10 Copyright © 2012, IGI Global. Copying or distributing in print or electronic forms without written permission of IGI Global is prohibited. Chapter 2 1. INTRODUCTION This chapter is concerned with the study of secrecy capacity and secure outage performance for the wireless channels, focusing on the recent research of secure communications where a legitimate user communicates with a legitimate receiver in the presence of an eavesdropper. Perfect secrecy is achieved when the transmitter and the legitimate receiver can communicate at some positive rate, while insuring that eavesdropper gets zero bits of information. Specifically, two different chan- nels, such as fading and additive white Gaussian noise (AWGN) channels are considered for the study. The open nature of wireless communication network makes it susceptible to eavesdropping and fraud. As a result, the privacy and security Md. Zahurul Islam Sarkar Queen’s University Belfast, UK Secure Communications over Wireless Networks ABSTRACT Nakagami-m fading channel is chosen to analyze the secrecy capacity for fading channels since the Nakagami-m distribution can model fading conditions, which are more or less severe than that of Rayleigh and has the advantage of including Rayleigh as a special case. At frst, secrecy capacity is defned in case of full channel state information (CSI) at the transmitter, where transmitter has access to both the main channel and eavesdropper channel gains. Secondly, secrecy capacity is defned with only main channel CSI at the transmitter. Then, optimal power allocation at the transmitter that achieves the secrecy capacity is derived for both the cases. Moreover, secrecy capacity is defned under open-loop transmission scheme, and the exact closed form analytical expression for the lower bound of ergodic secrecy capacity is derived for Nakagami-m fading single-input multiple-output (SIMO) channel. In addition, secrecy capacity is defned for the AWGN channel in order to realize the information-theoretic security of wireless channels with no fading. Finally, analytical expressions for the probability of non- zero secrecy capacity and secure outage probability are derived in order to investigate the secure outage performance of fading channels. DOI: 10.4018/978-1-4666-1797-1.ch002