Secrecy Rate Loss Research Articles

Secure Communication in Relay-Assisted Massive MIMO Downlink With Active Pilot Attacks

In this paper, the achievable secrecy rate of a relay-assisted massive multiple-input multiple-output (MIMO) downlink is investigated in the presence of a multi-antenna active/passive eavesdropper. The excess degrees-of-freedom offered by a massive MIMO base-station (BS) are exploited for sending artificial noise (AN) via random and null-space precoders. An active eavesdropper contaminates the uplink channel estimates by sending pilot sequences identical to those of the legitimate users/relay. This active pilot contamination makes the massive MIMO BS implicitly beamform the confidential signals toward the active eavesdropper during two-hop downlink transmissions. The achievable secrecy rates are derived by taking the detrimental effects of actively contaminated channel state information with estimation errors and spatially correlated fading at the multiple-antenna terminals into account. The secrecy rate loss incurred by active pilot attacks over passive eavesdropping is investigated, and the secrecy rate gap between random and null-space-based AN is compared. A novel transmit power control policy is designed to efficiently allocate transmit power at the BS/relay for payload data and AN sequences for maximizing the achievable secrecy rate. Our results reveal that active pilot contamination attacks significantly degrade the achievable secrecy rate in dual-hop transmissions, and the corresponding detrimental effects cannot be asymptotically mitigated in the infinite BS antenna regime.

Secure Massive MIMO Communication With Low-Resolution DACs

In this paper, we investigate secure transmission in a massive multiple-input multiple-output (MIMO) system adopting low-resolution digital-to-analog converters (DACs). Artificial noise (AN) is deliberately transmitted simultaneously with the confidential signals to degrade the eavesdropper's channel quality. By applying the Bussgang theorem, a DAC quantization model is developed which facilitates the analysis of the asymptotic achievable secrecy rate. Interestingly, for a fixed power allocation factor $\phi$, low-resolution DACs typically result in a secrecy rate loss, but in certain cases they provide superior performance, e.g., at low signal-to-noise ratio (SNR). Specifically, we derive a closed-form SNR threshold which determines whether low-resolution or high-resolution DACs are preferable for improving the secrecy rate. Furthermore, a closed-form expression for the optimal $\phi$ is derived. With AN generated in the null-space of the user channel and the optimal $\phi$, low-resolution DACs inevitably cause secrecy rate loss. On the other hand, for random AN with the optimal $\phi$, the secrecy rate is hardly affected by the DAC resolution because the negative impact of the quantization noise can be compensated for by reducing the AN power. All the derived analytical results are verified by numerical simulations.

RBA: Detection and Protection Analysis Using Region-Based Algorithm in Ultra-Dense Networks

Due to broadcast nature of wireless medium, increased density of users, base stations (BSs) and small cell size in the ultra-dense network (UDN), the users are susceptible to be attacked by malicious eavesdroppers (EDs). However, UDN is provisioned with exceptionally adequate performance for all diversity of users along with the appearance of low power small cells in abundance. This paper deals with the secure transmission in UDN for high speed (or vehicular) users under the influence of single or multiple EDs. Thereby to ensure secure communication, we design a detection algorithm based on pattern matching for high-speed users by computing the secrecy rate loss (SRL) and simultaneously estimating the ranks to determine the sensitive area for attack. We then also develop the mathematical approach through the formation of a correlation matrix. We formulate the secure and energy efficient algorithm called region-based algorithm (RBA), which will protect users by encrypting the information transmitted in the sensitive area of attack. Simulation results reveal that the proposed algorithm is energy efficient and secure. RBA outperforms the conventional approach of encryption and also helps in saving energy (reserved for encryption) more than 90%. We also propose the optimal utilization of saved encryption energy to further improve the secrecy rate of moving users in the region of attack. The simulation results verify our theoretical approach and proposed approach well meets the target QoS in the attacked zone, to overcome the impact of ED.

Secrecy Rate Analysis for Pilot Contamination Attacks in Massive MIMO With Limited RF Chains

Pilot contamination attacks in training-based massive multiple-input multiple-output systems with limited radio-frequency chains are investigated. A lower bound for the achievable secrecy rate in the presence of a multi-antenna active eavesdropper is derived in closed-form. Thereby, the secrecy rate loss due to the active attacks over the passive eavesdropping is quantified. Moreover, the secrecy rate loss due to hybrid precoding over the full-dimensional digital precoding is derived.

