A SIGNAL SELECTIVE CARRIER FREQUENCY ESTIMATION ALGORITHM FOR PSK SIGNALS*
Yang Liu†, Yong Tie, and Chen-Yan Liu
College of Electronic Information Engineering, Inner Mongolia University,
Hohhot, Inner Mongolia, China†E-mail: [email protected]
This paper addresses the estimation of carrier frequency for PSK signals in the presence of interfering signals and noise. The performance of conventional DFT algorithms suffers from severe degradation in the presence of interfering signals. We proposed a new signal-selective carrier frequency estimation algorithm for PSK signals based on the second-order cyclostationarity. The new method exploits cyclostationarity property of PSK signals with second-order cyclic statistics. Compared with the existing DFT algorithm, the new method is highly tolerant to interference and Gaussian noise. The performance of the new algorithm is studied using simulations in a variety of interference and noise conditions. Simulation results show that the proposed algorithm outperform the conventional DFT method in the presence of interference.
Keywords: Cyclostationarity; spectral correlation; PSK signals; carrier frequency.
1.Introduction
In practice, it is always assumed that the frequency offset is so small that the demodulated signal incurs only negligible phase rotations during the preamble duration [1]. Nevertheless, in broadband wireless communications systems, it is highly possible to receive a signal with a large frequency offset, which caused the traditional carrier recovery loop invalid because of its limited frequency acquisition range [2], [3]. In such conditions, a critical operation in the receiver is the estimation of the carrier frequency in order to perform accurate compensation in the demodulation process. This estimation process is generally performed directly on the received bandpass modulated signals.
One of the widely used large carrier frequency offset estimation methods is DFT algorithm, which is commonly employed in digital signal analysis instrumentation to guarantee that the residue carrier frequency offset within the capture bandwidth of the following carrier synchronization loop. A fast Fourier transform algorithm to estimate carrier frequency deviation based on the maximum likelihood parameter estimation approach for QPSK was proposed in [4]. Although this method can estimate the carrier frequency directly, its estimation accuracy is low. In order to improve the frequency and phase resolution capabilities, an interpolation algorithm for carrier frequency estimation based on FFT in burst M-PSK communication system is presented in [5]. The problem over frequency flat fading channels has been investigated in [6], a feed-forward technique exploiting the sample correlation function of the received signal was proposed. A class of frequency estimation algorithms intended for filter bank burst-mode multicarrier transmission over time-frequency selectively fading channels was introduced in [7]. The Cramer-Rao lower bound (CRB) for the joint estimation of the carrier phase and frequency offset from a noisy linearly modulated burst signal containing random data symbols as well as known pilot symbols was presented in [8].
Many frequency estimation schemes have been proposed for the additive white Gaussian noise and frequency selective and flat fading channels. However, it performs poorly against multiple signals that overlap within the same frequency band, and it is unable to produce separate unbiased estimates for multiple emitters that are located spatially close to each other, resulting in unresolvable frequency estimates. In many cases, the spatial proximity at which the DFT based methods fail is still too unacceptable large to ignore for carrier frequency applications. The limitations of the DFT methods motivate the need for new estimated carrier frequency estimation algorithms that can produce unbiased parameter estimates from spectrally overlapping signals regardless of their proximity.
Many man-made signals arising in communications, telemetry, radar and sonar applications exhibit cyclostationarity [9]. By exploiting this cyclostationarity property of such signals, a class of parameter estimation methods is introduced [10]. The signal-selective methods exploited the unique second-order cyclostationarity of the signal of interest (SOI), are inherent immune to interference and Gaussian noise. In order to alleviate the problems of interference, we introduce an approach to exploit cyclostationarity of signals with second-order cyclic statistics. We then propose a signal-selective carrier frequency estimation algorithm for PSK signals. The proposed algorithm takes advantages of cyclostationary methods, is robust against Gaussian noise and is immune to the interfering signals.
2.Signal Model
The signal model considered in this paper can be modeled as
where x(t) is the signal at the receiver antenna, s(t) is the signal of interest (SOI), and n(t) is signal not of interest (SNOI) including interfering signals and independent receiver noises.
The definition of cyclic autocorrelation function at certain cycle frequency α is defined as
where 〈•〉 is time-averaging operation and * denotes the conjugate [13]. The cyclic spectrum
is defined to be the Fourier transform of the cyclic autocorrelation
An intuitive understanding of cyclostationary processes can be gained by considering u(t) and v(t), where
The cross-correlation of u(t) and v(t) is
Substitution of Eq. (1) into Eq. (6)
which upon rearranging yields
From this result, an interpretation of the cyclic autocorrelation of a process is that it is the cross-correlation of frequency shifted versions of the original process
In order words, the spectrum density of correlation between spectral components at frequency f in u(t) and v(t) is identical to the density of correlation between spectral components at frequencies in x(t). A unique property of process exhibiting cyclostationarity is that their spectral content exhibits correlation between different frequencies.
3.Signal selective carrier frequency estimation algorithm for PSK signals
The demodulation of modulated signals requires knowledge of carrier frequency offset caused by oscillator instabilities. Several methods for frequency estimation have been investigated. The signals are always assumed as stationary random processes in traditional algorithms. However, it is indicated that most signal encountered in communications and telemetry syste...