**6. Conclusion**

which computes an autocorrelation matrix *D(m,n) = d\**

output buffer before it is being streamed to the host PC.

*S*0*S* <sup>∗</sup>

*S*1*S* <sup>∗</sup>

*S*2*S* <sup>∗</sup>

*Sn*�<sup>1</sup>*<sup>S</sup>* <sup>∗</sup>

*SnS* <sup>∗</sup>

<sup>0</sup> *S*0*S* <sup>∗</sup>

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

<sup>1</sup> *S*1*S* <sup>∗</sup>

<sup>2</sup> *S*2*S* <sup>∗</sup>

*D* ¼

matrix are accumulated from the *i*

operation on July 12th, 2012, **Figure 13**.

**algorithm**

**Figure 13.**

**20**

*18:00 PM EDT on July 12th, 2012.*

(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

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:

… … *S*0*S* <sup>∗</sup>

… … ⋮ … … ⋮

> … … ⋮ … … ⋮ … … ⋮

*M*�1

*th* row, where *i* and *j* are the first and

(38)

<sup>1</sup> *S*0*S* <sup>∗</sup> 2

<sup>2</sup> *S*1*S* <sup>∗</sup> 3

<sup>3</sup> *S*2*S* <sup>∗</sup> 4

*<sup>n</sup>*�<sup>2</sup> 0

where; *M* is the number of lags, *n* is the number of acquired samples, *S* denotes

To calculate the power spectrum of a certain range gate, the columns of the *D*

*th* row to the *j*

**5.2 Vertical wind velocity measurements using autocorrelation pre-processing**

In this section, wind velocity was measured in a vertical mode while preprocessing received signals using an autocorrelation algorithm. The autocorrelation algorithm calculates the autocorrelation of the received signals and streams out the lags matrix that can be gated according to user's range resolution's preference. That feature makes autocorrelation technique advantageous over the FFT technique, where range gates are fixed. Wind velocity was measured under this mode of

*Vertical wind velocity (m/s) vs. time and height measured at CCNY remote sensing laboratory between 14:01–*

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.

⋮ ⋮⋮

*<sup>n</sup>* 0 0

*<sup>n</sup>*�<sup>1</sup> *Sn*�<sup>1</sup>*<sup>S</sup>* <sup>∗</sup>

to a sample, and *S\** denotes to the complex conjugate of sample *S*.

*(n).d(n + m)* for m = 0 to M-1

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 City College of New York.

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 by a heterodyne balanced detector.

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

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

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 7 km instead of 3 km.
