**2.4 Fiber amplifier**

An erbium-doped fiber amplifier (EDFA) that has an average power of 340 mW and a peak power of 74.6 W is used. This peak value cannot be increased beyond 74.6 W because of the Stimulated Brillouin Scattering (SBS), which can take place when an intense laser beam travels through a medium such as an optical fiber. SBS is generated from the acoustic vibrations in the medium that are caused by variations of the electric field of a traveling laser beam. Usually a laser beam undergoes SBS in an opposite direction to the incoming beam, which in our case can go back to the laser amplifier and cause damage to it. The EDFA has two amplifier stages; preamplifier and power amplifier. Output power is adjusted in a current control mode by adjusting the current of the power amplifier stage.

*Ptotal* ¼ *Psig* þ *Pnoise* (14)

¼ 1 þ *SNR* (16)

(15)

Dividing this measured power spectrum by the power spectrum where no signal

*Psig Pnoise*

¼ 1 þ

Subtracting 1 from Eq. (16), gives the SNR. The previous technique is used in

All optical components are connected through PM optical fibers to ensure that

In this section, noise components of the heterodyne photodetector are analyzed, detailed SNR analysis is presented, and the optimum local oscillator power level is determined. The range dependence of SNR is also investigated, and system performance is evaluated. Analytical and experimental wideband SNR was compared. In Section 1, we present the SNR at the heterodyne detection and in Section 2 we

In optical heterodyne detection, The SNR of the Lidar system determines the system's ability to detect low level backscattered signals out of noise [9, 10]. Lidar heterodyne photoreceiver optimization is required to increase the receiving sensitivity [11].

the polarization state of the electric field of the local oscillator and that of the backscattered signals are very close, if not the same. Maintaining the polarization state throughout the different components of the system ensures a high level of the

*Ptotal Pnoise*

where SNR: is the signal to noise ratio.

*Non-flat gain response of the heterodyne balanced detector.*

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

**2.8 Polarized maintained (PM) fiber optic**

**3. Power analysis and SNR range dependence**

present the range dependence of the wideband SNR.

heterodyne detected signals.

**3.1 Transceiver noise analysis**

**9**

our signal processing to estimate backscattered signal power.

is present gives:

**Figure 3.**

### **2.5 Optical circulator**

The optical circulator ensures that the amplified output laser pulse is transmitted into the optical antenna and not into the detector. It also ensures that received backscattered signals and signals reflected off the fiber tip from the output pulse are directed into the receiver and not into the fiber amplifier. The back-reflection signal level at the fiber tip of the output port (port 2) of the optical circulator is very critical, because it can damage the optical detector.

### **2.6 Optical antenna**

A 4″ diameter lens with a focal length of 50 cm is used. The truncation ratio is approximately 0.88, and the lens' Rayleigh range is approximately 5 km, which means that the laser beam can be collimated for all desired range (100 m to 4 km). This lens is mounted on an aluminum rail with a fiber holder that houses the optical fiber. A 6″ mirror is also mounted on the same rail to steer the laser beam, and the entire setup is mounted on optical table.

#### **2.7 Balanced detector**

An InGaAs heterodyne balanced detector with a bandwidth extending from d.c. to 125 MHz is used to retrieve backscattered signals. The benefit of using a balanced detector is to subtract the two optical input signals from each other, which results in the cancelation of common mode noise. This allows for detection of small changes in the signal path from the interfering noise floor. The photo current is converted into voltage through the detector's transimpedance amplifier module. Detector's noise was measured using a spectrum analyzer while no optical signals were applied to its inputs, gain was set to 1, transimpedance was set to 1.4 kΩ, coupling was set to DC, and spectrum analyzer's frequency resolution was set to 3 MHz. Detector's noise was equal to 83 dBm, which is 1 dB below detector's specification of 3.6 pW Hz1/2. The detector has a non-flat gain response, **Figure 3**, i.e. the gain of the detector varies with the frequency of the input signals.

