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arXiv:2607.19729 · IEEE Transactions on Wireless Communications

Investigation of STEEP for Secure Communications Over SIMO and MISO Channels Subject to Full-Duplex Jamming and Eavesdropping

Md Saydur Rahman, Yingbo Hua

Published Jan 1, 2026• 0 citations
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Abstract

Secure communications over SIMO and MISO channels between wireless nodes are commonly encountered in applications and widely considered in the literature. This paper investigates such a problem by considering a newly proposed scheme called secrecy-message transmission by echoing encrypted probes (STEEP). We focus on a type of heavily eavesdropped channels where an aggressive eavesdropper (Eve) has multiple antennas and is capable of jamming and eavesdropping in the full-duplex mode. Assuming optimal jamming and eavesdropping by Eve, we present the secrecy rates achievable by STEEP in two forms: using SIMO channel in phase 1 and using MISO channel in phase 2, and vice versa. With any given channel condition between every pair of nodes and any finite jamming power by Eve, the secrecy rate of STEEP in either form is shown to be positive subject to a positive power in phase 1 and a sufficiently large power in phase 2. The connections between STEEP in either form and the conventional SIMO and MISO schemes are provided, and their secrecy rates are compared comprehensively subject to random fading channels and finite transmit powers.

DOI
10.1109/twc.2026.3706983

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•Jan 1, 2018•0 citations
Secure communications over SIMO and MISO channels between wireless nodes are commonly encountered in applications and widely considered in the literature. This paper investigates such a problem by considering a newly proposed scheme called secrecy-message transmission by echoing encrypted probes (STEEP). We focus on a type of heavily eavesdropped channels where an aggressive eavesdropper (Eve) has multiple antennas and is capable of jamming and eavesdropping in the full-duplex mode. Assuming optimal jamming and eavesdropping by Eve, we present the secrecy rates achievable by STEEP in two forms: using SIMO channel in phase 1 and using MISO channel in phase 2, and vice versa. With any given channel condition between every pair of nodes and any finite jamming power by Eve, the secrecy rate of STEEP in either form is shown to be positive subject to a positive power in phase 1 and a sufficiently large power in phase 2. The connections between STEEP in either form and the conventional SIMO and MISO schemes are provided, and their secrecy rates are compared comprehensively subject to random fading channels and finite transmit powers.
A scheme for secure communications, called “Secret-message Transmission by Echoing Encrypted Probes (STEEP)”, is revisited. STEEP is a round-trip scheme with a probing phase from one user to another and an echoing phase in the reverse direction. STEEP is shown to be broadly applicable to yield a positive secrecy rate in bits per channel use even if the receive channels at eavesdropper (Eve) are stronger than those between legitimate users in both forward and reverse directions. This paper focuses on STEEP in the following settings: using Gaussian probing signal and Gaussian linear encryption over MIMO Gaussian channel (G-STEEP); using phase-shift-keying probing signal and a nonlinear encryption over SISO channel (P-STEEP); and a variation of G-STEEP for multiple access communication (M-STEEP). In each of the settings, Eve is assumed to have any given number of antennas, and STEEP is shown to yield a positive secrecy rate subject to a sufficiently large power in the echoing phase, as long as Eve’s receive channel in the probing phase is not noiseless. It is also shown that G-STEEP, subject to asymmetric large powers in forward and reverse directions, has its secrecy rate approaching the secret-key capacity based on Gaussian probing signal over MIMO Gaussian channel. STEEP does not require secure feedback channel, collaborative third party, in-band full-duplex or reciprocal channels between users, but only needs a design for echoing encrypted probes, asymmetric power allocation and/or collaborative round-trip coding.
A transmission scheme for secure communications, called secret-message transmission by echoing encrypted probes (STEEP), can deliver a positive secrecy rate, even when eavesdropping channels are much stronger than that between users, subject to sufficient asymmetric power allocations from users. This paper considers an optimization problem for STEEP applied to MIMO (or MIMOME) channels between multi-antenna users and multi-antenna Eve. We reveal for the first time a significant increase of the achievable secrecy rate of MIMO STEEP using optimized precoders.
Unmanned Aerial Vehicle (UAV) assisted wireless communication has emerged as a highly promising element in the landscape of future wireless networks. This paper investigates the application of “Secret-message Transmission by Echoing Encrypted Probes (STEEP)” to secure UAV communications between a ground station (Alice) and a UAV (Bob). Even with the presence of strong jamming from a full-duplex eavesdropper (Eve), STEEP shows resilience and maintains a strong positive secrecy rate in bits per channel use in every channel coherence period as long as Eve's observations during the probing phase of STEEP are not noiseless. STEEP is a novel round-trip transmission scheme for secure communications, overcoming limitations where prior schemes fail to achieve a positive secrecy rate when Eve's receive channel is stronger than users'.
