Journal Radioengineering №1 for 2026 г.
Article in number:
Algorithm for controlling spatial power distribution in MIMO-radars with BPSK- and QPSK-signals
Type of article: scientific article
DOI: https://doi.org/10.18127/j00338486-202601-06
UDC: 629.052.3
Authors:

Yu.M. Meleshin1

1 MIET (Moscow, Zelenograd, Russia)

1 i@imym.ru

Abstract:

Modern radars built using multiple-input-multiple-output technology (hereinafter referred to as MIMO radars) are constructed using various signal-code structures and methods for ensuring the orthogonality of transmitting signals. The problems of controlling the spatial distribution of power for MIMO radar transmission while maintaining the orthogonality properties of transmitted signals are relevant, while an important direction in the development of MIMO radars is the transition to simple architectures using signals only with binary phase shift keying (BPSK) and quadratic keying (QPSK), such systems allow to abandon the use of digital-to-analog converters in transmitting channels and significantly simplify the implementation. This paper examines in detail the existing methods for controlling the power distribution for MIMO radars based on Zadoff-Chu sequences, which are constructed based on the synthesis of the alphabet of amplitude and phase values of both signals and the spatial precoding matrix. In this case, for the case with one direction, the problem is solved simply analytically, and for cases with several directions, the problem is solved by using optimization algorithms that change the extracted values from the alphabet and estimate the degree of divergence of the target distribution and the one obtained at each search iteration. Within the framework of this work, a replacement of the gradient descent optimization algorithm with a genetic algorithm is proposed, the operability of the proposed approaches is shown, and an increase in power in target directions from 3 to 7 dB is shown. A method for power control in MIMO radars with hardware limitations in terms of the phase values of transmitting element signals, in particular, only BPSK and QPSK, is proposed and investigated. As a result of modeling the proposed method, an increase in the radiated power in target directions from 2 to 3 dB for BPSK signals and from 2.2 to 3 dB (for 3 target directions) for QPSK signals is shown. It is shown that due to the specifics of the BPSK mode implementation, the final power distribution is always symmetrical, which indicates inefficient power distribution, however, even in this mode, the gain in radiated power towards target directions is considered a positive result. In the case of using QPSK signals, it is possible to achieve a significant gain even for 3 ... 5 spatial directions, while such signals can still be generated without using a digital-to-analog converter, using only two digital signals with two levels (for example, generated by FPGA) and a quadrature modulator in each transmitting channel. These results allow increasing the signal-to-noise ratio in operating modes with a priori information about target angular areas of interest, for example, in the additional search or target tracking mode.

Pages: 54-71
For citation

Meleshin Yu.M. Algorithm for controlling spatial power distribution in MIMO-radars with BPSK- and QPSK-signals. Radiotekhnika. 2026. V. 90. № 1. P. 54−71. DOI: https://doi.org/10.18127/j00338486-202601-06 (In Russian)

