1. Introduction

Pulsed coherent Doppler lidar plays an important role in clear-air atmosphere detection. Intensive progresses have been made in the last decades to improve the performance of Lidar in aspects of developing high-power optical amplification [1–3], low-noise optical detection [4] and all-fiber system stability [5]. However, the dilemma between range resolution and velocity accuracy remains as a key constrain in current pulsed coherent Doppler lidar. Traditional single frequency lidar (SFL) emits short pulses at a repetition of tens of kHz to reach a several-km detection range. Over the pulse repetition time (PRT), particles in the sensing volume usually move distances exceeding the laser coherent length, resulting in incoherent echoes of adjacent pulses. Thus, SFL applies Fast Fourier transformation (FFT) to contiguous samples within each pulse to get the Doppler spectrum [6]. In this way, the minimum achievable range resolution is determined by the sum of probing pulse length and coherent sampling length. Based on that, a way to improve the range resolution is to use fewer sampling points which, however, will lead to a bad spectral resolution. Another way is to use shorter pulses but will restrain the Lidar from efficiently measuring the estimated velocity. The main reason is that: the sensing volumes for two adjacent samples are staggered at a distance of sampling interval, so the ratio of common particles in adjacent sampling volumes is smaller for narrower pulses, which will result in severer contamination of the Doppler spectrum.

In order to improve the range resolution without deteriorating the velocity measurement sensitivity, some attempts were made in the last decades. Operations like zero-padding lead an interpolation effect of the original spectrum but do not physically improve the spectrum. Accumulation of spectral intensity can mitigate the impact of spectrum uncertainty, but at the expense of a decrease on the update rate of wind velocity measurement. For example, for a SFL possessing a laser pulse repetition frequency of 10 kHz, accumulation of 10,000 shots’ spectral intensity corresponds to a data update rate of 1s. Other algorithms like inverse techniques do help to achieve a higher resolution but have not considered the change of particles due to the movements of the physical sampling positions [7,8]. Noteworthy is that a so-called dual-frequency lidar (DFL) reported recently [9–12]. The beat frequency locates at microwave band thus DFL can adopt pulsed radar coherent processing procedures to get the Doppler spectrum [13]. The temporal window for coherent FFT process can be enlarged to achieve a high Doppler resolution without deteriorating range resolution. This coherent accumulation can effectively increase the processed spectrum intensity to M times with M pulses in use, making it more possible to detect weaker signals at a longer distance [14]. Apart from that, speckle noise can be greatly suppressed by introducing coherent dual-frequency signals [15].

Though DFL have already shown advantages in measuring solid targets [16,17], there are few researches aiming at distributed and soft target detection. To show the good potentials of DFL in detecting these targets, this paper focuses on comparing the performances of DFL and SFL in a fluctuated wind field under different conditions including wind field complexity, probing pulse width and signal to noise ratio (SNR), etc. Section 2 gives the Lidar echo formula and Doppler velocity retrieval algorithms. Section 3 presents a lot of comparisons on the simulated results of DFL and SFL.

2. Lidar signal and velocity retrieval algorithms

This section derivates the formula of Lidar signals in time domain and corresponding Doppler velocity estimating methods for traditional SFL and DFL.

2.1 Lidar signal in time domain

In real lidar systems, at least one stage of optical amplification is required to achieve sufficient emission pulse energy thus it is necessary to model the amplifier for the laser generation. Apart from that, laser diffraction, atmosphere absorption, backscattered radiation, optical mixing and quadratic detection are all included to obtain the Lidar signal formula.

2.1.1 Optical amplification model

Due to the advantages of low fiber loss, high atmosphere transmittance and safety for eyes, 1.5μm has been the most widely used laser band in wind detection Lidars. In terms of 1.55μm band, the erbium-doped fiber amplifier (EDFA) is used whose property can be characterized by the fiber parameters such as group velocity dispersion β₂, the third-order dispersion β₃ and nonlinear coefficient γ. To describe pulse propagation and amplification in EDFA, the generalized nonlinear Schrodinger equation (GNSE) used to describe the energy variation of laser pulse is

Table 1. Parameters of the EDFA model.

