Optimal Power Allocation in Block Fading Channels With Confidential Messages

Abstract

Abstract-The optimal power allocation for block fading (BF) networks with confidential messages is investigated under an M -block delay and power constraint. First, we study networks without channel state information (CSI) feedback to the transmitter and demonstrate that the optimal power allocation is the equidistribution of the power budget, denoted as the "blind policy". In blind scenarios secrecy can be achieved though receiver diversity; the probability of secrecy outage (PSO) is shown to decay exponentially with the the diversity order of the legitimate user. Then, we investigate networks with CSI feedback. For comparison purposes, we restate the acausal secure waterfilling algorithm with full CSI before moving to the causal feedback scenario. In the latter, an approximate "threshold policy" for the low SNR and an approximate "high power policy" for the high SNR regimes are derived. Furthermore, a novel universal transmission policy is proposed across all SNRs, denoted as the "blind horizon approximation" (BHA). Through numerical results, the BHA policy is shown to outperform both the threshold and high power policies when the legitimate user has an SNR advantage with respect to the eavesdropper, while it also compares well with the secure waterfilling policy.Index Terms-Secrecy capacity, probability of secrecy outage, block fading, BF-AWGN channel, causal channel state information feedback, dynamic program I. INTRODUCTION The increasing deployment of wireless networks introduces new challenges in the design of enhanced security next generation systems. A pressing need to develop alternative/complementary means to secure data exchange arises in many wireless settings with limited feedback and limited resources. Physical layer security (PLS) is an emerging technology from the area of information theory that can address open security issues in challenging wireless applications such as those envisaged for fifth generation (5G) networks. In PLS approaches [1], the issues of reliability and secrecy in the exchange of information are jointly addressed by employing novel double binning encoding schemes.PLS was pioneered by Wyner, who introduced the wiretap channel and established the possibility of creating perfectly secure communication links without relying on private (secret) keys [2]. Wyner termed the rates at which information can be transmitted secretly from the source to its intended destination as achievable secrecy rates, and the maximal achievable secrecy rate as the secrecy capacity (SC). Following Wyner's contribution, the SC of the scalar Gaussian wiretap channel was analyzed in [3]. In [4], Wyner's approach was generalized

Overcoming limitations of secret key generation in block fading channels under active attacks

“…This is a general result for the maximization of monotonic cost functions in blind scenarios; for details on a proof using dynamic programming see the blind scenario in Appendix B of [12]. Furthermore, with respect to Eve we investigate two possible scenarios.…”

“…Since nonnegative weighted summation preserves convexity, it is easy to check that C k (p * , γ) is convex in γ. The Karush-Kuhn-Tucker (KKT) necessary conditions for solving (12) provide us with a system of M quartic equations along the linear constraint. Although quartic equations can be solved analytically, obtaining a closed form solution for the Lagrange multiplier and γ as a function of M, P, P j is overly complex.…”

Optimal signalling strategies and power allocation for wireless secret key generation systems in the presence of a jammer

“…Proof: Following the proof in [15], the stochastic optimization objective function can be written as follows:…”

Physical Layer Security: A Paradigm Shift in Data Confidentiality

“…The key to achieving the SC of the fading channel is optimal power allocation, [9] for the ergodic fading channel and [18] for the the parallel Gaussian BCC. Finally, a positive SC can be achieved with only statistical channel state information of the eavesdropper's channel, by multiplexing the codewords across all fading realizations [4].…”

“…Furthermore, in cooperative networks with K legitimate users and E eavesdroppers the probability that the SC is below a target rate, denoted by P out , has been shown to exhibit an abrupt phase transition characteristic as shown in Fig.6 [4]. As a result, in large multi-user networks, the feasibility of PLS can be incorporated in the network architecture design.…”