A.V. Smolyakov1, A.S. Podstrigaev2
1,2 Saint Petersburg Electrotechnical University "LETI" (Saint Petersburg, Russia)
Multichannel digital receivers based on the signal processing technology involving undersampling are used for the instantaneous wideband analysis of the electronic environment. One of the most common algorithms for measuring input signal’s carrier frequency in such receivers includes unfolding of the signal’s spectrums from the first Nyquist zone of all receiver’s channels to the single frequency axis and searching for the frequency where the spectrum components from all of the receiver’s channels coincided. Performance of the signal detector, which uses this algorithm in its operation, was not studied. In the absence of a mathematical description of such a detector, evaluating the digital undersampling receiver’s sensitivity becomes possible only in the late stages of prototyping when it can be done through experimental study. Additionally, it is impossible to set a detection threshold in the receiver according to the Neyman-Pearson criterion, which hardens building constant false alarm rate (CFAR) systems based on this type's receivers.
This paper aims to develop the mathematical description of the digital undersampling receiver's detector and then, using this model, to get expressions and computer models to evaluate the characteristics of such receiver even in early stages of its development. This paper's main result is the developed mathematical tools necessary to evaluate the multichannel digital undersampling receiver’s signal detector performance. It is shown that the false alarm probability in such a detector does not exceed some value no matter how small the detection threshold is. The expression for evaluating the maximum false alarm probability by the receiver’s parameters is also presented in the paper alongside the true positive rate plots as a function of signal-to-noise ratio for the three-channel receiver.
These results can be used in evaluating the digital undersampling receiver’s characteristics in the early stages of its development. It allows one to choose optimal values of the receiver’s parameters which are hard and expensive to change after prototyping is done, and there is an opportunity to evaluate the receiver’s characteristics experimentally. Moreover, the obtained mathematical expressions make it possible to set the receiver's detection threshold according to the Neyman-Pearson criterion and build on its base a CFAR-systems widely used for wideband signal analysis.
Smolyakov A.V., Podstrigaev A.S. Detection performance characteristics of the digital undersampling receiver. Radiotekhnika. 2021. V. 85. № 9. P. 95−107. DOI: https://doi.org/10.18127/j00338486-202109-09 (In Russian)
- Patent for the Invention (US) № 5109188. Digital frequency measurement receiver with bandwidth improvement through multiple sampling of real signals. Sanderson R.B., Tsui J.B.Y. Publ. 24.03.1992.
- Patent for the Invention (US) № 5099243. Digital frequency measurement receiver with bandwidth improvement through multiple sampling of complex signals. Sanderson R.B., Tsui J.B.Y. Publ. 24.03.1992.
- Patent for the Invention (US) № 5109188. Instantaneous frequency measurement receiver with bandwidth improvement through phase shifted sampling of real signals. Sanderson R.B., Tsui J.B.Y. Publ. 28.04.1992.
- Patent for the Invention (US) № 5293114. Frequency measurement receiver with means to resolve an ambiguity in multiple frequency estimation. McCormick W.S., Tsui J.B.Y. Publ. 08.03.1994.
- Patent for the Invention (EP) № 1618407. Digital electronic support measures.. Beharrell G.P. Publ. 17.04.2013.
- Patent na izobretenie (RF) № 2516763. Sposob rasshirenija polosy chastot ocenki spektrov signalov.. Krenev A.N., Botov V.A., Gorjuncov I.S., Pogrebnoj D.S., Toporkov V.K. Opubl. 20.05.2014. Bjul. № 14 (in Russian).
- Huang S., Zhang H., Sun H., Yu L., Chen L. Frequency estimation of multiple sinusoids with three sub-Nyquist channels. Signal Processing. 2017. № 139. P. 96−101. DOI: 10.1016/j.sigpro.2017.04.013
- Botov V.A., Gorjuncov I.S., Pogrebnoj D.S., Krenev A.N., Toporkov V.K. Sposob rasshirenija polosy chastot obnaruzhenija radiosignalov v spektral'noj oblasti. Sistemy sinhronizacii, formirovanija i obrabotki signalov. 2013. № 2(4). S. 122-124 (in Russian).
- Lesnikov V.A., Naumovich T.V., Chastikov A.V., Garsh D.G. Vosstanovlenie spektra signala, iskazhennogo pri subdiskre-tizacii. DSPA: Voprosy primenenija cifrovoj obrabotki signalov. 2016. № 2(6). S. 239-243 (in Russian).
- Kondakov D.V., Lavrov A.P. Opredelenie chastotnogo spektra mnogokomponentnogo radiosignala v cifrovom priemnike s subdiskretizaciej. Radiotehnika. 2019. № 9(13). S. 20-26. DOI: 10.18127/j00338486-201909(13)-02 (in Russian).
- Lesnikov V.A., Naumovich T.V., Chastikov A.V. Vosstanovlenie analiticheskogo signala, iskazhennogo aliasingom pervogo porjadka. Sb. trudov IX Vseross. nauch.-tehnich. konf. «Problemy razrabotki perspektivnyh mikro- i nanojelektronnyh sistem – 2020». M.: IPPM RAN. 2020. № 3. S. 194-200 (in Russian).
- Liu C., Chen K., Zhang J., Wang Y., Wang H. Using FFT to reduce the computational complexity of sub-Nyquist sampling based wideband spectrum sensing. Journal of Physics: Conference Series. 2019. № 1237. DOI: 10.1088/1742-6596/1237/2/022004
- Sank D.T. Fast, Accurate State Measurement in Superconducting Qubits: PhD dissertation. University of California, Santa Barbara. 2014. URL: http://web.physics.ucsb.edu/~martinisgroup/theses/Sank2014.pdf
- Schoukens J., Renneboog J. Modeling the noise influence on the Fourier coefficients after a discrete Fourier transform. IEEE Transactions on Instrumentation and Measurement. 1986. № 3(35). С. 278 286. DOI:10.1109/tim.1986.6499210
- Tsui J. Special Design Topics in Digital Wideband Receivers. Norwood, MA: Artech House. 2010. P. 110-113.