Kalman filter is an important technology to realize information fusion between Inertial Navigation System (INS) and Global Navigation Satellite System (GNSS). One of the most important variables in the Kalman filter structure is the state variable, which is the basis of maintaining system stability. However, due to the inherent singularity in polar regions, the INS/GNSS integrated navigation system will not work properly in polar regions. Different coordinate systems are often used in trans-polar navigation to solve the problems in the polar regions, therefore the Kalman filter state variable transformation is inevitable in the process of entering or leaving the polar regions, which will bring instability and even failure to the system. Here, this paper proposes a Kalman filter state transformation algorithm for INS/GNSS polar integrated navigation based on Psi-angle error model to ensure the numerical stability of the Kalman filter during its state transformation. Key to this success is to establish the transformation relationship between different filter state variables as well as their covariance matrices in different navigation coordinate systems, then the state variables and the covariance matrices are transformed simultaneously. After presenting the state variable transformation algorithm and the system description, a numerical evaluation is carried out to assess the presented algorithm with regard to stability and accuracy.

Dual-axis rotational inertial navigation system (DRINS) can achieve self-calibration of error parameters to improve the navigation performance. However, the traditional self-calibration methods rely on the external reference information. This paper focuses on the dual DRINSs configuration and proposes a collaborative calibration algorithm. Considering the error parameters of redundant DRINS, the 60-D Kalman filter is established, in which the geometric constraint between systems are deployed to establish the observation equation without external reference information. A novel collaborative calibration scheme is designed based on the asynchronous rotation to make all the error states observable. Monte Carlo simulations and real system experiments are conducted to verify the effectiveness of the proposed algorithm. The result shows the algorithm works well.

The Kalman filter method plays a crucial role in enhancing the navigation accuracy of the dual-axis rotational inertial navigation system (RINS) through periodic estimation and compensation of device errors. Due to the particularity of polar geography, the traditional RINS mechanism in the local-level geographic frame loses efficacy in the polar region. This paper proposes a self-calibration Kalman filter algorithm based on the transverse ellipsoidal earth model to solve the self-calibration problem of RINS in polar region. This method firstly transforms the state of the local-level geographic frame to the transverse frame, and then constructs the prediction model and observation model of the Kalman filter based on the carrier state and error parameters in the transverse frame. In the self-calibration stage, a suitable rotation strategy is employed to stimulate the errors of RINS, and the proposed algorithm is utilized to estimate and compensate for the resulting errors. In addition, the traditional spherical earth model is improved to ellipsoidal earth model in this algorithm to avoid additional errors in the polar region. Monte Carlo experiments are carried out with simulation data at high latitudes, and then experiments at middle latitudes are carried out with ring laser gyro-based dual-axis RINS. The results demonstrate that the proposed method enables precise calibration of all error parameters, which aligns consistently with results obtained within the local-level geographic frame.

This paper investigates the multi-antenna covert communications assisted by a simultaneously transmitting and reflecting reconfigurable intelligent surface (STAR-RIS). In particular, to shelter the existence of covert communications between a multi-antenna transmitter and a single-antenna receiver from a warden, a friendly full-duplex receiver with two antennas is leveraged to make contributions where one antenna is responsible for receiving the transmitted signals and the other one transmits the jamming signals with a varying power to confuse the warden. Considering the worst case, the closed-form expression of the minimum detection error probability (DEP) at the warden is derived and utilized in a covert constraint to guarantee the system performance. Then, we formulate an optimization problem maximizing the covert rate of the system under the covertness constraint and quality of service (QoS) constraint with communication outage analysis. To jointly design the active and passive beamforming of the transmitter and STAR-RIS, an iterative algorithm based on semi-definite relaxation (SDR) method and Dinkelbach’s algorithm is proposed to effectively solve the non-convex optimization problem. Simulation results show that the proposed STAR-RIS-assisted scheme highly outperforms the case with conventional RIS, which validates the effectiveness of the proposed algorithm as well as the superiority of STAR-RIS in guaranteeing the covertness of wireless communications.

