Wireless Physical Layer Security with Imperfect Channel State Information: A Survey

Physical layer security is an emerging technique for improving wireless communication security, which is widely regarded as a complement to cryptographic technologies. To design physical layer security techniques for practical scenarios, uncertainty and imperfections in the channel knowledge need to be taken into account. This paper is a survey of recent research on physical layer security that considers imperfect channel state information （CSI） at communication nodes. We first give an overview of the main information-theoretic measures of secrecy performance with imperfect CSI. Then, we describe several signal processing enhancements in secure transmission designs. These enhancements include secure on-off transmission, beamforming with artificial noise, and secure communication assisted by relay nodes or in cognitive radio systems. Recent studies of physical layer security in large-scale decentralized wireless networks are also summarized. Finally, open problems for on-going and future research are discussed.

Robust MIMO Precoding for Cognitive Multiuser Relay Networks with Imperfect Channel State Information

In this paper, a novel robust precoder with imperfect channel state information(CSI)is proposed for multi-input multi-output(MIMO)cognitive multiuser networks equipped with relays. In the proposed model, the secondary users(SUs)are allowed to share the spectrum with the primary users(PUs)when the interference temperature(IT)is below a specific threshold. The transmitting strategy of relays is amplify-and-forward(AF), and the CSI error is characterized in terms of spherical uncertainty region. A minmax problem for the transmit power of the relays is considered when the mean square error(MSE)of SUs and the IT of PU meet their corresponding thresholds, and it is transformed into a semi-definite programming(SDP)problem to search for the solution. Numerical simulations demonstrate the effectiveness of the proposed precoder.

Adaptive Energy-Efficient Power Allocation for DAS with Imperfect Channel State Information and Antenna Selection

Considering that perfect channel state information(CSI) is difficult to obtain in practice,energy efficiency(EE) for distributed antenna systems(DAS) based on imperfect CSI and antennas selection is investigated in Rayleigh fading channel.A novel EE that is defined as the average transmission rate divided by the total consumed power is introduced.In accordance with this definition,an adaptive power allocation(PA) scheme for DAS is proposed to maximize the EE under the maximum transmit power constraint.The solution of PA in the constrained EE optimization does exist and is unique.A practical iterative algorithm with Newton method is presented to obtain the solution of PA.The proposed scheme includes the one under perfect CSI as a special case,and it only needs large scale and statistical information.As a result,the scheme has low overhead and good robustness.The theoretical EE is also derived for performance evaluation,and simulation result shows the validity of the theoretical analysis.Moreover,EE can be enhanced by decreasing the estimation error and/or path loss exponents.

Resource allocation algorithm in LTE uplink SC-FDMA system for time-varying channel with imperfect channel state information

In long term evolution （LTE） uplink single carrier frequency division multiple access （SC-FDMA） system, the restriction that multiple resource blocks （RBs） allocated to a user should be adjacent, makes the resource allocation problem hard to solve. Moreover, with the practical constraint that perfect channel state information （CSI） cannot be obtained in time-varying channel, the resource allocation problem will become more difficult. In this paper, an efficient resource allocation algorithm is proposed in LTE uplink SC-FDMA system with imperfect CSI assumption. Firstly, the resource allocation problem is formulated as a mixed integer programming problem. Then an efficient algorithm based on discrete stochastic optimization is proposed to solve the problem. Finally, simulation results show that the proposed algorithm has desirable system performance.

Joint Optimization of Spectral and Energy Efficiency for Multi-Pair Full-Duplex Two-Way Relay Networks with Imperfect Channel State Information

An iterative algorithm is proposed for jointly optimizing spectral and energy efficiency in a multipair full-duplex (FD) two-way relaying (TWR) system with imperfect channel state information (CSI). Based on Dinkelbach method, a Taylor expansion based approximation method and the Generalized Lagrange Multiplier Method have been applied iteratively to obtain the near optimal relay amplified matrix and power allocation, respectively. And the simulation results illustrate the effectiveness of the proposed algorithm and the algorithm can converge quickly. © 2017, Shanghai Jiaotong University and Springer-Verlag Berlin Heidelberg.

