R.F. Khaliullin1, A.I. Sulimov2

1,2 Institute of Physics, Kazan Federal University (Kazan, Russia)

1 sven456634@gmail.com; 2 asulimo@gmail.com

MIMO (Multiple Input Multiple Output) technology is highly promising for the organization of modern wireless communication systems. It also holds potential for coherent multi-position radio sounding, which involves assessing the spatial and temporal characteristics of various environments. One particularly challenging environment to study is the multi-path environment found in urban areas. Currently, portable MIMO radio complexes are being actively utilized to address these challenges. These complexes employ multi-position ultra-wideband probing techniques to capture the impulse response of the communication channel. However, before investing in expensive experimental hardware for MIMO sounding, it is advisable to evaluate the potential accuracy of estimation and determine the optimal parameters of probing signals through simulation modeling.

Regrettably, existing MIMO radio system models inadequately account for the spatial correlation effect between parallel antenna channels. This correlation arises due to clusters of scattering objects present in the probed multipath environment, which are separated by closely spaced antennas. Consequently, the objective of this study is to simulate the estimation of the impulse response matrix in a MIMO radio system using the maximum likelihood method, while considering the spatial correlation among the antenna channels.

The second objective is to evaluate the impact of the aforementioned spatial correlation effect on the throughput capacity of the MIMO radio system. Achieving these goals necessitated the development of a simulation model for the propagation environment of multipath signals. This model approximates the environment as a spatial Markov chain with a Poisson distribution of scatterers. When transitioning from one antenna to an adjacent antenna, a random jump was applied to the physical state of the channel based on the spatial correlation characteristics of the multipath environment. To incorporate this effect, scatterers were generated in the reference radio channel between the first transmit and receive antennas. Subsequently, additional scatterers were generated for the adjacent antenna channel between the first transmit and second receive antennas, taking into account the coefficient of spatial correlation. This process was repeated for each pair of neighboring transmit and receive antennas.

The research resulted in the development of a methodology for generating an array of statistically dependent impulse responses for MIMO systems with arbitrary configurations and random numbers of scatterers in the channel. The implementation of optimal estimation of the impulse response matrix using the maximum likelihood method demonstrated that, for a sample size of 1000 samples and a signal-to-noise ratio (SNR) of 18 dB, the error in recovering a single sample of the channel's impulse response is no more than 12.7%. Calculations based on generated realizations of the random multipath environment revealed that scaling the system does not lead to a proportional increase in throughput capacity. This effect can be attributed to the spatial correlation between closely spaced antenna channels.

Khaliullin R.F., Sulimov A.I. Simulation of the impulse response estimation for a MIMO radio system with multi-path effect. Radiotekhnika. 2023. V. 87. № 12. P. 99−109. DOI: https://doi.org/10.18127/j00338486-202312-11 (In Russian)