This paper investigates the multi-antenna covert communications assisted by a simultaneously transmitting and reflecting reconfigurable intelligent surface (STAR-RIS). In particular, to shelter the existence of communications between transmitter and receiver from a warden, a friendly full-duplex receiver with two antennas is leveraged to make contributions to confuse the warden. Considering the worst case, the closed-form expression of the minimum detection error probability (DEP) at the warden is derived and utilized as a covert constraint. Then, we formulate an optimization problem maximizing the covert rate of the system under the covertness constraint and quality of service (QoS) constraint with communication outage analysis. To jointly design the active and passive beamforming of the transmitter and STAR- RIS, an iterative algorithm based on globally convergent version of method of moving asymptotes (GCMMA) is proposed to effectively solve the non-convex optimization problem. Simu-lation results show that the proposed STAR-RIS-assisted scheme highly outperforms the case with conventional RIS.

This paper studies covert communications between a pair of legitimate transmitter-receiver against a watchful warden over fading channels. There coexist multiple friendly helper nodes who are willing to protect the covert communication from being detected by the warden. An uncoordinated jammer selection scheme is proposed where those helpers whose instantaneous channel gains to the legitimate receiver fall below a pre-established selection threshold will be chosen as jammers radiating jamming signals to defeat the warden. Afterwards, we jointly design the optimal selection threshold and transmission rate for maximizing covert throughput under the premise that the detection error of the warden exceeds a certain level. Numerical results demonstrate that the maximal covert throughput improves significantly as the total number of helpers increases.

In multiple access systems, physical layer security is degraded since more attacking targets are available for the eavesdropper. Fortunately, it has been recently demonstrated that non-orthogonal multiple access (NOMA) could improve secure transmission performance. However, it is still unknown how to design a transmission scheme for maximizing the sum rate when the channel state information is imperfectly known at the transmitter. To fill this gap, we formulate a maximization problem of sum rate while incorporating versatile metrics such as outage probability, quality of service, and transmit power. By leveraging the first-order and log-concavity properties of the Marcum Q-function, the maximum sum rate of the secure NOMA transmission scheme is efficiently obtained. Simulation results validate the strength of this newly established scheme when compared with conventional orthogonal multiple access scheme.

In a wiretap channel, due to the passive nature of eavesdropper and the inevitable errors during channel estimation or feedback, the channel state information is usually imperfectly known at the transmitter. While probabilistic constrained secure transmission provides an elegant formulation to tackle these uncertainties, current works mostly focus on the fixed-rate secure transmission design. To exploit the dynamic channel state information for performance enhancement, this paper investigates a variable-rate transmission scheme with adjustable rate and power, under the outage probabilistic constraints and upper bounding rate constraint. By leveraging the first-order and log-concavity properties of the Marcum Q-function, closed-form optimal secure transmission design is obtained. Furthermore, the optimality of the proposed method empowers us to concisely quantify the performance gain brought by rate variation. Numerical results show that the proposed scheme achieves significantly lower average outage probability and higher throughput than the fixed-rate scheme no matter with or without upper bound rate limitation.

The problem of power allocation with uncoordinated cooperative jamming is addressed in this paper to enhance the physical layer security of the single-input-single-output wiretap channel with single-antenna jammers. Differing from the existing works concerning the secrecy rate maximization, this paper studies the problem of minimizing the secrecy outage probability with fixed secrecy rate, where the channel state information concerning the eavesdropper is only known statistically. This problem is formulated as an optimization problem of power allocation for the jamming signals. We prove that the optimization problem is convex in essence, and the optimal solution is thus conveniently obtained by using the methods of golden section search and bi-section search. Simulation results show that the proposed approach is very efficient and can significantly enhance the physical layer security by reducing the secrecy outage probability.

