# Radiometric Identification of Signals by Matched Whitening Transform
## 1 Introduction  
Radiometric identification is the problem of attributing a signal to the source; often brand or model. Source identification is accomplished by RF fingerprinting of devices by looking for signatures that may arise from manufacturing tolerances, imperfections or normal statistical variations in production. There is considerable work in signal classification and modulation recognition [1, 2]. However, radiometric identification does not neatly fit in either of the two categories. In many ways, radiometric identification is a more difficult problem as signals originating from different sources may have similar characteristics such as modulation, bit rates, pulse shapes, etc. This fact makes subtle device variations the main signature for radiometric identification. Such variations, however, are small, imperceptible and difficult to model. Why radiometric identification is of interest are many fold. The military has been interested in this capability for some time as a means of identifying friendly from hostile radar [3, 4]. Satellite communication may be faced with intentional or unintentional jamming from rogue sources. Knowing the source and the brand of the interferer may help identify the defending source. Radiometric identification is also a valuable tool in securing wireless devices. Spoofing attempts in wireless networks and IoT devices can be thwarted if the source of the signal could be identified and blocked [5, 6]. It is more difficult to mimic device characteristics that are embedded in signals than to replicate modulation or pulse shaping. Radiometric identification can be formulated in the context of a statistical classifier. The classical approach follows feature extraction, dimensionality reduction by techniquessuch as PCA and finally multiple discriminant analysis classifier [7; 8]. In [9], Square Integral Bispectra (SIB) is used to extract the unique stray features of individual transmitted signals, followed by PCA to extract a low-dimensional feature vector. It has been observed that features retained after dimensionality reduction are not necessarily optimal for classification. A combined optimization of dimensionality reduction and fingerprint classification is proposed in [10]. The idea is to drive dimensionality reduction by minimizing the classification error and maximizing the mutual information between the reduced dimensionality features and the class label simultaneously. The RF fingerprint features are extracted from the statistics of the normalized instantaneous amplitude, phase and frequency of the signal resulting in feature vectors with up to 960 dimensions. The dimensionality reduction problem remains, however. Feature extraction for transmitter identification algorithms have been developed to operate in either transient [11] or steady state phases [12]. The transient phase is an analog state of the signal occurring right after the transmitter is activated whereas the steady state phase is characterized by modulation. More recent work on radiometric identification has been influenced by the rise of deep learning (DL) tools. Examples are RF fingerprinting [13], IoT device fingerprinting [14], spectrum sensing [15] and RF device identification in cognitive networks [16]. What is still needed in all such work is the extraction of feature vectors followed by time consuming dimensionality reduction. The feature vectors extracted in [10], for example, have 960 dimensions before dimensionality reduction. In other words, the main problem still remains. The use of DL is often accomplished by the programming of off-the-shelf tools or use of various convolutional neural networks (CNN) routines implemented in Matlab. For example, the compressed bispectrum is identified as the feature then used to train a three layer CNN [17]. What differs are the number of layers, taps, filters, activation functions etc. Another example along this vein appears in [18] where Keras API is used with TensorFlow on the backend to distinguish distracted drivers.