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Assuming the laser pulse before amplification is of Gaussian shape as:

2.1.2 Laser wave propagation model

Figure 2 shows the whole process of coherent lidar detection. All components are described in the Cartesian coordinate system (z,ρ) where ρ=(x,y). The light propagates along axis z with z=0 being the center of the telescope aperture. Vectors in the planes parallel to the telescope aperture, the light receiving plate (equals to the fiber optical circular (CIR)) and the photodetector (PD) are denoted as ${\boldsymbol \rho }^{\prime}$, ${\boldsymbol \rho }^{\prime\prime}$ and ${\boldsymbol \rho }^{\prime\prime\prime}$. Amplified light is divided into the probing and reference beams. Starting from the port 2 of the CIR, the probing pulses are emitted through the telescope. After expanding and collimating, the laser beam becomes Gaussian-shape in telescope aperture, then propagates through and senses the atmosphere volumes. The laser wave backscattered by the particles in the atmosphere is collected by the telescope and, after mixing with the reference beam at optical coupler 2 (OC2), reaches the PD. The process of laser beam from ${\boldsymbol \rho }^{\prime\prime}$ to ${\boldsymbol \rho }^{\prime}$ (①) meets the Fraunhofer diffraction while that from ${\boldsymbol \rho }^{\prime}$ to ${{\boldsymbol \rho }_i}$ obeys Fresnel diffraction [20].

 

Fig. 1. Output pulses from EDFA of different width.

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Fig. 2. Laser propagation path between lidar system and atmosphere.

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Since the Fraunhofer and Fresnel diffractions are reciprocal, the probing beam propagating from CIR to atmosphere is equivalent to the backpropagated reference beam. In other words, the coherent echo intensity can be calculated by multiplying the reference and probing laser field at the telescope aperture. Thus, the normalized coherent echo signal can be expressed as [21]

In which λ is the laser wavelength, ${a_0}$ is the beam radius determined at the e⁻¹ intensity level in the perpendicular plane of the telescope aperture, η is the quantum efficiency, hν is the photon energy, and h is Plank’s constant, B_F is the passband of PD, P_L is the reference beam power, α_i is the backscatter amplitude of the $i$ th particle. The atmospheric transmission $T({z_i}) = \exp [ - \int\limits_0^{{\textrm{z}_i}} {\sigma (r)dr} ]$ describes absorption and scattering by air molecules and aerosol particles along the propagation path, where $\sigma (r)$ is the radiation extinction coefficient. The three exponent terms: the phase ${\psi _i}\textrm{ = }\arg [{\tilde{I}_0}({z_i},{\boldsymbol{\mathrm{\rho}}_i}(t))]$ generally distributes evenly in the interval [0,2π], does not exert effective influence on the echo; the last term corresponds to the pulse shape of the received echo; the second term $4{\pi }\textrm{j}{z_i}(t)/\lambda$ reflects the instantaneous phase caused by the motion of the $i$ th particle located at ${z_i}(t)$, from which the Doppler frequency shift can be derived.

The operating principle of DFL is: the laser pulse containing two frequencies f₁, f₂ emits to the atmosphere and the received backscattered signal contains two Doppler frequency shifts Δ₁, Δ₂ proportional to f₁, f₂. The backscattered echoes containing frequencies f₁+Δ₁, f₂+Δ₂ and reference beams with frequencies f₁, f₂ are combined together in OC and then sent to the PD to undergo a squaring operation. Since the two frequencies f₁, f₂ are coherent, optical interference will occur, if the bandwidth of PD is narrow, only beams with frequencies of Δ₁ and Δ₂ can pass through. The signals are then acquired by analog-to-digital converter (ADC) and mixed by calculating (Δ₁+Δ₂)². The lowest frequency term Δ₂–Δ₁ corresponds to the Doppler shifted signal of the equivalent microwave beat frequency. Thus, the coherent length should be related to the beat frequency instead of the laser, and echoes between pulses are generally coherent. For dual-frequency pulsed signals, assuming that the backscattering coefficient of aerosol particles, atmospheric transmittance and quantum efficiency of detector are the same for the two frequencies, then all the terms in DFL echoes are the same except the wave number changes from $k = {{2{\pi }} / \lambda }$ to ${{2{\pi }({f_1} - {f_2})} / c}$, bringing difference to the Doppler phase shift term as:

It is noted that, several hypotheses are given in deriving formulas (4) and (5):

The major parameters mentioned above are shown in Table 2.