This paper presents further insights into a recently developed round-trip communication scheme called “Secret-message Transmission by Echoing Encrypted Probes (STEEP)”. A legitimate wireless channel between a multi-antenna user (Alice) and a single-antenna user (Bob) in the presence of a multi-antenna eavesdropper (Eve) is focused on. STEEP does not require full-duplex, channel reciprocity or Eve's channel state information, but is able to yield a positive secrecy rate in bits per channel use between Alice and Bob in every channel coherence period as long as Eve's receive channel is not noiseless. This secrecy rate does not diminish as coherence time increases. Various statistical behaviors of STEEP's secrecy capacity due to random channel fading are also illustrated.
This paper examines the properties of the lower and upper bounds established by Maurer, Ahlswede and Csiszar (MAC) for secret-key capacity in the case of channel probing over single-input and single-output (SISO) channels. Inspired by the insights into MAC's bounds, a scheme called secret-message transmission by echoing encrypted probes (STEEP) is proposed. STEEP consists of two phases: in phase 1, Alice sends random probes over a probing channel to Bob; in phase 2, Bob echoes back an estimated version of the probes, but encrypted by a secret, over a high-quality return channel. Provided that Eve is unable to obtain the exact probes transmitted by Alice in phase 1, STEEP guarantees a positive secrecy rate from Bob to Alice over the return channel even if Eve's channel strength during channel probing is stronger than Bob's. STEEP is applicable to both physical layer and upper layers in connected networks.
As the technology and computing power advance day by day, physical layer security in wireless communications gains more importance. It allows the security of wireless communications based on information theoretical guarantees without the need for cryptography. One important practical challenge for physical layer security arises from the fact that no information about the passive eavesdroppers is available to the legitimate nodes. Without such information, optimizing the transmission parameters has always been a difficult task. In this study we aim to address various challenging aspects about this issue and propose a new perspective into the analysis of secrecy with a focus on jamming. We start from the case of eavesdropper's channel state information (CSI) known to users in a three-node single-antenna multi-subcarrier network and present an improved optimization algorithm compared to previous methods. Then we expand our horizon to the case of multiple-antenna nodes with eavesdropper's CSI unknown to users. We investigate a secure wireless communication scheme which combines two of the most effective strategies to combat eavesdropping, namely mixing information with artificial noise at the transmitter and jamming from a full-duplex receiver. While such setup has been investigated in related works, new and important insights are revealed in this study. We investigate the design of optimal jamming parameters to achieve higher secrecy.We then derive a closed-form expression for asymptotic normalized instantaneous secrecy rate of our model. Based on the results of the asymptotic analysis, we propose an alternative less complex tractable optimization problem for the design of optimal transmission parameters to achieve higher secrecy. We show that even with the optimal parameters, secrecy is compromised if Eve is able to increase her number of antennas. To address this issue, we provide a comprehensive analysis of a new scheme called anti-eavesdropping channel estimation (ANECE) which prevents Eve from acquiring accurate channel estimations. We show that the usage of such scheme, makes it extremely hard for Eve to drive secrecy to zero. Numerical analyses and simulations are presented to support the arguments made in this study.We then derive a closed-form expression for asymptotic normalized instantaneous secrecy rate of our model. Based on the results of the asymptotic analysis, we propose an alternative less complex tractable optimization problem for the design of optimal transmission parameters to achieve higher secrecy. We show that even with the optimal parameters, secrecy is compromised if Eve is able to increase her number of antennas. To address this issue, we provide a comprehensive analysis of a new scheme called anti-eavesdropping channel estimation (ANECE) which prevents Eve from acquiring accurate channel estimations. We show that the usage of such scheme, makes it extremely hard for Eve to drive secrecy to zero. Numerical analyses and simulations are presented to support the arguments made in this study.We then derive a closed-form expression for asymptotic normalized instantaneous secrecy rate of our model. Based on the results of the asymptotic analysis, we propose an alternative less complex tractable optimization problem for the design of optimal transmission parameters to achieve higher secrecy. We show that even with the optimal parameters, secrecy is compromised if Eve is able to increase her number of antennas. To address this issue, we provide a comprehensive analysis of a new scheme called anti-eavesdropping channel estimation (ANECE) which prevents Eve from acquiring accurate channel estimations. We show that the usage of such scheme makes it extremely hard for Eve to drive secrecy to zero. Numerical analyses and simulations are presented to support the arguments made in this study.