Efficient Cycle Frequency Acquisition of a Cyclostationary Signal with the FACA Method

Abstract

The cycle frequencies of a cyclostationary signal can be used for the signal identification and classification, separation of the overlapped signals in cycle domain, and so on. Efficient cycle frequency acquisition depends on the fast measurement of cyclic autocorrelation function (CAF) or spectral correlation function (SCF) of the signal. Presently the relative efficient CAF and SCF measuring methods mainly include the cyclic correlogram, the well-known fast Fourier transform accumulation method (FAM), and so on. Motivated by these methods, a new efficient cycle frequency acquisition method which integrates the fast Fourier transform (FFT) algorithm with the autocorrelated cyclic autocorrelation function, named FACA, is presented. With the presented method, we can acquire the cycle frequencies of a cyclostationary signal more efficiently with a given level of reliability. Meanwhile, by enlarging the FFT window width of the FACA method we can get the same cycle frequency resolution as the benchmarked method FAM, but the computation cost still can be spared at this case.

A Novel Sampling Frequency Offset Estimation Algorithm for OFDM Systems Based on Cyclostationary Properties

“…In the proposed CB-SFS algorithm we use the cycle frequencies estimation algorithm proposed in [12, Sec. III], [13], which is based on the autocorrelated CAF. In the following, we briefly review this algorithm: The CAF corresponding to the sampled signal Y DT [n] can be estimated as [12,Eqns. (3), ( 4)]:…”

“…In [12,Appendix], [13,Sec. 3.2] it is shown that for sufficiently large values of N c , the autocorrelated CAF (28) approaches the expression (assuming synchronized sampling)…”

“…On the other hand, it directly follows from Table 2 that the computational complexity increases linearly as N seg increases. It thus follows that the value of N seg is selected as a compromise between these two opposite effects, and that it is generally preferred to use the minimal N seg which facilitates the required estimation accuracy, see [13,Sec. 3.3].…”

“…Lastly, we note that N seg is restricted to be a power of 2 in order facilitate the application of the FFT in the evaluation of Eqn. (27), leading to a more computationally efficient implementation, see also [13,Sec. 3.3].…”

“…The fact that using pilots to facilitate synchronization reduces the spectral efficiency of the communications link, motivated the present work in which we introduce a novel, efficient cyclostationarity-based sampling frequency synchronization (CB-SFS) algorithm, which exploits the cyclostationarity of the received signal without using a dedicated pilot sequence, while requiring a reasonable complexity as compared to the previously proposed algorithms. The novelty of the proposed algorithm follows as it does not estimate the sampling frequency directly, but instead it adjusts the cycle frequencies of the sampled received signal, estimated via [12], [13], to align with those of the transmitted signal. Note that the cycle frequencies of the transmitted signal are completely determined by the signal generation scheme, hence are available at the receiver.…”