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arXiv:1904.12237

Ergodic Secrecy Rate of Antenna-Selection-Aided MIMOME Channels with BPSK/QPSK Modulations

Chongjun Ouyang, Zeliang Ou, Pei Yang, Zhang, Lu, Zhang, Xin, Hongwen Yang

Published Apr 28, 2019• 0 citations
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Abstract

This paper analyzes transmit antenna selection (TAS) under Rayleigh flat fading for BPSK/QPSK modulations in multiple-input multiple-output wiretap channels, also termed as multiple-input multiple-output multiple-eavesdropper (MIMOME) channels. In our protocol, a single antenna is selected to transmit the secret message and selection combing (SC) or maximal-ratio combing (MRC) is utilized at the legitimate receiver or the eavesdropper. Novel closed-form expressions for the ergodic secrecy rates are derived to approximate the exact values, which hold high precision and compact forms. Besides theoretical derivations, simulations are provided to demonstrate the feasibility and validity of the proposed formulas.

DOI
10.48550/arxiv.1904.12237

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This paper analyzes transmit antenna selection (TAS) under Rayleigh flat fading for BPSK/QPSK modulations in multiple-input multiple-output wiretap channels, also termed as multiple-input multiple-output multiple-eavesdropper (MIMOME) channels. In our protocol, a single antenna is selected to transmit the secret message and selection combing (SC) or maximal-ratio combing (MRC) is utilized at the legitimate receiver or the eavesdropper. Novel closed-form expressions for the ergodic secrecy rates are derived to approximate the exact values, which hold high precision and compact forms. Besides theoretical derivations, simulations are provided to demonstrate the feasibility and validity of the proposed formulas.
This paper studies the secrecy performance of multiple-input multiple-output (MIMO) wiretap channels, also termed as multiple-input multiple-output multiple-eavesdropper (MIMOME) channels, under transmit antenna selection (TAS) and BPSK/QPSK modulations. In the main channel between the transmitter and the legitimate receiver, a single transmit antenna is selected to maximize the instantaneous Signal to Noise Ratio (SNR) at the receiver. At the receiver and the eavesdropper, selection combining (SC) is utilized. Additionally, suppose that the transmitted message is modulated by BPSK/QPSK modes. We first derive the closed-form approximated expression for the ergodic secrecy rate under Rayleigh fading, assuming that the channel state information of the eavesdropper (CSIE) is available at the transmitter. Next, analytical formulas for the approximated and asymptotic secrecy outage probability are also developed when CSIE is unavailable (NCSIE). Simulation results are provided to demonstrate the approximation precision of the derived results above. Furthermore, the asymptotic results reveal that the secrecy diversity order degrades into 0 due to the finite-alphabet inputs, which is totally different from that driven by the Gaussian inputs.
Transmit antenna selection (TAS) is an emerging technology in physical layer security. To provide new insights into the achievable secrecy performance of TAS in practical communication systems, this paper investigates the average secrecy rate (ASR) and secrecy outage probability (SOP) under practical modulation schemes in TAS aided multiple-input multiple-output multiple-antenna eavesdropper (MIMOME) wiretap channels over Rayleigh fading. Particularly, this research concentrates more on the square M-ary quadrature amplitude modulation (M-QAM). Furthermore, in the considered MIMOME channel, a single antenna is selected to transmit the secret message, and selection combining (SC) or maximal-ratio combining (MRC) is utilized at the legitimate receiver and the eavesdropper. Based on this system model, novel expressions for the ASR and SOP are formulated to characterize the secrecy performance of the finite-alphabet driven MIMOME channel. Besides exact analysis, an asymptotic analysis is performed using the considered performance metrics in high signal-to-noise ratio (SNR) regime. Theoretical analyses suggest that the asymptotic ASR and SOP converge to finite constants in high SNR regime due to the discrete constellation constraint, and we find that the asymptotic behaviour of discrete inputs differs from that of Gaussian inputs. Furthermore, we derive concise expressions to characterize the rate of convergence (ROC) of the ASR and SOP, respectively. To unveil more system design insights, we discuss the relationship between the ROC and several important system parameters such as the antenna number and the modulation order.
