Deep learning based Doppler frequency offset estimation for 5G-NR downlink in HSR scenario①

YANG Lihua(杨丽花), WANG Zenghao, ZHANG Jie, JIANG Ting

(∗College of Communication and Information Engineering, Nanjing University of Posts and Telecommunications, Nanjing 210003, P.R.China)

(∗∗College of Electronic and Information Engineering,Nanjing University of Aeronautics and Astronautics,Nanjing 210016,P.R.China)

Abstract In the fifth-generation new radio (5G-NR) high-speed railway (HSR) downlink, a deep learning (DL) based Doppler frequency offset (DFO) estimation scheme is proposed by using the back propagation neural network (BPNN). The proposed method mainly includes pre-training, training,and estimation phases, where the pre-training and training belong to the off-line stage, and the estimation is the online stage. To reduce the performance loss caused by the random initialization, the pre-training method is employed to acquire a desirable initialization, which is used as the initial parameters of the training phase. Moreover, the initial DFO estimation is used as input along with the received pilots to further improve the estimation accuracy. Different from the training phase, the initial DFO estimation in pre-training phase is obtained by the data and pilot symbols. Simulation results show that the mean squared error (MSE) performance of the proposed method is better than those of the available algorithms, and it has acceptable computational complexity.

Key words: fifth-generation new radio (5G-NR), high-speed railway (HSR), deep learning(DL), back propagation neural network (BPNN), Doppler frequency offset (DFO) estimation

0 Introduction

With the rapid development of high-speed railway(HSR), the HSR wireless communication has attracted more and more attentions around the world[1-2],and HSR has been used as one of the important usage scenarios of the fifth-generation new radio (5G-NR)communication network. In the 5G-NR system, the HSR is expected to achieve a moving speed of up to 500 km/h. However, the high mobility will significantly limit the coverage area and transmission rate, and most current wireless communication systems are designed for the low or medium mobility scenarios. Therefore, it is necessary to design a reliable and efficient communication system for 5G-NR HSR (up to 500 km/h) scenario[3-5].

In 5G-NR HSR scenario, the Doppler shift will become large due to the increase in vehicle speed and the use of high carrier frequency bands. The large Doppler shift will cause more serious inter-carrier interference, which seriously affects the performance of the HSR communication system[6-7]. Therefore, the anti-Doppler frequency shift technology is very important in 5G-NR HSR environment, where the Doppler frequency offset (DFO) estimation and compensation technology is the basis.

Although many DFO estimation methods in highspeed mobile scenarios have been developed, most of them are carried out for HSR scenarios under 4G-LTE systems[8-11]. Due to the increase in vehicle speed and the use of high carrier frequencies, the Doppler frequency shift of 5G-NR HSR scenario is larger than that of 4G-LTE HSR scenario, so the existing estimation schemes in 4G-LTE HSR scenario cannot be directly used for 5G-NR HSR scenario.

Currently, there have been a few DFO estimation methods for the 5G-NR HSR scenario[6,12-13], where the Ref.[6] gave a DFO estimation and compensation algorithm based on position and pre-compensation for the millimeter-wave HSR system, which calculated the Doppler shift according to the position and speed of the train. However, it relies on high-precision positioning,while the positioning error cannot be avoided in practice. In Ref. [12], a DFO elimination method was presented for a millimeter-wave HSR mobile communication system, where the frequency offsets of the received signals of the head and the tail antennas located on the train are assumed to be the same, but have opposite direction. By multiplying the received signals from head and tail antennas, it can eliminate the Doppler shift. However,when the train passes the base station, the DFO will rapidly change, and the time of the head-to-tail antennas passing through the base station is different, so its performance will be deteriorated when the train is handed over. In Ref.[13], a pilotbased maximum likelihood DFO estimation method was given, which estimates the DFO by segmenting the pilot and solving the maximum likelihood function, but it requires a large computational complexity to obtain high estimation accuracy. To meet the requirements of pilot special segmentation, the scheme in Ref.[13]has a strict limit on the length of the pilot symbols, so it is not suitable for systems where the pilot structure has been determined.

In addition, artificial intelligence, especially deep learning (DL), has been applied into the fields of computer vision, natural language processing, speech recognition, etc.[14]. Moreover, the DL is also applied to the wireless communication systems, such as channel estimation, signal detection and channel decoding,etc. In the previous work, a DL-based DFO estimation method has been presented in Ref.[15], which is mainly divided into two stages, off-line training and online estimation. In the previous work, the training samples are constructed only by the received pilot signals, and then the training samples are employed to train the back propagation neural network (BPNN) in an off-line manner. Based on the trained network, the DFO can be estimated. Although the algorithm in Ref.[15] has a better estimation accuracy than the existing schemes, its performance still needs to be further improved.

