bsuirДоклады БГУИРDoklady BGUIR1729-76482708-0382БГУИРbsuir-880Research ArticleСтатьиВЕРОЯТНОСТЬ ОШИБОК ПРИ ПРИЕМЕ СИГНАЛОВ ПО УПЛОТНЕННЫМ КАНАЛАМ СВЯЗИ С ОРТОГОНАЛЬНЫМ ЧАСТОТНЫМ РАЗДЕЛЕНИЕМProbability of errors when receiving signals on sealed communication channels with orthogonal frequency separationТузлуковВ. П.TuzlukovV. P.slava.tuzlukov@mail.ruБелорусская государственная академия авиацииBelarusian state academy of aviation201703062019057784Copyright © Тузлуков В.П., 20192019Тузлуков В.П.Tuzlukov V.P.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://doklady.bsuir.by/jour/article/view/880

Проводится математический анализ вероятности ошибок приема сигналов, передаваемых по уплотненным каналам связи с ортогональным частотным разделением при наличии замираний в канале связи, распределенных в соответствии с законом распределения Накагами- m . В отличие от предшествующих публикаций в настоящей работе рассматривается воздействие неравномерного распределения фазы замираний в канале связи на вероятность ошибок приема сигналов. Представлено унифицированное математическое выражение производящей функции моментов для замираний канала связи в частотной области, распределенных в соответствии с законом Накагами- m , при неравномерных распределениях фазы замираний в канале связи. Таким образом, классические методы определения производящей функции моментов могут непосредственно использоваться для получения точных математических выражений вероятности ошибок приема сигналов для различных видов модуляции и разнесения сигналов.

A mathematical analysis of the probability of errors in the reception of signals transmitted over compressed communication channels with orthogonal frequency separation in the presence of fading in the communication channel distributed in accordance with the Nakagami-m distribution law is made. Unlike previous publications, the present work considers the effect of non-uniform distribution of the phase of fading in the communication channel on the probability of errors in signal reception. A unified mathematical expression of the generating function of the moments for fading of the communication channel in the frequency domain, distributed according to the Nakagami-m law, is presented for uneven fading phase distributions in the communication channel. Thus, the classical methods of determining the generating function of moments can be used directly to obtain exact mathematical expressions for the probability of signal reception errors for various types of modulation and signal diversity.

производящая функция моментоввероятность ошибокзамирания в канале связиорт-огональное частотное разделение каналовmoment generating functionerror probabilityfading channelsorthogonal frequency-division multiplexingReferencesNakagami M. The m-distribution - a general formula of intensity distribution of rapid fading // Statistical Methods in Radio Wave Propagation. 1962. Vol. 40, No. 11. P. 757-768.Nakagami M. The m-distribution - a general formula of intensity distribution of rapid fading // Statistical Methods in Radio Wave Propagation. 1962. Vol. 40, No. 11. P. 757-768.Aulin A. Characteristics of a digital mobile radio channel // IEEE Transactions on Vehicle Technology. 1981. Vol. 30, No. 1. P. 45-53.Aulin A. Characteristics of a digital mobile radio channel // IEEE Transactions on Vehicle Technology. 1981. Vol. 30, No. 1. P. 45-53.Charash U. Reception through Nakagami fading multipath channels with random delays // IEEE Transactions on Communications. 1979. Vol. 27, No. 4. P. 657-670.Charash U. Reception through Nakagami fading multipath channels with random delays // IEEE Transactions on Communications. 1979. Vol. 27, No. 4. P. 657-670.Suzuki H. A statistical model for urban multipath // IEEE Transactions on Communications. 1977. Vol. 25, No. 7. P. 673-680.Suzuki H. A statistical model for urban multipath // IEEE Transactions on Communications. 1977. Vol. 25, No. 7. P. 673-680.Dwivedi V., Singh G. Error-rate analysis of the OFDM for correlated Nakagami-m fading channel by using maximal-ratio combining diversity // International Journal of Microwave and Wireless Technology. 