Abstract
This study presents a general and closed-form expression for the bit error probability (BEP) of Gray-coded M-ary phase shift keying (MPSK) in the presence of phase noise in additive white Gaussian noise (AWGN) channel. Closed-form expressions are obtained by converting the AWGN channel noise to equivalent phase noise, under the approximation that the AWGN channel noise and the phase error are both Gaussian distributed. The only existing work in the literature with similar assumption only calculates the BEP for M ≤ 16. The proposed analysis in this study will facilitate the BEP calculation for higher order MPSK.
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Kam, P. Y., Teo, S. K., Some, Y. K., & Tjhung, T. T. (1993). Approximate results for the bit error probability of binary phase shift keying with noisy phase reference. IEEE Transactions on Communications, 41(7), 1020–1022. https://doi.org/10.1109/26.231929
Some, Y. K., & Kam, P. Y. (1995). Bit-error probability of QPSK with noisy phase reference. IEE Proceedings: Communications, 142(5), 292–296. https://doi.org/10.1049/ip-com:19952188
Jang, Y., Yoon, D., & Lee, S. K. (2013). Generalized BER expression of MPSK in the presence of phase error. IEEE Communications Letters, 17(12), 2213–2216. https://doi.org/10.1109/LCOMM.2013.102913.131514
Wang, Q., & Kam, P. Y. (2014). Simple, unified, and accurate prediction of error probability for higher order MPSK/MDPSK with phase noise in optical communications. Journal of Lightwave Technology, 32(21), 3531–3540. https://doi.org/10.1109/JLT.2014.2347395
Jang, Y., Jeong, J., & Yoon, D. (2016). Bit error floor of MPSK in the presence of phase error. IEEE Transactions on Vehicular Technology, 65(5), 3782–3786. https://doi.org/10.1109/TVT.2015.2437792
Jafari, H., Miar-Naimi, H., & Kazemitabar, J. (2020). Generalised expression for the symbol error floor of M-ary phase shift keying in the presence of phase noise. I/Q imbalance and DC-offset. IET Communications, 14(14), 2319–2325. https://doi.org/10.1049/iet-com.2020.0001
Silva, P. E. G., de Souza, R. A. A., da Costa, D. B., Moualeu, J. M., & Yacoub, M. D. (2020). Error probability of M-Phase signaling with phase noise over fading channels. IEEE Transactions on Vehicular Technology, 69(6), 6766–6770. https://doi.org/10.1109/TVT.2020.2987201
Silva, P. E. G., de Souza, R. A. A., Nardelli, P. J., Moualeu, J. M. M., & da Costa, D. B. (2022). Performance of MPSK modulation with imperfect phase-recovery under severe fading conditions. Electronics Letters. John Wiley and Sons Inc. https://doi.org/10.1049/ell2.12432
Lu, J. (1999). M-PSK and M-QAM BER computation using signal-space concepts. IEEE Transactions on Communications, 47(2), 181–184. https://doi.org/10.1109/26.752121
Jeong, W., Lee, J., & Yoon, D. (2011). New BER expression of MPSK. IEEE Transactions on Vehicular Technology, 60(4), 1916–1924. https://doi.org/10.1109/TVT.2011.2114903
Viterbi, A. J. (1963). Phase-locked loop dynamics in the presence of noise by fokker-planck techniques. Proceedings of the IEEE, 51(12), 1737–1753. https://doi.org/10.1109/PROC.1963.2686
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Jafari, H., Kazemitabar, J. & Miar-Naimi, H. Generalized Closed-Form Expression for the Bit Error Probability of MPSK with Phase Noise. Wireless Pers Commun 130, 2441–2450 (2023). https://doi.org/10.1007/s11277-023-10386-4
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DOI: https://doi.org/10.1007/s11277-023-10386-4