**4.7 Vertical wind velocity measurement using FFT pre-processing algorithm**

Received signals are pre-processed on the FPGA by dividing backscattered signals into 128 samples per a range gate, corresponding to a 48 m range resolution,

**Figure 6.** *Time domain scattered signal off a hard target.*

**Figure 7.** *Time domain scattered signal off the atmosphere.*

#### **Figure 8.**

*The research van where the Doppler lidar instrument is installed for field measurements.*

ranging from 96 m to approximately 3 km. Power spectra of the gated signals are estimated by calculating the FFT and then accumulating the resulted power spectrum for 10,000 shots. Accumulated power spectra are streamed to the host PC for further processing and archiving. Wind velocities are calculated by estimating the Doppler frequency shift of the received signals' power spectrum. Three different techniques are used for velocity estimate; spectral peak search, power spectrum peak curve fitting, and MLE algorithm.

Range correcting received signals' power allows for comparison our results with

*Ratio of received signals power to shot noise power V.s. time and height measured at CCNY on August, 17th,*

*Vertical wind velocity profile (m/s) measured at CCNY on August, 17th, 2011 from 14:35–16:35 PM EDT*

the results of a 1 μm direct detection lidar, which was operated at the remote sensing laboratory of the City College of New York during the same time of operation. **Figure 11A** and **B** show a good agreement of signal intensity profile's and cloud patterns with that of the CDL at 14:30, 15:50 and 16:15. It is also noticed that signal intensity increased significantly at a height of approximately 2700 m at 14:30 and 16:20 due to clouds at that height. Both lidars also show a gradual increase of aerosol concentration as a function of time between 16:00 and 16:30. The Doppler lidar's signals power spectrum comparison with the direct detection measurements proves that the obtained power spectrum is valid, and as a result, the frequency shift has to be due to: (a) RF signals going into the AOMs, and (b) Doppler shift caused by wind. Since the LO is stable (laser's line width is approximately 3 kHz), and the jitter between the RF signal and the ADC's clock is less than 100 kHz, then measured frequency shifts are solely due to Doppler shifts caused by wind velocity. As mentioned in Section 2, the power spectrum of received signals needs to be corrected for the detector's non-flat gain shape. This is done by dividing the power spectrum of received signals by a power spectrum of reference signals. The reference signals are obtained using the detector while LO is turned on and no received signals are present (final amplifier is turned off), i.e. this power spectrum only

**Figure 9.**

**Figure 10.**

**17**

*estimated by Gaussian curve fitting.*

*Coherent Doppler Lidar for Wind Sensing DOI: http://dx.doi.org/10.5772/intechopen.91811*

*2011 from 14:35–16:35 PM EDT.*

represents shot noise. The SNR can be represented as follows:

In the following section, vertical measurement results of wind velocity measured during the month of August of 2011 are introduced and discussed. The vertical wind velocity profile was measured on August 17th, 2011 from 14:35-to-16:35 EDT. Scattered signals' power spectrum is flattened by dividing it by the power spectrum of input signals to the photo-detector when no scattered signals are present. A signal intensity threshold is chosen below which any returned signals power spectrum is ignored. In **Figure 9**, vertical wind velocity is estimated by fitting the power spectrum profile around the peak value to a Gaussian curve shape and finding the centroid of the fitted shape. It is also shown that updrafts and downdrafts are very visible, which is typical weather condition during a summer afternoon.

Backscattered signals' power was estimated by integrating the area under the power spectrum curve, **Figure 10**. The signal power was then range corrected by dividing estimated power by the overlap integral function given that the laser beam was focused at a known distance (approximately 2 km), which was determined by scattering off a hard target (clouds).