1. Molisch A.F. Wireless Communications. 2 ed. Wiley. IEEE. 2011. 844 p.
2. Sljusar V. Sistemy MIMO: principy postroenija i obrabotka signalov. Jelektronika NTB. 2005. № 8. S. 52-58 (in Russian).
3. Darsena D., Gelli G., Verde F., et al. Design and performance analysis of multiple-relay cooperative MIMO networks. Journal of Communications and Networks. 2019. V. 21(1). Р. 25-32.
4. Kadan F.E., Haliloglu O.A. Performance bound for maximal ratio transmission in distributed MIMO. IEEE Wireless Communications Letters. 2023. V. 12(4). Р. 585-589.
5. Duan G.Q., Wang D.W., Ma X.Y., Su Y. Three-dimensional imaging via wideband MIMO radar system. IEEE Geoscience and Remote Sensing Letters. 2010. V. 7(3). Р. 445-449.
6. He Q., Wang Z., Hu J., Blum R.S. Performance gains from cooperative MIMO radar and MIMO communication systems. IEEE Signal Processing Letters. 2019. V. 26(1). Р. 194-198.
7. Ganis A., Navarro E.M., Schoenlinner B., et al. A Portable 3-D imaging FMCW MIMO radar demonstrator with a 24×24 antenna array for medium-range applications. IEEE Transactions on Geoscience and Remote Sensing. 2018. V. 56(1). Р. 298-312.
8. Ponomarev G.A., Kulikov A.M., Tel'puhovskij E.D. Rasprostranenie UKV v gorode. Tomsk: MP «Rasko». 1991. 223 s. (in Russian).
9. Shhelkunov N.S. Issledovanie i razrabotka analiticheskoj modeli kanala MIMO na osnove rezul'tatov jeksperimental'nyh izmerenij: special'nost' 2.2.15 «Sistemy, seti i ustrojstva telekommunikacij»: Avtoref. diss. … kand. tehn. nauk. Novosibirsk: Sibirskij gos. un-t telekommunikacij i informatiki. 2022. 108 s. (in Russian).
10. Parsons J.D. The mobile radio propagation channel. 2nd ed. John Wiley & Sons. 2000. P. 433
11. Duel-Hallen A. Fading channel prediction for mobile radio adaptive transmission systems. Proceedings of the IEEE. 2007. V. 95. № 12. Р. 2299-2313.
12. Seijo O., Val I., Lopez-Fernandez J.A. Portable full channel sounder for industrial wireless applications with mobility by using sub-nanosecond wireless time synchronization. IEEE Access. 2020. V. 8. P. 175576–175588.
13. Costa N., Haykin S. Multiple-input multiple-output channel models: theory and practice. N.Y.: John Wiley & Sons. 2010. 225 р.
14. Kim M., Jeon H., Lee H., Chung H.J. Performance comparison of MIMO channel sounder architecture in between TDM scheme and FDM scheme. Proc. WiCOM. 2007. Shanghai. China. P. 192-195.
15. Garcia-Pardo C., Molina-Garcia-Pardo J.-M., Rodriguez J.-V., Llacer L.J. Comparison between time and frequency domain MIMO channel sounders. Proc. 72nd IEEE VTC. 2010-Sep.-69. Р. 1-5.
16. Voroshilin E.P., Lebedev V.Ju. Jeksperimental'naja ocenka impul'snoj reakcii kanala rasprostranenija radiovoln v santimetrovom diapazone. Doklady TUSUR. 2008. № 2(18). Ch. 2. S. 5-9 (in Russian).
17. Mukunthan P., Dananjayan P. Modified PTS with FECs for PAPR reduction in MIMO-OFDM system with different subblocks and subcarriers. International Journal of Computer Science Issues. 2011. V. 8(4). P. 444-452.
18. Bing H. Higher rank principal kronecker model for triply selective fading channels with experimental validation. IEEE Transactions on Vehicular Technology. 2015. V. 54. P. 1654-1663.
19. Yong S.С., Jaekwon K., Won Y.Y., Chung G.K. MIMO OFDM wireless communication with Matlab. Wiley-IEEE Press. 2010. P. 544.
20. Kay S.M. Fundamentals of statistical signal processing: estimation theory. University of Rhode Island Kingston: RI 02881. 1993. 595 p.
21. Ermolayev V.T., Flaksman A.G., Mavrichev E.A. Estimation of channel matrix rank for multielement antenna arrays working in multipath fading environment. Proc. 1st IEEE Int. Conf. on Circuits and Systems for Communication (ICCSC’02). St. Petersburg, Russia. 2002. Р. 416-419.
22. Bykov V.V. Cifrovoe modelirovanie v statisticheskoj radiotehnike. M.: Sovetskoe radio. 1971. S. 149-152 (in Russian).
23. Mihajlova O.K., Korogodin I.V., Lipa I.V. Universal'nyj generator dal'nomernyh kodov signalov sputnikovyh navigacionnyh radiosistem. Radiotehnika. 2019. № 9. S. 35-41. DOI: 10.18127/j00338486-201909(14)-04 (in Russian).
24. Kuznecov V.S., Shevchenko I.V., Volkov A.S., Solodkov A.V. Generacija ansamblej kodov Golda dlja sistem prjamogo rasshirenija spektra. Trudy MAI. 2017. № 96 (in Russian).
25. Tkac A., Wieser V. Channel estimation using measurement of channel impulse response. IEEE. 2014. P. 113-117.