2011. Vol. 3, No. 6. P. 717-726.Dwivedi V., Singh G. Error-rate analysis of the OFDM for correlated Nakagami-m fading channel by using maximal-ratio combining diversity // International Journal of Microwave and Wireless Technology. 2011. Vol. 3, No. 6. P. 717-726.Jain G., Dubey R. BER performance of OFDM system over Nakagami-m fading channels with different modulation schemes // International Journal of Advances Research in Computer Engineering & Technology (IJARCET). 2012. Vol. 1, No. 6. P. 111-116.Jain G., Dubey R. BER performance of OFDM system over Nakagami-m fading channels with different modulation schemes // International Journal of Advances Research in Computer Engineering & Technology (IJARCET). 2012. Vol. 1, No. 6. P. 111-116.Yacoub M., Fraidenraich G., Santos J. Nakagami-m phase envelope joint distribution // IEE Electronics Letters. 2005. Vol. 41, No. 5. P. 17-18.Yacoub M., Fraidenraich G., Santos J. Nakagami-m phase envelope joint distribution // IEE Electronics Letters. 2005. Vol. 41, No. 5. P. 17-18.Yacoub M. Nakagami-m phase-envelope joint distribution: a new model // IEEE Transactions on Vehicle Te-chnology. 2010. Vol. 59, No. 3. P. 1552-1557.Yacoub M. Nakagami-m phase-envelope joint distribution: a new model // IEEE Transactions on Vehicle Te-chnology. 2010. Vol. 59, No. 3. P. 1552-1557.Mallik R. A new statistical model of the complex Nakagami-m fading gain // IEEE Transactions on Communications. 2010. Vol. 58, No. 9. P. 2611-2620.Mallik R. A new statistical model of the complex Nakagami-m fading gain // IEEE Transactions on Communications. 2010. Vol. 58, No. 9. P. 2611-2620.Sood N., Sharma A., Uddin M. On channel estimation of OFDM-BPSK and -QPSK over Nakagami-m fading channels // Signal Processing: An International Journal (SPIJ). 2016. Vol. 4, No. 4. P. 239-246.Sood N., Sharma A., Uddin M. On channel estimation of OFDM-BPSK and -QPSK over Nakagami-m fading channels // Signal Processing: An International Journal (SPIJ). 2016. Vol. 4, No. 4. P. 239-246.Kumar I., Rao P. Efficient BER analysis of OFDM system over Nakagami-m fading channel // International Journal of Computer Engineering in Research trends (IJCERT). 2015. Vol. 2, No. 11. P. 745-750.Kumar I., Rao P. Efficient BER analysis of OFDM system over Nakagami-m fading channel // International Journal of Computer Engineering in Research trends (IJCERT). 2015. Vol. 2, No. 11. P. 745-750.Santos Filho J., Yacoub M. On the second-order statistics of Nakagami fading simulators // IEEE Transactions on Communications. 2009. Vol. 57, No. 12. P. 3543-3546.Santos Filho J., Yacoub M. On the second-order statistics of Nakagami fading simulators // IEEE Transactions on Communications. 2009. Vol. 57, No. 12. P. 3543-3546.Ma Y., Zhang D. A method for simulating complex Nakagami fading time series with nonuniform phase and prescribed autocorrelation characteristics // IEEE Transactions on Vehicle Technology. 2010. Vol. 59, No. 1. P. 29-35.Ma Y., Zhang D. A method for simulating complex Nakagami fading time series with nonuniform phase and prescribed autocorrelation characteristics // IEEE Transactions on Vehicle Technology. 2010. Vol. 59, No. 1. P. 29-35.Mishra M., Sood N., Sharma A. New BER analysis of OFDM system over Nakagami-n (Rice) fading channel // International Journal of Computer Science, Engineering and Information Technology (IJCSEIT). 2011. Vol. 1, No. 3. P. 12-20.Mishra M., Sood N., Sharma A. New BER analysis of OFDM system over Nakagami-n (Rice) fading channel // International Journal of Computer Science, Engineering and Information Technology (IJCSEIT). 2011. Vol. 1, No. 3. P. 12-20.Kang Z., Yao K., Lorenzelli F. Nakagami-m fading modeling in the frequency domain for OFDM system analysis // IEEE Communications Letters. Vol. 7, No. 10. P. 484-486.Kang Z., Yao K., Lorenzelli F. Nakagami-m fading modeling in the frequency domain for OFDM system analysis // IEEE Communications Letters. Vol. 7, No. 10. P. 484-486.Du Z., Cheng J., Beaulieu N. Accurate error-rate performance analysis of OFDM on frequency-selective Nakagami-m fading channels // IEEE Transactions on Communications. 2006. Vol. 54, No. 2. P. 319-328.Du Z., Cheng J., Beaulieu N. Accurate error-rate performance analysis of OFDM on frequency-selective Nakagami-m fading channels // IEEE Transactions on Communications. 