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IEEE Transactions on Vehicular Technology

Tournament-Based Index Obfuscation for Secure Space Shift Keying MIMO Systems

Raed Mesleh, Mohammad Ali Abudayah, Saud Althunibat

Published May 4, 2026• 0 citations
Publisher

Abstract

A tournament-based index obfuscation framework is proposed and analyzed for space shift keying (SSK) multiple-input multiple-output (MIMO) systems. Algebraic properties of Paley tournaments are exploited to construct deterministic yet nontrivial permutations of the transmit antenna indices. These permutations are refreshed on a per-channel basis through a channel-dependent cyclic shift derived from reciprocity. As a result, a matched index-domain channel is observed at the legitimate receiver, whereas an eavesdropper is forced to operate under a mismatched decoding metric. In contrast to conventional physical-layer security techniques, the proposed framework operates exclusively in the index domain and preserves the inherent energy-efficiency and low-complexity advantages of SSK. In practical SSK implementations where the number of transmit antennas is not a power of two, only a subset of valid antenna indices is used for information mapping, while the remaining antennas participate only in the obfuscation mechanism. Reliability and secrecy are characterized through average bit error rate, mutual information, generalized mutual information, secrecy rate, equivocation, and information leakage. Both passive and active adversarial scenarios are considered. Passive attacks include uninformed mismatched eavesdropping as well as partially correlated eavesdropping channels that emulate spatial proximity and common scattering. Active training-phase attacks, including pilot contamination and forced permutation manipulation, are also examined and mitigated through tournament-structure consistency checks leading to block acceptance/rejection. The proposed cyclic-shift realization is shown to operate effectively when the legitimate nodes observe consistent channel information, while its sensitivity to channel estimation mismatch is also discussed. Numerical results demonstrate that reliable communication is preserved at the legitimate receiver, while a substantial loss in the eavesdropper' achievable rate is induced even under correlated and active attack conditions. For benchmarking purposes, a comparison with artificial-noise based SSK is also included, highlighting the fundamental difference between power-domain and index-domain physical layer security mechanisms.

