Title :
The impact of constellation cardinality on Gaussian channel capacity
Author :
Wu, Yihong ; Verd, Sergio
Author_Institution :
Dept. of Electr. Eng., Princeton Univ., Princeton, NJ, USA
fDate :
Sept. 29 2010-Oct. 1 2010
Abstract :
Denote by Cm(snr) the Gaussian channel capacity with signal-to-noise ratio SNR and input cardinality m. We show that as m grows, Cm(snr) approaches C(snr) = 1/2 log(1 + snr) exponentially fast. Lower and upper bounds on the exponent are given as functions of SNR. We propose a family of input constellations based on the roots of the Hermite polynomials which achieves exponential convergence.
Keywords :
Gaussian channels; channel capacity; polynomials; Gaussian channel capacity; Hermite polynomials; SNR; constellation cardinality; exponential convergence; lower bounds; signal-to-noise ratio; upper bounds; Approximation methods; Channel capacity; Convolution; Entropy; Polynomials; Random variables; Upper bound;
Conference_Titel :
Communication, Control, and Computing (Allerton), 2010 48th Annual Allerton Conference on
Conference_Location :
Allerton, IL
Print_ISBN :
978-1-4244-8215-3
DOI :
10.1109/ALLERTON.2010.5706965