Wireless Secure Communication With Beamforming and Jamming in Time-Varying Wiretap Channels

For physical layer security with multiple antennas over wireless channels, we consider an artificial noise-aided secure beamforming system. A transmitter can send the confidential information to the legitimate user more securely without eavesdropping when an artificial jamming signal interfering eavesdroppers is transmitted with the confidential information signal. The transmitter splits its transmit power for both the information and jamming signals with a power splitting factor. Under such a system model, we investigate the impacts on secrecy performance of a power splitting factor, the numbers of antennas and eavesdroppers, and noise variance at the legitimate receivers and eavesdroppers by analyzing the expected secrecy rate. The optimal power splitting factor and limiting secrecy rate with large number of antennas are also derived. Moreover, we examine the expected secrecy rate loss caused by channel variation over time. It is shown that the secrecy rate loss is independent of system parameters like a power splitting factor, the numbers of antennas and eavesdroppers in a high signal to interference plus noise ratio (SINR) region. In a low SINR region, on the other hand, the secrecy rate loss changes with system parameters. Simulation results verify these observations on ergodic secrecy rate and its loss due to time-varying channels.

Optimal Power Allocation for Secrecy Rate Maximization in Broadcast Wiretap Channels

We investigate physical layer security in wireless communication networks, where a transmitter Alice sends a confidential message to an intended user Bob, while coexisting with a normal transmitter DT, a normal receiver DR, and a passive eavesdropper Eve. Compared with the conventional cooperative jamming (CJ) scheme, DT has dual responsibilities. One is to broadcast public information to its service subscriber DR, and the other is to confound the unauthorized eavesdropper Eve to ensure desired secure communication. Considering the secrecy outage restriction of Bob and the quality of service demand of DR, we propose an optimal resource management strategy. Users with different security requirements take hierarchical secure measures. For example, banking transaction needs to adopt high strength security measures, and personal voice communication resorts to low-level security protection strategies. Numerical simulations show that the proposed secure design outperforms the CJ scheme in terms of effective service rate and effective energy efficiency with a little secrecy rate loss, which is suitable for the low-level security real-time communication.

Enhancing secrecy rates in a wiretap channel

Reliable communication imposes an upper limit on the achievable rate, namely the Shannon capacity. Wyner's wiretap coding ensures a security constraint and reliability, but results in a decrease of achievable rate. To mitigate the loss in secrecy rate, we propose a coding scheme in which we use sufficiently old messages as key and prove that multiple messages are secure with respect to all the information possessed by the eavesdropper. We also show that we can achieve security in the strong sense. Next, we study a fading wiretap channel with full channel state information of the eavesdropper's channel and use our coding/decoding scheme to achieve a secrecy capacity close to the Shannon capacity of the main channel (in the ergodic sense). Finally, we study a case where the transmitter does not have instantaneous information of the channel state of the eavesdropper, but only its distribution.

Secure Massive MIMO Transmission With an Active Eavesdropper

In this paper, we investigate secure and reliable transmission strategies for multi-cell multi-user massive multiple-input multiple-output (MIMO) systems with a multi-antenna active eavesdropper. We consider a time-division duplex system where uplink training is required and an active eavesdropper can attack the training phase to cause pilot contamination at the transmitter. This forces the precoder used in the subsequent downlink transmission phase to implicitly beamform towards the eavesdropper, thus increasing its received signal power. Assuming matched filter precoding and artificial noise (AN) generation at the transmitter, we derive an asymptotic achievable secrecy rate when the number of transmit antennas approaches infinity. For the case of a single-antenna active eavesdropper, we obtain a closed-form expression for the optimal power allocation policy for the transmit signal and the AN, and find the minimum transmit power required to ensure reliable secure communication. Furthermore, we show that the transmit antenna correlation diversity of the intended users and the eavesdropper can be exploited in order to improve the secrecy rate. In fact, under certain orthogonality conditions of the channel covariance matrices, the secrecy rate loss introduced by the eavesdropper can be completely mitigated.

