ACOUSTIC OFDM SYSTEMS Sadia Ahmed and Huseyin Arslan Electrical Engineering Department, University of South Florida E-mail:
[email protected] and
[email protected] Abstract—Frequency offset and Doppler effect cause loss of orthogonality in Orthogonal Frequency Division Multiplexing (OFDM), which in turn may severely degrade receiver performance. Traditionally, most of the literature dealt with non-varying Doppler effect over OFDM subcarriers. However, in terrestrial ultra-wideband (UWB) OFDM radio frequency (RF) and in high data rate underwater acoustic communication (UAC), the effect of Doppler varies considerably over OFDM band. This paper will investigate the frequency offset and the varying effect of Doppler through analysis and simulation in both domains in order to maintain orthogonality or to compensate loss of orthogonality. To the best knowledge of the authors, this type of detailed analysis is not present in these domains, and thus this paper provides a valuable contribution. Index Terms—Doppler Effect, Frequency Offset, OFDM, Orthogonality, Underwater Acoustics, UWB-OFDM
I. I NTRODUCTION Prior Art on Doppler in OFDM There is a growing interest in the varying effects of Doppler over OFDM subcarriers due to the increasing demand on high data rate and mobility. A few papers addressed these effects and are discussed below. The relationship between Doppler effect and the subcarriers is presented for UWB-OFDM in [1]. Mathematical expressions are derived for the upper bound of Intercarrier Interference (ICI) and the lower bound of Signal to Interference Ratio (SIR). In [2], a Doppler parameter estimation method is presented where the authors used null subcarriers to estimate Doppler parameters. Maximum likelihood estimator (ML) with rotational invariance techniques (ESPRIT) are used to estimate the signal parameters. A resampling technique is proposed in [3] to compensate the varying Doppler effect across different subcarriers. An adaptive OFDM signal detection method is proposed in [4] that uses low complexity post-FFT signal processing over multiple arrays. The OFDM blocks are separated by zero pads and Doppler is assumed constant over each OFDM block. Contribution of This Paper This paper will present the following, c 2008IEEE 978-1-4244-2677-5/08/$25.00
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The frequency domain expressions for the received signal, ICI, and SIR incorporating both frequency offset and varying Doppler effect are derived in terms of channel frequency response. The condition is derived when the Doppler effect and the frequency offset are equivalent. Simulation is carried out using simulated Rayleigh channel and realistic channel responses. Although, due to lack of standard channel models, the number of realizations in actual UAC channels is limited. Acoustic velocity variation is also considered in the UAC simulation. The simulation is carried out in terrestrial and in UAC systems and are compared with each other.
The rest of the paper is organized as follows. In Section II, the Doppler challenges in the terrestrial and UAC OFDM are presented. In Section III, the mathematical analysis of Doppler effect and frequency offset is presented. In Section IV, the simulation results are provided, and in Section V, the conclusion is presented. II. D OPPLER
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T ERRESTRIAL
AND IN
UA OFDM
In the terrestrial environment, the relative velocity of the transmitter/receiver and/or surrounding objects contribute to Doppler effect. For narrowband terrestrial systems, the bandpass frequency is relatively high (for example, in the range of GHz) compared to the baseband subcarrier frequencies. In such cases, the individual subcarrier frequency variation from the bandpass frequency is insignificant. Hence, the effect of Doppler shift on the OFDM signal is considered to be equal to the Doppler shift on the bandpass frequency. The Doppler spread consists of the combined effect of many scatterers, where the shift owing to each scatter is given by FDa = CVaa f0a cosθa . The variable Va represents the relative velocity, Ca represents the RF velocity, f0a denotes the bandpass frequency, and θa represents the scattering angle. According to literature [5], [6], and the prior study addressed in section I, the Doppler effect in UAC is caused by two different sources. The Doppler shift is
a function of the relative velocity, vw of the the transducers/hydrophones, and other objects, variable acoustic velocity denoted by cw , and signal frequencies. In underwater OFDM, the bandpass frequency is comparable (for example, in Hz or kHz) to the baseband subcarrier frequencies (for example, in Hz or kHz). In such cases, the individual subcarrier frequency variation from the bandpass frequency is significant. Therefore, the effect of Doppler shift on OFDM signal will vary over subcarriers. The shift on the k th subcarrier in baseband OFDM can be expressed as, FDw =
vw fk cosθm , cw
(1)
where fk is the k th subcarrier frequency and θm is the scattering angle of the mth scatterer. The Doppler spread is primarily caused by the relative velocity of wind on the surface waves and by the internal currents [5], [6]. The total Doppler effect in UAC is a combination of Doppler shift and Doppler spread, where the average Doppler shift is much larger than the overall Doppler spread [5]. Compared to the narrowband terrestrial, Doppler in UAC is much more severe. This is primarily due to, A) Very low acoustic velocity (compared to RF, i.e. cw
