Use of nonlinear spectral estimation in the problem of determining the mutual delay of signals

Abstract

We consider an algorithm of nonlinear spectral estimation based on the maximum-entropy method using the procedure of explicit obtaining of the Lagrange multipliers with reference to the problem of determining the time and frequency shifts of radio signals of communication systems. Modification of a method for constructing the uncertainty function on the basis of a nonlinear algorithm of spectral estimation with a fixed body of computations is proposed.

An Efficient Algorithm for Joint Evaluation of the Time Delay and Frequency Shift of the Frequency-Modulated Signals

“…(11) is the ratio of the maximum value to the average level of the sample Q(f, τ ) at the frequencies corresponding to the maximum absolute value of the distributions given by Eqs. (7) and (8). Its value characterizes the manifestation degree of the correlation peak and, correspondingly, the degree of confidence with respect to the time-delay determination result.…”

“…Figure 3 shows the criterion S as a function of the SNR for the FSK signals when determining the time delay on the basis of Eq. (7), as well as modified algorithm (8) for various relative frequency shifts Δf . The solid black, the solid gray, and the dashed curves correspond to frequency shifts of 500 Hz, 1000 Hz, and 5000 Hz, respectively.…”

“…The proposed modification (8) of the calculation algorithm allows one to improve the estimation reliability of the mutual time delay for a comparable calculation efficiency of the algorithms for the FSK signals with the SNR exceeding −3 dB. Note that the difference in the behavior of the criterion S when the frequency shift varies in a range of 500 Hz to 5 kHz (due to the influence of the low-frequency filtering procedure with decimation when performing calculations on the basis of Eq.…”

“…(3), any definition of the mutual uncertainty function, which is given in [1][2][3][4], can be used. When processing the short realizations of the signals, the efficiency of the time-delay determination can be improved using the nonlinear spectral estimation in the algorithms of the joint measurement of the time and frequency signal shifts [8]. In this work, we propose the algorithm for determining the time delay, which is based on the modification of the method for calculating the uncertainty function [4].…”