In this paper, we apply angle-domain Doppler compensation for high-mobility wideband massive multi-input multi-output (MIMO) uplink communications. The time-varying multipath channel is considered between high-speed terminal and static base station (BS), where multiple Doppler frequency offsets (DFOs) are associated with distinct angle of departures (AoDs). With the aid of large-scale uniform linear array (ULA) at the transmitter, we design a beamforming network to generate multiple parallel beamforming branches, each transmitting signal pointing to one particular angle. Then, the transmitted signal in each branch will experience only one dominant DFO when passing over the time-varying channel, which can be easily compensated before transmission starts. We theoretically analyze the Doppler spread of the equivalent uplink channel after angle-domain Doppler compensation, which takes into account both the mainlobe and sidelobes of the transmit beam in each branch. It is seen that the channel time-variation can be effectively suppressed if the number of transmit antennas is sufficiently large. Interestingly, the asymptotic scaling law of channel variation is obtained, which shows that the Doppler spread is proportional to the maximum DFO √ and decreases approximately as 1/√(M) (M is the number of transmit antennas) when M is sufficiently large. The numerical results are provided to corroborate the proposed scheme.

In this paper, we design a novel angle-domain adaptive filtering (ADAF)-based frequency synchronization method for massive multiple-input multiple-output (MIMO) multiuser uplink, which is suitable for users with either separate or overlapped angle-of-arrival (AoA) regions. We first introduce the angle-constraining matrix (ACM), which consists of a set of selected match-filter (MF) beamformers pointing to the AoAs of the interested user. Then, the adaptive beamformer can be acquired by appropriately designing the ADAF vector. Such beamformer can achieve a two-stage adaptive multiuser interference (MUI) suppression, i.e., inherently suppressing the MUI from distant users by ACM in the first stage and substantially mitigating the MUI from adjacent overlapping users by ADAF vector in the second stage. For both separate and mutually overlapping users, the carrier frequency offset (CFO) estimation and subsequent data detection can be performed individually for each user, which reduces the computational complexity. Moreover, ADAF is rather insensitive to imperfect AoA knowledge, making itself promising for multiuser uplink transmission. Numerical results are provided to show the effectiveness of the proposed method, as well as its superiority over existing competitors.

In this paper, we propose a Doppler pre-compensation scheme for high-mobility orthogonal frequency division multiplexing (OFDM) uplink, where a high-speed terminal transmits signals to the base station (BS). Considering that the time-varying multipath channel consists of multiple Doppler frequency offsets (DFOs) with different angle of departures (AoDs), we propose to perform DFO pre-compensation at the transmitter with a large-scale uniform linear array (ULA). The transmitted signal passes through a beamforming network with high- spatial resolution to produce multiple parallel branches. Each branch transmits signal towards one direction thus the transmitted signal is affected by one dominant DFO when passing over the time-varying channel. Therefore, we can compensate the DFO for each branch at the transmitter previously. Theoretical analysis for the Doppler spread of the equivalent uplink channel is also conducted. It is found that when the number of transmit antennas is sufficiently large, the time-variation of channel can be efficiently suppressed. Therefore, the performance will not degrade significantly if we apply the conventional time- invariant channel estimation and equalization methods at the receiver. Simulation results are provided to verify the proposed scheme.

This paper proposes a new nonadaptive (NADP) transmission scheme with adjustable power allocation based on the instantaneous channel state information (CSI) of the main channel for the multiple-input-single-output-single-eavesdropper (MISOSE) system. With the assistance of the adjustable power allocation ratio, we can improve the secure transmission performance under the constraints of secrecy outage probability (SOP) and upper bound rate (UBR). To verify the superiority of our new approach, we consider the multi-antenna communication systems with NADP scheme and give the optimal solution for achieving the maximum secrecy throughput based on a two-dimensional (2-D) searching method. In addition, a good suboptimal solution is also provided to reduce the time complexity of the optimal solution. Simulation results are provided and confirm that the proposed NADP scheme has significant advantages over the existing work especially when the transmit power is high.

