Transmit diversity and performance analysis for aeronautical broadband satellite communication systems

Abstract

This paper analyzes the downlink transmission performance of an aeronautical broadband satellite communication system operating at millimeter wave (mmWave) band. Specifically, by considering that two adjacent satellites cooperatively communicate with an airplane employing an antenna array, we first propose a simple transmit scheme combining Alamouti space time block coding (STBC) with receive beamforming (BF) to improve the system performance. Then, by considering the phase shift errors in phased array antenna deployed at the airplane, we analyze the equivalent output signal-to-noise ratio (SNR) of the considered communication system. Further, with the help of the moment generating function (MGF) approach, we derive the average symbol error rate (ASER) of the system with the proposed transmit scheme, where the satellite links undergo correlated shadow-Rician (SR) fading. Finally, computer simulations are conducted to confirm the validity of the theoretical analysis and reveal the effect of phase errors on the performance of the aeronautical broadband communication system.

Introduction

Air traveler’s comfort and convenience have been the main concern of airlines and aircraft industry [1], [2], [3]. Currently, the aeronautical broadband communication takes two common forms, namely, the ground-based communication scheme (e.g. air-to-ground) [4], [5], [6] and the satellite-based communication scheme [7]. However, there are several drawbacks existing in the ground-based solution. Firstly, due to the limited coverage area of the base station, aircrafts need to implement frequently BS switch throughout the communication, leading to significant rate variation. Secondly, unfriendly geographies may make it more difficult to deploy BS. Thirdly, the altitude of the aircrafts must be less than the maximum communication distance of BS, which restricts the altitude of the aircrafts.

Compared with the ground-based communication scheme, satellite communication (SatCom), featuring global coverage and long transmission distance, becomes an indispensable method to deal with the above mentioned disadvantages in nowaday aeronautical communication [8], [9], [10], [11], [12]. Besides, in order to provide seamless connection and continuous services for global coverage, internet access, high throughput satellite (HTS) is playing an important part in aeronautical broadband satellite communication (ABSatCom) systems.

Recently, many works related to ABSatCom have been published in open literature [13], [14]. On the premise of reducing cost, the author of [13] proposed to apply the spot beam technology with similar size to Ka band in Ku band HTS, so as to obtain the same or even better system performance than Ka band. In [14], orthogonal frequency division multiplexing (OFDM) modulation technology was employed in the considered network to reduce the impact of Doppler on system performance. However, previous works [13], [14] both selected Ku band or even L band for communication, which cannot meet the requirements of high-speed data rate. Meanwhile, it was also faced with the threat that the spectrum resources in these frequency band increasingly tense. Thus, we need to obtain more spectrum resources from higher frequency band, such as millimeter wave (mWave) band [15], [16], [17]. In this context, the HTS system operating in mmWave band has become a hot research topic. In [18], the authors proposed to use the mmWave band for HTS in term of taking capacity and cost into account. In order to solve the issue of communication outage due to the operation of mmWave band, the authors of [19] and [20] proposed two different schemes based on smart gateway diversity. However, it should be noticed that with increasing the frequency, directional pattern will be improved as well as the narrower beamwidth. On the other hand, considering that the low profile and easy employment, the phased array antenna is often exploited at the airplane. Many works related to the phase antenna system have been investigated in [21], [22], [23]. Specifically, the author of [21] employed the adaptive path identification approach to characterize the communication links, and then investigate the impact of the phased array geometries on the transmission. In [22], the author studied the sample matrix inversion algorithm based on the phased array to reduce the jamming. The influence of phased array architectures on beamforming was revealed in [23].

Although the aforementioned works have investigated the system performance or beamforming algorithm of phased array-based network [21], [22], [23], they have not considered the phase errors in antenna array. It is worth mentioning that as the antenna directivity is misaligned due to the phase shift errors, the radiation intensity could be reduced together with array gain [24]. This observation motivates the work presented in this paper. Our contributions can be listed as follows:

• By employing the cooperation technology of two adjacent satellites, we propose the Alamouti space time block coding (STBC) based transmit diversity scheme for an ABSatCom operating at mmWave. Besides, the antenna array employed at the airplane is divided into two sub-arrays to receive the intended signal from the satellite, respectively. Compared with most of the related works [13], [14], our scheme can obtain the diversity order with low implement complexity while improving the system performance.

• Unlike the existing works that ignore the effect of phase shift errors in phased array antenna [21], [22], [23], we derive the equivalent signal-to-noise ratio (SNR) expression of the considered system with phase shift errors by using the proposed Alamouti STBC scheme. Thus, we consider a more general and practical scenario in comparison with the related works.

• By using the moment generating function (MGF) approach, we derive the closed-form expression for the average symbol error ratio (ASER) of the considered system with Alamouti STBC transmit diversity scheme. Here we consider two typical phase error models, namely, uniform distribution and Gaussian distribution, and suppose correlated SR fading for satellite channels, as opposed to the related works [8], [25] where independent and identically distributed (i.i.d.) SR fading is assumed. Numerical and simulation results highlight the impact of phase shift error on the system performance of ABSatCom.

The rest of this paper is organized as follows. In Section 2, we introduce the system model and problem formulation. In Section 3, we derive the closed-form expression of ASER for the considered system. Section 4 provides the simulation results along with discussions. Finally, conclusions are presented in Section 5.

Notation

Vectors and matrices are represented by bold lowercase and uppercase typeface, respectively. ${\left(\cdot \right)}^{\ast }$, ${\left(\cdot \right)}^T$, and ${\left(\cdot \right)}^H$ denote the conjugate, transpose and Hermitian transpose operation, respectively. $\left|\cdot \right|$ and $\Vert \cdot \Vert$ indicate absolute and Euclidean norm, respectively. $E\left[\cdot \right]$ and $diag\left\{\cdot \right\}$ represent the expectation and the diagonal matrix, respectively. ${ℂ}^{M\times N}$ denotes the complex space of $M\times N$, $N\left(\mu ,{\sigma }^2\right)$ and $ℂ\mathbb{N}\left(\mu ,{\sigma }^2\right)$ represent the real-valued and complex-valued Gaussian distribution the mean $\mu$ and covariance ${\sigma }^2$, respectively. ${\mathbf{R}}^{1/2}$ denotes the matrix square root of matrix $\mathbf{R}$, ${\mathbf{I}}_N$ denotes the $N$-dimensional unit matrix, $J_1\left(\cdot \right)$ and $J_3\left(\cdot \right)$ denote the first-kind Bessel function of order 1 and order 3, respectively.