Currently, the existing DL-based algorithms are mainly carried out from two aspects, one is to obtain better estimation results by using different neural networks[16-17], and the other is to obtain good results from designing the input values of the network[18-19]. To improve the performance of DFO estimation, a novel DLbased method is proposed from designing the initial value or input value of the network in the paper, which belongs to the second aspect.

The proposed DL-based method mainly contains three phases, i.e., pre-training, training and estimation stages. In the pre-training phase, the training samples are constructed by the received signal and initial DFO estimation, where the initial DFO is estimated by the data and pilot signals. In the training phase,only the received pilots and initial DFO estimation is used to train the BPNN, and the initial DFO estimation is obtained by the pilots. Due to the pre-training and initial DFO estimation, the performance of proposed method is greatly improved.

The rest of this paper is organized as follows. Section 1 introduces the system model. Section 2 presents the proposed method in detail. The simulation results and conclusions are given in Section 3 and Section 4 respectively.

1 Signal model

In a 5G-NR downlink single input single outputorthogonal frequency division multiple access (SISOOFDMA) system, assume that thenth transmitted time domain signal during themth OFDMA symbol in theith subframe issi(m,n).Since the Ricean-fading channel is often employed as the HSR channel[20-22],the discrete-time multipath Ricean-fading channel during themth OFDMA symbol in theith subframe is given as[23]

wherewi(m,n) is the additive white Gaussian noise(AWGN) with the covarianceσ2w.

Since the change of frequency offset during one OFDMA symbol is relatively small, the frequency offset in one subframe can be regarded as a constant. Moreover, the processing of the DFO estimation in each subframe is the same. Therefore, the subscriptith and superscriptmth can be omitted to derive conveniently in the following.

2 Proposed DFO estimation method

In the section, the architecture of BPNN is given first, and then the proposed method will be introduced in detail.

2.1 BPNN

In the field of DL, BPNN is a multi-layer feedforward neural network, which is trained by the error back propagation algorithm, and it has strong nonlinear mapping ability and a wide range of applications. Considering the complex correlation of data in high-speed mobile scenario, BPNN is employed to estimate DFO in the proposed method.

Fig.1 shows the structure of BPNN withLlayers,which containsL-2 hidden layers. In Fig.1, the input of thebth node of thelth layer can be expressed as

wherearepresents a set of nodes in the (L-1)th layer connected to the nodeb.w(l)b,ais a weight vector between the nodeband each node ina.Iais the input vector of the (L-1)th layer node.

Fig.1 The structure of BPNN

In BPNN, the output of the node is the value obtained by weighting all the inputs and then processing them through the transfer function, so the output of the nodebth of thelth layer is

wheref(·) represents the transfer function, and different transfer functions can be selected according to the specific application. In the proposed method, the Tansig and Purelin transfer functions are respectively employed in the hidden layer and output layer, i.e.,

2.2 DL-based DFO estimation algorithm

The proposed method contains pre-training, training, and estimation stages, which can be seen from Fig.2, where ΓR(·) represents the reshaping function given in Eq.(8). BPNN is firstly trained by an off-line manner at the pre-training and training stages.At the estimation stage, DFO will be estimated in real time by using little pilots. Moreover, the initial DFO estimation is also used as input to further improve the estimation accuracy.

Fig.2 The proposed algorithm

(1) Pre-training phase. To reduce the performance loss caused by the random initialization, the pretraining approach is firstly employed to obtain a desirable initialization, which is used as the initial parameters of the training stage.

In pre-training stage, assume that theuth training sample set of BPNN is

where 0 ≤u≤U-1,Uis the number of the training sample sets.R(k) represents the received signal at thekth subcarrier, which is obtained by IFFT ofr(m,n)given in Eq.(4) and includes pilot and information symbols.Nuis the number of the used subcarrier for one OFDMA symbol, which includesNppilot andNu-Npinformation symbols.f^dis the estimated Doppler frequency offset by the algorithm given in Ref.[11] with information symbols known.

The input data must be reshaped because BPNN can only work in real domain. Assume that ΓR(Ζ) is the input reshaping function, i.e.,

In the training phase, the training samples are the received pilots and estimated DFO, where the DFO is estimated only by the pilots. However, training samples are the estimated DFO and received signal in the pre-training phase, where the DFO is estimated by the information and pilot symbols, which can improve the estimation accuracy. Moreover, the proposed DL-based estimator adoptsf^das part of the input such that the BPNN can further improve the performance.