#### **Figure 9.**

*Vertical wind velocity profile (m/s) measured at CCNY on August, 17th, 2011 from 14:35–16:35 PM EDT estimated by Gaussian curve fitting.*

#### **Figure 10.**

ranging from 96 m to approximately 3 km. Power spectra of the gated signals are estimated by calculating the FFT and then accumulating the resulted power spectrum for 10,000 shots. Accumulated power spectra are streamed to the host PC for further processing and archiving. Wind velocities are calculated by estimating the Doppler frequency shift of the received signals' power spectrum. Three different techniques are used for velocity estimate; spectral peak search, power spectrum

*The research van where the Doppler lidar instrument is installed for field measurements.*

*Spatial Variability in Environmental Science - Patterns, Processes, and Analyses*

In the following section, vertical measurement results of wind velocity measured during the month of August of 2011 are introduced and discussed. The vertical wind velocity profile was measured on August 17th, 2011 from 14:35-to-16:35 EDT. Scattered signals' power spectrum is flattened by dividing it by the power spectrum of input signals to the photo-detector when no scattered signals are present. A signal intensity threshold is chosen below which any returned signals power spectrum is ignored. In **Figure 9**, vertical wind velocity is estimated by fitting the power spectrum profile around the peak value to a Gaussian curve shape and finding the centroid of the fitted shape. It is also shown that updrafts and downdrafts are very

visible, which is typical weather condition during a summer afternoon.

Backscattered signals' power was estimated by integrating the area under the power spectrum curve, **Figure 10**. The signal power was then range corrected by dividing estimated power by the overlap integral function given that the laser beam was focused at a known distance (approximately 2 km), which was determined by

peak curve fitting, and MLE algorithm.

*Time domain scattered signal off the atmosphere.*

**Figure 7.**

**Figure 8.**

**16**

scattering off a hard target (clouds).

*Ratio of received signals power to shot noise power V.s. time and height measured at CCNY on August, 17th, 2011 from 14:35–16:35 PM EDT.*

Range correcting received signals' power allows for comparison our results with the results of a 1 μm direct detection lidar, which was operated at the remote sensing laboratory of the City College of New York during the same time of operation. **Figure 11A** and **B** show a good agreement of signal intensity profile's and cloud patterns with that of the CDL at 14:30, 15:50 and 16:15. It is also noticed that signal intensity increased significantly at a height of approximately 2700 m at 14:30 and 16:20 due to clouds at that height. Both lidars also show a gradual increase of aerosol concentration as a function of time between 16:00 and 16:30. The Doppler lidar's signals power spectrum comparison with the direct detection measurements proves that the obtained power spectrum is valid, and as a result, the frequency shift has to be due to: (a) RF signals going into the AOMs, and (b) Doppler shift caused by wind. Since the LO is stable (laser's line width is approximately 3 kHz), and the jitter between the RF signal and the ADC's clock is less than 100 kHz, then measured frequency shifts are solely due to Doppler shifts caused by wind velocity.

As mentioned in Section 2, the power spectrum of received signals needs to be corrected for the detector's non-flat gain shape. This is done by dividing the power spectrum of received signals by a power spectrum of reference signals. The reference signals are obtained using the detector while LO is turned on and no received signals are present (final amplifier is turned off), i.e. this power spectrum only represents shot noise. The SNR can be represented as follows:

#### **Figure 11.**

*Range corrected backscattered signal power V.s. time and height (a) and the 1 μm direct detection lidar signal power vs. height and time (b). Both signals power profiles show a good agreement around 14:35, 15:60, and 16:15, where clouds' patterns are observed at the same heights. Aerosols concentration profiles also show a good agreement in the two measurements.*

$$\text{SNR} = \frac{P\_{\text{sig}}^{(N)}}{P\_{\text{noise}}} \tag{32}$$

**5. FPGA programming and wind measurements analyzed using**

*R*ð Þ¼ *τ*

*G f* ð Þ¼

is the Fourier transform (power spectrum).