To correct for this non-flat gain shape, received signals' power spectrum is divided by the power spectrum of detector's output while no signal is present. The measured power when signal is present can be represented as:

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

AOMs on during the 300 ns of the 20 kHz RF driving pulse to generate a laser pulse

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

An erbium-doped fiber amplifier (EDFA) that has an average power of 340 mW and a peak power of 74.6 W is used. This peak value cannot be increased beyond 74.6 W because of the Stimulated Brillouin Scattering (SBS), which can take place when an intense laser beam travels through a medium such as an optical fiber. SBS is generated from the acoustic vibrations in the medium that are caused by variations of the electric field of a traveling laser beam. Usually a laser beam undergoes SBS in an opposite direction to the incoming beam, which in our case can go back to the laser amplifier and cause damage to it. The EDFA has two amplifier stages; preamplifier and power amplifier. Output power is adjusted in a current control mode

The optical circulator ensures that the amplified output laser pulse is transmitted

A 4″ diameter lens with a focal length of 50 cm is used. The truncation ratio is approximately 0.88, and the lens' Rayleigh range is approximately 5 km, which means that the laser beam can be collimated for all desired range (100 m to 4 km). This lens is mounted on an aluminum rail with a fiber holder that houses the optical fiber. A 6″ mirror is also mounted on the same rail to steer the laser beam, and the

An InGaAs heterodyne balanced detector with a bandwidth extending from d.c. to 125 MHz is used to retrieve backscattered signals. The benefit of using a balanced detector is to subtract the two optical input signals from each other, which results in the cancelation of common mode noise. This allows for detection of small changes in the signal path from the interfering noise floor. The photo current is converted into voltage through the detector's transimpedance amplifier module. Detector's noise was measured using a spectrum analyzer while no optical signals were applied to its inputs, gain was set to 1, transimpedance was set to 1.4 kΩ, coupling was set to DC, and spectrum analyzer's frequency resolution was set to 3 MHz. Detector's noise was equal to 83 dBm, which is 1 dB below detector's specification of 3.6 pW Hz1/2. The detector has a non-flat gain response, **Figure 3**, i.e. the gain of the

To correct for this non-flat gain shape, received signals' power spectrum is divided by the power spectrum of detector's output while no signal is present.

into the optical antenna and not into the detector. It also ensures that received backscattered signals and signals reflected off the fiber tip from the output pulse are directed into the receiver and not into the fiber amplifier. The back-reflection signal level at the fiber tip of the output port (port 2) of the optical circulator is very

with 200 ns Full Width at Half Maximum (FWHM).

by adjusting the current of the power amplifier stage.

critical, because it can damage the optical detector.

detector varies with the frequency of the input signals.

The measured power when signal is present can be represented as:

entire setup is mounted on optical table.

**2.4 Fiber amplifier**

**2.5 Optical circulator**

**2.6 Optical antenna**

**2.7 Balanced detector**

**8**

**Figure 3.** *Non-flat gain response of the heterodyne balanced detector.*

$$P\_{\text{total}} = P\_{\text{sig}} + P\_{\text{noise}} \tag{14}$$

Dividing this measured power spectrum by the power spectrum where no signal is present gives:

$$\frac{P\_{\text{total}}}{P\_{\text{noise}}} = \mathbf{1} + \frac{P\_{\text{sig}}}{P\_{\text{noise}}} \tag{15}$$

$$= \mathbf{1} + \text{SNR} \tag{16}$$

where SNR: is the signal to noise ratio.

Subtracting 1 from Eq. (16), gives the SNR. The previous technique is used in our signal processing to estimate backscattered signal power.

#### **2.8 Polarized maintained (PM) fiber optic**

All optical components are connected through PM optical fibers to ensure that the polarization state of the electric field of the local oscillator and that of the backscattered signals are very close, if not the same. Maintaining the polarization state throughout the different components of the system ensures a high level of the heterodyne detected signals.

## **3. Power analysis and SNR range dependence**

In this section, noise components of the heterodyne photodetector are analyzed, detailed SNR analysis is presented, and the optimum local oscillator power level is determined. The range dependence of SNR is also investigated, and system performance is evaluated. Analytical and experimental wideband SNR was compared. In Section 1, we present the SNR at the heterodyne detection and in Section 2 we present the range dependence of the wideband SNR.

#### **3.1 Transceiver noise analysis**

In optical heterodyne detection, The SNR of the Lidar system determines the system's ability to detect low level backscattered signals out of noise [9, 10]. Lidar heterodyne photoreceiver optimization is required to increase the receiving sensitivity [11].

