Compressive Temporal Higher Order Cyclostationary Statistics

Abstract

The application of nonlinear transformations to a cyclostationary signal for the purpose of revealing hidden periodicities has proven to be useful for applications requiring signal selectivity and noise tolerance. The fact that the hidden periodicities, referred to as cyclic moments, are often compressible in the Fourier domain motivates the use of compressive sensing (CS) as an efficient acquisition protocol for capturing such signals. In this work, we consider the class of Temporal Higher Order Cyclostationary Statistics (THOCS) estimators when CS is used to acquire the cyclostationary signal assuming compressible cyclic moments in the Fourier domain. We develop a theoretical framework for estimating THOCS using the low-rate nonuniform sampling protocol from CS and illustrate the performance of this framework using simulated data.

Automatic Modulation Recognition Using Compressive Cyclic Features

“…Fortunately, the development of CS enlightens a way to relieve this burden. By employing the sparsity of CMs, Lim and Wakin [11] estimated CMs from compressive measurements, then derived CC through cyclic moment to cumulant formula [9]. Because of the requirement of all the necessary nth-and lower-order CMs, it seems cumbersome.…”

“…In practice, based on the strategy of non-uniform sampling (NUS) [17], compressive measurements can be directly acquired from the continuous waveform x(t). Moreover, a novel signal acquisition setup proposed in [11] was available to generate various compressive signal lag products. As a result, we just need to divide x(t) into W temporal windows, let them undergo the aforementioned setup, respectively, and then the TMs and TCs can be calculated successively.…”

“…Providing a proper tradeoff between SNR and γ, the CS-based AMR can be totally treated as an alternative of the classical CC-based AMR, and affords dramatic savings of computational complexity and storage requirements. Figures 3 and 4 compare the performance of the proposed algorithm to the CS-based AMR proposed in [11] for γ = 0.2. It is apparent that these two curves almost converge, and the former slightly outperforms the latter in both cases.…”

“…It is apparent that these two curves almost converge, and the former slightly outperforms the latter in both cases. This mainly results from the fact that in the algorithm of [11], several lower-order CMs need to be estimated, which yields bias accumulation in the computation of CCs. With the SNR degrading, these two classifiers both exhibit unacceptably poor performance when SNR ≤ 0 dB (not shown in Figures 3 and 4).…”

“…However, this method is restricted in the modulation pool consisting of a few lower-order modulations. Lim and Wakin [11] proposed a CS-based AMR algorithm by exploiting the sparsity of cyclic moments (CMs). In this approach, higher-order CC was indirectly derived by initially estimating several lower-order CMs.…”