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IEEE Transactions on Communications

Noisy and Dynamic-Index Partitioned Modulation for Physical Layer Security

Lina Mroueh, Idowu Ajayi

Published Aug 20, 2025• 2 citations
Publisher

Abstract

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.

DOI
10.1109/tcomm.2025.3600556

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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.
In this paper, we propose a new transmission scheme, referred as Bit Interleaved Coded Modulation with Indexed Partitions (BICM-IPM), to secure the transmission on a wiretap channel with a passive eavesdropper. The BICM-IPM is designed to degrade the quality of QAM symbols transmission on a wiretap channel, while preserving the quality at the legitimate receiver. To achieve this, the QAM constellation is divided into several disjoint subsets, each one indexed by a channel-dependent dynamic secret key, known at the sender (Alice) and the legitimate receiver (Bob), but not at the eavesdropper (Eve). The symbols are then decoded at the legitimate receiver considering only the alphabet containing the symbols relative to the partition. However, in the absence of the index-partition knowledge at the eavesdropper, all the constellation symbols will be considered. Thus, the detection zones around Bob’s symbols will be larger than those at Eve. To further degrade the wiretap channel, we propose to inject a uniformly distributed random noise in a domain space totally included in Bob’s detection zone, but exceeding Eve’s one. Our analytical and numerical results show that the BICM-IPM creates a Bit Error Rate (BER) floor of 50% independent of the Signal-to-Noise Ratio (SNR) on the Eavesdropper’s link, while preserving the legitimate link for which the BER decreases with the SNR. This creates a maximal entropy at the eavesdropper side that is close to decoding a random binary sequence.
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.
Abstract In this article, we propose a random quadrature spatial modulation (RQSM) scheme to achieve secure transmission in multiple‐input multiple‐output multiantenna eavesdropper channels. We consider the case in which the eavesdropper has more antennas than that of the legitimate receiver, leading to a strong wiretap channel. In this case, the conventional secure quadrature spatial modulation schemes based on the artificially interfering signals are vulnerable to eavesdropping. On the contrary, the proposed RQSM scheme is able to achieve the physical‐layer security without transmitting artificial noises. Specifically, the bits‐to‐symbol mapping of the proposed RQSM is randomized according to the instantaneous channel state information of the legitimate link. Since in a rich scattering environment, the legitimate and the wiretap channels are generally independent of each other due to the spatial decorrelation property. Thus, the eavesdropper can be considered ignorant of the legitimate channel and cannot decode the confidential messages correctly. We derive the ergodic secrecy rate of the proposed RQSM scheme and show that the secrecy performance does not degrade as the number of antennas at the eavesdropper increases, which also outperforms the conventional jamming strategies. In addition, the bit error rate of the RQSM is also analyzed, which shows that security is achieved without sacrificing the system's reliability. Numerical results validate the theoretical derivations and demonstrate the effectiveness of the proposed RQSM scheme.
In this paper, a physical layer security (PLS) scheme based on quadrature channel modulation (QCM) called secure QCM (SQCM) is proposed for time division duplex (TDD) multi-input multi-output (MIMO) media based modulation (MBM) systems to resist eavesdropping. By exploiting the abundant legitimate channel realizations generated by the radio frequency (RF) mirrors, secure mappings between the original information bits and the transmit patterns are designed, where the transmit patterns include the transmit antenna activation pattern (AAP), mirror activation pattern (MAP) and symbol modulation pattern. The secure mappings used by the transmitter change for each transmission and are unavailable at the eavesdropper due to the independent fading of the legitimate link and the eavesdropping link. Based on the secure mappings, the proposed SQCM conveys the source information bits securely through the complex modulation symbol and instantaneous channel realizations by using a single RF chain. The ergodic secrecy rate is analyzed and a closed-form approximation is derived. Simulation results show that the closed-form approximation coincides with the experimental ergodic secrecy rate, and the achievable ergodic secrecy rate is not influenced by the number of eavesdropping antennas or the channel advantage of the eavesdropping link. Compared to the secure MBM scheme using the traditional artificial noise (AN) technique, the proposed SQCM scheme shows significant performance gain without consuming jamming power when the eavesdropper has more antennas than the legitimate receiver. Compared to the precoded MBM and probabilistic optimized MBM schemes exploiting the eavesdropper's CSI, the proposed SQCM scheme has better secrecy performance in all SNR region and medium-to-high SNR regions respectively without requiring the eavesdropper's CSI.
In this paper, we investigate the physical layer security based on space shift keying (SSK) in which bit-to-spatial mapping of antenna indices dynamically adapts according to the partial channel state information (CSI) of the legitimate channel at the transmitter (Tx). Further, the Tx also adapts transmit power allocation to each transmit antenna according to partial CSI. Since an eavesdropper (Eve) is not (usually) aware of the legitimate CSI, it cannot successfully decode the antenna index; thus, transmission over the legitimate channel is secured from the wiretapping of Eve. An important virtue of the proposed scheme is that the Tx does not require full CSI of the legitimate and eavesdropper channels to secure the confidential information. The proposed work focuses on the secrecy rate (SR) and bit error rate (BER) of the considered multiple-input single-output system over Rayleigh fading channels. Approximate expressions of Bob's data rate for 2-ary and 4-ary SSK modulations are derived in closed-form. Furthermore, an upper-bound of Bob's data rate for Na-ary SSK modulation is also derived. In order to obtain the secrecy rate for the proposed scheme, we also evaluate Eve's data rate. Analytical results of SR and BER demonstrate the robustness of the proposed scheme. All numerical results are thoroughly verified by using extensive Monte Carlo simulations.
This paper proposes a method to provide secrecy for digital communications with arbitrarily large quadrature amplitude modulation (QAM) constellations for transmission over a Gaussian fading wiretap channel. This is accomplished by breaking the constellation down into nested quadrature phase-shift keying (QPSK) symbols and randomizing the assignment between message bits and modulated symbols using channel state information (CSI). If enough random bits can be generated from CSI it becomes possible to uniquely map an arbitrary message to any symbol in the large QAM constellation. The proposed method can thereby provide perfect secrecy while maintaining high reliability by exclusively assigning minimum-distance-mapped constellations through the randomization for use by the legitimate decoder.