We investigate signaling and linear precoding designs for secure downlink communications in a multiuser MIMO (MU-MIMO) network. The network is tapped by an external eavesdropper (Eve) who is equipped with a large number of antennas. In addition to the transmission of several (unicast) information signals to downlink users (Bobs), the transmitter (Alice) generates friendly jamming (FJ), aiming to prevent Eve from decoding Alice’s signals. To mitigate both multiuser interference (MUI) and FJ on Bobs, MU-MIMO systems often rely on zero-forcing (ZF) precoders. A condition for the application of such precoders is that the network must beunderloaded, i.e., Alice has more antennas than all Bobs combined. Foroverloadedscenarios, ZF-based precoding cannot guarantee nullification of both MUI and FJ at legitimate receivers. Accordingly, we propose a combined signaling-and-precoding scheme that can also be applied to an overloaded MU-MIMO network. In an underloaded scenario, our technique is shown to impose a more stringent antenna requirement on Eve than a classical ZF-based precoding, i.e., Eve must utilize more antennas if she is to successfully eavesdrop on Alice’s transmissions. Although our scheme is comparable to antenna selection (AS) approaches in terms of Eve’s antenna requirement, it incurs much less delay and complexity by avoiding frequent on/off switching of the RF chains at Bobs. For underloaded scenarios, we provide security analysis that establishes the conditions under which our scheme is superior to the ZF scheme. Using computer simulations, we validate the advantages of our design and contrast it with ZF and AS schemes in terms of the symbol error rate, the EVM, and the achievable rate in both underloaded and overloaded scenarios.

Carrier frequency offset (CFO) arises from the intrinsic mismatch between the oscillators of a wireless transmitter and the corresponding receiver, as well as their relative motion (i.e., Doppler effect). Despite advances in CFO estimation and tracking techniques, estimation errors are still present. Residual CFO creates a time-varying phase error, which degrades the decoder's performance by increasing the symbol error rate. The impact is particularly visible in dense constellation maps (e.g., high-order QAM modulation), often used in modern wireless systems such as 5G NR, 802.11ax, and mmWave, as well as in physical security techniques, such as modulation obfuscation (MO). In this paper, we first derive the probability distribution function for the residual CFO under Gaussian noise. Using this distribution, we compute the maximum-likelihood demodulation boundaries for OFDM signals in a non-closed form. For modulation schemes with unequal-amplitude reference constellation points (e.g., 16-QAM and higher, APSK, etc.), the “optimal” boundaries have irregular shapes, and more importantly, they depend on the time since the last CFO correction instance, e.g., reception of frame preamble. To approximate the optimal boundaries and provide a practical (real-time) demodulation scheme, we explore machine learning techniques, specifically, support vector machine (SVM). Our SVM approach exhibits better accuracy and lower complexity in the test phase than other state-of-the-art machine-learning approaches. As a case study, we apply our CFO-aware demodulation to enhance the performance of a MO technique. Our analytical results show a gain of up to 3dB over conventional demodulation schemes, which exceeds 3dB in complete system simulations. Finally, we implement our scheme on USRPs and experimentally corroborate our analytic and simulation-based findings.

Carrier frequency offset (CFO) arises from the intrinsic mismatch between the operating frequencies of the transmitter and the receiver, as well as their relative speeds (i.e., Doppler effect). Despite advances in CFO estimation techniques, estimation errors are still present. Residual CFO creates time-varying phase error. Modern wireless systems, including WLANs, 5G cellular systems, and satellite communications, use high-order modulation schemes, which are characterized by dense constellation maps. Accounting for the phase error is critical for the demodulation performance of such schemes. In this paper, we analyze the post-estimation probability distribution of residual CFO and use it to develop a CFO-aware demodulation approach for a set of modulation schemes (e.g., QAM and APSK). For a given distribution of the residual CFO, symbols with larger amplitudes are less densely distributed on the constellation map. We explore one important application of our adaptive demodulation approach in the context of PHY-layer security, and more specifically modulation obfuscation (MO) mechanisms. In such mechanisms, the transmitter attempts to hide the modulation order of a frame's payload from eavesdroppers, which could otherwise exploit such information to breach user privacy or launch selective attacks. We go further and complement our CFO-aware demodulation scheme by optimizing the design of a low-complexity MO technique with respect to phase errors. Our results show that when combined, our CFO-aware demodulation and optimized MO techniques achieve up to 5 dB gain over conventional demodulation schemes that are not obfuscated and are oblivious to residual CFO.

