Градієнтна оптимізація двопараметричної віконної функції Найквіста для зменшення позасмугогово випромінювання в OFDM системі

Abstract

The relationship between Nyquist pulses in the time domain and Nyquist window functions used in orthogonal frequency division multiplexing (OFDM) technology has been investigated. One of the ways to approximate the transition region of Nyquist window functions using piecewise linear functions has been analyzed. This method allowed increasing the number of degrees of signal freedom through the introduction of two additional parameters. The spectral density of the selected two-parameter Nyquist window function has been determined. Optimization of the synthesized signal by the criterion of minimum energy in the first side lobes of its spectral density has been performed. To solve the optimization problem, the gradient descent method with minimization of the function at each stage of the iteration by the golden section method is chosen. In the MATLAB programming environment, program has been created that works according to the selected optimization algorithm. With the maximum allowable relative error ε =10–3, the number of iterations of the gradient search method is 2 iterations. It is established that at the optimal values of the signal parameters the amount of energy concentrated in the first three side lobes of its spectral density is 12.6 dB less than for the rectangular window function. The graphs for the synthesized window function with optimal parameters in time and frequency domain are given in this paper. The use of the two-parameter Nyquist window function with reduced level of spectral density of the side lobes allows reducing the level of out-of-band radiation of the OFDM signal and increasing the resistance of the system with many subcarriers to frequency offsets caused by the mutual movement of the transmitter and receiver. It should be noted that the chosen gradient search algorithm is universal and can be used to optimize the Nyquist window functions by different criteria and regardless of the number of signal parameters.