Tight Analytical and Asymptotic Upper Bound for the BER and FER of Linear Codes Over Exponentially Correlated Generalized-Fading Channels

• Published in: IEEE transactions on communications Vol. 67; no. 6; pp. 3852 - 3864
• Main Authors: Mouchtak, Yassine, El Bouanani, Faissal, da Costa, Daniel Benevides
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.06.2019; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Asymptotic analysis; Asymptotic properties; Bit error rate; Block codes; Channels; Codes; convolutional codes; Correlation; Covariance matrices; Covariance matrix; Eigenvalues; Eigenvalues and eigenfunctions; exponentially correlated generalized-fading channel; Fading; frame error rate; linear block codes; Lower bounds; Maximum likelihood decoding; performance analysis; Rayleigh channels; Signal to noise ratio; Upper bound; Upper bounds
• ISSN: 0090-6778; 1558-0857
• DOI: 10.1109/TCOMM.2019.2901461

In this paper, the upper bound and asymptotical approximation for the bit error rate (BER) as well as for the frame error rate of linear block codes under maximum-likelihood decoding operating over exponentially correlated (EC) generalized-fading channels are proposed. Particularly, our analysis takes the convolutional codes as an example and three different fading scenarios are considered, namely Rice, Nakagami-<inline-formula> <tex-math notation="LaTeX">m </tex-math></inline-formula>, and Weibull fading. Such scenarios have a common property that is spherically invariant random process (SIRP). Our analysis relies on the derivation of new lower bounds per each eigenvalue since the BER as well as the FER expressions are written in terms of the pairwise error probability, which by its turn depends on the eigenvalues of the channel covariance matrix. Based on that, the upper bounds and asymptotic expressions of the considered metrics subject to the three above fading models are derived, which show to be tighter than the previous results published elsewhere in the literature, especially for the high signal-to-noise ratio regions.