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Channel estimation is a challenging task, especially in high mobility applications due to the rapid variation of the propagation environment. This paper presents a new technique that exploits past channel impulse responses (CIRs) in order to trace and compensate Doppler frequency in mobile applications, enabling robust estimation of time-varying channel. Based on the fact that channel taps at different time instants can be fitted with a sinusoidal wave, a joint estimator is proposed to estimate the channel parameters. Therefore, the efficiency of the channel estimation can be improved and stringent delay requirements for the communication systems can also be satisfied. Simulation results show that system performance in terms of bit error rate (BER) is significantly improved with the proposed algorithm.

Channel estimation is of crucial importance for reliable coherent detection in high mobility applications, such as vehicular-to-vehicular (V2V) or vehicular-to-infrastructure (V2I) communications [

One of the first studies reported in the literature for the estimation of Doppler frequency is [

In this paper, we have studied a joint CIR and Doppler frequency estimator that exploit multiple observations of the past CIRs, which can be used to track the CIR in the current estimation period. At first, a multiframe time-domain correlation technique is used to obtain the time-domain estimates of the past CIRs, as shown in Figure

Multiframe based observation of channel impulse responses.

Note that the proposed method does not rely on the estimation of ACF as in conventional techniques, that is, prone to erroneous estimation of Doppler due to model imperfections such as presence of line-of-sight component and nonisotropic scattering. In addition, the proposed method uses local time-domain pilot signals to obtain multiframe observations of the channel, therefore free of model imperfections, that is, a major drawback for the conventional techniques [

The rest of the paper is organized as follows. Section

Let us consider a multipath channel as shown in Figure

Typical multipath channel impulse responses observed at different time instants.

Over a short interval of time, for example, when observation times

A multiframe technique is used to obtain multiple observations of the past CIRs [

In order to obtain the reference CIR, we have used time-domain channel estimation for the OFDM system, tailored for DVB-T system [

Let us consider that the channel samples observed at time instants

Let us assume that an estimate of Doppler frequency in iteration

Similarly,

Using the above two approximations in (

The above equation is nonlinear in the parameters, but it may be linearized using the assumption that Doppler is constant over the observation period; that is,

It is obvious that in order to obtain a unique solution for each of the parameters, at least three observations are necessary. The simple technique is to repeatedly solve the above linear system; that is, at iteration

The algorithm follows an iterative process to find the parameters that minimize the sum of squared differences as the following:

Once

The initial guess for

For a moving vehicle, there could be a constrained set on the Doppler frequency based on the mobility pattern of the vehicle. Basically, it could be determined by the maximum acceleration or deceleration of the vehicle. Therefore, the Doppler shift can be initialized based on the study of mobility pattern in a particular scenario, that is, highway. The constrained can be formulated as

If the Doppler phase remains constant over the observation period, taking the difference between the phase of the successive channel estimate would leave the initial phase. For a faster convergence, guess for initial phase can be computed from the differential phase rotations obtained from the past CIRs as follows:

In general, these successive differences for

It should be noted that the convergence would be much faster than the conventional joint estimation technique, as in the conventional technique only one estimation is used to obtain the initial guesses of the channel parameters.

The performance of channel estimation following this technique will be determined by the number of observations obtained as well as the estimation error introduced in the past observations. Let us consider that past observed CIR has an error

It is important that we study the number of observations needed to obtain certain performance threshold of the estimator. For a certain CRB, the above equation can be rewritten as

The above solutions provide the bounds on the number of the observations required in order to maintain the CRB for a given SNR level and sampling frequency.

In this section, we will study the change in Doppler frequency over the observation period and its impact on the performance of the estimator. If the Doppler frequency does not change appreciably over the observation period, the previous technique can be used to estimate the channel parameters. However, the Doppler frequency may change over the observation period, depending on the mobility pattern of the users and angle of arrivals for each path.

It is obvious that the speed of a vehicle is a time-varying function and so is the Doppler frequency for each path. The relationship between the change of Doppler frequency and the speed of a vehicle can be derived as follows [

The above equation would determine the variation of Doppler frequency for each multipath in a CIR over the time difference between successive CIRs. Under high mobility application, in fact, a short interval of time may introduce a significant variation of Doppler shifts for the successive CIRs depending on the duration of the data frame structure; however, change in Doppler frequency will be dominated by the change in the angle of arrivals for each multipath.

Therefore, considering the variation in Doppler, (

The small variation in Doppler shift over the observation period can be considered as a noise in the estimation process. Therefore, the noise introduced in the estimation process will be higher than the stable Doppler case. Let us consider that the variance of the noise in this case is given by

Digital Video Broadcasting-Terrestrial (DVB-T) system is used to evaluate the performance of the proposed technique. It is assumed in the simulation that the past channel responses may experience a constant or varying Doppler under a receiver velocity from 50 km/h to 100 km/h. DVB-T standard transmission for 2 K mode with 8 MHz bandwidth and 800 MHz carrier frequency is used for the simulation of the proposed technique. The sampling period for the chosen data transmission is 7/64

Figure

Comparison of estimated Doppler frequency with true Doppler in presence of different estimation errors (constant Doppler case).

Figure

Comparison of estimated Doppler frequency with true Doppler in presence of different estimation errors (varying Doppler case).

Figure

Cramer-Rao bound on the variance of the proposed channel estimator.

Figure

Improvement of DVB-T system performance in terms of BER with the proposed algorithm in ITU Vehicular Channel Model B.

Figure

Improvement of DVB-T system performance in terms of BER with the proposed algorithm for an arbitrary channel, under a receiver mobility of 100 km/h.

In this paper, a robust Doppler frequency and channel estimation technique is presented that is, suitable for mobile communications. The technique exploits past observed CIRs in order to jointly estimate channel parameters. It is found that the estimated Doppler frequency is very close to the known Doppler frequency as observed in the simulation results. Further, the Doppler frequency estimation algorithm has been evaluated with estimation error variance introduced by the past CIRs. As expected, it is found that with the decrease of estimation error, the Doppler frequency estimation becomes more accurate. CRB of the proposed channel estimator is also evaluated with the number of past observations under different SNR values. It is observed that even in highly mobile channels, with the compensation of Doppler frequency-induced impairment, the system BER performance can be significantly improved. In addition, because of the joint estimation of the channel parameters, the estimation is more efficient and much simpler to implement. The proposed technique is suitable for emerging V2V or V2I communication systems, where delay requirement and high reliability are essential.

This work was supported in part by a Canada Graduate Scholarship—Doctoral (CGSD) from the Natural Sciences and Engineering Research Council (NSERC), Canada.