Name
Abstract | ||
|---|---|---|
In this paper, we derive a closed form equation for the joint probability distribution \({{f_{{R}_{z}}},{\varTheta _{z}}}({r_{z}},{\theta _{z}})\) of the amplitude \({R_{z}}\) and phase \({\varTheta _{z}}\) of the ratio \({Z=\frac{X}{Y}}\) of two independent non-zero mean Complex Gaussian random variables \(X\sim CN(\nu _{x} \mathrm {e}^{j\phi _{x}},{\sigma ^{2}_{x}})\) and \(Y\sim CN(\nu _{y} \mathrm {e}^{j\phi _{y}},{\sigma ^{2}_{y}})\). The derived joint probability distribution only contains a confluent hypergeometric function of the first kind \({_1F_{1}}\) without infinite summations resulting in computational efficiency. We further derive the probability distribution for the ratio of two non-zero mean independent real Rician random variables containing an infinite summation generated by the estimation of the Cauchy product of equivalent series of two modified Bessel functions. |
Year | DOI | Venue |
|---|---|---|
2018 | 10.1007/s11045-017-0519-3 | Multidim. Syst. Sign. Process. |
Keywords | Field | DocType |
Complex Gaussian random variable,Ratio distribution,Rice distribution | Discrete mathematics,Ratio distribution,Random variable,Confluent hypergeometric function,Probability distribution,Cauchy product,Complex normal distribution,Mathematics,Bessel function | Journal |
Volume | Issue | ISSN |
29 | 4 | 0923-6082 |
Citations | PageRank | References |
1 | 0.63 | 3 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Esmaeil S. Nadimi | 1 | 9 | 5.90 |
| Mohammad H. Ramezani | 2 | 2 | 2.08 |
| Victoria Blanes-Vidal | 3 | 6 | 3.46 |