We propose a distributed interference management method for a single-stream MIMO interference network that is tapped by an external eavesdropper. Along with its information signal, each legitimate transmitter creates a bogus signal, known as transmit-based friendly jamming (TxFJ), to confuse the eavesdropper. Although generating TxFJ protects the link from eavesdropping, it creates interference at other unintended but legitimate links. Using non-cooperative game theory, we design a distributed method for maximizing the sum of secrecy rates. Each link is a player in the game. It seeks to maximize its secrecy rate subject to a given information-rate constraint and power budget. The strategy profile of each player is to control the amount of TxFJ it generates. Because a pure non-cooperative game may not have Nash equilibria that result in (Pareto-)optimal secrecy sum-rate, we propose a modified price-based game, in which each link is penalized for generating interference on other legitimate links. Under the exact knowledge of eavesdropping channels, we show that the price-based game has a comparable secrecy sum-rate to a centralized approach. We then relax the assumption of knowledge of eavesdropping channels and leverage mixed-strategy games to provide robust solutions to the distributed secrecy sum-rate maximization problem.

We consider joint optimization of artificial noise (AN) and information signals in a MIMO wiretap interference network, wherein the transmission of each link may be overheard by several MIMO-capable eavesdroppers. Each information signal is accompanied with AN, generated by the same user to confuse nearby eavesdroppers. Using a noncooperative game, a distributed optimization mechanism is proposed to maximize the secrecy rate of each link. The decision variables here are the covariance matrices for the information signals and ANs. However, the nonconvexity of each link's optimization problem (i.e., best response) makes conventional convex games inapplicable, even to find whether a Nash equilibrium (NE) exists. To tackle this issue, we analyze the proposed game using a relaxed equilibrium concept, called quasi-NE (QNE). Under a constraint qualification condition for each player's problem, the set of QNEs includes the NE of the proposed game. We also derive the conditions for the existence and uniqueness of the resulting QNE. It turns out that the uniqueness conditions are too restrictive, and do not always hold in typical network scenarios. Thus, the proposed game often has multiple QNEs, and convergence to a QNE is not always guaranteed. To overcome these issues, we modify the utility functions of the players by adding several specific terms to each utility function. The modified game converges to a QNE even when multiple QNEs exist. Furthermore, players have the ability to select a desired QNE that optimizes a given social objective (e.g., sum rate or secrecy sum rate). Depending on the chosen objective, the amount of signaling overhead as well as the performance of resulting QNE can be controlled. Simulations show that not only can we guarantee the convergence to a QNE, but also due to the QNE selection mechanism, we can achieve a significant improvement in terms of secrecy sum rate and power efficiency, especially in dense networks.

The article considers the joint optimization of artificial noise (AN) and information signal precoders in a MIMO wiretap interference network where the transmission of each user may be overheard by several MIMO-capable eavesdroppers. We use the theory of non-cooperative games to propose a distributed framework to optimize the covariance matrices of the information signal and AN at each link. To tackle the non-convexity of each link/player's optimization problem, we recruit a relaxed equilibrium concept in game theory, called quasi-Nash equilibrium (QNE). Under the assumption of no coordination between links, we derive sufficient conditions for the existence and uniqueness of the resulting QNE. It turns out that the uniqueness of QNE is not always guaranteed, especially in the case of high interference. Hence, multiple QNEs might exist, and an ordinary updating process (e.g., Gauss-Seidel, Jacobi, or asynchronous update) does not guarantee the convergence to a QNE. Instead, by using the Tikhonov regularization method for variational inequality problems, we modify our algorithm to guarantee the game's convergence to a QNE even in the case of having multiple QNEs. The modified algorithm also allows the links to select between multiple QNEs so as to reduce the received interference at the legitimate receivers. Simulations are then used to confirm the above theoretical findings and the efficacy (in terms of secrecy sum-rate, convergence guarantee, and energy efficiency) of the latter algorithm.

In this paper, we expand the scope of PHY-layer security by investigating TX-based friendly jamming (FJ) for the wiretap channel in multi-link settings. For the single-link scenario, creating a TX-based FJ is an effective and practical method in improving the secrecy rate. In a multi-link setting, several information signals must be transmitted simultaneously. Thus, the design must guarantee that the FJ signal of a given transmitter does not interfere with unintended but legitimate receivers. Under the assumption of exact knowledge of the eavesdropping channel, we first propose a distributed price-based approach to improve the secrecy sum-rate of a two-link network with one eavesdropper while satisfying an information-rate constraint for both link. Simulations show that price-based FJ control outperforms greedy FJ, and is close to the performance of a centralized approach. Next, we propose a method based on mixed strategic games that can offer robust solutions to the distributed secrecy sum-rate maximization problem under the assumption of an unknown eavesdropping channel. Lastly, we use simulations to show that in addition to outperforming the greedy approach, our robust optimization also satisfies practical network considerations. In particular, the transmission time for the robust optimization can be determined flexibly to match the channel's coherence time.