Confidential Cooperative Communication With Trust Degree of Potential Eavesdroppers

For a confidential communication, we develop the transmission strategies by taking into account trust degree among users, which shows how much a user can be trusted in terms of an eavesdropping attack. For a single potential eavesdropper (PE) case, we derive an optimal power allocation for confidential message and jamming signal to maximize an expected secrecy rate with respect to the trust degree. In order to further increase the expected secrecy rate, by exploiting relaying transmission via PE, we derive the optimal transmission strategy and corresponding power allocation based on the threshold of trust degree. Furthermore, to investigate the effect of the accuracy of trust degree, we analyze the expected secrecy rate loss caused by an estimation error of the trust degree and provide the robust power allocation based on imperfect trust degree. Finally, we extend the results to the case of confidential communication in the presence of multiple PEs. Our analytical and numerical results show that the proposed strategies achieve substantially higher secrecy rates than that without exploiting the trust degree of users.

On Performance and Feedback Strategy of Secure Multiuser Communications With MMSE Channel Estimate

In this paper, we investigate a multiuser MIMO downlink with imperfect channel state information (CSI) from the physical-layer security provision. In a classical transmitter (Alice)–legitimate receiver (Bob)–eavesdropper (Eve) model using artificial noise to disturb Eve’s reception, we consider a general scenario where all nodes are equipped with multiple antennas, and Bob’s CSI is acquired by pilot-assisted channel estimation. For designing the secure transmit beamforming, we utilize random matrix quantization (RMQ) to quantize Bob’s channel estimate, and then Bob feeds it back to Alice. Due to the effects of imperfect CSI at Alice, the secrecy performance is upper bounded in the high signal-to-noise ratio (SNR) regions. In order to avoid the interference-limited phenomenon, we present a scaled strategy for the secrecy system utilizing derived upper bound on the secrecy rate loss. Moreover, it is shown that our derived results can be easily extended to a special case where both legitimate and eavesdropping receivers equip a single antenna each, where random vector quantization (RVQ) is utilized instead. By employing our proposed feedback strategy, the secrecy rate increases with transmit power, and the certain secrecy requirement can be guaranteed.

Hybrid Spatio-Temporal Artificial Noise Design for Secure MIMOME-OFDM Systems

This paper investigates artificial noise (AN) injection along the temporal and spatial dimensions of a legitimate system to secure its transmissions from potential eavesdropping. In particular, we consider a multiple-input multiple-output (MIMO) orthogonal frequency-division multiplexing (OFDM) system in the presence of a multiple-antenna passive eavesdropper and characterize both the secrecy rate and average secrecy rate of the legitimate system. We assume that the legitimate transmitter knows the full channel state information (CSI) of the links connecting it with its legitimate receiver but does not know the instantaneous CSI of the passive eavesdropper. Closed-form expressions for the secrecy rate and average secrecy rate are derived for the asymptotic case of a large number of transmit antennas. We compare the degrading effects of spatial and temporal AN on the eavesdropper's rate. We also investigate the power allocation between the data and the AN and the power allocation between the spatial and the temporal AN. An upper bound on the secrecy rate loss due to the presence of the eavesdropper is also derived, and computer simulations are carried out to demonstrate the performance of our proposed AN scheme.

Guaranteeing Positive Secrecy Capacity for MIMOME Wiretap Channels With Finite-Rate Feedback Using Artificial Noise

While the impact of finite-rate feedback on the capacity of fading channels has been extensively studied in the literature, not much attention has been paid to this problem under secrecy constraint. In this work, we study the ergodic secret capacity of a multiple-input multiple-output multiple-antenna-eavesdropper (MIMOME) wiretap channel with quantized channel state information (CSI) at the transmitter and perfect CSI at the legitimate receiver, under the assumption that only the statistics of eavesdropper CSI is known at the transmitter. We refine the analysis of Lin et al. 's random vector quantization (RVQ) based artificial noise (AN) scheme, where a heuristic upper bound on the secrecy rate loss (compared to the perfect CSI case) was given. We propose a lower bound on the ergodic secrecy capacity. We show that the lower bound and the secrecy capacity with perfect CSI coincide asymptotically as the number of feedback bits and the AN power go to infinity. For practical applications, we propose a very efficient quantization codebook construction method for the two transmit antennas case.

