Effects of Correlation of Channel Gains on the Secrecy Capacity in the Gaussian Wiretap Channel

Authors

Abhishek Lokur, University of Nebraska - LincolnFollow

First Advisor

Dr. H. Andrew Harms

Second Advisor

Prof. Won Mee Jang

Third Advisor

Dr. Lamar Yang

Date of this Version

2019

Document Type

Article

Citation

Lokur, A. (2019). Effects of the Correlation of Channel Gains on the Secrecy Capacity in the Gaussian Wiretap Channel (Master's Thesis). University of Nebraska-Lincoln, USA

Comments

A THESIS Presented to the Faculty of The Graduate College at the University of Nebraska In Partial Fulfillment of the Requirements For the Degree of Master of Science, Major: Telecommunications Engineering, Under the Supervision of Professor H. Andrew Harms. Lincoln, Nebraska: July, 2019

Copyright © 2019 Abhishek Pradeep Lokur

Abstract

Secrecy capacity is one of the most important characteristic of a wireless communication channel. Therefore, the study of this characteristic wherein the system has correlated channel gains and study them for different line-of-sight (LOS) propagation scenarios is of ultimate importance.

The primary objective of this thesis from the mathematical side is to determine the secrecy capacity (SC) for correlated channel gains for the main and eavesdropper channels in a Gaussian Wiretap channel as a function from main parameters (μ, Σ, ρ). f(h₁, h₂) is the joint distribution of the two channel gains at channel use (h₁, h₂), f_i(h_i) is the main distribution of the channel gain h_i. The results are based on assumption of the Gaussian distribution of channel gains (g_M, g_E). The main task of estimating the secrecy capacity is reduced to the problem of solving linear partial differential equations (PDE). Different aspects of the analysis of secrecy capacity considered in this research are the Estimation of SC mathematically and numerically for correlated SISO systems and a mathematical example for MIMO systems with PDE.

The variations in Secrecy Capacity are studied for Rayleigh (NLOS) distribution and Rician (LOS) distribution. Suitable scenarios are identified in which secure communication is possible with correlation of channel gains. Also, the new algorithm using PDE has a higher speed and than analog algorithms constructed on the classical statistical Monte Carlo methods. Taking into account the normality of the distribution of system parameters, namely the channel gain (g_M, g_E), the algorithm is constructed for systems of partial differential equations which satisfies the secrecy criterion.

Advisor: H. Andrew Harms