This paper studies the artificial noise (AN) aided secure transmission design in a multiple-input- single-output multicast channel where a common message is transmitted to multiple receivers and only statistical channel state information of the eavesdropper is available. In this scenario, there may be no valid null space which allows the AN not to affect the legitimate receivers, and the traditional null-space AN scheme may not be applicable. To find the optimal design, we formulate a secrecy outage probability (SOP) constrained secrecy rate maximization problem which applies to an arbitrary number of the receivers. We adopt a novel approximation of the intractable SOP constraint and establish an efficient algorithm which solves the approximated problem to global optimality. The effectiveness of AN as well as the proposed solution is confirmed by simulation results. It is shown that the AN aided approach performs much better than pure beamforming even when there is no valid null space.

The artificial noise (AN) aided beamforming design in the MISOME (multiple-input, single-output, multiple-eavesdropper) wiretap channel is studied from the perspective of secrecy outage. Unlike many existing works which directly adopted the traditional null-space AN scheme, we start with a general assumption on the structure of the transmit signal, and seek to find the optimal structure by solving a secrecy outage probability (SOP) constrained secrecy rate maximization problem. By generalizing several existing conclusions regarding a single-antenna eavesdropper, we prove that the null-space AN scheme is indeed optimal for an arbitrary number of the eavesdropper's antennas from the perspective of secrecy outage. The power allocation problem is also studied and the closed-form optimal solution is obtained. It is found that the increase in the eavesdropper's antenna number is equivalent to requiring a smaller SOP.

In this paper, the outage performance of nonorthogonal multiple access (NOMA) is investigated in a downlink space division multiple access (SDMA) network with a multi-antenna base station and randomly deployed users. The NOMA technology is concurrently exploited with SDMA to further improve spectral efficiency. With limited channel state information (CSI) feedback taken into account, an analytical framework is proposed to evaluate outage performance for a given user. An expression for the outage probability is derived in closed form. Moreover, the diversity order and the effect of the number of feedback bits on the outage performance of NOMA are analyzed. Numerical results are demonstrated to verify our analytical findings and show that different from the perfect CSI case there always exists performance floor in the considered network due to limited feedback.

In this paper, we investigate physical-layer security in a wireless ad hoc network in which a large number of legitimate transmitter-receiver pairs coexist with randomly distributed eavesdroppers; each legitimate receiver works in either half-duplex (HD) or full-duplex (FD) mode. We aim to increase the number of secure links per unit area in the network of interest by determining the allocation between HD- and FD-mode links. We use tools from stochastic geometry theory and analyze the connection outage probability and the secrecy outage probability for an arbitrary legitimate link by deriving analytical expressions, based on which we then figure out the optimal fraction of FD-mode links that maximizes the area secure link number given a pair of wiretap code rates. We further develop insights into this optimal fraction and derive a closed-form expression for it assuming perfect self-interference cancellation. Numerical results are demonstrated to validate our theoretical findings.

This paper investigates the physical layer security in a multiple-input-single-output multicast channel, where a common message is transmitted to multiple receivers and only statistical channel state information of the eavesdropper is available. We consider transmitting some artificial noise (AN) along with the information-bearing signal to improve secrecy. To find the optimal AN design, we formulate a secrecy outage probability (SOP) constrained secrecy rate maximization problem. For solving this problem, we adopt a novel transformation of the intractable SOP constraint and establish an efficient algorithm which solves the transformed problem to global optimality. We also propose a low-complexity refinement method to reduce the conservatism incurred by the transformation and an efficient algorithm to find a suboptimal solution when the information-bearing signal is transmitted using single-stream beamforming. Our solution is found to be a valuable generalization of the traditional null-space AN scheme. According to our simulation results, when the number of receivers is less than that of transmit antennas, distributing AN uniformly in the null space of the legitimate channel vectors is near-optimal. When there is no valid null space, transmitting AN will interfere with some legitimate receivers, and the secrecy performance can also be improved with carefully designed AN.

