Algorithm for nonlinear digital filtering of harmonic filling of phase-shift keyed signals

Abstract

In this work, we propose a method for nonlinear digital filtering of phase-shift keyed signals with different carrier frequencies on the basis of separating the phase discontinuities of the input signals. The method allows one to avoid compensation for unknown frequency shift in the problems of determining the time delay of signals in the case of multichannel propagation. The efficiency of the proposed method is shown for the signals which are short informative packages with the phase-shift keying against the noise background in the presence of the Doppler effect.

An algorithm for digital preprocessing of QPSK signals in the problem of mutual time delay estimation

“…The algorithms for preprocessing of FSK signals, which were proposed in [3][4][5], are based on the use of a suboptimal digital narrow-band filtering system, which is generally nonlinear and is adjusted for transmission of the signal carrier frequency and suppression of all other frequencies. In the case of an input signal in the form of a complex sinusoid of given frequency f 0 the output of the filtering system is constant, and the response to phase-shift keying (phase shift by π rad) is maximum.…”

“…Moreover, the response strongly depends on the frequency shift. These constraints make it necessary to generalize the earlier proposed processing method [3][4][5] by introduction of auxiliary narrow-band filters tuned to respective characteristic frequencies f ± 0 of the spectrum of signal (1) with ψ = ±π/2. The frequencies f ± 0 are chosen on the basis of the maximization criterion for the response to respective phase-shift keying, and their position is determined by the form of the modulus of the spectrum S(f ) and the properties of the filtering system.…”

“…A quadrature filter based on generalization of Capon's minimum-variance approach was proposed in [3,5]. Capon's approach consists in construction of a nonlinear filter whose output signal has the minimum variance under the condition of a unit transmission coefficient at a given frequency:…”

“…Nevertheless, the idea of Capon's method can serve as the basis for construction of nonlinear filters that are free of the above-mentioned constraints [7]. On the basis of a linear filter, one can construct a quadrature filter whose output signal is determined by the expression [3] …”

“…This paper is devoted to generalization of the earlier proposed algorithms [3][4][5] of preprocessing of binary PSK signals to the case of quadrature phase-shift-keyed (QPSK) signals. The proposed scheme is qualitatively similar to demodulation of PSK signals and consists in processing of an input signal x[n] using a system of three bandpass filters forming a complex output signal Y [n] (Fig.…”