The impact of feedback errors on the security performances of multiple-input multiple-output (MIMO) wiretap channels is analyzed. For the legitimate MIMO system, two schemes are considered: 1) transmit antenna selection/maximal ratio combining (TAS/MRC) and 2) transmit antenna selection/receive antenna selection (TAS/RAS). The eavesdropper uses either MRC or RAS techniques. We derive closed-form expressions for the exact secrecy outage probability (SOP) and the probability of strictly positive secrecy capacity (PSPSC). In order to obtain the secrecy diversity order and the secrecy array gain, on asymptotic SOP expression is also derived.
We propose and analyze transmit antenna selection (TAS) to enhance physical layer security in a wiretap channel with multiple antennas at the transmitter, the receiver, and the eavesdropper. We consider the practical scenario of passive eavesdropping, where the transmitter does not have any channel state information (CSI) of the eavesdropper's channel. In the main channel between the transmitter and the receiver, we select a single antenna at the transmitter that maximizes the instantaneous signal-to-noise ratio (SNR) at the receiver. At the receiver and the eavesdropper, we consider two combining techniques: 1) maximal-ratio combining (MRC) and 2) selection combining (SC). For non-identical Rayleigh fading between the main channel and the eavesdropper's channel, we first derive new closed-form expressions for the exact and asymptotic secrecy outage probabilities. The asymptotic results accurately reveal the secrecy diversity order and the secrecy array gain. Next, we derive new closed-form expressions for the probability of positive secrecy and characterize the ε-outage secrecy capacity. We show that, under TAS/MRC and TAS/SC protocols, the secrecy outage probability approaches zero and the ε-outage secrecy capacity increases with increasing number of transmitter antennas.
In this paper, a novel transmit antenna selection scheme for multiple input multiple output (MIMO) wiretap channels is proposed. This new scheme achieves higher secrecy performance by exploiting eavesdropper's channel state information. The key idea behind our proposal is to perform the antenna selection aiming to maximize the overall secrecy rate instead of maximizing the instantaneous signal-to-noise ratio of the main channel. In our analysis, we assume that the legitimate receiver and the eavesdropper employ a maximal-ratio combining technique to combine the received signals from the transmitter. Considering Nakagami-m fading channels, a closed-form expression for the secrecy outage probability is derived, which can be used as a quality of service metric. Further, an asymptotic analysis is carried out and the diversity/array gains are obtained. The ergodic secrecy rate is also investigated for the case of multiple input single output wiretap channels. Representative numerical examples are plotted and validated through Monte Carlo simulations. Insightful discussions are drawn from the proposed analysis.
This paper investigates the secrecy performance of maximal ratio combining (MRC) and selection combining (SC) with imperfect channel state information (CSI) in the physical layer. In a single-input multipleoutput (SIMO) wiretap channel, a source transmits confidential messages to the destination equipped with M antennas using the MRC/SC scheme to process the received multiple signals. An eavesdropper equipped with N antennas also adopts the MRC/SC scheme to promote successful eavesdropping. We derive the exact and asymptotic closed-form expressions for the ergodic secrecy capacity (ESC) in two cases: (1) MRC with weighting errors, and (2) SC with outdated CSI. Moreover, two important indicators, namely high signal-to-noise ratio (SNR) slope and high SNR power offset, which govern ESC at the high SNR region, are derived. Finally, simulations are conducted to validate the accuracy of our proposed analytical models. Results indicate that ESC rises with the increase of the number of antennas and the received SNR at the destination, and fades with the increase of those at the eavesdropper. Another finding is that the high SNR slope is constant, while the high SNR power offset is correlated with the number of antennas at both the destination and the eavesdropper.