Cheng Wang, Gaofeng Cui, Weidong Wang, Yinghai Zhang

Key Laboratory of Universal Wireless Communications, Ministry of Education, Beijing University of Posts and Telecommunications

* The corresponding author, Email： cuigaofeng@bupt.edu.cn

I. INTRODUCTION

In the past decade, satellite has been widely used in communication systems with the advantage of its wide coverage. However, satellite systems in the early years are employed as the complement to the terrestrial wireless communication systems. For example, the Inmarsat mainly provided services to seagoing ships in the 1980s [1]. With the development of communication techniques, the data rate of satellite systems has been increased signi ficantly. In [2], satellite systems are used to provide communication services to the areas without terrestrial wireless communication systems. Furthermore, many business companies (e.g., OneWeb, O3b, SpaceX) start to provide broadband Internet access based on satellite.

Recently, satellite systems evolve from single-carrier techniques to multi-carrier techniques to improve the spectral efficiency[3-5]. As is known, orthogonal frequency di-vision multiplexing (OFDM) technique is a typical multi-carrier technique used in many wireless communication systems [6-8]. With the capability of providing high spectral efficiency in the multi-path environment, OFDM is chosen as the multi-carrier technique in the 4G terrestrial wireless communication systems [9]. Meanwhile, OFDM is also proposed as the satellite component of IMT-Advanced systems by China [5]. However, OFDM has the drawback of high peak-to-average power ratio (PAPR). Due to the nonlinear high power ampli fiers (HPAs) of satellite systems, a large input backoff (IBO) is needed to deal with the signal distortion in OFDM systems [10]. The authors of [11] give an overview of PAPR reduction techniques for OFDM systems, however, these techniques may lead to either low spectral efficiency or high complexity.

Another way that can be used to reduce the PAPR is the constant envelope OFDM (CEOFDM) technique [12]. By modulating a real-valued OFDM signal to the phase of a constant envelope signal, the PAPR of CE-OFDM signal is 0dB. Therefore, the HPAs of satellite can achieve high power efficiency. The low complexity linear receiver, which is based on Taylor series expansion, is proposed for CEOFDM systems in [13]. The authors of [14]design the CE-OFDM based mm-wave system. The authors of [15] present the optimum performance of CE-OFDM signals in both additive white Gaussian noise (AWGN) channel and frequency-selective channel. However, the CE-OFDM technique can only reach nearly 50% spectral efficiency of the OFDM technique [12].

In order to improve the spectral efficiency of CE-OFDM technique, a dual-stream CEOFDM technique is proposed in [16]. Besides,it can also keep the PAPR of the waveform being lower than 3dB. Hence, the dual-stream CE-OFDM technique can be considered as a type of quasi-constant envelope OFDM(QCE-OFDM) technique with high spectral efficiency. Therefore, the satellite systems based on QCE-OFDM are worthwhile to be investigated. In satellite systems, the communication links are always affected by the carrier frequency offset (CFO) and the carrier phase offset (CPO). The CFO is caused by the Doppler effect, and the CPO is caused by the non-ideal oscillator. In this paper, we investigate the joint CFO and CPO estimation in QCE-OFDM satellite systems. The main contributions of this paper are as follows.

● The effects of CFO and CPO in QCEOFDM satellite systems are analyzed.

● The joint CFO and CPO estimation method is designed according to the linear relationship among CFO and CPO as well as data symbols.

● The optimal pilot symbol structure is proposed for the joint CFO and CPO estimation.

The rest of this paper is organized as follows. Section II presents the related works.Section III introduces the signal model and analyzes the effects of CFO and CPO in QCEOFDM satellite systems. Section IV presents the joint CFO and CPO estimation method.Section V proposes the optimal pilot symbol structure for the joint CFO and CPO estimation method. Section VI and VII introduce the simulation analysis and the conclusions,respectively.

In this paper, the authors ananlyze the effects of carrier frequency offset and carrier phase offset in Quasi-Constant Envelope OFDM satellite systems. The optimal pilot structure in frequency domain is proposed in this paper.

II. RELATED WORKS

Since CFO and CPO will deteriorate the biterror-rate (BER) performance, the estimation and the compensation of CFO and CPO are essential for communication systems. For single-carrier systems, the estimation method and the corresponding CRBs for phase and frequency offset of phase-shift keying (PSK)packets are presented in [17]. The CRBs for QAM phase and frequency estimation are illustrated in [18]. The authors of [19] propose an optimal blind joint CFO and CPO estimation method, which is based on the nonlinear least-squares algorithm. For multi-carrier systems, training sequences are generally used to estimate the CFO and CPO. A robust frequency and timing synchronization scheme for OFDM is presented in [20], where the authors construct a training sequence whose length is two symbols. There are two identical parts in the first symbol, which is used to estimate the fractional CFO. Meanwhile, the second symbol is used to estimate the integer CFO.In order to reduce the overhead, the authors of[21-22] propose the CFO estimation methods based on one symbol, which is consisted of several identical parts. The optimal training sequence structures for CFO estimation in AWGN channel and frequency-selective channel are presented in [23] and [24], respectively. However, the estimation method of CPO is not considered in [23] and [24]. A joint CFO and CPO estimation method based on the sequential Monte-Carlo and expectation-maximization (EM) approaches is proposed in [25].Whereas, the method in [25] has high computation complexity. The authors of [26] propose a joint CFO and CPO estimation method,which is based on the expectation conditional maximization algorithm. However, the training symbol used in [26] has high PAPR. In[27], an estimation method of CFO in QCEOFDM satellite systems is proposed without the consideration of CPO. The authors of [28]propose the maximum-likelihood (ML) estimators of CFO and CPO. A CFO estimation method, which is based on the repeated preamble, is proposed in [29]. The scattered pilots-based frequency synchronization scheme and the blind frequency synchronization scheme are proposed for multi-user OFDM systems in [30] and [31], respectively. Whereas, the schemes in [30] and [31] assume that the receiver has a large number of antennas based on the massive multi-input multi-output(MIMO) technique. However, the applicatio

