Fully complex deep learning classifiers for automatic modulation recognition in non-cooperative environment

Abstract

Automatic Modulation Recognition (AMR) refers to a technique that finds the modulation type of an observed radio signal and has been recognized as an essential and fundamental process at the initial step in many military and civilian applications. One of the main obstacles in AMR is its non-cooperative environment. In such an environment, recognizing the modulation type is burdensome because it is usually hard to obtain preliminary information about the signal source or the received signal. Recently, several studies have attempted to improve the modulation recognition capability in this harsh environment by applying deep learning (DL), which is currently rapidly developing, to the AMR classifiers. Unfortunately, it is not easy to directly apply the conventional DL's benefits to AMR applications. The radio signals in modern communication systems consist of orthogonal components of I (in-phase) and Q (quadrature). The problem is that these components are theoretically equivalent to a complex number's real and imaginary parts. Until now, most DL tools have been based on real values

that is, they can't inherently handle complex data. Accordingly, the conventional AMR classifiers based on these real-valued DL tools inevitably have to process I and Q data separately. However, in this real data processing, the real-based classifiers fundamentally accompany performance limitations of AMR since it is challenging to learn complex-related features such as the size, phase, and location of each signal element appearing in the two-dimensional complex domain. This study proposes fully complex DL classifiers as a novel method for AMR. First, we newly define two core complex operations for constructing new classifiers: complex-valued (a) max-pooling and (b) softmax. In this step, we also analyze the applicability of the formerly proposed complex operations and the complex training possibility. Next, we experimentally derive AMR-optimized structures and present enhanced AMR architectures: (c) convolutional neural network (CNN) based and (d) residual neural network (ResNet) based fully complex-valued classifiers. Then, the proposed classifiers' performance is evaluated in various aspects: effectiveness of complex signal processing, in-depth analysis of AMR accuracy, effect of dataset size on AMR performance, computational complexity, and AMR performance in a commercial wireless environment. The analysis results show that complex-valued classifiers can provide faster learning speed, higher optimization, and better generalization at acceptable learning and recognition costs. In particular, the proposed classifiers significantly improve the AMR accuracy for the modulation types closely related to complex information (i.e., PSK, APSK, QAM), even in small datasets. Furthermore, to more thoroughly analyze the reasons for the performance improvement of the complex classifiers, we suggest an advanced visualizable tool: (e) the complex-valued gradient-weighted class activation maps (C-Grad-CAM). By visually representing the influence of the final decision on the input signal, this tool can provide an intuitive basis for complex data processing gains. We hope that C-Grad-CAM delivers valuable insights into explaining the inner workings of the complex classifiers, commonly considered black boxes.