Joint Energy-Efficient Power Allocation and Beamforming Design for mm Wave-NOMA System with Imperfect CSI

The joint power allocation(PA)and beamforming(BF)design problem is studied to maximize the energy efficiency of a two-user downlink millimeter-wave system with non-orthogonal multiple access under imperfect channel state information(CSI).By means of block coordinate descent,convex-concave procedure,and successive convex approximate,we propose a suboptimal joint PA and BF design scheme to address this non-convex problem.Simulation results verify that the proposed joint PA and BF design scheme is more effective when compared to some existing schemes.

Power control scheme for multiple antenna systems with space-time coding in Rayleigh fading channels

Two optimal power control （PC） schemes under the power constraint for space-time coded multiple input multiple output systems over the flat Rayleigh fading channel with the imperfect channel state information （CSI） are presented. One is based on the minimization of a bit error rate （BER）, and the other is based on the maximization of a fuzzy signal-to-noise ratio. In these schemes, different powers are allocated to individual transmit an- tennas rather than equal power in the conventional one. For the first scheme, the optimal PC procedure is developed. It is shown that the Lagrange multiplier for the constrained optimization in the power control does exist and is unique. A practical iterative algorithm based on Newton＇s method for finding the Lagrange multiplier is proposed. In the second scheme, some existing schemes are included, and a suboptimal PC procedure is developed by means of the asymptotic performance analysis. With this suboptimal scheme, a simple PC calculation formula is provided, and thus the calculation of the PC will be straightforward. Moreover, the suboptimal scheme has the BER performance close to the optimal scheme. Simulation results show that the two PC schemes can provide BER lower than the equal PC and antenna selection scheme under the imperfect CSI.

HIGH SNR SUM CAPACITY ANALYSIS OF BD MIMO BC SYSTEMS WITH IMPERFECT CSI

We investigate the sum capacity of Block Diagonalization precoding Multiple Input Mul-tiple Output Broadcast Channels(BD MIMO BC) with imperfect Channel State Information(CSI) at the base station.Since it is difficult to obtain the exact expression,a lower and an upper bounds of the sum capacity under Gaussian channel estimation errors are drived instead.Analyses show that the gap between two bounds is considerably tight at all Signal to Noise Ratio(SNR) region.From the lower bound of the sum capacity,we can see that the multiplexing gain tends to be zero at high SNR region,which indicates that the BD MIMO BC system with channel estimation errors is interference-limited at high SNR.

ROBUST OPTIMIZATION OF TRANSMIT/RECEIVE BEAMFORMER FOR MIMO DOWNLINK WITH IMPERFECT CSI AT BASE STATION

A robust scheme is proposed to jointly optimize transmit/receive beamformers for Mul-tiple Input Multiple Output(MIMO) downlinks where the available Channel State Information(CSI) at Base Station(BS)(CSIBS) is imperfect.The criterion is to minimize the sum Mean Square Error(sum-MSE) over all users under a constraint on the total transmit power,which is a non-convex and non-linear problem.Observing from the first order optimization condition that the optimal trans-mit/receive beamformers are mutually dependent,the transmit/receive beamformers for each user are updated iteratively until the sum-MSE is minimized.Simulation results indicate that the proposed scheme can effectively mitigate the system performance loss induced by imperfect CSIBS.

Underwater video transceiver designs based on channel state information and video content

Underwater hostile channel conditions challenge video transmission designs. The current designs often treat video coding and transmission schemes as individual modules. In this study, we develop an adaptive transceiver with channel state information(CSI) by taking into account the importance of video components and channel conditions. The design is more effective than the traditional ones. However, in practical systems, perfect CSI may not be available. Therefore, we compare the imperfect CSI case with existing schemes, and validate the effectiveness of our design through simulations and measured channels in terms of a better peak signal-to-noise ratio and a higher video structural similarity index.

