**4.3 FFT pre-processing algorithm**

In this pre-processing algorithm, received signals are time gated into portions corresponding to spatial range gates, FFT is estimated for each range gate, and the corresponding power spectra are accumulated over 10 k laser shots. Power spectrum can be calculated using the FFT as follows:

The normalized Fourier transform of a time domain signals*f(t)* can be expressed as:

$$F\_T(w) = \frac{1}{\sqrt{T}} \int\_0^T f(t) \, e^{-iwt} \, dt \tag{28}$$

corresponding to the peak power [23]. If the backscattered signal's mean frequency shift and the frequency corresponding to the peak power do not coincide, the velocity estimate can be off by as much as one-half of a frequency resolution.

Initially the following procedure was followed when measurements were taken at the remote sensing laboratory of the CCNY to assure the fiber's optimum alignment with respect to the lens. In this procedure, the laser pulses were shot at a hard target (100 m), and the scattered signal was obtained and monitored on the oscilloscope. **Figure 6** shows the scattered signal off a hard target in time domain. Maximizing the magnitude of the hard target's scattered signal through adjusting fiber's x, y, and z positions achieves the optimum fiber's location to focus the beam at about 100 m (the hard target's distance). To focus the beam at a different distance, the z position of the fiber holder can be adjusted accordingly. We then direct the laser beam away from the hard target to obtain atmospheric backscattering, **Figure 7.**

In this section, real-time wind measurements are reported. Real-time measurements are recoded continuously, thanks to FPGA pre-processing techniques that allow for streaming of either power spectrum or autocorrelation of received signals instead of raw data. The instrument was installed in our research vehicle that is located at the City College of New York at upper Manhattan, New York (latitude: 40.49°N, longitude: 73.56°W). Laser pulses are transmitted into the atmosphere through an opening in the vehicle's roof, **Figure 8**. The following subsections introduce vertical wind velocity measurements using FFT and autocorrelation preprocessing techniques. Horizontal wind speed measurement is also introduced.

**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,

**4.5 Setup procedure to observe scattered signals**

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

**4.6 Real-time wind measurement**

**Figure 6.**

**15**

*Time domain scattered signal off a hard target.*

The discrete spectral density can then be found as:

$$\text{PSD}(\boldsymbol{w}) = \lim\_{T \to \infty} \mathbb{E}\left[ \left| F\_T(\boldsymbol{w})^2 \right| \right] \tag{29}$$

Eq. (29) shows that the squared modulus of the Fourier transform is the power spectrum. Therefore, we program the FPGA to calculate the square modulus of the output of the FFT block. Our ADC vendor provided us with an FPGA logic design that streams digitally converted signals (sampled at 400 MHz rate) across the PCI express bus to the host PC. This logic design accepts an external trigger signal to start data acquisition. A 20 kHz signal synchronized with laser pulses is used to trigger the data acquisition process. The ADC card operates in a frame mode in which it acquires a frame of incoming data every time it receives an external trigger's interrupt. A frame size of 8192 samples is chosen, which corresponds to approximately 3.1 km. Xilinx Fast Fourier Transform 7.1 circuit block is used in a pipelined-streaming-io mode to calculate FFT for a vector of 128 samples of time gated scattered signals (corresponding to a 48 m spatial resolution). Logic circuits that calculate the modules of the FFT complex output are also implemented and integrated with this design.

#### **4.4 Host computer signal processing**

Once accumulated power spectra are streamed from the FPGA across the PCI express bus, data post processing is carried out on the host PC to estimate various parameters such as radial wind velocity, backscattered signal strength, and velocity statistics. Data archiving and visualization are also carried out on the host PC.

The Doppler lidar estimate of the radial component *v* (m.s�<sup>1</sup> ) of the velocity vector is obtained from the mean-frequency *Δf* (Hz) of the Doppler lidar signal as:

$$v = \frac{\lambda}{2} \Delta f \tag{30}$$

where λ (m) is the laser wavelength. As a result, the maximum radial velocity that can be measured is given by:

$$
\upsilon\_{\text{max}} = \frac{\lambda}{2} f\_{\text{max}},
\tag{31}
$$

which is approximately 30 m s�<sup>1</sup> .

The main parameter of interest in Doppler wind measurement is the mean frequency shift of the backscattered signal, because it is directly proportional to the mean velocity of moving aerosol particles within the atmosphere [20, 21]. Doppler frequency shift can be estimated by finding the centroid of the discrete power spectrum of the backscattered signal after removing the amplifier gain shape [22]. One easily calculated method of finding this frequency from a discrete power spectrum is to find the frequency of the highest power, i.e. the frequency
