Xuanfan Shen, Yong Liao,＊, Xuewu Dai, Ming Zhao, Kai Liu, Dan Wang

1 Center of Communication and TT&C, Chongqing University, Chongqing 400044, China

2 The State Key Laboratory of Integrated Services Networks, Xidian University, Xi’an 710071, China

3 Faculty of Engineering and Environment, Northumbria University, Newcastle upon Tyne, NE1 8ST, United Kingdom

4 Key Laboratory of Dependable Service Computing in Cyber Physical Society, Chongqing University, Ministry of Education,Chongqing 400044, China

5 Chongqing Key Laboratory of Mobile Communication Technology, Chongqing University of Posts and Telecommunication,Chongqing 400065, China

Abstract: This paper addresses the problem of channel estimation in 5G-enabled vehicular-to-vehicular (V2V) channels with high-mobility environments and non-stationary feature.Considering orthogonal frequency division multiplexing (OFDM) system, we perform extended Kalman filter (EKF) for channel estimation in conjunction with Iterative Detector& Decoder (IDD) at the receiver to improve the estimation accuracy. The EKF is proposed for jointly estimating the channel frequency response and the time-varying time correlation coefficcients. And the IDD structure is adopted to reduce the estimation errors in EKF. The simulation results show that, compared with traditional methods, the proposed method effectively promotes the system performance.

Keywords: orthogonal frequency division multiplexing (OFDM); non-stationary channel estimation; extended Kalman filter (EKF);Iterative Detector & Decoder (IDD); vehicular-to-vehicular (V2V)

I. INTRODUCTION

With the rapid deployment of intelligent vehicular around the world, the researches about 5G-enabled cooperative intelligent vehicular(5GenCIV) framework have attracted a lot of attention[1]. It is mentioned that it is necessary to provide a reliable and safe wireless communication service for 5GenCIV in [1], and the communication systems with low-latency and high-mobility meet the basic demand for 5GenCIV. And [2]-[5] points out that accurate precision and estimation for channel is able to improve the transmission delay and system throughput under highway scenarios. Therefore, providing reliable channel estimation and precision is crucial for 5GenCIV.

However, in high-mobility environment it is a challenging work to estimate the channel state information (CSI) accurately. [6]-[9]show the essential feature and parameter model of non-isotropic vehicle-to-vehicle (V2V)channel. And it is also pointed out that there is non-stationary character in high-mobility channel and the time correlation coefficients of channel are time-varying.

From a system point of view, the channel is indeed a time-varying dynamic system characterized by its channel response, and the channel estimation is a system state estimation problem, in which the channel response is the state variable of the channel system. The Kalman Filter (KF) has been widely used as a state estimation technique and several KF-based channel estimation methods have been proposed in [10]-[12]. On one hand, in most of KF-based methods, the state transition matrix is constructed by zero-order Bessel function depending on the conclusion about time correlation coefficients of Jakes model.However, in high-mobility environments, the channel response is non-stationary, and the time correlation coefficcients are time-varying.So, traditional KF-based channel estimation methods are not practical in high-mobility environments. On the other hand, as for the Kalman Filter (KF)-based channel estimation,the estimation accuracy also depends on the accuracy of measurement matrix. In [10] and[12]-[14], the Decision-directed method is adopted to construct measurement matrix of KF, but the performance is limited due to error propagation of Decision-directed. And we find that Iterative Detector & Decoder (IDD) is a receiver structure which could be applied to construct a more proper measurement matrix for KF by utilizing thea posterioriLog-likelihood ratios (LLRs) from Soft-input Soft-output (SISO) decoder. The method named“LLR-directed” is purposed in this paper could improve channel estimation performance by the redundancy of channel coding.

To cope with the challenges of non-stationary channel estimation, the main contributions of this paper are outlined as follows: For high-mobility environments, the non-stationary channel is modeled as a time-varying autoregressive (AR) process. And an EKF is proposed for joint estimating of both the channel frequency response (CFR) and the time-varying time correlation coefficients. To further improve the channel estimation accuracy, the IDD technique is integrated with the EKF(IDD-EKF). And we study the performance of proposed method for different cases of user mobility.

The rest of this paper is organized as follows. In Section II, both the system model and channel model are presented. In Section III,we propose the IDD-EKF channel estimation method, including state space model, updating equation, and measurement matrix of EKF. In Section IV, the performance of the proposed method is compared with the traditional methods in high-mobility environment by MATLAB. Finally, the conclusion is discussed in Section V.

