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arXiv:2608.01758 · IEEE International Symposium on Personal, Indoor and Mobile Radio Communications (PIMRC)

Pseudo-Noise Superposition for Finite-Alphabet Physical Layer Security

Fernando Moya Caceres, Chamath Divarathne, Yapeng Xie, Michael Aygur, Sithamparanathan Kandeepan, Akram Al‐Hourani, Saman Atapattu

Published Sep 1, 2026• 0 citations
arXivHTMLPDF

Abstract

Physical-layer security based on pseudo-noise (PN) superposition is a promising approach for mitigating eavesdropping in future wireless systems. However, under Shannon's capacity formulation with Gaussian signaling, achieving secrecy typically requires allocating substantial transmit power to PN, resulting in a significant reduction in achievable information rate and limiting practical applicability. This limitation is alleviated when finite-alphabet modulation schemes, such as M-ary Quadrature Amplitude Modulation ($M$-QAM), are employed, as expected in practical 6G transceivers. In this work, we analyze the information rate performance of PN-assisted systems under $M$-QAM signaling using mutual information and derive the corresponding achievable secrecy rate. The impact of PN power allocation on both the legitimate user and the eavesdropper is investigated across different modulation orders and channel conditions. Monte Carlo simulations are conducted to evaluate system behavior under varying user and eavesdropper channel conditions and to examine how PN power allocation influences secrecy performance. The results show that, at sufficiently high signal-to-noise ratio (SNR), the information rate becomes largely insensitive to PN power allocation, enabling near-perfect secrecy with $M$-QAM modulation-highlighting a key departure from Shannon-capacity-based secrecy analyses and underscoring the practicality of finite-alphabet security mechanisms for 6G wireless systems.

