# A CNN-MPSK Demodulation Architecture with Ultra-Light Weight and Low-Complexity for Communications
###### Abstract  
Modulation is an indispensable component in modern communication systems and multiple phase shift keying (MPSK) is widely studied to improve the spectral efficiency. It is of great significance to study the MPSK modulations of symmetric phases in practice. Based on convolutional neural networks (CNNs), we propose a generic architecture for MPSK demodulation, referred to as CNN-MPSK. The architecture utilizes a single-layer CNN and a pooling trick to crop network parameters. In comparison with conventional coherent demodulation, the CNN-MPSK eliminates three modules, i.e., carrier multiplication, bandpass filter and sampling decision. Thus, we can avoid \(\pi\)-inverted phenomenon from the multiplication of two carrier waves with different phases, as the carrier multiplication is not employed. In addition, we can reduce errors introduced by sampling decision. Furthermore, we conduct bit-error-rate tests for binary-PSK, 4 PSK, 8 PSK, and 16 PSK demodulation. Experimental results reveal that the performance of CNN-MPSK is almost the same to that of conventional coherent demodulation. However, the CNN-MPSK demodulation reduces computational complexity from \(\mathbf{O}(n^{2})\) to \(\mathbf{O}(n)\) as compared to the latter one. Additionally, the proposed scheme can be readily applied for demodulation of non-symmetric MPSK constellations that maybe distorted by linear and nonlinear impairments in communication systems. c 2022 14 April 2022 25 April 2022  
frequency offset, symbol rate, and multipath fading. The traditional convolutional neural networks (CNNs) achieve similar performance to residual networks, but with the increased trainable parameters [7]. A novel two-step training for CNN-based automatic modulation classification (CNN-AMC) was then proposed in order to handle complex tasks [8]. Simulation results indicate that the CNN-AMC approximates the optimal maximum likelihood (ML)-AMC. Regarding inference speed, the deep learning-based approach is more than a hundred times faster than ML-AMC by using parallel computation. The relatively simple neural network architectures were presented for space-time-block-codes multiple-input multiple-output systems (MIMO), which are sparse autoencoders-based deep neural networks (DNN) and radial basis function networks (RBFN) [9]. RBFN and DNN weights are optimized using the Broyden-Fletcher-Goldfarb-Shannon algorithm and the least square approach. For the classification of digitally modulated signals in varying channel conditions, [PERSON] and [PERSON] [10] proposed a fully linked two-layer feed-forward DNN with layerwise unsupervised pretraining. This system uses multiple hidden nodes and independent autoencoders for learning feature maps. The proposed DNN has good classification accuracy even when trained and tested at different signal-to-noise ratios (SNRs). To be more efficient in low SNR conditions, the deep belief network and spiking neural network were utilized to reduce execution latency associated with deep learning architectures [11]. Each feature-based AMC classifier is then studied to determine the upper and lower performance bounds within this adaptive framework. By employing a CNN-based technique, an intelligent eye-diagram analyzer was proposed to recognize modulation formats and estimate optical SNR [12]. Aided by oscilloscope in simulation, the eye diagram images of four modulation formats can be obtained over a wide optical SNR range. It was showed that CNN achieves higher accuracy than other machine learning algorithms such as decision trees, \(k\)-nearest neighbors, back-propagation neural networks, and support vector machines. Using the strengths of the CNN and the long short-term memory (LSTM), the AMC is developed by dual-stream construction, which efficiently explores the feature interaction and spatial-temporal properties of raw complex temporal signals [13]. In particular, the signals first go through preprocessing to be converted to the temporal inphase/quadrature format and amplitude/phase representation.