Table 2. Parameters in the Lidar echo equation

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A typical ${I_0}({z_i},{\boldsymbol{\mathrm{\rho}}_i})$ along propagating axis z and transverse axis ρ is shown in Fig. 3. For a given initial two-dimensional position to each particle and a Gaussian-shape wind field described in Eq. (13) in which velocity varies with z, after propagation, intensities of the received echoes can reduce by 20dB or even more. Although the phase of scattered signal by each particle varies between 0 and 2π randomly, the phase superposition of all scattered signals from a large number of particles generally approaches π. Thus, the simulated signal intensities are not affected by the random phase, but depend mainly on the atmospheric transmission that is proportional to the transmission distance. Thus, the simulated signal intensities should be almost identical for different pulses.

 

Fig. 3. Intensity of I₀.

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2.2 Doppler spectra for SFL and DFL

Detailed echo sampling and processing methods of SFL and DFL are displayed in Fig. 4 and Fig. 5 respectively. In Fig. 4, the two straight lines $r = ct$ and $r = c(t - {T_p})$ denote the propagation routes of the pulse front edge and trailing edge in the time-range coordinates, where ${T_p}\textrm{ = 2}{\sigma _p}$ is the pulse width. On the bottom is the pulse temporal-amplitude envelope with a pulse width of Tp. The dotted lines with a slope of -c, indicate the backscattering of laser wave from particles to the Lidar. The received echo at each moment ${T_p}\textrm{ + }i{T_s}$ is the summation of the particle scattering signals within a pulse width range, weighted according to the pulse waveform. These Lidar echoes carry information about the radial velocities of aerosol particles entrained by the background wind field.

 

Fig. 4. Sampling and processing diagram of SFL in the time-range coordinate.

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Fig. 5. Sampling and processing diagram of DFL in the time-range coordinate.

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For SFL, after (N+1)-time continuous sampling with the time interval of ${T_s}$, these contiguous sampling sequences Z_s(t_m,k) ∼ Z_s(t_m,k + N) from the k^th sample of pulse in time t_m are used to determine the estimation of autocorrelation function as:

Then spectral density of the echo signal power can be estimated by the Fourier Transformation of the autocorrelation function as:

Weighted average is conducted based on the averaged spectral density to get the Doppler frequency shift, then according to Doppler formula, the estimated velocity is ${V_g} = \frac{\lambda }{2} \cdot {{\sum\limits_n {{f_n} \cdot {{\bar{S}}_s}({f_n})} } / {\sum\limits_n {{{\bar{S}}_s}({f_n})} }}$. Thus the minimum processing range unit, typically regarded as the range resolution is $({T_p}\textrm{ + }N{T_s})c/2$. The shared region of sampling particles inside each range bin occupies $({T_p} - N{T_s})c/2$. In this way, adjacent samples used for coherence in SFL correspond to scattered particles belonging to different volumes. Moreover, the retrieved velocity is the uneven average of the wind speed in the sampling area. The denser sampling in the central area enables a higher velocity resolution while the sparse sampling in the edge of processing unit lowers the velocity resolution. Inaccuracy of spectrum estimation may also exist in the sampling and processing way of SFL. As a windowing operation is implied in the classic spectrum estimation method, energy leakage will inevitably appear due to the presence of side lobes of the window spectrum, making the estimation of frequency unreliable. Apart from that, when the number of sampling points is small, the frequency resolution is low. The modern spectral estimation method is highly dependent on the order of the prediction model and performs bad either when the number of sampling points is small.

The pulse-to-pulse coherence processing method adopted by DFL is shown in Fig. 5. Particle echoes from the i^th sample of (M+1) PRTs Z_D(0,i) ∼ Z_D(MPRT,i) are used to estimate the Doppler spectrum with FFT:

N is the number of pulse groups used to do incoherent accumulation. The angular frequency is ${\omega _D} = \frac{{2\pi n}}{{M\textrm{ + }1}} \cdot \frac{1}{{PRT}}$, where (M+1) is the number of coherent samples being used. Since pulse-to-pulse coherence is conduct in DFL, ${\omega _D}$ depends on pulse repetition frequency ${1 / {PRT}}$ instead of sampling frequency. Similarly, estimated wind velocity can be calculated according to the weighted Doppler frequency shift of DFL. Using this radar-processing method, the spectrum over the range resolution of ${T_p}c/2$ is available at sampling interval. Since the movement of particles resulting from the time delay of (M+1) PRT is slight compared with that in SFL, it can be considered that the processed echoes come from particles locating within the same region. Based on the above analysis, DFL is supposed to have finer range resolution determined only by the length of probing pulses, and avoid the velocity distortion from movement of sampling position.

