Combined digital filtering of harmonic content of phase-shift keyed signals in the problem of estimation of the time delay

Abstract

We propose a two-step method for digital filtering of phase-shift keyed signals filtering in the problem of determination of the time delay during the multichannel propagation. The first step is realized as an information-optimal linear filter with complex coefficients, while the second step, as a quadratic filter based on the minimum-variance criterion. The efficiency of the proposed method is demonstrated for short PSK signals with various carrier frequencies against the background of additive and multiplicative noise. The developed algorithm can easily be implemented in real time on the basis of a digital signal processor.

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:…”

“…The signal-to-noise ratio in the studied channel varied from −15 to 15 dB. For the simulation, we used the earlier proposed filtering algorithm [5] (line 1 in Fig. 4), its generalization, which is proposed in this paper (line 2 in Fig.…”

“…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.…”