II. SYSTEM MODEL

Consider an OFDM system withNsubcarriers,Nppilot subcarriers, andIOFDM symbols in a sub-frame. We consider a first-order time-varying AR process for the non-stationary channel. It can be expressed as

Clark model is regarded as foundation in most studies on channel AR model, and the time correlation coefficientai,kcan be expressed asin power-normalized stationary channel, whereJ0(·) is zero-order Bessel function,fddenotes the maximum Doppler frequency andTsis sample spacing of system. However, for non-stationary channel,ai,kis a time-varying parameter rather than a constant which is only related to the intervalNTsof adjacent symbols.

The OFDM baseband system could be modeled as follows.is defined as a transmitted symbol atkth pilot subcarrier on theith OFDM symbol, and the vector of transmitted symbols at pilot subcarriers isAs we assume that the channel impulse response in an OFDM symbol is constant, the channel matrix isThe system model can be expressed as

III. EKF FOR CHANNEL ESTIMATION

In this section, a minimum variance estimator based on EKF for the channel response at pilot subcarriers is derived. In particular, we present an iterative channel estimation method based on EKF.

3.1 State space model of EKF

Considering a time-varying channel described in (1) and the system model in (2), the CFR at pilot subcarriers can be described as a state space model of Kalman filter

The measurement matrix for pilot symbol is known, but it is necessary to be estimated or constructed for data symbols. Bothare mutually independent,zero-mean, Gaussian complex white noises,with covarianceTo track the non-stationary channel, the time-varying state transition matrix Aiis estimated together with the channel response hi.

In order to facilitate the description, we de fine the state transition vectorfollow

Assuming a random walk model for the parameter ai, (3) becomes

whereεi?1denotes the process noise of aiand it is an independent, zero-mean Gaussian noise with covariance

In order to jointly estimate the state and parameters, a new augmented state ziis de fined asThen, the channel state space model (5) turns into an augmented system

Applying the first-order Taylor approximation to the nonlinear state transition function aroundin (7), the state (6) becomes

3.2 Update equation of EKF

Applying the standard KF to the model (8) is straight-forward. The resulting EKF algorithm for the joint estimation of CFR hiand time correlation coefficcients aiworks in a prediction- correction cycle.

The prediction projects forward (in time)the current estimates zi?1and error covariance Pi?1at the (i-1) th OFDM symbol to obtain thea prioriestimates zi|i?1and Pi|i?1for the nextith OFDM symbol. zi|i?1and Pi|i?1can be expressed as

The correction adjusts thea prioriestimatesto an improveda posterioriestimates by using an actual measurement of received symbol yiat theith OFDM symbol. It can be described as follows

where Kiis the Kalman gain of the EKFdenotes the conjugate transpose of matrix anddenotes inverse of matrix).

3.3 Measurement matrix of EKF

The Decision-directed is adopted widely in KF-based channel estimation to construct the measurement matrix. When the Decision-directed makes a wrong decision, the estimated measurement matrix would be different from the actual transmitted symbols, which may lead to error decision in the process of update in EKF, and these errors would be propagated with the iteration of EKF. The key point to avoid error propagation is to contrast a measurement matrix more close to the transmitted data symbols. The SISO decoder is able to correct error bits, so the output of decoder,aposterioriLLRscould be used for constructing a more proper measurement matrix for EKF with LLR-directed. The LLR-directed utilizes the redundancy of channel code to improve the accuracy of channel estimation,and the detail is as follow.

First of all, thea posterioriLLRsfrom decoder are converted into bit probabilities via the following equation:

The coded bits are assumed to be statistically independent, so the symbol probabilities can be deduced

whereSmis the modulation symbol corresponding to the bit sequenceand log2Mis the modulation order. With hard mapping, the symbol with the highest probabilityis chosen from the elements of the modulation alphabet:

3.4 Processing flow

Figure 1 illustrates the block diagram of proposed IDD-EKF for OFDM downlink channel estimation. And the procedure of the proposed LLR-directed non-stationary OFDM channel estimation is summarized as follows.

While the OFDM symbols are detected by receiver, channel estimator is initialized. In first stage, for reducing the complexity, LS is adopted to estimate the CFR as preliminary estimation, and the detector switches to the Initialization. After detecting, thea prioriLLRsof each bit are outputted by detector and fed to SISO decoder. And the decoder corrects error bits anda posterioriLLRsare delivered to EKF by LLR-directed to construct the measurement matrix. In this stage, EKF is initialized. Then, in the second stage, CFR is estimated and interpolated by EKF with iterative prediction-correction cycle.Thea prioristate estimate zi|i?1is achieved by (9) and (10). In the iteration of the OFDM data symbols,is fed back to the EKF to calculatea posterioristate estimate ziby(11)-(13). And the detector switches to the updating stage. CFR of the sub-frame from EKF is used for detecting and decoding. At last, the bit stream is outputted by decoder.