To sum up, theoretically, the Doppler frequency shift estimated from the spectral density corresponds to a weighted summation of radial velocities of the particles assembling in the sensing volume. However, the unique sampling and processing ways of SFL limited by short coherence length, bring inevitable velocity error as well as dilemma of velocity and range resolution. For DFL, since the beat frequency locates at microwave band, echoes can be dealt by coherent radar processing way, which may improve the velocity resolution without deteriorating the range resolution. Combing the echo signal model and processing estimators, performance of SFL and DFL in measuring complex wind field can be assessed and compared in detail.

3. Simulation results and discussion

In this section, simulation results for SFL and DFL under different parameters/conditions are discussed and compared.

3.1 Performance analysis of traditional SFL

In this section, we analyze the dependence of velocity error on different factors, i.e. wind field distribution, pulse width, sampling rate.

3.1.1 Dependence of velocity error on the complexity of the wind field

Described in Eq. (13) is a Gaussian-shaped wind field which becomes more sharply-varying if the variance ${\delta ^2}$ decreases. As plotted in Fig. 6(a), the Gaussian-shaped wind centered at 3km is considered in this simulation where the maximum velocity is 20m/s ($Vc$). When ${\delta ^2}\textrm{ = 100}$, the velocity drop between the center and the edge of processing area is around 20m/s.

In the simulation, pulses of 200ns width are emitted with a 30m effective pulse length (${T_p}c/2$). The pulse repetition frequency is 20kHz. The sampling frequency is 100MHz corresponding to 1.5m sampling interval, thus, 7 samples are needed to measure the range resolution of 39m according to $({T_p}\textrm{ + }N{T_s})c/2$. As shown in Fig. 6(a), each sample covers a length of pulse length with the center marked by the red cross. Velocity spectra obtained by accumulating 3200 pulses is shown in Fig. 6(b). The theoretical wind velocities retrieved by integrating the wind field (${V_g}$) are 8.82, 11.96 and 13.78 m/s when the variance ${\delta ^2}$ drops from 300 to 100. Meanwhile, the velocity spectrum broadens gradually and the absolute error rises from 1.05, 1.60 to 2.31 m/s. In other words, although the range resolution remains the same, it is hard to accurately detect more complex wind field using the same probing pulse width as well as number of sampling points for SFL framework.

 

Fig. 6. The aerosol particle velocities under three normal distributions (a); the velocity spectra of SFL corresponding to the three distributions (b).

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While detecting field exceeding one range resolution, the overlapping method allows one to obtain ensemble-mean velocity within pulse width in a sampling interval $Ts$. In order to investigate performance of SFL during continuous processing, a dual-profile wind field model contains two small-size profiles (less than 39m) over a large range of 100m is set as shown in Fig. 7(a). The two envelopes are still Gaussian with a certain distance and the sizes can be controlled by the variance ${\delta ^2}$(this time ${\delta ^2}\textrm{ = 100}$). For a case with a pulse duration of 200ns, applying FFT to every 7 contiguous samples and accumulating 3200 PRTs, the calculated velocity distribution displays in Fig. 7(b). The autocorrelation coefficient of the calculated and real velocity is R=0.9271. The measured positive and negative peak velocities are all obviously lower than theoretical ones. This means that the current SFL scheme is not qualified to well retrieve the Doppler velocity when complex wind field is taken into account.

 

Fig. 7. Wind field models containing two small-size profiles (a) and comparison between theoretical and calculated velocities (b).

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3.1.2 Dependence of velocity error on pulse width variation

Furthermore, pulse width is reduced to increase the number of sampling points in order to find whether the detection accuracy can be improved. Similarly, the wind field is set as Vel_Dist3 in Fig. 6(a) with the velocity variance and detection range being ${\delta ^2}\textrm{ = 300}$ and 39m, respectively. The sampling frequency remains as 100MHz when the probing pulse duration varies from 20ns to 200ns. As shown in Fig. 8(a), the spectrum of 20ns-39m (the first item represents the pulse width, the second item represents the range resolution) is observed to be with a big variance where 25 contiguous sampling points are used to meet the present range resolution of 39m. Though the number of sampling points used for FFT calculation has been increased to 25 when a narrower pulse width (20ns) is taken into account, the performance of estimated velocity is not improved. The main reason is that, for this case, there is no shared sensing volume for the 25 samples. This means that the scattered wave of these samples are from different group of particles, which will inevitably result in a bad coherence. Utilizing a large pulse width, the velocity spectrum of 200ns-39m becomes smoother and narrower, presenting a single peak which corresponds to a velocity close to $Vc$. However, adopting wide pulse makes it hard to get a good range resolution even if fewer sampling points are used.

