Adaptive Time-Frequency Synthesis for Waveform Discernment in Wireless Communications

The discernment of waveforms for the purpose of identifying the underlying wireless technologies and validating if observed transmissions are legitimate or not remains a challenge within the communications sector and beyond. Conventional techniques struggle to robustly process Signals under Test (SuTs) in real-time. A particular difficulty relates to the selection of an appropriate window size for the processed data when pertinent contextual information on SuTs is not known a priori. The disadvantage of applying a predetermined fixed window size is that of length and shape (i.e., coarse resolution). In contrast, an adaptive window size offers more optimally tuned resolution. Towards this end, we propose a novel approach that uses an Adaptive Resolution Transform (ART) to either maintain a constant (prespecified) resolution, via a Variable Window Size and Shape (VWSS), or adjust the resolution (again using the VWSS technique) to match latency requirements. Central to this approach is the utilization of Continuous Wavelet Transforms (CWTs), which do not substantively suffer from those energy leakage issues found in more commonly used transforms such as Discrete Wavelet Transforms (DWT). A robust numerical implementation of CWTs is presented via a particular class of Convolutional Neural Networks (CNNs) called Robust Convex Relaxation (RCR)-based Convolutional Long Short-Term Memory Deep Neural Networks (a.k.a., CLSTMDNNs or CLNNs). By employing small convolutional filters, this class leverages deeper cascade learning, which nicely emulates CWTs. In addition to its use for convex relaxation adversarial training, the RCR framework also improves the bound tightening for the successive convolutional layers (which contain the cascading of ever smaller 'CWT-like' convolutional filters). In this paper, we explore this particular architecture for its discernment capability among the SuT time series being compared. To operationalize this architectural paradigm, non-conventional Nonnegative Matrix Factorization (NMF) and Multiresolution Matrix Factorization (MMF) is used in conjunction to facilitate the capture of the structure and content of the involved matrices so as to achieve higher resolution and enhanced discernment accuracy. The desired WT (a.k.a., Corresponding WT or CORWT) resulting from the MMF is implemented as a translation-invariant CWT PyWavelet to better illuminate the intricate structural characteristics of the SuT and facilitate the analysis/discernment of their constituent Waveforms of Interest (WoIs). A precomputed hash and lookup table is utilized to facilitate WoI classification and discernment in quasi-real-time.