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IEEE Transactions on Information Forensics and Security

Parallel PAM for Secure Transmission

Hongliang He, Nengcheng Chen

Published Jan 1, 2025• 2 citations
Publisher

Abstract

Physical layer security is a promising approach to enhancing the security of multi-user networks. However, user interference causes constellation points from different users to overlap, limiting both network reliability and security. To address this, we propose a parallel pulse amplitude modulation (PAM) scheme that ensures constellations are regularly superimposed at the legitimate receiver while appearing chaotic to the eavesdropper. Consequently, the eavesdropper experiences a consistently high bit/symbol error rate, whereas the legitimate receiver maintains a very low error rate. Furthermore, we extend the parallel PAM scheme to both the in-phase and quadrature components of the signal, forming a heterogeneous quadrature amplitude modulation (QAM) scheme. This enhances transmission efficiency while preserving security. We analyze the bit/symbol error rates at both the legitimate receiver and the eavesdropper, deriving a lower bound for the eavesdropper’s error rate. Finally, simulation results validate our theoretical analysis.

DOI
10.1109/tifs.2025.3552035

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Physical layer security is a promising approach to enhancing the security of multi-user networks. However, user interference causes constellation points from different users to overlap, limiting both network reliability and security. To address this, we propose a parallel pulse amplitude modulation (PAM) scheme that ensures constellations are regularly superimposed at the legitimate receiver while appearing chaotic to the eavesdropper. Consequently, the eavesdropper experiences a consistently high bit/symbol error rate, whereas the legitimate receiver maintains a very low error rate. Furthermore, we extend the parallel PAM scheme to both the in-phase and quadrature components of the signal, forming a heterogeneous quadrature amplitude modulation (QAM) scheme. This enhances transmission efficiency while preserving security. We analyze the bit/symbol error rates at both the legitimate receiver and the eavesdropper, deriving a lower bound for the eavesdropper’s error rate. Finally, simulation results validate our theoretical analysis.
In this paper, we propose a noisy and dynamic-index partitioned modulation (IPM) to secure a quadrature amplitude modulation (QAM) constellation transmission over a non-degraded wiretap channel. Unlike approaches that rely on multi-antenna systems or tight amplitude-phase tracking, IPM partitions QAM into multiple disjoint subsets that are separately indexed by a dynamic key, known at the transmitter (Alice) and the legitimate receiver (Bob), but not at the eavesdropper (Eve). The proposed IPM maps the information bits into multiple sequences, each one lying in a different partition of the QAM constellation space. This mapping is performed through a cross-bit labeling that we define to increase the confusion at the eavesdropper, while minimizing the bit error rate (BER) at the legitimate receiver. As the eavesdropper is not aware of the dynamic index pointing to the different partitions, the IPM creates larger Voronoï detection zones around Bob’s symbol compared to Eve. To induce further confusion at Eve, we inject random uniform noise into IPM symbols. The noise varies in a domain that is fully included in Bob’s larger detection zone, but it exceeds Eve’s detection zone. The performances of the noisy IPM scheme in terms of error rate and secrecy rate are analytically and numerically evaluated. Our results show that the IPM scheme creates on the Eavesdropper’s link an error floor, independently of its signal-to-noise ratio (SNR). However, the IPM scheme preserves the legitimate link, for which the BER decreases as the SNR increases. Indeed, the secrecy rate remains positive for all SNR values and achieves an asymptotical constant plateau value.
This paper studies a practical design of probabilistic constellation shaping (PCS) for enhancing the performance of physical layer security in visible light communications (VLC). In particular, we consider a wiretap VLC channel employing a probabilistically shapedM-ary pulse amplitude modulation (PAM) constellation. Considering the requirements for reliability of the legitimate user’s channel, flickering-free transmission, and symmetric constellation distribution, the optimal constellation distributions to maximize modulation-constrained secrecy capacity or the bit error rate (BER) of eavesdropper’s channel are investigated for both scenarios of known and unknown eavesdropper’s channel state information (CSI). To formulate the