 

Fig. 8. Velocity spectra of different pulse width under a same range resolution (a); two types of velocity errors versus pulse width (b). Legends in (a): among the first three legends, the first item represents the pulse width, the second item represents the range resolution, legends $Vg$ and $Vc$ represent the integrated and central velocity of the preset wind field, respectively. The left Y-axis in (b) is the difference between the estimated velocity and $Vg$, while the right one is the difference between the estimated velocity and $Vc$.

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According to Fig. 8(b), the dependence of velocity error on pulse width is further explained. Fixing the detection range and varying the pulse width, the difference of estimated velocity $Ve$ and the integral wind speed $Vg$ is expressed as $V_g^{error}$ on the left, and the difference between $Ve$ and $Vc$ is shown as $V_c^{error}$ on the right. $V_g^{error}$ and $V_c^{error}$ show an opposite varying trend along with the increase of pulse width. The error changing process can be divided into several stages: Firstly, when the pulse is narrow (40-140ns), the sampling process is more equivalent to sweeping the entire detection range via a single pulse. The sampling echoes have less overlapped region, thus the measured velocity is closer to the integral value $Vg$. While the pulse width enlarges, the number of particles being repeatedly sampled increases. correspondingly, the estimated velocity starts from near $Vg$ and then steadily approaches $Vc$. Secondly, when the pulse width becomes wider (140-220ns), shared region between samples appears. When the proportion of shared region increases, the error of measured velocity will gradually decrease. Noteworthy is that the error changes in the left and right ends throughout the figure. When the pulse is too narrow, particles within the sampling echoes change totally, causing the appearance of velocity error singularity in 20ns as shown in Fig. 8(b). On the other hand, along with the broadening of pulse width, sampling points that used in FFT drops. If the pulse width is too large, number of samples will be too small to get a high velocity accuracy, which explains the increment of $V_g^{error}$ for pulse width 220-260ns when complex wind field is taken into account. To summarize, a narrow pulse width combining with more sampling points will result in a smaller $V_g^{error}$, and a large ratio of overlapping particles can also lead to small $V_g^{error}$. Therefore, a trade-off has to be made between the pulse duration and number of adjacent echoes calculating for FFT while the SFL scheme is adopted.

3.1.3 Dependence of velocity error on sampling rate

Finally, the sampling rate is varied to investigate the influence of the number of points used in FFT. Seen from Fig. 9, except for 50 MHz, velocity error keeps steady in larger sampling rates under the combination of these two pulse widths and detection distances. So the way of increasing the sampling rate to add the number of sampling points, cannot reduce the velocity error. As discussed in section 3.1.2, the pulse duration influences the velocity error obviously, and the ratio of overlapping particles in each range resolution also has some impact on the velocity error. For pulse width of 200ns, number of samples increases from 6 to 16 accordingly to meet the range resolution assumption (39m to 54m), which makes the decrease of the ratio of the shared region in the given processing unit. Thus, stabilized velocity error almost doubles from 200ns-39m to 200ns-54m. On the contrary, for pulse width of 100ns, whether using 16 or 26 samples to conduct FFT (corresponds to 39m or 54m range resolution), there is no shared region among the detected particles in each processing unit. So, the velocity error remains the same level between 100ns-39m and 100ns-54m.

 

Fig. 9. velocity error versus sampling rate under different combinations of pulse width and detection range.

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3.2 Performance of DFL

As described in Section 3.1, DFL can process the retrieved pulse-to-pulse echoes coherently, which makes it possible to obtain high range resolution and accurate velocity. Detailed analysis is as follows.

3.2.1 Dependence of velocity error on pulse width variation

In this section, the dual-profile wind field described in Fig. 7(a) is taken into account. We also use 3200 pulses to get the Doppler spectrum of a given range bin. The frequency difference used in DFL is 20 GHz. The pulses are divided into 100 groups, and 32 pulses in each group are used to get the Doppler spectrum with traditional radar data processing framework, then the spectra of these 100 groups are accumulated to get the final spectrum of this range bin. Other parameters remain the same as in SFL. Change the probing pulse width (20ns, 100ns, 200ns) and fix the range resolution as 39m, then the obtained Doppler velocities are shown in Fig. 10.