IV. SIMULATION RESULTS AND ANALYSIS

In this section, simulation is performed to validate the performance of the proposed IDDEKF channel estimation for OFDM systems.It was mentioned in [7] that the WINNER II channel models have introduced the concept of time-evolution to explicitly simulate the non-station of the fading channels. A highspeed channel model de fined by WINNER-II D1 is adopted to con figure the non-stationary channel with additive white Gaussian noise.The system bandwidth is 5MHz, and the total number of subcarriers is 300. The system operates at 2.8GHz. The 16-QAM modulation is employed. And the log-MAP algorithm is used for decoding and the decoding iteration is 6. A KF-based channel estimation method proposed in [11] which adopts Decision-directed and sets the state transmitted matrix as constant is compared with IDD-EKF in this paper.

Figure 2 shows the comparison of NMSE of LS estimation, traditional KF-based channel estimation [11] as well as IDD-EKF at different speeds. It is observed that the NMSE of the three methods are very close at the speed of 50km/h. Compared to KF-based estimation, the average SNR gain of IDD-EKF is less than 2dB, as the channel fading is flat in low-mobility environments where the Clark model can still be useful for the approximate the actual channel response. However, a gain in SNR of IDD-EKF is more than 2dB comparing with the KF at the speed of 300km/h. In high-mobility environments, KF could not track the changes of non-stationary channel, because the time-correlation property of channel response between two pilot symbols is fixed. On the contrary, IDD-EKF adjusts the state transition matrix in time with the diversity in time domain of channel. Therefore,IDD-EKF channel estimation achieves higher accuracy in high-mobility environments.

As mentioned above, error propagation may occur during the process of Decision-directed.Figure 3 illustrates the distribution of mean errors of the LS method, KF-based method in[11] and IDD-EKF. And the continuous error peaks in time domain is the re flection of error propagation. The most of the error peaks in figure 3(a) are higher than (b) and (c). Figure 3(b)shows that the error propagation in Decision-directed KF marked by ellipses. In figure 3(c),the error peaks decrease at the symbols which are the same as marked in figure 3(b). It is obvious that the in fluence of error propagation on estimation precision is effectively eliminated and the error peaks are shorter than KF-based one. The decoder corrects the error bits and the measurement matrix of EKF is constructed by thea posterioriLLRs with LLR-directed. It is demonstrated that LLR-directed is able to improve the estimate accuracy.

Fig. 1. Channel estimator by IDD-EKF.

Fig. 2. NMSE verse SNR performance comparison at 50km/h & 300km/h.

Fig. 3. CFR estimation mean errors in 100km/h with SNR=25dB. (a) for the LS scheme, (b) for KF-based scheme [11], and (c) for the IDD-EKF scheme.

Figure 4 shows the bit error rate (BER) of LS estimation, KF-based channel estimation[11], and IDD-EKF at 50km/h and 300km/h respectively. At 50km/h, comparing with LS method, the average SNR gain of KF-based estimation is 2dB, and the SNR gain in IDDEKF is 3dB. And the performance of IDDEKF is almost close to the performance of realistic and perfect channel state information(CSI). There is no conspicuous SNR gain of IDD-EKF compared with KF, because the error propagation is not obvious in low-mobility environments. In contrast with KF method,the gain in SNR of IDD-EKF is more than 3dB in high-mobility environments (300km/h). It is evident that the hypothesis that time correlation coefficcients as constant is unpractical in non-stationary channel. It limits the performance of channel estimation. And IDDEKF could adjust state transition matrix with time-varying channel, and construct measurement matrix to obtain more accuracy estimates with LLR-directed.

V. CONCLUSION

For 5G-enabled V2V channels with high-mobility environments and non-stationary feature, we performed a joint design of channel estimation, detection and decoding based on EKF and IDD technology. The proposed method jointly estimates the time correlation coefficcients and CFR, which is appropriate for non-stationary channel estimation. And the LLR-directed avoid error propagation, which could improve the estimation accuracy. The simulation results show that IDD-EKF promotes channel estimation performance effectively compared with traditional methods in high-mobility environments.

ACKNOWLEDGMENT

This work was supported by the National Natural Science Foundation of China (No.61501066, No. 61572088, No. 61701063),Chongqing Frontier and Applied Basic Research Project (No. cstc2015jcyjA40003,

Fig. 4. BER verse SNR performance comparison at 50km/h & 300km/h.

No. cstc2017jcyjAX0026, No. cstc2016jcyjA0209), the Open Fund of the State Key Laboratory of Integrated Services Networks(No. ISN16-03), and the Fundamental Research Funds for the Central Universities(No.106112017CDJXY 500001).