A New Representation for the Symbol Error Rate
Abstract
The symbol error rate of the minimum distance detector for an arbitrary multi-dimensional constellation impaired by additive white Gaussian noise is characterized as the product of a completely monotone function with a non-negative power of the signal to noise ratio. This representation is also shown to apply to cases when the impairing noise is compound Gaussian. Using this general result, it is proved that the symbol error rate is completely monotone if the rank of its constellation matrix is either one or two. Further, a necessary and sufficient condition for the complete monotonicity of the symbol error rate of a constellation of any dimension is also obtained. Applications to stochastic ordering of wireless system performance are also discussed.
Cite
@article{arxiv.1206.3189,
title = {A New Representation for the Symbol Error Rate},
author = {Adithya Rajan and Cihan Tepedelenlioglu},
journal= {arXiv preprint arXiv:1206.3189},
year = {2013}
}
Comments
26 pages, 3 figures. Parts of this work have been presented in the Asilomar Conference on Signals, Systems, and Computers, 2012, and the IEEE International Symposium on Information Theory, 2012. This work was supported in part by the National Science Foundation under Grant CCF 1117041