Secure MIMO Communications Under Quantized Channel Feedback in the Presence of Jamming

We consider the problem of secure communications in a MIMO setting in the presence of an adversarial jammer equipped with $n_j$ transmit antennas and an eavesdropper equipped with $n_e$ receive antennas. A multiantenna transmitter, equipped with $n_t$ antennas, desires to secretly communicate a message to a multiantenna receiver equipped with $n_r$ antennas. We propose a transmission method based on artificial noise and linear precoding and a two-stage receiver method employing beamforming. Under this strategy, we first characterize the achievable secrecy rates of communication and prove that the achievable secure degrees-of-freedom (SDoF) is given by $d_s = n_r - n_j$ in the perfect channel state information (CSI) case. Second, we consider quantized CSI feedback using Grassmannian quantization of a function of the direct channel matrix and derive sufficient conditions for the quantization bit rate scaling as a function of transmit power for maintaining the achievable SDoF $d_s$ with perfect CSI and for having asymptotically zero secrecy rate loss due to quantization. Numerical simulations are also provided to support the theory.

On the secrecy rate of limited feedback beamforming over multiple-input single-output wiretap channels

The secrecy rate of limited feedback beamforming is studied for a Multiple-Input Single-Output (MISO) wiretap channel with a multi-antenna eavesdropper. We first obtain the secrecy rate of limited feedback beamforming achieved at the legitimate receiver. We then derive a lower bound for the asymptotic secrecy rate in the large system limit. From this bound, we observe a threshold for the ratio of eavesdrop antennas to transmit antennas to obtain a positive secrecy rate. We further show that the secrecy rate loss due to limited feedback decays with the number of feedback bits per transmit antenna.

Adaptive Limited Feedback for MISO Wiretap Channels With Cooperative Jamming

This paper studies a multi-antenna wiretap channel with a passive eavesdropper and an external helper, where only quantized channel information regarding the legitimate receiver is available at the transmitter and helper due to finite-rate feedback. Given a fixed total bandwidth for the two feedback channels, the receiver must determine how to allocate its feedback bits to the transmitter and helper. Assuming zero-forcing transmission at the helper and random vector quantization of the channels, an analytic expression for the achievable ergodic secrecy rate due to the resulting quantization errors is derived. While direct optimization of the secrecy rate is difficult, an approximate upper bound for the mean loss in secrecy rate is derived and a feedback bit allocation method that minimizes the average upper bound on the secrecy rate loss is studied. A closed-form solution is shown to be possible if the integer constraint on the bit allocation is relaxed. Numerical simulations indicate the significant advantage that can be achieved by adaptively allocating the available feedback bits.

The Role of Feedback in Two-Way Secure Communications

Most practical communication links are bidirectional. In these models, since the source node also receives signals, its encoder has the option of computing its output based on the signals it received in the past. On the other hand, from a practical point of view, it would also be desirable to identify the cases where such an encoder design may not improve communication rates. This question is particularly interesting for the case where the transmitted messages and the feedback signals are subject to eavesdropping. In this paper, we investigate the question of how much impact the feedback has on the secrecy capacity by studying two fundamental models. First, we consider the Gaussian two-way wiretap channel and derive an outer bound for its secrecy capacity region. We show that the secrecy rate loss can be unbounded when feedback signals are not utilized except for a special case we identify, and thus conclude that utilizing feedback can be highly beneficial in general. Second, we consider a half-duplex Gaussian two-way relay channel where the relay node is also an eavesdropper, and find that the impact of feedback is less pronounced compared to the previous scenario. Specifically, the loss in secrecy rate, when ignoring the feedback, is quantified to be less than 0.5 bit per channel use when the relay power goes to infinity. This achievable rate region is obtained with simple time sharing along with cooperative jamming, which, with its simplicity and near optimum performance, is a viable alternative to an encoder that utilizes feedback signals.

