Fully Complex Deep Learning Classifiers for Signal Modulation Recognition in Non-Cooperative Environment

Abstract

Deep learning (DL) classifiers have significantly outperformed traditional likelihood-based or feature-based classifiers for signal modulation recognition in non-cooperative environments. However, despite these recent improvements, the conventional DL classifiers still have an unintended problem in handling the received signal in which the in-phase and quadrature components are separated. Even though the two components seem to be individually uncorrelated to each other, they are definitely the theoretical real and imaginary parts of a signal sample in the complex domain. Thus, it may be helpful for a classifier to regard and treat the modulated signal as a complex data array representing beneficial mutual information between the two real data arrays. In this paper, we propose two types of fully complex convolutional neural network (CNN) and residual neural network (ResNet) classifiers that deal with the complex data instead of the two separated data. First, we organize and define the core complex operations for implementing the complex DL classifiers. Next, the architectures of the proposed classifiers are realized by applying the structural optimizations and the regularization technique. Then, the various aspects of the classifiers' performance are analyzed and explained for providing comprehensive and deep understandings: (a) the effectiveness of the complex signal handling, (b) the in-depth evaluation of classification accuracy, (c) the impact of the data size on performance, and (d) the computational complexity. The experimental results show that the proposed classifiers can provide the faster learning speed, the higher optimization, and the better generalization with sacrificing acceptable learning and classification costs. Especially, our approaches remarkably improve the performance on the mutually correlated modulation types (i.e., the phase-related modulations: PSK, APSK, and QAM) even in the less-scale datasets.

A Novel Complex-Valued Hybrid Neural Network for Automatic Modulation Classification

“…The goal of GRU is to address the issues of gradient disappearance and gradient explosion in the training process of lengthy sequences. In this paper, the modulus of the real and imaginary features extracted from the previous network layer is taken as the input of this network layer to realize the complex-valued GRU, whose expression is shown in Equation (12). Generally, to normalize the predictions to a probability distribution, softmax is typically the final step in DL-AMC models.…”

“…Generally, to normalize the predictions to a probability distribution, softmax is typically the final step in DL-AMC models. In this paper, an extension of the real softmax to the complex domain is achieved by using the magnitude of the complex data shown in Equation ( 13) [12]. (8) According to Equations ( 6) and ( 8), it could be found that Z can be obtained by a linear combination of the columns and Z DL , which can be shown in Equation (9).…”

“…Generally, to normalize the predictions to a probability distribution, softmax is typically the final step in DL-AMC models. In this paper, an extension of the real softmax to the complex domain is achieved by using the magnitude of the complex data shown in Equation ( 13) [12].…”

“…Usually, most of the collected signals, such as electromagnetic, optical waves, and RF signals, are complex numbers [9]. For example, in the actual situation, the modulation signal in the communication field is complex and consists of in-phase (I) and quadrature (Q) channel data, where the phase component represents the time course or position difference and the amplitude represents the energy or power of the wave [10][11][12]. Since complex-valued neural networks (CVNNs) can directly process phase and amplitude information and can completely extract wave information, the data expression ability can be improved by using CVNNs, which is more suitable for processing wave-related information processing models than real-valued neural networks (RVNNs) [13,14], and provides a new solution for dealing with problems with complex characteristics or calculations on a complex domain.…”

“…At the same time, a complex-valued DNN is proposed, which has a lower error rate and fewer parameters than real-valued DNN and complex ResNets [5]. In 2022, to better improve the performance of the DL-AMC models based on CVNNs, S. Kim et al [12] extended max-pooling and softmax to complex operations. To handle complex-valued data, complex-valued CNN and complex-valued ResNet were developed based on the basic architecture of real-valued CNN and ResNet.…”