(3) Estimation phase. The estimation stage is the process of DFO estimation in an online manner by using the network model obtained in the training stage.Moreover, the input data in the estimation stage has same structure as that in the training stage. By feeding the input data into the trained BPNN, one can obtain the DFO estimation.

3 Simulation results

3.1 MSE performance

To evaluate the performance of the proposed method, a 5G-NR for HSR scenario is considered[24-26].The simulation parameters are given as follows: the length of one slot is 250 μs, and each slot contains 14 OFDMA symbols. The length of FFT is 1024, and the carrier frequency is 30 GHz. The pilot uses the centralized placement. The cyclic prefix (CP) length is 128.The sub-carrier spacing is 60 kHz, and the vehicle speed is 500 km/h. The single path Ricean channel model is considered, and the Ricean factors are 5 and 10. In comparison with the proposed method, the previous work in Ref.[15], the pilot segment based DFO estimation method in Ref.[11], and the pilot based maximum likelihood estimation ( ML) method in Ref.[13] are also simulated.

Fig.3 MSE performances of the DL-based DFO estimation method with different training methods and training parameters (Ricean factor is 10)

Fig.3 gives the mean squared error (MSE) performances of the DL-based DFO estimation method with different training methods and training parameters. In Fig.3,the DL-based without pre-training and only using pilot symbols is the previous work given in Ref.[15].In the simulation, the number of used pilot is 72 for DL-based without pre-training, and the number of used pilot for pre-training and training are 72 and 16 respectively for both DL-based with pre-training and proposed method. Compared with the DL-based without pretraining given in Ref.[15], the DL-based with pretraining method has a better performance due to its using pre-training. However, the proposed method has a best performance due to employing the pre-training and initial estimation

Fig.4 shows the MSE performance under the different numbers of training sample sets for the proposed method. In the simulation, the number of pilotsNpin each sample set is the same, andNp=16. In Fig.4,one can see that the accuracy of DFO estimation is improved as the number of sample setsUincreases,which indicates that the larger training sample sets can improve the learning efficiency of the neural network,but it will also increase the complexity of offline training. Therefore, the choice of the number of training sample sets should be a compromise between performance and computational complexity in practice.

Fig.4 MSE performance under different numbers of training sample sets for the proposed method (Ricean factor is 10)

Fig.5 shows the MSE performance of the DFO estimation by the network trained under different signalto-noise ratios (SNRs) conditions for the proposed method. When the SNR is lower than 12 dB, the performance of proposed method with the network trained under the fixed SNR of 10 dB is better than that of the network trained under the 20 dB, and when the SNR is greater than 12 dB, the performance of the network trained under the 20 dB is better. When training the network with varying SNRs, the proposed method can maintain good performance regardless of whether SNR is low or high. Therefore, when DFO estimation is performed, in order to maintain better estimation performance, a suitable neural network can be selected according to different SNRs for estimation.

Fig.5 MSE performance of proposed method by training under different SNRs (Rican factor is 10)

Fig.6 shows the MSE performances of the different DFO estimation methods with the different Ricean factors. In simulation,U=4000 andNp=32 for the proposed method, andNp=1024 and the number of the segments is 2 both for the schemes in Ref.[11]and Ref.[13]. From Fig.6, the proposed method can obtain the best performance but only using a little pilot, while the algorithms in Ref.[11] and Ref.[13]are limited by the number of pilot segments, so they have a poor estimation performance. Moreover, the performance of all methods will be improved as Ricean factor increases.

Fig.6 MSE performances of different DFO estimation methods with different Ricean factors

3.2 Complexity analysis

Assume thatL=3 andT=100, the number of neurons in the two hidden layers is 20 and 50 respectively. In the case, the complexity of the proposed method in the off-line stage is larger than those of the algorithms in Ref.[11] and Ref.[13], while its complexity in online stage is close to those of the algorithms in Ref.[11] and Ref.[13]. However, the proposed method only needs to train the neural network once in an off-line manner for the same wireless environments,and the network can be used to obtain the DFO estimation in an on-line manner. Moreover, the estimation performance of the proposed method is best, which can be seen from Fig.6.

4 Conclusions

A DL-based DFO estimation method is proposed for 5G-NR HSR scenario. After training the network in an off-line manner, the proposed method only uses little pilots to obtain the high-precision DFO estimation in an online manner, which has low computational complexity. The proposed method is not only suitable for 5G-NR HSR scenarios, but also can be employed to estimate the DFO in existing and future high-speed mobile communication scenarios.