It was shown that heterodyne detection sensitivity can reach its maximum value if local oscillator power is set to an optimum level [10]. The following analysis presents different heterodyne photodetector's noise components and gives an estimate to SNR.

The noise at the output of the optical detector consists of: (1) thermal noise (Johnson noise), (2) shot noise due to local oscillator induced current, and (3) laser's relative intensity noise (RIN).

Thermal noise is related to the detector and does not depend on the local oscillator power (*Plo*). Thermal noise is expressed as:

$$\ = \frac{4kTB}{R\_l} \tag{17}$$

directly proportional to *Plo*. Hence SNR increases with increasing *Plo*. On the other hand, when *Plo* is large, the third term in the denominator dominates, and *SNR* is inversely proportional to *Plo*. The *SNR* then decreases with increasing *Plo*. This means that *SNR* will increase as local oscillator power increases until it reaches a maximum value (where *Plo* is optimum), after which it starts to decrease. The optimum value of *Plo* can be determined by plotting the SNR as a function of *Plo* assuming room temperature, *Rin* = 152 dB as provided by our laser vendor, *Rb* = 25 dB, *η<sup>q</sup>* = 0.8, and *Rl* = 50 Ω. It is shown that *SNR* is maximum when *Plo* is approximately = 10 mW, however, we chose to set *Plo* to approximately 5 mW to

In this section, we study the range dependence of SNR for the coherent laser radar (CLR) heterodyne detection using a mono-static configuration, and we compare analytical and experimental results. Mono-static configuration was believed to have an improved performance due to the correlation of the transmitted and back scattered fields. This correlation is the result of wave-front tilts self correction in a mono-static configuration [13–15]. The SNR range dependence of a CLR monostatic system is evaluated by using the concept of backprojected local oscillator (BPLO), which is the imaginary local oscillator field distribution projected at the target side of the receiver aperture, receiver lens, originating from the detector [13, 16, 17]. Frehlich and Kavaya [13] derived an equation that describes SNR as a function of range assuming a Gaussian Lidar system i.e., transmitter and LO fields are deterministic, detector response function is uniform, and the detector collects all LO and backscattered power incident on the receiver aperture. The SNR was then found by calculating the overlap integral between the BPLO and the backscattered fields on the receiver plane assuming a distributed aerosol target assuming ideal conditions, i.e. shot noise limited detector and a deterministic beam. To take into account the effects of refractive turbulence on CLR performance, different techniques of wave propagation in random medium were used [18]. Analysis shows that the SNR is proportional to the product of direct detection power and heterodyne efficiency. The calculation of received power and SNR requires mutual coherence function of the backscattered field incident on the receiver. As for natural aerosol targets, backscattered field at each aerosol particle has a random phase, and the mutual coherence function of the total backscattered

avoid operating the detector near its damage threshold, **Figure 4**.

**3.2 Coherent Lidar signal range dependence**

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

**Figure 4.**

**11**

*Normalized* SNR *as a function of local oscillator power* Plo*.*

where: *k* is Boltzmann's constant,*T* is temperature in degrees Kelvin, B is detector's bandwidth, and *Rl* is detector's load resistor.

Shot noise, unlike signal powers that cancel through the balanced detector, the uncorrelated shot noise adds [12], resulting a mean-square noise at the output of the detector given by:

$$\quad=2eiB\tag{18}$$

where: *i* is the detector's current caused by the local oscillator power. This current can be calculated as follows:

$$
\dot{a} = \epsilon n\_{\epsilon} \tag{19}
$$

where, *ne* is the number of electrons, which is given by:

$$n\_e = \eta\_q e\_{ph} \tag{20}$$

where, *nph* is the number of photons incident on the detector, *η<sup>q</sup>* is detector's optical efficiency.

