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Electronics Letters

Joint optimisation of secret key capacity and sparse channel estimation based on pilot power allocation

Chenhao Qi, Arumugam Nallanathan, Lenan Wu

Published Jun 1, 2015• 2 citations
Publisher

Abstract

Pilot power allocation is investigated under the framework of physical layer secure communications in time‐division duplex systems, where the secret keys are generated from the estimates of sparse wireless channels. The joint optimisation of secret key capacity and sparse channel estimation performance based on pilot power allocation is formulated as a convex optimisation problem. Considering the fairness between these two sides, a scaling factor is introduced. Then, a scheme is proposed to fast solve the problem by looking up a table and using existing optimisation solvers. Simulation results show that a proper scaling factor can make a trade‐off between the secret key capacity and sparse channel estimation performance.

DOI
10.1049/el.2014.4078

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Pilot power allocation is investigated under the framework of physical layer secure communications in time‐division duplex systems, where the secret keys are generated from the estimates of sparse wireless channels. The joint optimisation of secret key capacity and sparse channel estimation performance based on pilot power allocation is formulated as a convex optimisation problem. Considering the fairness between these two sides, a scaling factor is introduced. Then, a scheme is proposed to fast solve the problem by looking up a table and using existing optimisation solvers. Simulation results show that a proper scaling factor can make a trade‐off between the secret key capacity and sparse channel estimation performance.
Physical layer security (PLS) is an approach that provides secrecy based on information-theoretic model which does not account for any computation capability assumption or pre-installed standardized secret key generation algorithm and it is a good additional protection on the top of the existing security scheme. This work includes four different topics which are about improving PLS with full-duplex radio. In the first topic, we develop a fast algorithms for computing power allocations in subcarriers, subject to power and rate constraints, to maximize the secrecy capacity of a three-node network consisting of a source, a full-duplex capable destination and an eavesdropper. The optimal power allocation at the destination is found to be significant especially when its power budget is high. The second topic is about the analysis of a two-phase scheme for secret information transmission with the technique of anti-eavesdropping channel estimation (ANECE), which requires full duplex transceiver and it can better handle Eve with any number of antennas. The analysis is based on the assumption that everyone has a prior statistical knowledge of the channel state information (CSI) anywhere and it yields lower and upper bounds on secure degrees of freedom as functions of the number of antennas on Eve and the size of information packet. For the third topic, we present optimal designs of the pilots for ANECE based on two criteria. The first is to optimize the minimum mean squared error (MMSE) channel estimation for the users, and the second is to maximize the mutual information between the pilot-driven signals observed by the users. Closed-form optimal pilots are shown under both criteria but subject to a symmetric and isotropic condition. Algorithms for computing the optimal pilots are shown for general cases. In the fourth topic, we analyze the secure degree of freedom and the asymptotic expression of the achievable secret key rate from a two-phase key generation scheme which consists of channel training phase and secure information transmission phase. Based on the asymptotic form, we develop an effective algorithm for coherence time allocation between the two phases to maximize the achievable secret key rate.
Abstract With the rapid development of wireless communication, the use of the inherent features of wireless channels to enhance and supplement existing security mechanisms has attracted widespread attention. In this work, a key generation scheme based on power allocation optimisation is proposed. The subchannel state information obtained from channel probing is employed to allocate signal power. Furthermore, an improved channel probing process is designed to implement the optimisation scheme of power allocation. Theoretical analysis and simulation results show that this optimisation scheme can obtain higher key capacity, and the superiority is more prominent when the signal‐to‐noise ratio is low. Besides, the key bits mismatch rate of the proposed optimisation scheme is decreased and the corresponding key generation rate is higher compared with the benchmark.
Abstract Generating a secret key from the physical layer is one of the most challenging topics in cryptography. Secret key generation rate (SKGR) and secrecy rate (SR) are two important concepts for any secure communication scheme. In this paper, we first propose a new power allocation strategy to minimize the power consumption under a given SKGR constraint for orthogonal frequency division (OFDM) based communication systems. Due to the non-convex nature of the SKGR expression, we convert the optimization problem into a convex problem. In the continuation of this paper, we investigate the effects of the proposed power allocation strategy on the SR performance. Simulation results demonstrate that using the obtained optimum power vector, which was calculated in the key generation phase, we achieve a better level of SR in the data communication phase. The simulation results also verify that the average SR performance obtained by the proposed method is superior to the geometric programing (GP)-based method.
Summary Extracting secret keys from the common randomness of wireless channels has attracted prominent attention recently. Orthogonal frequency‐division multiplexing (OFDM) systems can provide extra randomness in view of the use of multiple subchannels. So far, the secret key capacity of OFDM systems is still an open issue. In this paper, the secret key capacity of OFDM systems based on the subchannel state information is analyzed, and an expression of the secret key capacity is derived under the assumption that the subchannels are independent. To increase the secret key capacity, a power allocation scheme based on geometric program is proposed. Furthermore, an underlying propagation protocol is designed to realize the power allocation scheme. Performance simulations show that the proposed scheme achieves greater secret key capacity in comparison with equal power allocation scheme, especially at low signal‐to‐noise ratio region. Besides, the secret key bits mismatch rate during the secret key generation based on the power allocated subchannels is decreased.
Through a wireless channel, two users can transmit pilot signals to each other, and then utilize the received signals to agree upon a secret key through communications in a public channel without leaking any secret about this key to anyone else. This paper addresses the optimization of the two pilots to maximize the capacity of secret key generation for a MIMO channel with any given receive and transmit correlation matrices. This study shows how the globally optimal pilots can be obtained if the transmission power is either low or high. For an arbitrary transmission power, the algorithm developed is at least locally optimal. Comparison to pilots based on minimum channel estimation errors and uniform power distribution is also presented. It is also shown that the designed pilots meet the requirement for anti- eavesdropping channel estimation.
The joint transmitter and PS factor optimal design scheme for secure transmission in multiple‐input multiple‐output (MIMO) full‐duplex relay network powered by simultaneous wireless information and power transfer (SWIPT) is studied. An optimisation problem is presented, aimed at maximising the system security capacity by jointly optimising transmitter and PS factor while satisfying the energy harvest constraint in both perfect and imperfect channel state information (CSI). In perfect CSI case, the optimisation function is formulated with energy harvest constraint, and semidefinite relaxation (SDR) is introduced to solve the non‐convex optimisation problem. In imperfect CSI case, it is assumed that only the first and second order statistics of the eavesdropper's channels are available, but the specific distribution is unknown. In this case, the security capacity of the system is maximised while satisfying the security outage probability and energy harvest constraint. The SDR solution based on equivalent conic reformulation is proposed. And the simulation results demonstrate the effectiveness of the optimal designs in both CSI cases.