 

Fig. 10. Doppler-velocity profiles of DFL under different pulse width.

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When the probing pulse width is 200 ns, the retrieved velocity varies slighter than the theoretical curve around in the positive and negative peaks. Obviously, the probing pulse width determines the range-resolution in DFL velocity measurement and the calculated velocity curve fits the theoretical better when using narrow pulses because the averaged range bin is thinner. Especially, around the peaks and valleys where wind speed changes dramatically, we can still get good estimate of velocity if the pulse duration is set as 20ns.

3.2.2 Dependence of velocity error on the complexity of the wind field

Seen from Fig. 11(a), a dual-profile wind field accompanied with some fluctuations in sine-shape $flu\textrm{ = sine(}R\textrm{)}$ is used in DFL simulation to increase the complexity of wind field. The probing pulse width is 20ns, which corresponds to an effective pulse length of 3m. While the sampling is 1.5m, 65 samples are needed to measure the whole 100m-range. For wind fields under different conditions, the retrieved velocity profile is in good agreement with theoretical curve. For the cases with more disturbances, the correlation coefficient R between the calculated and theoretical velocity reaches 0.9988 in Fig. 11(b), which is much better than that in Fig. 7(b). These phenomena well verify the good performance of the DFL scheme.

 

Fig. 11. Wind field models containing two small-size profiles (a) and comparison between theoretical and calculated velocities under the two wind conditions (b). One wind field is set with ${\delta ^2}\textrm{ = 100}$ and sine-shape fluctuations, the other wind field is under ${\delta ^2}\textrm{ = 300}$ without fluctuations. The calculated velocity in (b) is under condition of ${\delta ^2}\textrm{ = 100}$ with fluctuations.

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3.2.3 Dependence of velocity error on the number of pulses used in FFT for DFL

Generally speaking, when more pulses, which correspond to a longer coherent time, are used to get the Doppler spectrum with FFT, the spectral width is supposed to be thinner. This phenomenon holds for the data processing in DFL. As shown in Fig. 12(a), the Doppler spectrum in each range bin becomes thinner when more consecutive pulses are used to obtain the spectrum with FFT, which is helpful for better extracting the Doppler velocity. As displayed in Fig. 12(b), for different pulse durations, the mean velocity error among all samples gradually decreases along with the increase of number of adopted coherent pulses. In the case of wide pulses, the velocity averaged error is generally large and fluctuates greatly while different number of coherent pulses are in use. But all in all, the impact of pulse width on velocity measurement is relatively greater than the number of coherent pulses. However, considering the background wind field contains sharply-varying small profiles, velocity error of around 0.2m/s is already a quite satisfactory result and hard to achieve under SFL scheme.

 

Fig. 12. Accumulated DFL Spectrum along the range (a), the central red line is theoretical wind field and the white horizontal line divides each sample; mean error among all range bins versus number of coherent pulses (b).

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3.3 Gain of DFL on SNR compared to SFL scheme

Apart from the improvement on range resolution, velocity accuracy and ability in detecting complex wind field, DFL scheme has the potential to detect further and weaker echoes than SFL, because the DFL scheme uses coherent integration of spectrum rather than the incoherent integration used in SFL scheme.

3.3.1 Dependence of spectrum power intensity on accumulative number

According to radar data processing theory [13], DFL adopts coherent accumulation of M consecutive pulses to get the Doppler spectrum which may increase the spectrum intensity P_DF² by M² times. While the incoherent accumulation in SFL can only increase the spectrum intensity P_SF² by M∼M² times and the gain turns closer to M when sufficient pulses are used. If no accumulation of spectra is used when the number of FFT pulses varies from 0 to 128, the ratio of spectral power between DFL (P_DF) and SFL mode (P_SF) is demonstrated in Fig. 13. When the pulse width varies among 20-200ns, the value of P_DF/P_SF is less than $\sqrt M$ when a small number of coherent pulses are in use, but the ratio becomes larger than $\sqrt M$ with more used coherent pulses. Especially for 20ns pulse width, P_DF/P_SF overtakes M when the number of coherent accumulations exceeds 64, indicating a good coherent effect. Therefore, by adopting radar processing method, DFL can obtain stronger echo signal which makes it possible to get a longer detection range.