This paper studies the artificial noise (AN) aided beamforming design in the multiple-input, single-output, and multiple-eavesdropper wiretap channel from the perspective of secrecy outage. Unlike many existing works, which directly adopted the traditional null-space AN scheme, we start with a general assumption on the structure of the transmit signal, and seek to find the optimal structure by solving a secrecy outage probability (SOP) constrained secrecy rate maximization problem. By generalizing several existing conclusions regarding a single-antenna eavesdropper, we prove that the null-space AN scheme is indeed optimal for an arbitrary number of the eavesdropper’s antennas from the perspective of secrecy outage. Furthermore, the optimal power allocation between the information-bearing signal and the AN is found under both general conditions and the conservative assumption that the eavesdropper can be arbitrarily close to the transmitter or his receiver noise power can be arbitrarily low. It is also found that the increase in the eavesdropper’s antenna number is equivalent to requiring a smaller SOP under the conservative assumption. The results in this paper can help generalize existing design solutions for single-antenna eavesdroppers to multi-antenna eavesdroppers.

In this paper, we investigate the physical-layer security of slow fading wiretap channel with channel estimation errors. We aim to maximize the reliable secrecy rate under constraints of secrecy outage probability and reliability outage probability. To this end, we propose an adaptive (ADP) transmission scheme in which the communication rate and secrecy rate are adaptively adjusted based on the estimated imperfect channel state information (CSI) of the legitimate channel. The optimal solution is obtained by solving a single-variable maximization problem, where the objective function is log-concave. Numerical results are provided to verify our approach as well as to show the impact of imperfect CSI on the secrecy throughput.

This paper studies the dirty-paper coding (DPC) based secure transmission in a multiuser broadcast channel. Since the encoding order of DPC determines which information-bearing signals must be treated as noise by potential eavesdroppers, adopting DPC enables the accurate characterization of the intrinsic secrecy as well as secrecy outage of multiuser broadcasting. Furthermore, the information-bearing signals can be designed to provide secrecy in addition to supporting normal (unclassified) transmission. To show this, we consider the scenario where one user requests secure transmission and the other users request normal transmission, and propose a hybrid secure transmission scheme which combines zero-forcing DPC and artificial noise (AN). By solving the secrecy rate maximization problem under constraints on the secrecy outage probability and the normal communication rates, we find that in addition to supporting the normal transmission, the proposed scheme has the potential to achieve a secrecy rate close to that of the traditional AN-based beamforming.

In this paper, we provide a comprehensive analysis of the multi-antenna transmission in a K-tier downlink heterogeneous cellular network (HCN). We first propose a reliability-oriented mobile access policy with an access threshold, in which each user connects to the strongest base station in terms of the truncated long-term received power. Under this policy, we derive for a random user explicit analytical expressions of the exact out-age probability along with its computational convenient lower and upper bounds. Asymptotic analysis on the outage probabilities shows that introducing the access threshold efficiently improves outage performance. We further investigate the area network throughput from the perspective of outage. Our theoretic analysis and numerical validations show that throughput performance can be enhanced by properly designing the access threshold.

A practical uncoordinated cooperative jamming (UCJ) scheme with multiple single-antenna helpers is proposed in this paper to enhance the physical layer security of single-input-multiple-output (SIMO) wiretap channel. In the scheme, both the intended receiver and the eavesdropper are equipped with multiple antennas and apply the minimum mean-square error (MMSE) combiner. The multiple uncoordinated single-antenna helpers transmit jamming signals independently to confound the eavesdropper, and we focus on power allocation for the helpers to solve the secrecy rate maximization (SRM) problem. Assuming that the statistical channel state information (CSI) concerning the eavesdropper is available, a convex conservative secrecy outage probability (SOP) constraint is derived and then used to solve the SRM problem with DC (difference of convex function) programming method. Furthermore, a bisection-like refinement method is provided to find a quality solution of the SRM problem with the original SOP constraint. Numerical results show that the proposed scheme has good secrecy performance especially when the number of helpers is large.