n of massive MIMO technique in satellite systems requires further research. A pilot based CFO estimation method is proposed in [32] for cooperative OFDM systems. A fractional frequency offset estimation scheme is designed in [33] for non-cooperative OFDM systems.Nevertheless, the CFO estimation range is not presented in [32], and the CPO estimation is not considered in both [32] and [33].

According to the analysis above, how to design the joint CFO and CPO estimation method according to the characteristics of QCEOFDM satellite systems is worth researching.

III. SIGNAL MODEL AND PROBLEM ANALYSIS

The QCE-OFDM transmission signal in OFDM signal to the phase of a constant envelope signal.

Fig. 1 The transceiver of QCE-OFDM satellite systems

Fig. 2 BER performance with and without CFO and CPO

The transmitter of QCE-OFDM can be considered as multiplexing two CE-OFDM signals by the phase shifting. The receiver of QCE-OFDM is based on the Taylor series expansion. Assuming that the CFO and CPO are equal to zero, the received signal vector in (1) can be divided to two streams, including the real part stream and the imaginary part stream. These streams can be expressed as

In (6), the CFO is represented by shows the BER performance with and without CFO and CPO in AWGN channel. From Fig.2, the CFO and CPO will result in the serious BER performance degradation of QCE-OFDM satellite systems.

IV. JOINT ESTIMATION METHOD

Fig. 3 shows the joint estimation structure of CFO and CPO. It consists of three modules,including the arctangent module and the phase unwrapper module, as well as the discrete Fourier transform (DFT) module. Section 4.1 presents the linear relationship among CFO and CPO as well as data symbols. Then, Section 4.2 proposes the joint estimation method based on the linear relationship.

4.1 Linear relationship among CFO and CPO as well as data symbols

where the sine and cosine functions meet [34]

The linear relationship is

4.2 Joint Estimation Method

According to [36], the minimum variance unbiased (MVU) estimators and the corresponding CRBs ofΔfandθare shown as

V. OPTIMAL PILOT SYMBOL STRUCTURE DESIGN METHOD

5.1 CRB Theoretical Analysis

According to (12),

Fig. 3 The joint estimation structure of CFO and CPO

After substituting (16) into (13), the CRBs can be expressed as

5.2 Optimal pilot structure

According to the properties in Section 5.1, if the overhead of pilot symbol is fixed, we can get the optimal pilot symbol structure as is shown in Fig. 5.

From Fig. 5, the optimal pilot positions optimal pilot symbol structure under arbitrary fixed pilot overhead is obtained.

Table I Simulation parameters

Fig. 4 The values of

Fig. 5 The optimal pilot symbol structure

Fig. 6 The MSE performance of CFO

VI. SIMULATION RESULTS AND ANALYSIS

The mean squared error (MSE) and the BER are used to evaluate the performance of the proposed pilot symbol structure. The Minn method in [22] and the ML method in [28] as well as the repeated preamble (RP) method in[29] are employed for the MSE comparison.The multi-path fading channel obeys the Rician distribution. The simulation parameters are listed in Table 1.

The MSE performance of CFO is shown in Fig. 6. The CFO is normalized to the subcarrier spacing and the CPO is an arbitrary value data symbol is used as the pilot symbol, and this situation can be considered as the blind estimation case. In addition, Fig. 6 shows that the CNR threshold of the phase demodulator is nearly 8dB. Due to the threshold effect of the phase demodulator, the estimation of CFO is accurate when CNR is larger than the CNR threshold.

From Fig. 6, the MSE performance of the Minn method is better than the proposed meththe proposed method is less than 1dB compared with the ML method and the RP method.However, the pilot overhead of the proposed method is less than the ML method and the RP method.

Overall, the proposed joint CFO and CPO estimation method and the optimal pilot symbol structure can achieve good performance,in terms of large estimation range and high estimation accuracy.

Fig. 7 The CRB of CPO

VII. CONCLUSIONS

In this paper, we analyze the effects of CFO and CPO in QCE-OFDM satellite systems.Then, the linear relationship among CFO and CPO as well as data symbols is presented. According to this linear relationship, the MVU estimators and the corresponding CRBs are obtained. Therefore, the joint estimation method of CFO and CPO is given. Furthermore, the optimal pilot symbol structure in the frequency domain is proposed. In addition, this paper proves that the proposed pilot symbol structure can minimize the CRBs of CFO and CPO under the fixed pilot overhead. Simulation results show that the joint estimation method and the proposed pilot structure can achieve good performance in QCE-OFDM satellite system.

Fig. 8 The BER performances of QCE-OFDM satellite systems

ACKNOWLEDGEMENTS

This work was supported by the National Natural Science Foundation of China (No.91438114, No. 61372111 and No. 61601045).

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