 

Fig. 13. Ratio between DFL and SFL spectral power against number of FFT pulses.

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3.3.2 Dependence of velocity error on SNR

Furthermore, noises are added in the echoes to compare detection ability of SFL and DFL under noise environment. The noise intensity (${I_n}$) is set by dividing the echo signal intensity in the central sensing area and a given SNR. Combining the noise ($Noise\textrm{ = }{I_n} \cdot \textrm{(randn(0,}{N_{particles}}\textrm{) + j} \cdot \textrm{randn(0,}{N_{particles}}\textrm{))}$) and coherent signal $Zs$ yields the received echoes. 100m-long dual-profile wind field in ${\delta ^2}\textrm{ = 100}$(same as described in Fig. 7(a)) is used with the sampling rate being 100MHz. 7 adjacent sampling points and 32 consecutive laser pulses are used to do FFT in SFL and DFL respectively. SFL accumulates 320 pulses and DFL perform 10 groups of incoherent spectrum accumulation. For the case of 20ns pulse width, in DFL, the range resolution is 3m, and the sample interval is 1.5m, 65 sampling points are required to cover the 100m wind field. The mean velocity errors of all 65 samples under DFL and SFL processing methods are shown in Fig. 14(a). The trends of the two error curves can be divided into 3 regions: in Region 1 where the SNR is low (around -25 to -9 dB), SFL and DFL both perform bad with almost the same absolute velocity error of 5∼6 m/s; along with the growth of SNR in Region 2, the velocity errors of DFL and SFL both decline significantly but the mean velocity error of DFL experiences a larger decline rate; in Region 3 where the SNR exceeds 12 dB, errors of SFL and DFL both remain stable at 3 m/s and 0.3 m/s respectively with slight fluctuations. The minimum averaged velocity error of SFL is ten times larger than that of DFL. To sum up, compared with SFL, DFL allows to get a stable and accurate detection in lower SNR.

 

Fig. 14. Mean velocity error of SFL and DFL versus SNR.

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In order to evaluate the potential performance of DFL and SFL in an environment with strong noise interference, the accumulated SFL and DFL spectra under SNR = 15 dB and SNR= -15 dB is shown in Fig. 15(a) and (b), respectively. The white lines parallel to the velocity axis demarcates each sampling interval. When the SNR is relatively high, the velocity results of DFL almost restore the set wind velocity. Meanwhile the spectra width of SFL is wider and the center of the spectra is farther away from the set velocity. Under SNR=-15dB, although the average measuring errors under the two methods are both close to 6m/s in Fig. 14 Region 1, SFL in the left of Fig. 15(b) possesses a messier spectrum obviously. For DFL on the right, the velocity distribution along range can be seen to relatively match the preset wind field. Thanks to the coherent accumulation, processed echo from DFL is enlarged more times under the same SNR, enable a long-range detection with higher accuracy.

 

Fig. 15. Accumulated SFL and DFL spectrum along the range under SNR=15 dB (a) and SNR=–15 dB (b), the central red line is the theoretical wind field and the white horizontal line divides each sample.

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4. Conclusions

Based on the analysis on traditional SFL, this paper proposes a DFL scheme which uses the radar-processing algorithms for detecting complex wind field. Current SFL inevitably brings velocity error because it uses adjacent samples rather than adjacent pulses to obtain the Doppler spectra. In details, sampling particles used to get the Doppler spectrum of a range bin belongs to different detection volumes, making the ensembled-mean velocity offset from center of each range resolution. Also, range resolution is hard to improve due to the limitation of pulse width and necessary-used sample points.

The frequency difference locating in the radar band allows DFL to conduct pulse-to-pulse coherence and sufficient coherent accumulation. Taking advantage of this processing scheme, DFL not only possesses high range resolution, velocity accuracy and ability in detecting complex wind field, but also performs far exceeding SFL in relatively low SNR conditions if a narrow pulse is used.

All in all, theoretical analysis of DFL and SFL schemes in this paper shows the preferable performance of DFL in detecting complex wind field with both high range and velocity resolutions, as well as its good adaption to traditional low SNR environments. Theoretically, if high quality of Dual-frequency signal can be generated, and the transmission, reception and process of the signal are all in good conditions, high coherence between pulses should remain. However, the coherence might degenerate due to the nonlinear and other unfriendly effects in practice. This is an issue deserving special attention, and efforts will be made to investigate these effects in detail in our near future work schedule.