Nested code sequences of Barker — Mersenne — Raghavarao

Introduction: The problem of noise-free encoding for an open radio channel is of great importance for data transfer. The results presented in this paper are aimed at stimulating scientific interest in new codes and bases derived from quasi-orthogonal matrices, as a basis for the revision of signal processing algorithms.Purpose: Search for new code sequences as combinations of codes formed from the rows of Mersenne and Raghavarao quasi-orthogonal matrices, as well as complex and more efficient Barker — Mersenne — Raghavarao codes.Results: We studied nested code sequences derived from the rows of quasi-orthogonal cyclic matrices of Mersenne, Raghavarao and Hadamard, providing estimates for the characteristics of the autocorrelation function of nested Barker, Mersenne and Raghavarao codes, and their combinations: in particular, the ratio between the main peak and the maximum positive and negative “side lobes”. We have synthesized new codes, including nested ones, formed on the basis of quasi-orthogonal matrices with better characteristics than the known Barker codes and their nested constructions. The results are significant, as this research influences the establishment and development of methods for isolation, detection and processing of useful information. The results of the work have a long aftermath because new original code synthesis methods need to be studied, modified, generalized and expanded for new application fields.Practical relevance: The practical application of the obtained results guarantees an increase in accuracy of location systems, and detection of a useful signal in noisy background. In particular, these results can be used in radar systems with high distance resolution, when detecting physical objects, including hidden ones.

LPI Radar Waveform Recognition Based on CNN and TPOT

The electronic reconnaissance system is the operational guarantee and premise of electronic warfare. It is an important tool for intercepting radar signals and providing intelligence support for sensing the battlefield situation. In this paper, a radar waveform automatic identification system for detecting, tracking and locating low probability interception (LPI) radar is studied. The recognition system can recognize 12 different radar waveform: binary phase shift keying (Barker codes modulation), linear frequency modulation (LFM), Costas codes, polytime codes (T1, T2, T3, and T4), and polyphase codes (comprising Frank, P1, P2, P3 and P4). First, the system performs time–frequency transform on the LPI radar signal to obtain a two-dimensional time–frequency image. Then, the time–frequency image is preprocessed (binarization and size conversion). The preprocessed time–frequency image is then sent to the convolutional neural network (CNN) for training. After the training is completed, the features of the fully connected layer are extracted. Finally, the feature is sent to the tree structure-based machine learning process optimization (TPOT) classifier to realize offline training and online recognition. The experimental results show that the overall recognition rate of the system reaches 94.42% when the signal-to-noise ratio (SNR) is −4 dB.

Research and Analysis of Autocorrelation Functions of Code Sequences Formed on the Basis of Monocyclic Quasi-Orthogonal Matrices

Introduction: Barker codes representing binary sequences (codes) of finite lengths 2, 3, 4, 5, 7, 11 and 13 are widely used in solving the problem of increasing the noise immunity of radar channels. However, the code sequences for n > 13 are unknown. Sequences derived from quasi-orthogonal Mersenne matrices also have not been used for these purposes.Purpose: Studying the ways to compress a complex modulated signal by Mersenne sequences obtained from the first rows of a monocyclic quasi-orthogonal Mersenne matrix, as an alternative to Barker codes.Results:It has been found out that the characteristics of autocorrelation functions for Mersenne codes 3, 7 and 11 exceed those for Barker codes. This is a basis for ensuring greater noise immunity of probing signals in radar channels, as well as for increasing the probability of their correct detection, proving the expediency of their application for amplitude and phase modulation of radio signals.Practical relevance:The obtained results allow you to increase the compression characteristics in radar systems when solving the problem of detecting targets under noise and interference. The wide application of Barker codes of length 3, 7 and 11 in digital data transmission systems provides a special interest in similar Mersenne codes when implementing noise-resistant data transmission in radio channels in a complex electromagnetic environment. Discussion: An unresolved problem is the non-symmetry of elements in a coding Mersenne sequence. This problem can be solved either by special synthesis of a phase-modulated signal or by finding new approaches to their compression.