Approximation for Average Error Probability of BPSK in the Presence of Phase Error

Authors: Yeonsoo Jang, Dongweon Yoon, Ki Ho Kwon, Jaeyoon Lee, Wooju Lee

Abstract:

Phase error in communications systems degrades error performance. In this paper, we present a simple approximation for the average error probability of the binary phase shift keying (BPSK) in the presence of phase error having a uniform distribution on arbitrary intervals. For the simple approximation, we use symmetry and periodicity of a sinusoidal function. Approximate result for the average error probability is derived, and the performance is verified through comparison with simulation result.

Keywords: Average error probability, Phase shift keying, Phase error

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1083627

References:

[1] A. Demir, A. Mehrota, and J. Roychowdhury, "Phase Noise in Oscillators: A Unifying Theory and Numerical Methods for Characterization," IEEE Transactions on Circuit and Systems, Vol. 47, No. 5, pp 655-674, May 2000.
[2] A. Armada, and M. Calvo, "Phase Noise and Sub-Carrier Spacing Effects on the Performance of an OFDM Communication System," IEEE Communications Letters, Vol. 2, No. 1, Jan. 1998.
[3] M. Najib, "Lower Bound on Error Performance for BPSK and QPSK Systems with Imperfect Phase Recovery," IEEE International Conference on Communications, pp 1253-1258, Atlanta, USA, Jun. 1998.
[4] Y. Some, and P. Kam, "Bit-error Probability of QPSK with Noisy Phase Reference," IEE Proceedings-Communications, vol. 142, pp 292-296, Oct. 1995.
[5] G. Kaplan, and U. Ram, "Bounds on Performance for the Noisy Reference PSK Channel," IEEE Transactions on Communications, Vol. 38, No. 10, Oct. 1990.
[6] B. Sklar, Digital Communications: Fundamentals and Applications, Prentice-Hall, 2001.
[7] R. Ziemer, and W. Tranter, Principles of Communications: Systems Modulation and Noise, Wiley, 2002.
[8] " The Wolfram functions site."
[Online]. Available: http://functions.wolfram.com