$$e\_{ph} = \frac{P\_{lo}}{h\nu} \tag{21}$$

$$\therefore < i\_{sh}^2 > = \frac{2\eta\_q e^2 B P\_{lo}}{h\nu} \tag{22}$$

Laser relative intensity noise (RIN) is a property of the laser source, which is related to square value of local oscillator power through the following relationship:

$$\ = \left(R\_{in}\right)R\_b\left(\frac{e\eta\_q}{h\nu}\right)^2B(P\_{lo})^2\tag{23}$$

where: *Rb* is *RIN* suppression ratio through the use of balanced detection. The SNR can now be expressed as:

$$\text{SNR} = \frac{}{ +  + } \tag{24}$$

$$=C\left[\mathbf{1} + \frac{2kT\hbar\nu}{\eta\_q e^2 P\_{lo} R\_l} + \frac{\eta\_q R\_{in} R\_b P\_{lo}}{2h\nu}\right]^{-1} \tag{25}$$

where: *C* is an independent term of local oscillator power = *<sup>η</sup><sup>q</sup> Bh<sup>υ</sup> Ps*. When *Plo* is small, the second term in the denominator of Eqs. (3)–(9) dominates, and *SNR* is *Coherent Doppler Lidar for Wind Sensing DOI: http://dx.doi.org/10.5772/intechopen.91811*

It was shown that heterodyne detection sensitivity can reach its maximum value if local oscillator power is set to an optimum level [10]. The following analysis presents different heterodyne photodetector's noise components and gives an estimate to SNR. The noise at the output of the optical detector consists of: (1) thermal noise (Johnson noise), (2) shot noise due to local oscillator induced current, and (3) laser's

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

Thermal noise is related to the detector and does not depend on the local oscil-

*th* <sup>&</sup>gt; <sup>¼</sup> <sup>4</sup>*kTB Rl*

where: *k* is Boltzmann's constant,*T* is temperature in degrees Kelvin, B is detec-

Shot noise, unlike signal powers that cancel through the balanced detector, the uncorrelated shot noise adds [12], resulting a mean-square noise at the output of the

*sh* > ¼ 2*eiB* (18)

*i* ¼ *ene* (19)

*ne* ¼ *ηqeph* (20)

(17)

(21)

(22)

(24)

(25)

*Bh<sup>υ</sup> Ps*. When *Plo* is

<sup>2</sup> (23)

<*i* 2

> < *i* 2

where, *ne* is the number of electrons, which is given by:

∴ <*i* 2

*RIN* > ¼ ð Þ *Rin Rb*

*SNR* <sup>¼</sup> <sup>&</sup>lt; *<sup>i</sup>*

2*kThυ ηqe*<sup>2</sup>*PloRl*

small, the second term in the denominator of Eqs. (3)–(9) dominates, and *SNR* is

<*i* 2 *th* > þ < *i*

where: *C* is an independent term of local oscillator power = *<sup>η</sup><sup>q</sup>*

¼ *C* 1 þ

<*i* 2

where: *i* is the detector's current caused by the local oscillator power. This

where, *nph* is the number of photons incident on the detector, *η<sup>q</sup>* is detector's

*eph* <sup>¼</sup> *Plo hν*

Laser relative intensity noise (RIN) is a property of the laser source, which is related to square value of local oscillator power through the following relationship:

where: *Rb* is *RIN* suppression ratio through the use of balanced detection. The

*sh* <sup>&</sup>gt; <sup>¼</sup> <sup>2</sup>*ηqe*<sup>2</sup>*BPlo hν*

> *eηq hυ* � �<sup>2</sup>

> > 2 *s* >

2 *sh* > þ <*i*

þ

" #�<sup>1</sup>

*B P*ð Þ*lo*

2 *RIN* >

*ηqRinRbPlo* 2*hυ*

relative intensity noise (RIN).

detector given by:

optical efficiency.

SNR can now be expressed as:

**10**

lator power (*Plo*). Thermal noise is expressed as:

tor's bandwidth, and *Rl* is detector's load resistor.

current can be calculated as follows:

directly proportional to *Plo*. Hence SNR increases with increasing *Plo*. On the other hand, when *Plo* is large, the third term in the denominator dominates, and *SNR* is inversely proportional to *Plo*. The *SNR* then decreases with increasing *Plo*. This means that *SNR* will increase as local oscillator power increases until it reaches a maximum value (where *Plo* is optimum), after which it starts to decrease. The optimum value of *Plo* can be determined by plotting the SNR as a function of *Plo* assuming room temperature, *Rin* = 152 dB as provided by our laser vendor, *Rb* = 25 dB, *η<sup>q</sup>* = 0.8, and *Rl* = 50 Ω. It is shown that *SNR* is maximum when *Plo* is approximately = 10 mW, however, we chose to set *Plo* to approximately 5 mW to avoid operating the detector near its damage threshold, **Figure 4**.

