On the PDF of the sum of random vectors
- 1 January 2000
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Communications
- Vol. 48 (1) , 7-12
- https://doi.org/10.1109/26.818866
Abstract
There are various cases in physics and engineering sciences (especially communications) where one requires the envelope probability density function (PDF) of the sum of several random sinusoidal signals. According to the correspondence between a random sinusoidal signal and a random vector, the sum of random vectors can be considered as an abstract mathematical model for the above sum. Now it is desired to obtain the PDF of the length of the resulting vector. Considering the common and reasonable assumption of uniform distributions for the angles of the vectors, many researchers have obtained the PDF of the length of the resulting vector only for special cases. However in this paper, the PDF is obtained for the most general case in which the lengths of vectors are arbitrary dependent random variables. This PDF is in the form of a definite integral, which may be inappropriate for analytic manipulations and numerical computations. So an appropriate infinite Laguerre expansion is also derived. Finally, the results are applied to solve a typical example in computing the scattering cross section of random scatterers.Keywords
This publication has 56 references indexed in Scilit:
- Probability of erasure in non-Rayleigh fading channels-a simulation studyIEEE Transactions on Communications, 1995
- Statistics of the scattering cross-section of a small number of random scatterersIEEE Transactions on Antennas and Propagation, 1995
- Nonparametric density estimation and detection in impulsive interference channels. I. EstimatorsIEEE Transactions on Communications, 1994
- On circularityIEEE Transactions on Signal Processing, 1994
- The Analysis of Directional Time Series: Applications to Wind Speed and DirectionPublished by Springer Nature ,1989
- Dual algorithms for fast calculation of the Fourier-Bessel transformIEEE Transactions on Acoustics, Speech, and Signal Processing, 1981
- Detection in the presence of spherically symmetric random vectorsIEEE Transactions on Information Theory, 1976
- Tables of Bessel TransformsPublished by Springer Nature ,1972
- The Probability Distribution of the Amplitude of a Constant Vector Plus a Rayleigh-Distributed VectorProceedings of the IRE, 1955
- Distribution of the sum of randomly phased componentsQuarterly of Applied Mathematics, 1948