Outage-Aware Sum Rate Maximization in Movable Antennas-Enabled Systems

TL;DR

This paper investigates the movable antennas (MAs)-enabled multiple-input-single-output (MISO) systems, where the base station (BS) equipped with multiple MAs serves multiple single-antenna user and adopts the statistical CSI based zero-forcing beamforming design.

Abstract

In this paper, we investigate the movable antennas (MAs)-enabled multiple-input-single-output (MISO) systems, where the base station (BS) equipped with multiple MAs serves multiple single-antenna user. The delay-sensitive scenario is considered, where users refrain from periodically sending training signals to the BS for channel estimations to avoid additional latency. As a result, the BS relies solely on the statistical channel state information (CSI) to transmit data with a fixed rate. Under this setup, we aim to maximize the outage-aware sum rate of all users, by jointly optimizing antenna positions and the transmit beamforming at the BS, while satisfying the given target outage probability requirement at each user. The problem is highly non-convex, primarily because the exact cumulative distribution function (CDF) of the received signal-to-interference-plus-noise ratio (SINR) of each user is difficult to derive. To simplify analysis and without comprising performance, we adopt the statistical CSI based zero-forcing beamforming design. We then introduce one important lemma to derive the tight mean and variance of the SINR. Leveraging these results, we further exploit the Laguerre series approximation to successfully derive the closedform and tight CDF of the SINR. Subsequently, the outageaware sum rate expression is presented but still includes complex structure with respect to antenna positions. Facing this challenge, the projected gradient ascent (PGA) method is developed to iteratively update antenna positions until convergence. Numerical results demonstrate the effectiveness of our proposed schemes compared to conventional fixed-position antenna (FPA) and other competitive benchmarks.

Figures (8)

• Figure 1: Illustration of the considered system model.
• Figure 2: Comparison of the CDF of ${\gamma _1}({\bf{t}},{{\bf{W}}^{{\rm{ZF}}}}({\bf{t}}))$ via Monte Carlo, the derived approximation via (31) and the first-order method via (32), where $N = 5$, $M = 4$, ${{\bf{t}}_1} = {[0,0]^T}$, ${{\bf{t}}_2} = {[0,0.5\lambda ]^T}$, ${{\bf{t}}_3} = {[0.5\lambda ,0]^T}$, ${{\bf{t}}_4} = {[0.5\lambda ,0.5\lambda ]^T}$, ${{\bf{t}}_5} = {[\lambda ,0]^T}$, ${\theta _1} = {\phi _1} = 0$, ${\theta _2} = {\phi _2} = 0.5$, ${\theta _3} = {\phi _3} = 1$, ${\theta _4} = {\phi _4} = 1.5$, $\left\{ {{P_m}} \right\}_{m = 1}^M = 10$ dBm, $\left\{ {{\beta _m}} \right\}_{m = 1}^M = {10^{ - 9}}$, ${\sigma ^2} = {10^{ - 9}}$ dBm and $\left\{ {{K_m}} \right\}_{m = 1}^M = K$.
• Figure 3: Comparison of the outage-aware transmission rate of the first user via Monte Carlo and our proposed approximation via (39), where $\left\{ {{P_m}} \right\}_{m = 2}^M = 10$ dBm, the target outage probability is set as $\delta = 0.2$, and other parameters are the same as those in Fig. 2.
• Figure 4: The convergence behavior of our proposed PGA method, where $N = 5$, $L = \lambda$, $K = 15$ and $\delta = 0.2$.
• Figure 5: Outage-aware sum rate versus the side length of the moving region $L$, where $N = 5$, $K = 15$ and $\delta = 0.2$.

Theorems & Definitions (1)

• proof