Transmitter beamforming and artificial noise with delayed feedback: Secrecy rate and power allocation

Utilizing artificial noise (AN) is a good means to guarantee security against eavesdropping in a multi-input multi-output system, where the AN is designed to lie in the null space of the legitimate receiver's channel direction information (CDI). However, imperfect CDI will lead to noise leakage at the legitimate receiver and cause significant loss in the achievable secrecy rate. In this paper, we consider a delayed feedback system, and investigate the impact of delayed CDI on security by using a transmit beamforming and AN scheme. By exploiting the Gauss-Markov fading spectrum to model the feedback delay, we derive a closed-form expression of the upper bound on the secrecy rate loss, where N <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">t</sub> = 2. For a moderate number of antennas where N <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">t</sub> >; 2, two special cases, based on the first-order statistics of the noise leakage and large number theory, are explored to approximate the respective upper bounds. In addition, to maintain a constant signal-to-interference-plus-noise ratio degradation, we analyze the corresponding delay constraint. Furthermore, based on the obtained closed-form expression of the lower bound on the achievable secrecy rate, we investigate an optimal power allocation strategy between the information signal and the AN. The analytical and numerical results obtained based on first-order statistics can be regarded as a good approximation of the capacity that can be achieved at the legitimate receiver with a certain number of antennas, N <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">t</sub> . In addition, for a given delay, we show that optimal power allocation is not sensitive to the number of antennas in a high signal-to-noise ratio regime. The simulation results further indicate that the achievable secrecy rate with optimal power allocation can be improved significantly as compared to that with fixed power allocation. In addition, as the delay increases, the ratio of power allocated to the AN should be decreased to reduce the secrecy rate degradation.

Linear Precoding for Finite-Alphabet Signaling Over MIMOME Wiretap Channels

In this paper, we investigate the secrecy rate of finite-alphabet communications over multiple-input-multiple-output-multiple-antenna eavesdropper (MIMOME) channels. Traditional precoding designs based on Gaussian input assumption may lead to substantial secrecy rate loss when the Gaussian input is replaced by practical finite-alphabet input. To address this issue, we investigate linear precoding designs to directly maximize the secrecy rate for MIMOME systems under the constraint of finite-alphabet input. By exploiting the theory of Karush-Kuhn-Tucker (KKT) analysis and matrix calculus, we first present necessary conditions of the optimal precoding design when instantaneous channel-state information (CSI) of the eavesdropper is known at the transmitter. In this light, an iterative algorithm for finding the optimal precoding matrix is developed, utilizing a gradient decent method with backtracking line search. Moreover, we find that the beamforming design in MIMONE systems, which is a secrecy-capacity-achieving approach for Gaussian signaling, no longer provides the maximum secrecy rate for finite-alphabet input data. This case is substantially different from the Gaussian input case. In addition, we derive the closed-form results on the precoding matrix, which maximizes the secrecy rate in the low signal-to-noise ratio (SNR) region, and reveal the optimal precoding structure in the high-SNR region. A novel jamming signal generation method that draws on the CSI of the eavesdropper to additionally increase the secrecy rate is further proposed. The precoding design with only statistical CSI of the eavesdropper available at the transmitter is also considered. Numerical results show that the proposed designs provide significant gains over recent precoding designs through a power control policy and the precoding design with the Gaussian input assumption in various scenarios.

On the Impact of Quantized Channel Feedback in Guaranteeing Secrecy with Artificial Noise: The Noise Leakage Problem

The impact of quantized channel direction information (CDI) on the achievable secrecy rate is studied for multiple antenna wiretap channels. By assuming that the eavesdropper's channel is unknown at the transmitter, we adopt the transmission scheme where artificial noise (AN) is imposed in the null space of the legitimate receiver's channel to disrupt the eavesdropper's reception. It has been shown that, in the ideal case where perfect CDI is available at the transmitter, the achievable secrecy rate can be made arbitrarily large by increasing the transmission power. However, when only quantized CDI is available, the AN that was originally intended to jam the eavesdropper may now leak into the legitimate receiver's channel, causing significant secrecy rate loss. For a given number of feedback bits B and transmission power P, we derive the optimal power allocation among the message-bearing signal and the AN to maximize the secrecy rate under AN leakage. We show that, when B is sufficiently large, one should allocate power evenly among the message-bearing signal and the AN; whereas when B is small, one should be more conservative in allocating power to the AN. Moreover, by showing that the achievable secrecy rate under quantized CDI is bounded by a constant, we derive a scaling law between B and P that is necessary to maintain a constant secrecy rate loss compared to the perfect CDI case. The scaling of B is shown to be logarithmic of P. These results are first derived for the multiple-input single-output single-antenna-eavesdropper scenario and are later extended to the multiple-input multiple-output multiple-antenna-eavesdropper case. Numerical simulations are provided to verify our theoretical claims.