References
  1. Gul M.M.U., Ma X., Lee S. Timing and frequency synchronization for OFDM downlink transmissions using Zadoff Chu sequences. IEEE Trans. Wireless Commun. Mar. 2015. V. 14. № 3. Р. 1716–1729.
  2. Popovic B.M. Spreading sequences for multicarrier CDMA systems. IEEE Trans. Commun. Jun. 1999. V. 47. № 6. Р. 918–926.
  3. Ipanov R.N., Baskakov A.I., Olyunin N., Ka M.H. Radar Signals with ZACZ based on pairs of D-Code sequences and their compression algorithm. IEEE Signal Processing Letters. 2018. V. 25. № 10. P. 1560-1564. DOI: 10.1109/LSP.2018.2867734.
  4. Ljalin K.S., Hasanov M.S., Meleshin Ju.M., Kuz'min I.A. Spektral'nyj metod podavlenija bokovyh lepestkov avtokor-reljacionnoj funkcii dlinnyh psevdosluchajnyh binarnyh posledovatel'nostej. Trudy MAI. 2018. № 103. S. 23 (in Russian).
  5. Meleshin Ju.M., Hasanov M.S., Karpov V.N. MIMO RLS na baze linejno-chastotno modulirovannyh signalov s bystroj sglazhennoj fazokodovoj manipuljaciej. Cifrovaja obrabotka signalov. 2024. № 4. S. 63-68 (in Russian).
  6. Zajcev G.V., Kondranina N.S., Litvinov D.M. Ocenka harakteristik metoda nesoglasovannoj fil'tracii, minimiziruju-shhego integral'nyj uroven' bokovyh lepestkov fazokodomanipulirovannyh signalov. Cifrovaja obrabotka signalov. 2017. № 1 (in Russian).
  7. Shi C., Ding L., Wang F., Salous S., Zhou J. Joint target assignment and resource optimization framework for multitarget tracking in phased array radar network. IEEE Syst. J. Sep. 2021. V. 15. № 3. Р. 4379–4390.
  8. Hassanien A., Vorobyov S.A. Transmit energy focusing for DOA estimation in MIMO radar with colocated antennas. IEEE Trans. Signal Process. Jun. 2011. V. 59. № 6. Р. 2669–2682.
  9. Wang X., Wang L., Li X., Bi G. Nuclear norm minimization framework for DOA estimation in MIMO radar. Signal Process. Jun. 2017. V. 135. Р. 147–152.
  10. De Maio Aubry A., Huang Y. MIMO radar beampattern design via PSL/ISL optimization. IEEE Trans. Signal Process. Aug. 2016. V. 64. № 15. Р. 3955–3967.
  11. Imani S., Ghorashi S.A. Transmit signal and receive filter design in co-located MIMO radar using a transmit weighting matrix. IEEE Signal Process. Lett. Oct. 2015. V. 22. № 10. Р. 1521–1524.
  12. Gregorio F.H., et al. Analysis and compensation of nonlinear power amplifier effects in multi-antenna OFDM systems. Espoo, Finland: Helsinki Univ. of Technology. 2007.
  13. Aldayel O., Monga V., Rangaswamy M. Successive QCQP refine ment for MIMO radar waveform design under practical constraints. IEEE Trans. Signal Process. Jul. 2016. V. 64. № 14. Р. 3760–3774.
  14. Huang Y., Liu C., Song Y., Yu X. DFT codebook-based hybrid precoding for multiuser mmWave massive MIMO systems. EURASIP J. Adv. Signal Process. Dec. 2020. V. 2020. № 1. Р. 1–13.
  15. Liu, Lau V. Phase only RF precoding for massive MIMO systems with limited RF chains. IEEE Trans. Signal Process. Sep. 2014. V. 62.
    № 17. Р. 4505–4515.
  16. Mukkavilli K.K., Sabharwal A., Erkip E., Aazhang B. On beamforming with finite rate feedback in multiple-antenna systems. IEEE Trans. Inf. Theory. Oct. 2003. V. 49. № 10. Р. 2562–2579.
  17. Raghavan V., Hanly S.V., Veeravalli V.V. Statistical beamforming on the Grassmann manifold for the two-user broadcast channel. IEEE Trans. Inf. Theory. Oct. 2013. V. 59. № 10. Р. 6464–6489.
  18. Gaydos M.G., Love D.J., Kim T. Constant modulus precoded MIMO radar based on zadoff-chu sequences. IEEE Transactions on Radar Systems. 2024. V. 2. Р. 677-689. DOI: 10.1109/TRS.2024.3409029.
  19. Proakis J.G. Digital signal processing: principles, algorithms, and applications. Chennai. India: Pearson. 2001.
  20. Grillet P.A. Abstract algebra. V. 242. New York. NY. USA: Springer. 2007.
  21. Chu D.C. Polyphase codes with good periodic correlation properties. IEEE Trans. Inf. Theory. Jul. 1972. V. IT-18. № 4. Р. 531–532.
  22. Beyme S., Leung C. Efficient computation of DFT of Zadoff–Chu sequences. Electron. Lett. 2009. V. 45. № 9. Р. 461–463.
  23. Jordan J. Intro to optimization in deep learning: gradient descent. Paperspace. Series: Optimization. 2018. URL: https://blog.pa-perspace.com/intro-to-optimization-in-deep-learning-gradient-descent/.
  24. Kashirina I.L., Demchenko M.V. Issledovanie i sravnitel'nyj analiz metodov optimizacii, ispol'zuemyh pri obuchenii nejronnyh setej. Vestnik Voronezhskogo gos. un-ta. Ser. Sistemnyj analiz i informacionnye tehnologii. 2018. № 4. S. 123-132 (in Russian).
  25. Gasnikov A.V. Sovremennye chislennye metody optimizacii. Metod universal'nogo gradientnogo spuska. Izd. 2-e, dop. M.: Moskovskij fiziko-tehnicheskij institut (gosudarstvennyj universitet). 2018. 181 s. (in Russian).
  26. Diveev A.I., Konstantinov S.V. Jevoljucionnye algoritmy dlja reshenija zadachi optimal'nogo upravlenija. Vestnik Rossijskogo universiteta druzhby narodov. Ser. Inzhenernye issledovanija. 2017. T. 18. № 2. S. 254-265 (in Russian).
  27. Goldberg D.E. Genetic Algorithms in search, optimization, and machine learning. AddisonWesley. 1989. 412 p.
Date of receipt: 21.08.2025
Approved after review: 06.10.2025
Accepted for publication: 29.12.2025
Download