2006. Vol. 54, No. 2. P. 319-328.Tuzlukov V. Signal detection theory. New York: Springer-Verlag. 2001. 746 p.Tuzlukov V. Signal detection theory. New York: Springer-Verlag. 2001. 746 p.Luo J., Zeidler J., McLaughlin S. Performance analysisof compact antenna arrays with MRC in correlated Nakagami fading channels // IEEE Transactions on Vehicle Technology. 2001. Vol. 50, No. 1. P. 267-277.Luo J., Zeidler J., McLaughlin S. Performance analysisof compact antenna arrays with MRC in correlated Nakagami fading channels // IEEE Transactions on Vehicle Technology. 2001. Vol. 50, No. 1. P. 267-277.Polprasert C., Ritcey J. A Nakagami fading phase difference distribution and its impact on BER performance // IEEE Transactions on Wireless Communications. 2008. Vol. 7, No. 7. P. 2805-2813.Polprasert C., Ritcey J. A Nakagami fading phase difference distribution and its impact on BER performance // IEEE Transactions on Wireless Communications. 2008. Vol. 7, No. 7. P. 2805-2813.de Souza R., Yacoub M. Bivariate Nakagami-m distribution with arbitrary correlation and fading parameters // IEEE Transactions on Wireless Communications. 2008. Vol. 7. No. 12. P. 5227-5232.de Souza R., Yacoub M. Bivariate Nakagami-m distribution with arbitrary correlation and fading parameters // IEEE Transactions on Wireless Communications. 2008. Vol. 7. No. 12. P. 5227-5232.New results for the multivariate Nakagami-m fading model with arbitrary correlation matrix and applications / G. Alexandropoulos [et al.] // IEEE Transactions on Wireless Communications. 2009. Vol. 8, No. 1. P. 245-255.New results for the multivariate Nakagami-m fading model with arbitrary correlation matrix and applications / G. Alexandropoulos [et al.] // IEEE Transactions on Wireless Communications. 2009. Vol. 8, No. 1. P. 245-255.Reig J. Multivariate Nakagami-m distribution with constant correlation model // AEU International Journal on Electronics and Communications. 2009. Vol. 63, No. 1. P. 46-51.Reig J. Multivariate Nakagami-m distribution with constant correlation model // AEU International Journal on Electronics and Communications. 2009. Vol. 63, No. 1. P. 46-51.Tuzlukov V. Signal processing in radar systems. Boca Raton, London, New York, Washington D.C.: CRC Press. 2012. 601 p.Tuzlukov V. Signal processing in radar systems. Boca Raton, London, New York, Washington D.C.: CRC Press. 2012. 601 p.Gradshteyn G., Ryzhik I. Tale of integrals, series, and products. 6th edition. Los Angeles: Academic Press. 2005. 1457 p.Gradshteyn G., Ryzhik I. Tale of integrals, series, and products. 6th edition. Los Angeles: Academic Press. 2005. 1457 p.Abramowitz M., Stegun I. Handbook of mathematical functions. 10th ed. Washington, D.C. 2010. 1048 p.Abramowitz M., Stegun I. Handbook of mathematical functions. 10th ed. Washington, D.C. 2010. 1048 p.Simon M., Alouini M. Digital communication over fading channels. 2nd ed. New York: John Wiley & Sons, Inc. 2005. 936 p.Simon M., Alouini M. Digital communication over fading channels. 2nd ed. New York: John Wiley & Sons, Inc. 2005. 936 p.Tuzlukov V. Contemporary issues in wireless communications. Chapter 4: Signal processing by generalized receiver in DS-CDMA wireless communication systems. INTECH. Croatia. 2014. P. 79-158.Tuzlukov V. Contemporary issues in wireless communications. Chapter 4: Signal processing by generalized receiver in DS-CDMA wireless communication systems. INTECH. Croatia. 2014. P. 79-158.Tuzlukov V. Communications systems: new research. New York: NOVA Science Publishers, Inc. 2013. 423 p.Tuzlukov V. Communications systems: new research. New York: NOVA Science Publishers, Inc. 2013. 423 p.Tuzlukov V. Advances in communications and media research. Chapter 6: detection of spatially distributed signals by generalized receiver using radar sensor array in wireless communications. New York: NOVA Science Publishers, Inc. 2015. P. 143-173.Tuzlukov V. Advances in communications and media research. Chapter 6: detection of spatially distributed signals by generalized receiver using radar sensor array in wireless communications. New York: NOVA Science Publishers, Inc. 2015. P. 143-173.

The authors declare that there are no conflicts of interest present.