The article presents the results of research into a method for representing complex data based on an overcomplete basis and l₀/l₁ norms. The proposed method is an extended modification of the neural-like MFNN (minimum fuel neural network) for the case of complex data. The influence of the choice of activation function on the performance of the method is analyzed. The results of the numerical simulation demonstrate the effectiveness of the proposed method for the case of sparse representation of complex data and can be used to determine the direction of arrival (DOA) for a uniform linear array (ULA).

This article outlines the results of comparison methods for representing complex data based on a redundant basis using the L0 norm and analyses the method of a modified MFNN (minimum fuel neural network) and the sparse representation method for the complex-data SL0 (smoothed L0 norm), based on the smoothed L0 norm. The example of numerical modeling for determining the direction of arrival (DOA) of sources received by an equidistant antenna array (ULA—Uniform Linear Array) shows that the SL0 method ensures a high convergence rate. However, unlike the MFNN-like neural network method, it does not guarantee convergence to the correct solution.

BACKGROUND: Related to the active development of unmanned vehicles, the task of development of effective sensors capable of creating three-dimensional models of the road scene becomes relevant. One of the types of such sensors is millimeter-wave radars with linear frequency modulation of the signal. Currently, they are mainly used to create two-dimensional models of the road scene in azimuth/range coordinates. However, the ability to scan in an elevation plane can significantly improve the recognition of low objects against the ground, which is especially important at agricultural machinery operation, especially in fields during harvesting. The transition to three-dimensional modeling of the road situation requires the ability to scan not only in azimuth, but also in elevation, which leads to a significant complication of the radar design. To reduce the complexity and cost of the radar, it is proposed to use the MIMO architecture (Multiple Input Multiple Output), but this method has a number of disadvantages, such as increased losses in signal energy and difficulties in synchronization in time or frequency domain of transmitters’ signals. AIM: The aim of the work is to conduct an experimental study and mathematical modeling of the radiation pattern characteristics of a combined microstrip two-dimensional antenna system with frequency scanning. To do this, we will use signal processing algorithms such as fast Fourier transform, correlation processing, and minimization of the L1 norm using a redundant basis (dictionary) and a combination of them are used. METHODS: This paper discusses signal processing methods for automotive radar designed to create a three-dimensional road scene. The radar uses an antenna array with a frequency-swinging beam pattern to scan in the vertical plane RESULTS: This paper presents the results of modeling and experimental studies conducted using algorithms based on the fast Fourier transform (FFT), the use of weight processing functions, and the modified MFNN (Minimum Fuel Neural Network) algorithm. CONCLUSION: This study demonstrates the effectiveness of constructing a three-dimensional road scene using frequency scanning of the beam pattern.

BACKGROUND: Recognition and representation of the road scene is a relevant task in the field of autonomous driving. One of the ways to improve the characteristics of the existing sensory hardware is the use of neural networks for signal processing. AIM: To conduct an experimental study of the possibilities of using the modified MFNN neural network to increase the resolution of a radar with a small number of channels, to compare it with the classical algorithm based on the fast Fourier transform (FFT), and, in addition, to compare the results with the data obtained from other types of sensors (lidars). METHODS: The algorithm of the road scene representation, in particular, the detection of pedestrians and cars, is used with a millimeter-range automotive radar and a method for determining data components in relation to the DOA problem, based on the MFNN neural network, modified for the case of representing signals taking complex values in the form of excessive basis coefficients minimizing these coefficients according to the L1 norm. The algorithm based on the fast Fourier transform (FFT) is used for comparative analysis. RESULTS: As a result of the conducted research, confirmation of the practical feasibility of the developed modifications of the MFNN method was obtained, and the advantage of using a neural network, consisting in increasing the degree of detail of objects, the accuracy of determining their shape and position using a radar with a small number of channels, was demonstrated. CONCLUSION: The obtained results can be used to develop solutions to improve the efficiency of detecting obstacles on the way of transport, automatic vehicle control, continuous environmental monitoring, and so on, which helps to improve the safety and efficiency of highly automated and autonomous systems.