### **3.2 Coherent Lidar signal range dependence**

In this section, we study the range dependence of SNR for the coherent laser radar (CLR) heterodyne detection using a mono-static configuration, and we compare analytical and experimental results. Mono-static configuration was believed to have an improved performance due to the correlation of the transmitted and back scattered fields. This correlation is the result of wave-front tilts self correction in a mono-static configuration [13–15]. The SNR range dependence of a CLR monostatic system is evaluated by using the concept of backprojected local oscillator (BPLO), which is the imaginary local oscillator field distribution projected at the target side of the receiver aperture, receiver lens, originating from the detector [13, 16, 17]. Frehlich and Kavaya [13] derived an equation that describes SNR as a function of range assuming a Gaussian Lidar system i.e., transmitter and LO fields are deterministic, detector response function is uniform, and the detector collects all LO and backscattered power incident on the receiver aperture. The SNR was then found by calculating the overlap integral between the BPLO and the backscattered fields on the receiver plane assuming a distributed aerosol target assuming ideal conditions, i.e. shot noise limited detector and a deterministic beam. To take into account the effects of refractive turbulence on CLR performance, different techniques of wave propagation in random medium were used [18]. Analysis shows that the SNR is proportional to the product of direct detection power and heterodyne efficiency. The calculation of received power and SNR requires mutual coherence function of the backscattered field incident on the receiver. As for natural aerosol targets, backscattered field at each aerosol particle has a random phase, and the mutual coherence function of the total backscattered

**Figure 4.** *Normalized* SNR *as a function of local oscillator power* Plo*.*

field is the integration of all mutual coherence functions from each aerosol particle. The SNR range dependence equation is expressed as [19]:

$$\text{SNR}(L) = \frac{\eta\_D(L)\lambda E\beta K^{2L/1000}\pi D^2}{8hBL^2} \tag{26}$$

wideband SNR range dependence. It is clear that both measured and theoretically calculated wideband SNR have a very good agreement. The parameters used in this

**4. FPGA programming and wind measurements analyzed using FFT**

For a 20 kHz PFR and a 14-bit ADC with a sampling rate of 400 MHz, data transfer rate from the data acquisition card to the host PC will be 800 Mbyte/s. This high data transfer rate is difficult to be achieved and requires additional hardware and software. Moreover, the amount of data collected in 1 day will be more than 69 Tbyte, which makes data archiving for just a few days nearly impossible. Due to the fast PFR, signal processing on the host computer cannot be achieved in real time, and will cause data to be lost. Therefore, programming the FPGA to calculate power spectra or correlograms of backscattered signals and accumulate the results over a large number of pulses (we chose 10 K pulses) will not only take the burden off the host PC and allow for real time analysis, but will significantly reduce data transfer rate across the PCI express bus to the host PC. In this approach, a signal processing algorithm is implemented and programmed onto the FPGA so that backscattered signals time gating, power spectrum calculation, and accumulation will all be simultaneously carried out on the hardware level as soon as signals are acquired by the ADC. Power spectrum of

backscattered signals can be estimated directly by calculating the FFT of the time gated signals, or by calculating the FFT of signals' autocorrelation. FFT pre-processing algorithm and wind measurement results using FFT technique will be explained in the following sections, while autocorrelation pre-processing algorithm and wind measurement results using autocorrelation technique will be explained in details in Section 5.

Backscattered signals are sampled at 400 MSPS using a 14-bit ADC card, which features two 14-bit, 400 MSPS A/D and two 16-bit, 500 MSPS DAC channels with a Virtex5 FPGA computing core and a PCI Express host interface. The Virtex5 FPGA can be programmed using VHDL and MATLAB using the Frame Work Logic toolset. The MATLAB Board Support Package (BSP) allows for real-time hardwarein-the-loop development using graphical, block diagram Simulink environment with Xilinx System Generator toolset. Software tools for host PC development can

A signal pre-processing algorithm is initially implemented as a logic design, which can be simulated and tested using Matlab/Simulink software. This logic design is then compiled using Xilinx system generator toolset to produce a hardware VLSI image, which can be downloaded into the FPGA. We chose to pre-process backscattered signals in two different techniques: (a) calculate the FFT of time gated signals then accumulate the resulting power spectrum, and (b) calculate the autocorrelation of the backscattered signals then accumulate the resulting autocor-

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

analysis are listed in **Table 1**.