DOI
10.1109/tvt.2026.3690306

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A tournament-based index obfuscation framework is proposed and analyzed for space shift keying (SSK) multiple-input multiple-output (MIMO) systems. Algebraic properties of Paley tournaments are exploited to construct deterministic yet nontrivial permutations of the transmit antenna indices. These permutations are refreshed on a per-channel basis through a channel-dependent cyclic shift derived from reciprocity. As a result, a matched index-domain channel is observed at the legitimate receiver, whereas an eavesdropper is forced to operate under a mismatched decoding metric. In contrast to conventional physical-layer security techniques, the proposed framework operates exclusively in the index domain and preserves the inherent energy-efficiency and low-complexity advantages of SSK. In practical SSK implementations where the number of transmit antennas is not a power of two, only a subset of valid antenna indices is used for information mapping, while the remaining antennas participate only in the obfuscation mechanism. Reliability and secrecy are characterized through average bit error rate, mutual information, generalized mutual information, secrecy rate, equivocation, and information leakage. Both passive and active adversarial scenarios are considered. Passive attacks include uninformed mismatched eavesdropping as well as partially correlated eavesdropping channels that emulate spatial proximity and common scattering. Active training-phase attacks, including pilot contamination and forced permutation manipulation, are also examined and mitigated through tournament-structure consistency checks leading to block acceptance/rejection. The proposed cyclic-shift realization is shown to operate effectively when the legitimate nodes observe consistent channel information, while its sensitivity to channel estimation mismatch is also discussed. Numerical results demonstrate that reliable communication is preserved at the legitimate receiver, while a substantial loss in the eavesdropper' achievable rate is induced even under correlated and active attack conditions. For benchmarking purposes, a comparison with artificial-noise based SSK is also included, highlighting the fundamental difference between power-domain and index-domain physical layer security mechanisms.
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.
The secure exchange of messages between different communication devices is a major issue of Internet-of-Things (IoT) applications in future smart cities. Current security mechanisms focus on multiple antennas technology, such as spatial modulation (SM), but in space shift keying (SSK), there is still a space to explore. In this article, we propose a secrecy-enhancing SSK scheme for IoT applications by applying security technologies in the physical layer wherein the number of transmit antennas is arbitrary rather than the value of power of two. In this scheme, the security performance of the communication system is improved by using two technologies, namely, artificial noise (AN) and antenna selection. We assume that the application scenario of the SSK system is under the classic eavesdropping model. First, we design ANs according to the channel state information (CSI) to interrupt the eavesdropper and benefit the legitimate receiver via the appropriate cancellation technology. Second, the antenna selection method is designed based on the signal to leakage noise ratio (SLNR) to further boost the secrecy performance by expanding the mutual information difference between the main channel and the eavesdropping channel. Results from our simulations indicate that by the use of the proposed scheme, significant secrecy enhancing can be achieved in terms of bit error ratio (BER) and secrecy rate (SR) when compared with existing schemes. This achieved secrecy enhancing can benefit the suitable IoT communication applications in the smart city environment to avoid the leakage of data transmission.
In this paper, we propose an adaptive antenna index (AI) mapping scheme with the aid of partial channel state information (CSI) (i.e., channel gain order information) of legitimate channel. Based on the received partial CSI that is unknown to an eavesdropper (Eve), transmitter (Tx) adapts AI mapping patterns. In addition, Tx also adapts transmit power allocation to each transmit antenna according to the partial CSI. Since Eve is unaware of the partial CSI of the legitimate channel, it cannot successfully decode the AI patterns; and transmission over the legitimate channel is secured from wiretapping of Eve. Further, we offer an accurate analytical framework for ergodic secrecy rate (ESR) and bit error rate (BER) of 2-ary space shift keying modulated multiple-input single-output system in the presence of a passive eavesdropper. Moreover, the analytical results of ESR and BER demonstrate the robustness of the proposed scheme. All numerical results are thoroughly verified by using the Monte Carlo simulations.
In multiple-input-multiple-output (MIMO) wireless communications, Space Shift Keying (SSK), Spatial modulation (SM) and Generalized Space Shift Keying (GSSK) are three novel MIMO modulation techniques, that can greatly reduce the complexity of MIMO systems. This paper investigates the physical-layer security in typical MIMO systems of these three modulations. We present an exhaustive analysis of secrecy rate for multiple antennas destination and eavesdroppers receivers. Without eavesdroppers channel information, both achievable secrecy rate and bit error rate (BER) are studied through joint modulated signal and jamming signal transmission. Our simulation results demonstrate that the proposed proactive source jamming method achieves improvement of secrecy rate and improved BER performance for multi-antenna users.
Security and privacy are vital challenges in Industrial Internet of Things (IIoT) systems due to the inherent broadcast property of industrial wireless communication. Therefore, how to improve the security of smart devices in IIoT systems has attracted widespread attention. In this article, a novel security optimization scheme for space shift keying (SSK)-based IIoT systems is proposed by applying secrecy enhancing techniques in the physical layer. Specifically, two methods are adopted in the proposed optimization scheme. First, the sender transmits artificial noise (AN) to interfere with the eavesdropper, while the legitimate receiver can eliminate AN. Second, the sender can select optimal antennas based on the proposed minmax criteria to transmit AN and information, which further promotes the security of industrial wireless communication. The optimal antenna selection pattern increases the difference of the average mutual information between the legitimate receiver and the eavesdropper. In addition, the proposed minmax antenna selection approach only requires the channel state information of the legitimate receiver, which satisfies the application scenario of unknown eavesdropper attacks in IIoT. Finally, we adopt a deep learning-based maximum likelihood (ML) detection algorithm to detect the optimal antenna index and analyze the bit error rate (BER) and secrecy rate (SR) of the proposed optimization scheme. Simulation results show that the proposed scheme can achieve similar SR improvements and superior BER performance compared with the state-of-the-art scheme, namely the signal-leakage-to-noise ratio (SLNR) scheme. The BER performance of the proposed scheme achieves a maximum of 100 times superior to that of the SLNR scheme when the signal-to-noise ratio (SNR) is 27 dB. Moreover, the proposed scheme outperforms the traditional antenna selection scheme (random selection) in terms of BER and SR.
Reliability and security are the main concerns in modern industrial wireless sensing systems because of the nature property of the industrial wireless sensing environment. Therefore, how to enhance the secrecy and make the industrial wireless sensing systems smart attract a lot of attention. In order to address the secrecy problem in industrial wireless sensing systems, this article proposes a secrecy enhancement mechanism based on space shift keying (SSK) communication in industrial wireless sensing systems where a transmitting node, a receiving node, and an eavesdropper are considered. To prevent the valid information from being attacked by the eavesdropper, the technologies of antenna selection (AS) and the artificial noise (AN) are jointly used in the proposed scheme to enhance the physical layer security (PLS). Eventually, the designed AN is canceled at the receiving node and remains at the eavesdropper. In addition, two kinds of AS methods, namely, signal-to-leakage-noise ratio (SLNR)-based method and Euclidean distance AS (EDAS)-based method are proposed for the proposed secrecy enhancement scheme. Specifically, the SLNR and EDAS methods are designed for the known eavesdropper channel case and the unknown eavesdropper channel case, respectively. Moreover, to make the scenario practical, the channel estimation error is fully considered in the sensing data transmission stage since the perfect channel state information (CSI) is rarely available in the actual sensing environment. The results from simulations demonstrate that the proposed scheme can enhance the system performances of secrecy rate (SR) and bit error rate (BER) when compared with the traditional random selection method.