V.I. Kulakova – Ph.D. (Eng.), Head of Department – Сhief Designer,

LTD «STC» (St. Petersburg)

E-mail: nika_kulakova@mail.ru

E.O. Mamonov – Engineer, 

LTD «STC» (St. Petersburg)

E-mail: velikiynovgorod1993@mail.ru

This paper analyses receiver phase coherence in a synthetic aperture direction finder (SADF) [1,2]. SADF operates with several  receivers which are mounted on different unmanned aerial vehicles (UAVs). Individual narrow-band stationary sources emitting in  frequency range from 30 MHz to 3 GHz are considered. The angular resolution in SADF is achieved by aperture synthesis technique. In this regard phase fluctuations caused by oscillators deserve special attention [4–6]. Section 1 of the paper describes radio signal processing in SADF (Fig. 1). The trajectory signal for matched filtering is given in Eq. 1. The phase fluctuations  (t) =δφrec1(t)–δφrec2(t) limit the maximum time of accumulation T. Table 1 shows the values of the required aperture synthesis time for a set of carrier frequencies Fc in order to achieve angular resolution δθ = 0,1º (UAV speed is 30 m/s). 

Section 2 shows that it is advisable to consider separately quadratic 2(t) and high-frequency h(t) components of phase fluctuations

(t). Then the conditions for coherent accumulation are established: max{|h(t)|} ≤ h with h = 6º and max{|2(t)|} ≤ 2 with 2 = 25º. 

Section 3 presents analytical investigation based on theoretic model for typical ultra stable oscillator [7] (Table 2, Fig. 2). This section shows simulation examples of (t) (Fig. 3) and h(t) (Fig. 4), as well as histograms for maximum synthesis time obtained for 200  examples of phase fluctuations (Fig. 5). Based on simulation results, maximum synthesis time is limited by high-frequency phase fluctuations h(t). Achievable angular resolution is 0,05º…0,04º (Table 3).

Section 4 is devoted to the experimental results and presents examples of (t) (Fig. 7) as well as histograms for maximum synthesis time (Fig. 8). Phase fluctuations in the experiments appeared to be greater in amplitude. There is also a noticeable quadratic phase component in the phase measurements, which is caused by the linear drift of the oscillator frequency. Based on experimental results, achievable angular resolution is 0,08º…0,04º (Table 3). 

The section makes the following conclusions. 

1. The theoretic model does not accurately describe the quadratic component of the phase fluctuations. In real conditions 2(t) and h(t) have comparable influence on the synthetic aperture duration. 
2. The model describes the phase fluctuations accurately at time intervals of up to 10–15 seconds, so it gives accurate results in the analysis of the maximum synthesis time for operating frequencies Fc ≥ 500 MHz. 
3. For frequencies Fc < 500 MHz the estimation of the maximum synthesis time according to the experimental results is about 1,7 times less than the simulation results.

1. Patent RU 2594759 G01S5/04. Sposob i ustrojstvo opredelenija koordinat istochnika radioizluchenija. Carik O.V., Terent'ev A.V., Kulakova V.I., Smirnov P.L. Zajav. 28.10.2015. Opubl. 27.07.2016. [in Russian]
2. Kulakova V.I. Rezul'taty razrabotki pelengatora s sintezirovannoj aperturoj dlja malogabaritnogo BLA. Trudy 24 Mezhdunar. nauch.tehnich. konf. «Radiolokacija, navigacija, svjaz'». Voronezh. T. 3. S. 280–280. [in Russian]
3. Kondratenkov G.S., Frolov A.Ju. Radiovidenie. Radiolokacionnye sistemy distancionnogo zondirovanija Zemli. M.: Radiotehnika. 2005. [in Russian]
4. Wang W.Q. Multi-Antenna Synthetic Aperture Radar / Boca Raton, FL: CRC Press, Taylor & Francis, cop. 2013.
5. Willis N.J. Bistatic Radar. 2nd ed. SciTech Publishing Inc. 2005.
6. Krieger G., Cassola M.R., Younis M., Metzig R. Impact of oscillator noise in bistatic and multistatic SAR. Proceedings of the IEEE International Geoscience and Remote Sensing Symposium. Korea. July 2005. P. 1043–1046.
7. Sajt AO «Morion», g. Sankt-Peterburg. Katalog. Precizionnyj maloshumjashhij kvarcevyj generator GK197-TS. URL: http://www.morion.com.ru/catalog_pdf/41-GK197-TS_VER_10.pdf. [in Russian]