DOI
10.1109/pimrc69400.2026.11711696

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Physical-layer security based on pseudo-noise (PN) superposition is a promising approach for mitigating eavesdropping in future wireless systems. However, under Shannon's capacity formulation with Gaussian signaling, achieving secrecy typically requires allocating substantial transmit power to PN, resulting in a significant reduction in achievable information rate and limiting practical applicability. This limitation is alleviated when finite-alphabet modulation schemes, such as M-ary Quadrature Amplitude Modulation (MMM-QAM), are employed, as expected in practical 6G transceivers. In this work, we analyze the information rate performance of PN-assisted systems under MMM-QAM signaling using mutual information and derive the corresponding achievable secrecy rate. The impact of PN power allocation on both the legitimate user and the eavesdropper is investigated across different modulation orders and channel conditions. Monte Carlo simulations are conducted to evaluate system behavior under varying user and eavesdropper channel conditions and to examine how PN power allocation influences secrecy performance. The results show that, at sufficiently high signal-to-noise ratio (SNR), the information rate becomes largely insensitive to PN power allocation, enabling near-perfect secrecy with MMM-QAM modulation-highlighting a key departure from Shannon-capacity-based secrecy analyses and underscoring the practicality of finite-alphabet security mechanisms for 6G wireless systems.
In this dissertation, we present novel physical (PHY) and cross-layer design guidelines and resource adaptation algorithms to improve the security and user experience in the future wireless networks. Physical and cross-layer wireless security measures can provide stronger overall security with high efficiency and can also provide better flexibility in response to the typically time-varying wireless environment. To better utilize limited wireless resources, we present approaches and techniques based on new performance criteria for wireless system optimization by thoroughly exploiting user information including its Quality of Service (QoS) requests and channel state information (CSI) to improve network throughput and security. In recent years, there has been a growing research interest in wireless system security from PHY layer perspective. In a wiretap channel model introduced in the seminal work by Wyner, a sender “Alice” wishes to transmit a secret message to the intended receiver “Bob” in presence of a passive eavesdropper “Eve”. Existing works have characterized maximum achievable secrecy rate or secrecy capacity for single- and multiple-antenna systems by applying Gaussian signaling and secrecy code. Despite the impracticality of Gaussian input, its compact closed-form expression of mutual information motivated the wide use of Gaussian input assumption in theoretical analysis. In contrast to the Gaussian codebook, practical wiretap codes must consist of finite-alphabet symbols. Because of this constraint, the achievable secrecy rate for a finite-alphabet input scenario would differ from the secrecy rate achievable by a Gaussian codebook. In this thesis, we quantify the effect of finite discrete-constellation on instantaneous and ergodic secrecy rate of multiple-antenna wire-tap channels. Our results demonstrate substantial performance difference between systems involving finite-alphabet inputs and systems with Gaussian inputs. In addition, we investigate the secrecy performance of multi-terminal wiretap systems when a codebook based transmission beamforming is implemented. We characterize the secrecy outage probability of a communication link under eavesdropping. We consider a limited feedback scenario where the transmitter uses a pre-defined codebook known to both the transmitter and the receiver for beamforming, and analyze the secrecy outage probability of the link when it being eavesdropped. Next, we consider the security of wireless multi-hop networks. Certainly, network security is an overarching issue that transcends all layers of communication protocol stack. Therefore, we tackle the problem of network security by proper user scheduling, routing, and resource management. Our approach of secrecy is complementary to the traditional cryptography based techniques. Together, they can provide stronger overall security and flexibility in selecting the desired solution and can reduce bandwidth and energy overhead as much as possible. Multi-hop wireless networks frequently employ the traditional routing and resource allocation strategies. Such strategies often fail to take into account the additional need for protection against security vulnerabilities due to the wireless medium. Thus, to address security concerns, we investigate the problem of eavesdropping control by proposing security-aware power allocation strategies and routing algorithms for multi-hop networks. The future wireless infrastructure will consists of a plethora of heterogeneous collections of applications and services. A differentiated service structure would therefore be an essential part of the future wireless infrastructure. In addition to the security consideration of wireless network, we focus on the heterogeneous structure of the network. We study the problem of cross-layer resource allocation and admission control in a multiuser heterogeneous OFDMA network providing both QoS-constrained user servicesand best-effort services. Such heterogeneous networks provide service to both High-Priority (HP) users and Best-Effort (BE) users. By clustering subcarriers, efficient algorithms for cluster and power allocation have been proposed. Our strategy maximizes the total network utility of the BE users while satisfying the QoS request for maximum number of HP users. The feasibility of the resource allocation problem depends on the number of HP users in the network. Since a large number of demanding HP users would render the resource allocation problem infeasible, a joint admission control and resource allocation scheme could be an efficient way of tackling both problems with less overhead. By incorporating admission control, we propose an efficient and optimal joint admission control and resource allocation algorithm.
Physical-layer security could efficiently prevent wiretapping for wireless communication from the information-theoretic perspective. However, most related works in this area are based on the assumption of Gaussian inputs, which are impractical for a practical communication system. In this paper, we study the physical-layer security with finite-alphabet inputs, wherein amplitude phase shift keying (APSK) constellation is considered to improve the achievable secrecy rate performance. It is concluded that the secrecy rate can be improved by using APSK, comparing to its quadrature amplitude modulation (QAM) counterpart, which is verified by both the minimum mean square error (MMSE) theoretic derivation and simulation results. A specific strategy of selecting constellation orders for secure communication is also presented.