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

**4.1 ADC card**

be performed using C++.

**4.2 FPGA programming algorithms**

relation matrix for 10 k laser shots.

**4.3 FFT pre-processing algorithm**

**13**

where; η<sup>D</sup> is the system efficiency, given by:

$$\eta\_D(L) = \frac{\eta\_{\text{total}}}{\left\{ \mathbf{1} + \left( \mathbf{1} - \frac{L}{L\_F} \right)^2 \left( \frac{\pi (A\_C D)^2}{4 \bar{\imath} L} \right)^2 + \left( \frac{A\_C D}{2S\_O(L)} \right)^2 \right\}}\tag{27}$$

where; the parameters of Eqs. (26) and (27) are introduced in **Table 1**.

The performance of a 4″ diameter antenna was evaluated both theoretically and experimentally while focusing the laser beam at approximately 1.8 km. Continuous 38 range gates having a length of 0.32 μs (48 m range resolution) were obtained between a minimum range of 128 m and a maximum range of approximately 2 km. The power spectra of received signals from 10,000 laser shots were accumulated and wideband SNR was estimated. **Figure 5** shows theoretical and experimental


**Figure 5.** *Wideband SNR range dependence (points, experimental; solid curve, theoretical).*

field is the integration of all mutual coherence functions from each aerosol particle.

*SNR L*ð Þ¼ *<sup>η</sup>D*ð Þ *<sup>L</sup> <sup>λ</sup>EβK*2*L=*1000*πD*<sup>2</sup>

*LF* <sup>2</sup> *<sup>π</sup>*ð Þ *ACD* <sup>2</sup>

where; the parameters of Eqs. (26) and (27) are introduced in **Table 1**.

**Parameter Descriptions Value**

B Bandwidth 100 MHz λ Wave length 1545.2 μm E Pulse energy 7 μJ D Effective aperture diameter 0.15 m τ Pulse width 200 ns <sup>β</sup> Atmospheric backscatter coefficient 8.3 � <sup>10</sup>�<sup>7</sup> m/sr K One way atmospheric transmittance 0.95 km LF Focal range of optical antenna 1.8 km Ac Correction factor 0.76 Cn<sup>2</sup> Refractive index structure constant <sup>2</sup> � <sup>10</sup>�<sup>14</sup> <sup>m</sup>�2/3 ηtotal Total system efficiency �2.2 dB *So(L)* Transverse coherent length �(1.1 *kw<sup>2</sup>*

4*λL* <sup>2</sup>

The performance of a 4″ diameter antenna was evaluated both theoretically and experimentally while focusing the laser beam at approximately 1.8 km. Continuous 38 range gates having a length of 0.32 μs (48 m range resolution) were obtained between a minimum range of 128 m and a maximum range of approximately 2 km. The power spectra of received signals from 10,000 laser shots were accumulated and wideband SNR was estimated. **Figure 5** shows theoretical and experimental

<sup>8</sup>*hBL*<sup>2</sup> (26)

*L Cn<sup>2</sup>* ) �3/5

<sup>þ</sup> *ACD* 2*SO*ð Þ *L*

<sup>2</sup> (27)

The SNR range dependence equation is expressed as [19]:

*<sup>η</sup>D*ð Þ¼ *<sup>L</sup> <sup>η</sup>total* <sup>1</sup> <sup>þ</sup> <sup>1</sup> � *<sup>L</sup>*

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

where; η<sup>D</sup> is the system efficiency, given by:

L Range (m)

*kw* Wave number = 2π/λ

*Parameters corresponding to analytical estimation of wideband SNR range dependence.*

*Wideband SNR range dependence (points, experimental; solid curve, theoretical).*

**Table 1.**

**Figure 5.**

**12**

wideband SNR range dependence. It is clear that both measured and theoretically calculated wideband SNR have a very good agreement. The parameters used in this analysis are listed in **Table 1**.