constraint on the channel reliability, tractable closed-form expressions for the upper bound and approximate BER ofM-ary PAM under an arbitrary symbol probability are derived. The design problem is shown to be non-convex due to the non-convex BER constraint. By proving that the upper bound BER is a concave function of the constellation distribution, a suboptimal solution based on the convex-concave procedure (CCCP) is presented. Our findings reveal that while the uniform signaling can only satisfy the BER constraint when the optical power is beyond a certain value, the proposed PCS design works in the entire region of the optical power. Some insights into the optimal constellation distribution with respect to the emitted optical power are also discussed.
Superposition modulation(SM) separates the transmitters and the bits to be sent into two parts, respectively, and aims that the low-order symbols modulated by different bit sequences reach the legitimate receiver (Bob) synchronously. Then the receiver receives a high-order superposition symbol superimposed by the low-order symbols. Its diversity makes a great fluctuation of communicating channels, which is a great feature for the physical-layer security. So the potential security of SM is deserved to be discussed. This paper investigates the security performance of SM scheme in a wiretap system, and its symbol error rete (SER) at the eavesdropper (Eve) is much higher compared with the traditional QAM scheme. Furthermore, we discuss the effect of channel estimation errors. It shows that SM scheme is as sensitive to estimation error as traditional QAM scheme for Eve, such that SM is still have a better secrecy performance. The results show agreement with computer simulations.
Physical layer security (PLS) offers a unique approach to protecting information confidentiality against eavesdropping by malicious users. This paper studies a joint design of adaptive M−ary pulse amplitude modulation (PAM) and precoding for performance improvement of PLS in visible light communications (VLC). It is known that higher-order modulation results in a better secrecy capacity at the expense of a higher bit-error rate (BER). On the other hand, a proper precoding design can also enhance secrecy performance. The proposed design, therefore, aims at the optimal PAM modulation order and precoder to maximize a utility function that takes into account the secrecy capacity and BERs of the legitimate user (Bob)’s and the eavesdropper (Eve)’s channel. Due to the lack of a closed-form expression for the utility function, a Q-learning-based design is proposed and evaluated. Compared to the non-adaptive approach under all different settings of Bob’s and Eve’s positions, simulation results verify that the proposed joint adaptive design achieves a good balance between the secrecy capacity and BER of Bob’s channel while maintaining a sufficiently high BER of Eve’s channel.
We apply the concept of artificial noise (AN) transmission in an untrusted relay network to enhance secure communication between the source and destination. Specifically, in addition to square quadrature amplitude modulated (QAM) signals broadcasted by the source, the relay simultaneously receives AN symbols designed and transmitted by the destination. For the relay, based on the assumption of additive white Gaussian noise, we derive the analytical symbol error rate (SER) expression, which is maximized for the optimal AN design. Under an average power constraint, we find the optimal phase and power distribution of the AN. Interestingly, our study shows that the Gaussian distribution is generally not optimal to generate AN and the results in this paper can be used as benchmarks for future analyses of AN-based techniques. More importantly, rather than conducting analysis from an information-theoretic perspective, our SER-based approach takes practical communication issues into account, such as QAM signalling.
In this paper, we propose a novel constellation rotation and superposition scheme to improve the security of wireless multiple-access wiretap channels. The basic idea is to overlay the signal constellations of all users on a common constellation after being rotated at a certain angle. Then offset the legitimate channel phase and make the legitimate channel coefficients the superposition of modules, while the eavesdropper’s channel coefficients are the superposition of vectors. In this way, it is more possible for the legitimate destination to achieve a higher signal-to-noise ratio (SNR) than the eavesdropper. We analyze the security performance of the proposed scheme and derive the bit error rates (BER) for the legitimate destination and the eavesdropper. The results show that an increase in the number of users is beneficial to improving security performance.