In this thesis, we study the physical layer security in downlink multi-user wireless networks. Traditionally, security has been addressed by cryptography at the higher layers of the communication stack. Security at the physical layer has been a major research topic in recent years. We study two different precoder designs alongside artificial noise (AN) to mitigate multi-user interference and deteriorate reception at the eavesdropper (Eve). We study the large scale analysis to calculate the secrecy sum-rate for these two cases and analyze the effect of AN on the system. First, we consider the worst case scenario, when eavesdropper's (Eve's) rate is not deteriorated by the interference caused by the legitimate users. Later, we investigate how interference from legitimate users would affect the large scale security sum rate. At the end, we assume more practical situation where the channel state information at the transmitter is not perfect due to feedback limitation and estimation error. We first study block diagonalization (BD) precoding. We derive the asymptotic secrecy sum-rate of BD for physical layer security in downlink multi-user wireless networks using artificial noise (AN). We first derive the secrecy sum-rate assuming that the channel of the eavesdropper is not known at the transmitter and derive the asymptotic secrecy sum-rate. Then we derive the optimum power allocation for asymptotic secrecy sum-rate. We design the system based on large scale analysis for different special cases. Simulation results show that the proposed precoders outperform channel inversion (CI) and regularized channel inversion (RCI) schemes at all SNRs. We also show that as the number of receive antennas of each user increases, the sum-rate gap between the proposed scheme and existing methods increases. We, then, study two methods of regularized block diagonalization (RBD) precoding using artificial noise (AN) for physical layer security in downlink multi-user MIMO wireless networks. We compare the complexity analysis of these two methods in terms of floating point operations per second (FLOPS). We derive the secrecy and asymptotic secrecy sum-rates for these schemes. We also derive closed form expressions for the asymptotic optimal power allocation to the AN signal and legitimate users. Simulations show RBD precoding outperform regularized channel inversion (RCI) in terms of secrecy sum-rate with a margin of 0.5 bits/s/Hz. Also, simulation results show our closed-form asymptotic secrecy sum-rates matches closely with the simulations for perfect and imperfect CSIT. We also study the effect of interference on BD precoding scheme. In the first two studies the worst case scenarios was considered and the effect of interference was not considered at the eavesdropper. We first derive the closed-form secrecy and asymptotic secrecy sum-rates for this scheme. Then, we derive the optimum power allocation. Using the derived optimum power allocation, we determine the conditions under which adding AN helps. We also investigate the optimum number of users, number of antennas at the eavesdropper, and the number of transmit antennas to fully study the conditions where using AN improves performance. We show that as the number of users increases or the number of receive antennas at the eavesdropper decreases, improved performance is achieved by allocating a smaller fraction of the total power to transmit the AN. The closed form expressions for the secrecy sum rate (SSR) and optimum power allocation closely match our simulation results. In Chapter 5, we study the effect of imperfect channel state information at the transmitter (CSIT) for each case studied in earlier chapters. We first study the effect of imperfect CSIT for BD precoding in both scenarios when interference does and does not exist at eavesdropper. We show that the imperfect CSI play the same role as interference for the desired users. Then, we study the effect of imperfect CSIT for RBD precoding when interference does not exist at eavesdropper. We show as channel estimation error increases, the secrecy sum-rate decreases. This is due to the fact that channel estimation error just affects the desired users' rate and has no effect on eavesdropper's performance. Finally, in the last chapter, we conclude our thesis and provide some road map for future--Author's abstract
Massive Multiple-Input Multiple-Output (MIMO) has become a crucial enabling technology for 5G and beyond, providing previously unheard-of increases in energy and spectrum efficiency. It is still difficult to guarantee secure communication in these systems, particularly when it comes to passive eavesdroppers whose base station is unaware of their channel state information. By taking advantage of the inherent randomness of wireless channels, Physical Layer Security (PLS) offers a promising paradigm; however, its efficacy in massive MIMO is heavily reliant on resource allocation and transmission strategies. In this work, the performance of secure transmission schemes, such as Maximum Ratio Transmission (MRT), Zero-Forcing (ZF), and Artificial Noise (AN)-aided beamforming, is examined when passive eavesdroppers are present. This work will use extensive Monte Carlo simulations to assess important performance metrics such as energy efficiency, secrecy outage probability, and secrecy sum rate under different system parameters (e.g., number of antennas, Signal-to-Noise Ratio (SNR), power allocation). The results aim to provide comparative insight into the strengths and limitations of different PLS strategies and to highlight open research directions to design scalable, energy-efficient, and robust secure transmission techniques in future 6G networks.
Physical layer security encompasses information theoretic approaches that could guarantee perfect secrecy in wireless communication systems. In this framework, helping interferer strategies rely on intentionally creating confusion at a potential eavesdropper by injecting a jamming signal. In cases where the information signal has a Gaussian probability density function (pdf) it has been demonstrated that the optimal jamming signal, under an overall power constraint, should also be Gaussian. However, in practical communication systems where data symbols are typically drawn from discrete uniform probability mass functions (pmf), commonly M-ary Quadrature Amplitude and M-ary Phase Shift Keying modulation schemes, the structure of the optimal jamming signal is still an open question. In the present work we aim at shedding light into this question. Our approach is based on formulating a secrecy capacity maximization problem by expressing the optimal arbitrary helping interferer pdf as a mixture of unknown Gaussians. The proposed approximation is well-suited for jamming signals of practical interest, i.e. Gaussian or M-QAM interferers and reveals that in certain scenarios it is advantageous to use jamming signals whose statistical structure resembles the data rather than the noise.
Orthogonal frequency division multiplexing (OFDM) systems have enjoyed widespread adoption as the physical layer standard for high data rate wired and wireless networks, due to their ability to efficiently cope with slowly varying dispersive channels. Therefore in searching for feasible implementations of physical layer security techniques, it is appropriate to analyze how existing information theoretic results can be applied to the OFDM structure This paper considers the information theoretic secrecy rates that are achievable in a wiretap OFDM channel when transmitting quadrature amplitude modulation (QAM) constellation symbols. The loss with respect to the secrecy rates obtained with Gaussian distributed inputs is evaluated for both nite constellation cardinalities and in the asymptotic approximation of arbitrarily high cardinality. Moving from the insight gained with this analysis, we propose bit-loading strategies to efficiently allocate the appropriate number of bits in each subchannel, by considering the twofold objective of minimizing the loss with respect to the Gaussian input secrecy capacity and minimizing the total bit load.