COMPUTATIONAL COMPLEXITY OF THE CORRELATION SIGNAL PROCESSING ALGORITHM WITH ADAPTATION TO THE INFORMATION TRANSMISSION RATE BASED ON PERFECT BINARY MATRICES

Abstract

When developing methods for generating and correlating signal processing of promising radio communications, one of the priority tasks is to ensure the minimum complexity of correlation signal processing at the reception. The paper proposes the structure of a device for correlation signal processing with adaptation for the information transmission rate based on perfect binary matrices. The correlation processing device includes: Cooley-Tukey direct and inverse transform devices, a memory device, a spectra multiplier and a solver. The total computational complexity of the algorithm for correlation processing of signals with adaptation to the information transmission rate based on perfect binary matrices is calculated. The dependences of the computational complexity of the algorithm for correlation processing of signals with adaptation to the information transfer rate based on perfect binary matrices and the algorithm for correlation processing by direct Fourier transform on the length of the code sequence are investigated. According to the results of the study, it was found that with the length of the code sequence exceeding eight bits, the computational complexity of the correlation processing algorithm by the direct Fourier transform is greater than the computational complexity of the correlation signal processing algorithm with adaptation to the information transfer rate based on perfect binary matrices. The gain achieved in the amount of computations of the proposed algorithm in comparison with the correlation processing algorithm by the direct Fourier transform is calculated. The dependence of the payoff is investigated, it is achieved in the amount of computations, on the length of the code sequence, as a result of which it is established that the payoff is directly proportional to the length of the code sequence and inversely proportional to the doubled sum of the binary logarithm of the length of the code sequence and one. When the length of the code sequence is more than eight bits, the gain achieved in the amount of computation is greater than one. Reducing the computational complexity of the signal correlation processing algorithm at the reception allows you to reduce the mass-dimensional characteristics of the entire system, its cost and power consumption. Prospects for further research are the study of the structural and energy secrecy of signals with adaptation to the information transmission rate based on perfect binary matrices.

Keywords

• special purpose radio communication systems
• correlation signal processing
• computational complexity of correlation signal processing
• cooley-tukey transform