Robust resource allocation for NOMA-assisted heterogeneous networks

As a promising technology to improve spectrum efficiency and transmission coverage,Heterogeneous Network(HetNet)has attracted the attention of many scholars in recent years.Additionally,with the introduction of the Non-Orthogonal Multiple Access(NOMA)technology,the NOMA-assisted HetNet cannot only improve the system capacity but also allow more users to utilize the same frequency band resource,which makes the NOMA-assisted HetNet a hot topic.However,traditional resource allocation schemes assume that base stations can exactly estimate direct link gains and cross-tier link gains,which is impractical for practical HetNets due to the impact of channel delays and random perturbation.To further improve energy utilization and system robustness,in this paper,we investigate a robust resource allocation problem to maximize the total Energy Efficiency(EE)of Small-Cell Users(SCUs)in NOMA-assisted HetNets under imperfect channel state information.By considering bounded channel uncertainties,the robust resource optimization problem is formulated as a mixed-integer and nonlinear programming problem under the constraints of the cross-tier interference power of macrocell users,the maximum transmit power of small base station,the Resource Block(RB)assignment,and the quality of service requirement of each SCU.The original problem is converted into an equivalent convex optimization problem by using Dinkelbach's method and the successive convex approximation method.A robust Dinkelbach-based iteration algorithm is designed by jointly optimizing the transmit power and the RB allocation.Simulation results verify that the proposed algorithm has better EE and robustness than the existing algorithms.

Energy-efficient power allocation for NOMA heterogeneous networks with imperfect CSI

In this paper,an optimal user power allocation scheme is proposed to maximize the energy efficiency for downlink non-orthogonal multiple access(NOMA)heterogeneous networks(HetNets).Considering channel estimation errors and inter-user interference under imperfect channel state information(CSI),the energy efficiency optimization problem is formulated,which is non-deterministic polynomial(NP)-hard and non-convex.To cope with this intractable problem,the optimization problem is converted into a convex problem and address it by the Lagrangian dual method.However,it is difficult to obtain closed-form solutions since the variables are coupled with each other.Therefore,a Lagrangian and sub-gradient based algorithm is proposed.In the inner layer loop,optimal powers are derived by the sub-gradient method.In the outer layer loop,optimal Lagrangian dual variables are obtained.Simulation results show that the proposed algorithm can significantly improve energy efficiency compared with traditional power allocation algorithms.

Resource allocation for physical-layer security in OFDMA downlink with imperfect CSI

We investigate the problem of resource allocation in a downlink orthogonal frequency-division multiple access （OFDMA） broadband network with an eavesdropper under the condition that both legitimate users and the eavesdropper are with imperfect channel state information （CSI）. We consider three kinds of imperfect CSI： （1） noise and channel estimation errors, （2） feedback delay and channel prediction, and （3） limited feedback channel capacity, where quantized CSI is studied using rate-distortion theory because it can be used to establish an information-theoretic lower bound on the capacity of the feedback channel. The problem is formulated as joint power and subcarrier allocation to optimize the maximum-minimum （max-min） fairness criterion over the users＇ secrecy rate. The problem considered is a mixed integer nonlinear programming problem. To reduce the complexity, we propose a two-step suboptimal algorithm that separately performs power and subcarrier allocation. For a given subcarrier assignment, optimal power allocation is achieved by developing an algorithm of polynomial computational complexity. Numerical results show that our proposed algorithm can approximate the optimal solution.

Energy Efficiency of Distributed Antenna Systems with D2D Communications Under Imperfect CSI

In this paper,we investigate the distributed antenna systems(DAS)based on device to device(DASD2D)communications under the imperfect channel state information(CSI).Our aim is to maximize the energy efficiency(EE)of the D2D users equipment(DUE)under the constraints of the maximum transmission power of D2D pairs and the quality of service(QoS)requirements of the cellular user equipment(CUE).The worst-case design is considered so that the QoS of the CUE can be guaranteed for every realization of the CSI error in the ellipsoid region.The EE objective function of the optimization problem is non-convex and non-linear,and thus this problem cannot be solved by the traditional optimization methods.To solve this problem,first we transform it to an EE maximization problem without uncertain parameters by exploiting the Markov and Cauchy-Schwartz inequality.Then using the fractional programming theory and difference of convex functions optimization method,the robust EE maximization algorithms based on the hard and soft protection method are developed to maximize the system’s EE performance,respectively.However,these two algorithms are designed at the cost of the reduced EE of the DUE.Therefore,in order to further improve the EE performance and make a trade-off between the EE performance and the robustness,the iterative update algorithms for the total power constraint and average interference constraint are developed to maximize the system’s EE performance,respectively.Simulation results demonstrate the effectiveness of the four proposed EE algorithms and illustrate the trade-off between the EE performance and robustness for the iterative update algorithms.