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

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).

$$R(\tau) = \bigcap\_{-\infty}^{\infty} f(t)f(t+\tau)dt\tag{36}$$

$$\mathcal{G}(f) = \bigcap\_{-\infty}^{\infty} \mathcal{R}(\tau) e^{-j2\pi f \tau} \, dt \tag{37}$$

where; *f t*ð Þ is a time domain signal, *R*ð Þ*τ* is the signal's autocorrelation, and *G f* ð Þ is the Fourier transform (power spectrum).

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 ) component, **Figure 12**.

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

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,

#### **Figure 12.**

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

*SNR* <sup>¼</sup> *<sup>P</sup>*ð Þ *<sup>N</sup> sig Pnois*

*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*

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

respectively. For a shot noise limited receiver system, the noise power is due to shot

*shot* <sup>¼</sup> <sup>&</sup>lt;*Pshot* <sup>&</sup>gt; � *<sup>σ</sup>*ð Þ *<sup>N</sup>*

where; <*Pshot* > is the average shot noise power, which is a fixed level charac-

when averaged N times (standard deviation of the shot noise for N accumulation).

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

signals power spectrum by a reference signals power spectrum and then subtracting

� <sup>1</sup> <sup>¼</sup> ð Þ *SNR*ffiffiffiffi *N* p þ

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.

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

*P*ð Þ *<sup>N</sup>*

In our analysis, we calculate the following parameter: *Pmeasured*

*Pmeasured Pref*

As a result, the value we calculate is equal to: <sup>1</sup> ffiffiffiffiffiffiffiffiffiffiffi

The average shot noise fixed power level is given by:

*sig* are the noise and signal power accumulated over N pulses,

*shot* (33)

*Pref* � 1 by dividing

10, 000 <sup>p</sup> = 0.024, which is the

(35)

*shot* is the shot noise variation around its fixed level

*Pshot* ¼ 2*eiB* (34)

ffiffiffiffi 2 *N* r

10, 000 <sup>p</sup> <sup>þ</sup> ffiffi

2 p ffiffiffiffiffiffiffiffiffiffiffi

where, *Pnois*, and *P*ð Þ *<sup>N</sup>*

*agreement in the two measurements.*

*shot*, which can be given by:

terized by the laser source, and *σ*ð Þ *<sup>N</sup>*

noise: *P*ð Þ *<sup>N</sup>*

**Figure 11.**

bandwidth.

single shot.

**18**

one, which results to:

(32)

which computes an autocorrelation matrix *D(m,n) = d\* (n).d(n + m)* for m = 0 to M-1 (lags) and n = 0 to N-1 (number of time domain samples, which is 8k samples/4 = 2 k), where *d\* = di(n) - j dq(n)* is the complex conjugate of *d(n).* The processing repeats for 10 k laser shots and the elements of D matrix are accumulated and then streamed to an output buffer before it is being streamed to the host PC.

Once the accumulated lags' matrix [Eq. (5)–(3)] is streamed to the host PC, further processing is conducted to calculate the power spectrum of received signals as follows:

$$D = \begin{bmatrix} S\_0 S\_0^\* & S\_0 S\_1^\* & S\_0 S\_2^\* & \dots & \dots & S\_0 S\_{M-1}^\* \\ \mathbf{S}\_1 \mathbf{S}\_1^\* & S\_1 \mathbf{S}\_2^\* & S\_1 \mathbf{S}\_3^\* & \dots & \dots & \vdots \\ \mathbf{S}\_2 \mathbf{S}\_2^\* & S\_2 \mathbf{S}\_3^\* & S\_2 \mathbf{S}\_4^\* & \dots & \dots & \vdots \\ \vdots & \vdots & \vdots & \dots & \dots & \vdots \\ \mathbf{S}\_{n-1} \mathbf{S}\_{n-1}^\* & S\_{n-1} \mathbf{S}\_{n-2}^\* & \mathbf{0} & \dots & \dots & \vdots \\ \mathbf{S}\_n \mathbf{S}\_n^\* & \mathbf{0} & \mathbf{0} & \dots & \dots & \vdots \end{bmatrix} \tag{38}$$

**6. Conclusion**

the City College of New York.

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

by a heterodyne balanced detector.

7 km instead of 3 km.

**Author details**

Sameh Abdelazim<sup>1</sup>

and Sam Ahmed<sup>2</sup>

**21**

In conclusion, an eye-safe all-fiber CDL system for wind sensing in urban areas was designed, developed, tested, and operated at the remote sensing Laboratory of

The system utilizes a 1.5 μm fiber optics laser, which benefits from the availability and affordability of telecommunication optical components. Two AOMs are connected in series to achieve a high extinction ratio and to shift the laser frequency by 42 MHz each, which produces a total shift of 84 MHz. An optical amplifier amplifies the laser pulse to produce approximately 12 μJ/pulse (200 ns FWHM at 20 kHz PFR). An optical circulator directs amplified laser pulses to its output port that is connected to the optical antenna, and directs received signals to an optical coupler to be mixed with a LO. Circulator's fiber tip was polished and angled to reduce internal reflection that can damage the detector. Optical mixed signals are detected

Received signals are sampled at 400 MHz through a 14-bit ADC equipped with an FPGA. Due to the very low energy per pulse (12 μJ/pulse), a high PFR (20 kHz) is used to allow for digging the very low signal out of noise. This high pulse rate makes it almost impossible to process the data in real time, therefore, the FPGA was programmed to pre-process received signals at the hardware level as the received

Two different pre-processing algorithms have been simulated and programmed into the FPGA; one algorithm calculates FFT of time gated received signals and accumulates the resulted power spectrum; the other algorithm calculates autocorrelation of the received signals and accumulates the result. The later algorithm allows for changing range gate (spatial resolution), which can be applied to signals scattered

The system was installed in a research vehicle and wind velocity was measured at the City College of New York. Wind velocity was measured in two different modes; vertical mode, and scan mode. Wind velocity was measured up to 3 km in a vertical mode during a very clear day. The system can be operated to measure wind velocity, processes received signals in real time, and display results while acquiring data. Improving the system can be achieved by increasing the measured range to

, Mark F. Arend<sup>2</sup>

© 2020 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium,

, Fred Moshary<sup>2</sup>

from very high altitudes (where signals are very weak) to improve the SNR.

signals are being acquired and before streaming to the host PC.

\*, David Santoro<sup>2</sup>

1 Fairleigh Dickinson University, New Jersey, USA

2 The City College of New York, New York, USA

\*Address all correspondence to: azim@fdu.edu

provided the original work is properly cited.

where; *M* is the number of lags, *n* is the number of acquired samples, *S* denotes to a sample, and *S\** denotes to the complex conjugate of sample *S*.

To calculate the power spectrum of a certain range gate, the columns of the *D* matrix are accumulated from the *i th* row to the *j th* row, where *i* and *j* are the first and last corresponding samples of that range gate, respectively. This accumulation process produces an M size autocorrelation vector, which is complex (in-phase and quadrature components). Since the autocorrelation is symmetric, we construct the second half of the autocorrelation vector by making its real part even and imaginary part odd. Finally, we find the power spectrum of that range gate's signals by calculating the FFT of the constructed complex autocorrelation vector.