In this paper, we propose a new efficient blind carrier frequency offset (CFO) estimator for multi-input multi-output orthogonal frequency division multiplexing (MIMO-OFDM) systems. A cost function is carefully designed which can be exactly expressed as a superposition of very few harmonically related cosine waves even with the effect of noise. By using this property, the minimization of the designed cost function can be solved in a quite computationally efficient manner without any exhausted grid searching procedure. We provide numerical results to corroborate the proposed studies. It is seen that the proposed estimator can achieve comparable estimation performance with existing competitors with substantially reduced computational burden.

The secrecy outage of a two-user slow fading broadcast channel is studied in this paper. We consider the scenario where independent and confidential messages are transmitted to each user using superposition coding in the presence of an external eavesdropper. We assume the instantaneous channel state information (CSI) of the eavesdropper's channel is not available and the secrecy outage can be claimed for each user. The secrecy outage probability of each user conditioned on the instantaneous CSI of the legitimate channel is studied and used to derive the achievable secrecy rate region under the conditional secrecy outage probability constraints. The average achievable secrecy rate, i.e. the secrecy throughput, is studied as the measure of performance under the slow fading. The optimal secrecy rate allocation strategy that achieves the boundary of the achievable secrecy throughput region is characterized for the general case and for the maximum sum secrecy throughput. Numerical results of the secrecy throughput regions are shown, and the parameters that influence the secrecy throughput are discussed.

In this paper, we investigate the security issue of a two-hop amplify-and-forward MIMO wireless relay networks in the existence of a multi-antenna eavesdropper. The optimal scheme to achieve the secrecy capacity involves a non-convex optimization and is still an open problem. Aiming to find an efficient way to enhance the secrecy rate, we propose a suboptimal joint source and relay linear precoding scheme. In the scheme, the source node adopt a generalized singular value decomposition (GSVD) based precoding to transmit the signal in the first phase, and the relay node forwards the received signal based on SVD in the null-space of the wiretap channel in the second phase. Power allocations in both phases are optimized to maximize the secrecy rate. An alternating iterative optimization algorithm is proposed to solve the problem. The algorithm is computationally efficient and guarantees to converge to a local optimum. Numerical evaluation results are provided to show the effectiveness of the iterative algorithm and the proposed secrecy scheme.

We investigate the physical layer security of a multiple-input single-output (MISO) channel in the presence of a multi-antenna passive eavesdropper. Traditionally, artificial noise (AN) scheme is an efficient security strategy without the channel state information (CSI) of the eavesdropper. In this paper, we propose and analyze an efficient security scheme called the artificial fast fading (AFF) scheme. The basic idea is to randomly weight the information symbols at different transmit antennas in a special manner so that the channel of the intended receiver is an AWGN channel while that of the eavesdropper is a fast fading channel. This prevents the eavesdropper obtaining the CSI using the blind channel estimation techniques so that it can only detect the information symbols in a non-coherent way, which greatly reduces the amount of information intercepted. More importantly, we derive the achievable secrecy rate of the sheme and provide a low bound of it, which can be numerically calculated. Compared with the exact secrecy rate of the AN scheme, even the low bound of the AFF scheme is larger, when the eavesdropper has more antennas than the transmitter.

Exploiting the idea of cooperative communications is an efficient way to improve the physical-layer security of a wireless transmission in the presence of passive eavesdroppers. In this paper, we propose a hybrid cooperative relaying and jamming scheme to enhance the security of a two-way relay network, where some intermediate nodes help to relay the signal to the legitimate terminals via distributed beamforming and the others jam the eavesdropper simultaneously. In such a way, both two cooperative phases of the data transmission are protected. Subjected to the more practical per-node power constraint of each node and without the channel state information (CSI) of the eavesdropper, we propose a scheme to enhance the secrecy of the two terminals. It is shown that the problem can be transformed into a semidefinite programming (SDP) problem with an additional rank-1 constraint. We then develop a penalty function method and an iterative algorithm to solve such a problem efficiently, instead of the popular semi-definite relaxation (SDR) and randomization techniques proposed in the previous literatures. Simulations show that the proposed hybrid scheme greatly improves the security of the two-way relay networks.