Achievable rate of UAV-based communication with uniform circular arrays in Ricean fading

Abstract

In future wireless communication systems, combining unmanned aerial vehicles (UAVs) with massive MIMO technology is a promising solution to meet ever-increasing data demand due to it has advantages of high reliability, cost effective, and flexible deployment. In this paper, we study the achievable rate of UAV-based communication under Ricean fading, where the transceivers of UAV is equipped with circular antenna array (UCA) configuration. We exploit an effective statistical-eigenmode space division multiple-access transmission (SE-SDMA) scheme with only the knowledge of the CSI at the UAV’s transceivers. An exact expression on the achievable rate of UAV-based communication systems with UCA configuration is derived, in which the transceivers utilizes the channel response vector as the beamforming precoder. Based on the derived theoretical results, we gain the relationships of the achievable SE and the system parameters, such that the achievable sum-rate tends to a saturation value in the high signal-to-noise ratio regime. In addition, we find that the high Ricean $K$-factor and the small values of inner product between different statistical channel vector are contribute to the achievable sum-rate of the UAV-based communication system.

Introduction

Future wireless communication systems are envisioned to offer ubiquitous and sustainable high data-rate communication services [1], [2], [3]. Recently, aerial communication systems based on unmanned aerial vehicles (UAVs) has attracted more and more attention due to it could provide high maneuverability and fast flexible deployment of communication infrastructure in the design of future communication systems. The UAVs deployed with on-board wireless transceivers can fly over the target area and enjoy high mobility, the wireless channels are typically modeled via the Ricean fading because line-of-sight (LoS) and scatter components exist in wireless transmission environment [4], [5], [6]. Therefore, the achievable rate analysis of UAV-based communication systems under Ricean fading becomes a problem of practical relevance.

In the design of wireless communication systems, a lot of research about UAV-based communication transceivers were focus on uniform linear arrays (ULAs) at the base station (BS) [7], [8], [9]. In practical setup, when the transceivers is installed with ULAs and equipped with a very large antenna arrays, it will leads to the physical size become huge, which is challenge to the deployment of UAV-based communication infrastructure [10], [11], [12]. To handle this issue, the UAV-based communication systems is expected to deploy with the uniform plane antenna array [13], such as L-shaped antenna arrays, uniform circular antenna arrays (UCA), and parallel antenna arrays, which achieves the three-dimensional (3D) beamforming and cuts down the physical space. To reap the benefits of using uniform plane antenna array at the UAV’s transceivers, we will now review the relevant state-of-the-art in the UAV-based MIMO communication. For instance, the authors of [14] studied the efficient deployment of UAV-based MIMO communication, which aims to maximize system’s performance and the wireless networks’s coverage. The work in [15] presented a system model for UAV-based communications. The authors in [16], [17] reported that the LoS links from the UAV and users’ terminals play dominant role in short-distance. By applying user scheduling algorithm in various UAV-based wireless networks, the performance of UAV-based MIMO communication system can be efficiently improved. In [18], the authors presented a novel framework for trajectory optimization and energy-efficient UAV-based communication. The work in [19] investigated the joint optimization of user scheduling and UAV trajectory, which aims to enhance the achievable rate of system. As a general comment, most issues pertaining to the achievable rate of UAV-based MIMO communication under LoS scenario have been largely and extensively characterized. Apart from that, some recent investigations have analyzed the SE performance in the UAV-based MIMO communication under Rayleigh fading. To the maximum achievable sum-rate, linear precoding becomes a effective way, but the main challenge is that the transmitting terminal master the exact channel state information (CSI) [20], [21]. Hence, the research of statistical channel state information for multiuser massive MIMO system is of premier significance under wireless transmission. This is because the perfect CSI is hard to be attained from users terminal, but can be easily attained at the UAV’s transceivers. Fortunately, the authors in [22] proposed an excellent SE-SDMA scheme by utilizing statistical channel state information. The advantage of this scheme lies in that it not only can obtain the optimal achievable rate of systems with SCSI at the UAV’s transceivers, but also can acquire the ideal CSI at the users, Therefore, leaving the SE-SDMA scheme for UAV-based MIMO communication have been treated as an effective suboptimal technique.

Beside the technical challenges mentioned above, antenna array configuration also is the important factor in the UAV-based wireless communication systems in practice. For the conventional MIMO system, the base station is usually equipped with ULAs configuration [23]. as the number of antenna elements grows large enough (formed as massive MIMO system [24], [25]). The fundamental problem of placing a massive number of antennas in a confined space, can be addressed by deploying the uniform plane antenna array. For instant, the antenna elements of uniform rectangular plane antenna arrays (URPA) can be arranged at the both horizontally and vertically direction In addition, compared with the ULAs configuration, the UCAs configuration has more advantages such as the ability to utilize the azimuth-elevation angles and the intrinsic symmetric structure in the azimuth coverage of 360 degrees, lower mutual coupling, more compact structure [26], so more and more researchers have paid attention to UCAs configuration in future wireless communications. The authors in [27] gave the closed-form lower bound expression of achievable downlink sum-rate of multiuser MIMO system equipped with the UCA configuration, but it just consider the LoS scenario. The work in [28] investigated the achievable sum rate of massive MIMO system under time-varying Rayleigh channel. However, the achievable rate of massive MIMO system with UCAs configuration has not been well studied for the three-dimensional spatial channel model. Naturally, deep investigation of the UCA configuration is very essential, while analyzing the achievable rate of UAV-based communication systems under Ricean fading.

From the above discussion, we clear sense that a straightforward and exact theoretical result for UAV-based MIMO systems with Ricean fading is missing from the open literature. This paper presents a general analytic framework for studying the achievable rate of UAV-based communications with a UCA configuration. The main contributions of this paper are summarized as follows:

• By utilizing the statistical channel state information and adopting general Ricean fading channel, there is a need for a new SE-SDMA scheme that can be used to analyze the performance of UAV-based communications with the UCA configuration. We exploit an effective SE-SDMA scheme with only the knowledge of the CSI at the UAV’s transceivers.

• Based on this scheme, a suboptimal beamforming precoder is proposed, which is on the basis of the signal-to-interference-and-noise ratio (SINR) in [29]. This precoder is used for deriving a closed-form formula of the achievable ergodic rate. Secondly, we thus investigate the achievable rate of UAV-based communication system with UCAs under Ricean fading and an exact expression on the achievable rate is given.

• Our results showcase that the achievable sum-rate tends to a saturation value in the high signal-to-noise ratio regime. Furthermore, we find that the high Ricean $K$-factor and the small values of inner product between different channel statistical vector are contribute to the achievable sum-rate of the UAV-based communication system.

Notation: Vector and Matrix are expressed as in lowercase and uppercase boldface, ${\left(\cdot \right)}^H$ and ${\left(\cdot \right)}^T$ denote the conjugate transpose and transpose, respectively, $\Vert \cdot \Vert$ and $\left|\cdot \right|$ stand for Euclidean norm and the absolute value, respectively, ${\mathbf{I}}_N$ is the $N\times N$ identity matrix, $\angle z$ denotes the phase of a complex number $z$, $\mathcal{CN}(\mu ,{\sigma }^2)$ represents a complex Gaussian distribution with mean $\mu$ and variance ${\sigma }^2$ while a Gaussian distribution with mean $\mu$ and variance ${\sigma }^2$ denotes as $\mathcal{N}(\mu ,{\sigma }^2)$; the expectation of a random variable is denoted as $\mathbb{E}\left\{\cdot \right\}$ while the matrix determinant and trace by $det\left(\cdot \right)$ and $\text{trace}\left(\cdot \right)$.