**O.V. Bolkhovskaya**1**, V.A. Sergeev**2**, A.A. Maltsev**3

1-3 National Research Lobachevsky State University of Nizhny Novgorod (Nizhny Novgorod, Russia)

In this paper, we consider the problem of detection and wavefront estimation for a known deterministic signal received by a multi-element antenna array. The problem of testing two hypotheses about the wavefront of the signal is solved. The first one is the null hypothesis H0 – the wavefront of the useful signal is plane with an unknown angle-of-arrival (AoA), which corresponds to the assumption of the point radiation source and its location in the far-field zone (Fraunhofer zone). The second one is the alternative hypothesis H1 – the wavefront of the useful signal is spherical, it is received from the unknown direction and distance from the point radiation source, which corresponds to the assumption that the source is located in the near-field zone (Fresnel zone).

To solve this complex problem of "detection – estimation – distinction", an approach based on a modified GLRT test (Generalized Likelihood Ratio Test) is used. It should be noted that the standard GLRT approach used to distinguish between two composite hypotheses [Lehmann 1959, Kay 1993] implies replacing unknown signal parameters with their maximum likelihood (ML) estimates for each of the formulated hypotheses and using the likelihood ratio as a decision statistics. In this paper, in contrast to the standard GLRT approach, two original decision statistics, based on the obtained ML estimates of the useful signal wavefront, are proposed. The first decision statistic ε2 is formed as the square modulus of the difference between the estimates of the wavefront vectors for each of the hypotheses. As the second statistic, the estimated value of the coefficient γ, which stands before the quadratic term of the nonlinear regression model of the phase trend approximation on the elements of the antenna array, is used. An analytical expression is found that establishes a direct relationship between the statistics ε2 and γ. A detailed study of the properties of the proposed decision statistics has shown that the statistic γ is more convenient for practical usage, since its distribution function, assuming the hypothesis H0, at relatively small values of the signal-to-noise ratio (SNR > 9 dB) becomes close to the Gaussian (Normal) probability density function (PDF). Therefore, the threshold values γth of this statistic can be easily obtained using a standard normal PDF.

A signal processing scheme for the multi-element antenna array is proposed. A linear equidistant M-element antenna array (M=8) with a distance between elements equal to half the wavelength is considered. The characteristics of the algorithms for estimating the wavefront of the signal, the signal AoA and the distance to the radiation source, as well as the radiation source detection in the near-field Fresnel zone are studied by intensive simulations.

The accuracy of estimating the signal AoA and the distance to the source are investigated. The levels of the SNR at which these estimates practically reach the theoretical Cramer-Rao lower bound (CRLB) are found.

As an example, the confident detection zones for a base station with an 8-element antenna array are constructed for a mobile device operating in the 2.4 GHz band in Wi-Fi (IEEE Std. 802.11) network. It is shown that for such a scenario, a device with a typical transmitter power of 1 mW will be confidently detected (with a probability of right detection equals 0.8) based on receiving and processing only the first 2-4 symbols of the short preamble of one transmitted packet with a false alarm probability of 0.05 at distances of about 62 meters (510 wavelengths).

*Bolkhovskaya O.V., Sergeev V.A., Maltsev A.A. A passive system for source detection and distance measurement based on signal wavefront estimation. Radiotekhnika. 2022. V. 86. № 9. P. 98−112. DOI: https://doi.org/10.18127/j00338486-202209-11 (In Russian)*

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