Movable Antennas-Assisted Secure Transmission Without Eavesdroppers' Instantaneous CSI

TL;DR

This work tackles secure downlink transmission when Alice uses movable antennas and lacks instantaneous eavesdropper CSI. By modeling the wiretap links with a Rician-to-Nakagami approximation and applying Laguerre-series-based Gamma approximations, the authors derive a tight secrecy outage probability expression and reformulate the optimization of transmit beamforming and MA positions. They introduce a novel linear surrogate for the inverse incomplete gamma function and solve the resulting nonconvex problem via an alternating projected gradient ascent (APGA) method, with a lower-complexity ZF-based benchmark (MA+ZF) for practical deployment. Numerical results show significant secrecy gains over fixed-position antennas, with MA configurations exploiting extra spatial degrees of freedom and converging efficiently under the proposed framework. The findings underscore the practicality of MA-enabled secure transmissions in scenarios with limited or statistical wiretap CSI, offering scalable strategies for future wireless secure designs.

Abstract

Movable antenna (MA) technology is highly promising for improving communication performance, due to its advantage of flexibly adjusting positions of antennas to reconfigure channel conditions. In this paper, we investigate MAs-assisted secure transmission under a legitimate transmitter Alice, a legitimate receiver Bob and multiple eavesdroppers. Specifically, we consider a practical scenario where Alice has no any knowledge about the instantaneous non-line-of-sight component of the wiretap channel. Under this setup, we evaluate the secrecy performance by adopting the secrecy outage probability metric, the tight approximation of which is first derived by interpreting the Rician fading as a special case of Nakagami fading and concurrently exploiting the Laguerre series approximation. Then, we minimize the secrecy outage probability by jointly optimizing the transmit beamforming and positions of antennas at Alice. However, the problem is highly non-convex because the objective includes the complex incomplete gamma function. To tackle this challenge, we, for the first time, effectively approximate the inverse of the incomplete gamma function as a simple linear model. Based on this approximation, we arrive at a simplified problem with a clear structure, which can be solved via the developed alternating projected gradient ascent (APGA) algorithm. Considering the high complexity of the APGA, we further design another scheme where the zero-forcing based beamforming is adopted by Alice, and then we transform the problem into minimizing a simple function which is only related to positions of antennas at Alice.As demonstrated by simulations, our proposed schemes achieve significant performance gains compared to conventional schemes based on fixed-position antennas.

Figures (13)

• Figure 1: System model.
• Figure 2: Comparison of the exact CDF of ${\sum\nolimits_{i = 1}^M {{{\left| {{{\bf{h}}_i}({\bf{x}}){\bf{w}}} \right|}^2}} }$ via Monto Carlo and the derived approximation via (18), where $N = 5$, $M = 3$, ${\bf{x}} = {[0,0.5\lambda ,\lambda ,1.5\lambda ,2\lambda ]^T}$, ${\bf{w}} = {{\bf{w}}_1}/\left\| {{{\bf{w}}_1}} \right\|$ with ${{\bf{w}}_1} = {\left[ {1 + j,2 + j3,2 + j,3 - j,4 + j5} \right]^T}$, $\left\{ {{\beta _i}} \right\}_{i = 1}^M = 1$, ${\theta _1} = \pi /6$, ${\theta _2} = \pi /4$, ${\theta _3} = \pi /10$ and $\left\{ {{K_i}} \right\}_{i = 1}^M = K$.
• Figure 3: ${\gamma ^{ - 1}}(\varepsilon ,{f_1}({\bf{w}},{\bf{x}}))$ and the proposed linear approximation model w.r.t. ${f_1}({\bf{w}},{\bf{x}})$ under different $\varepsilon$.
• Figure 4: The parameters $\kappa (\varepsilon )$ and $\rho (\varepsilon )$ w.r.t. $\varepsilon$.
• Figure 5: The achievable performance of the proposed algorithm under two typical cases.

Theorems & Definitions (5)

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