ð ∞

�∞

∞ð

*R*ð Þ*τ e*

where; *f t*ð Þ is a time domain signal, *R*ð Þ*τ* is the signal's autocorrelation, and *G f* ð Þ

Changing range gates (varying spatial resolution) is an advantage that previous FFT pre-processing algorithm does not have. In this technique (autocorrelation), digitized received signals are split into two paths. The first path is mixed with a cosine signal oscillating at 84 MHz to produce an in-phase (I) component; the other path is mixed with a sine signal oscillating at 84 MHz to produce a quadrature (Q )

**5.1 Autocorrelation (analog complex demodulator) pre-processing algorithm**

*Autocorrelation algorithm block diagram as implemented on the FPGA to produce an in-phase (I) and a*

Mixing the received signals (oscillating around 84 MHz +/� Doppler shift) with an 84 MHz cosine and sine waves produces two output signals; a high frequency (sum of the two frequencies) component and low frequency (difference of the two frequencies) component (the Doppler shift). A low-pass, finite impulse response (FIR), filter is used on each path to get rid of the unwanted high frequency. Filtered signals are then down-sampled (decimated) by a factor of 4, which will reduce our original sampling period from 2.5 n.s (400 MHz) to 10 n.s (100 MHz). This down conversion reduces the maximum detectable frequency (according to Nyquest theorem) to 50 MHz, which corresponds to a radial velocity of approximately 38 m/s. The resulting complex time sequence *d(n) = di(n) + j dq(n)* is input to the (M)-lag autocorrelator circuit,

�∞

The objective of processing received signals using this technique is to have the ability to change the spatial resolution. This is achieved by calculating the autocorrelation of received signals and using it to calculate the power spectrum of any desired range gate [24]. The power spectrum of received signals is found by calculating the FFT of the autocorrelation as shown in Eqs. (36) and (37).

*f t*ð Þ*f t*ð Þ þ *τ dt* (36)

�*j*2*π<sup>f</sup> <sup>τ</sup> dt* (37)

**autocorrelation**

*Coherent Doppler Lidar for Wind Sensing DOI: http://dx.doi.org/10.5772/intechopen.91811*

component, **Figure 12**.

**Figure 12.**

**19**

*quadrature (Q ) signals.*

where, *Pnois*, and *P*ð Þ *<sup>N</sup> sig* are the noise and signal power accumulated over N pulses, respectively. For a shot noise limited receiver system, the noise power is due to shot noise: *P*ð Þ *<sup>N</sup> shot*, which can be given by:

$$P\_{shot}^{(N)} = < P\_{shot}> \pm \sigma\_{shot}^{(N)}\tag{33}$$

where; <*Pshot* > is the average shot noise power, which is a fixed level characterized by the laser source, and *σ*ð Þ *<sup>N</sup> shot* is the shot noise variation around its fixed level when averaged N times (standard deviation of the shot noise for N accumulation). The average shot noise fixed power level is given by:

$$P\_{shot} = 2 \text{eiB} \tag{34}$$

where; *e* is the electronic charge, *i* is the photo-current, and *B* is the detector's bandwidth.

In our analysis, we calculate the following parameter: *Pmeasured Pref* � 1 by dividing signals power spectrum by a reference signals power spectrum and then subtracting one, which results to:

$$\frac{P\_{measured}}{P\_{ref}} - 1 = \frac{(\text{SNR})}{\sqrt{N}} + \sqrt{\frac{2}{N}} \tag{35}$$

Therefore, when accumulating 10,000 pulses and in order to extract signal out of noise, the signal power should be at least equal to noise power, i.e. SNR =1. As a result, the value we calculate is equal to: <sup>1</sup> ffiffiffiffiffiffiffiffiffiffiffi 10, 000 <sup>p</sup> <sup>þ</sup> ffiffi 2 p ffiffiffiffiffiffiffiffiffiffiffi 10, 000 <sup>p</sup> = 0.024, which is the value we set as a threshold below which received signals are ignored. It is also worth noting that the signal power we report is not really the signal power, but it's the signal power normalized to the shot noise, in other words, it is the SNR for a single shot.
