Design of a photonic-based multifrequency oscillator for radar applications

Corso di Laurea Magistrale in Ingegneria delle Telecomunicazioni

Tesi di laurea

“

Design of a photonic-based multifrequency oscillator for radar applications

”

Relatori

Candidato

Prof. Filippo GIANNETTI Ortensio FORMISANO

Prof.ssa Antonella BOGONI

CONTENTS

List of Figures

1

Abstract

5

Preface

7

1. Distributed radar systems

10

1.1 Radar architecture 1.1.1 Radar Front-end 1.1.2 Radar Transceiver 1.2 Radar principle of operation 1.3 Radar Equation

1.4 Radio-Frequencies and Radar applications

1.5 MIMO radar systems with widely separated antennas 1.5.1 Phased-array, multistatic or MIMO radar?

1.5.2 MIMO communication systems and MIMO radars 1.6 Applications and issues of current radar technologies

2. Microwave photonics in radar systems

26

2.1 Microwave photonics devices 2.1.1 Semiconductor lasers 2.1.2 Mach-Zehnder Modulator 2.1.3 Optical Amplifiers

2.1.4 Photodetectors

2.2 Multi-frequency optical sources 2.1.1 Mode locked laser

2.3 Photonics-based RF functions

2.3.2 Photonics-based detection and digitization 2.4 Photonics-based radar

2.5 ROBORDER project

3. Coherent multi-frequency oscillators

44

3.1 Optical generation of microwave signals 3.2 Phase-lock loop

3.3 Optical injection locking

3.4 Cavity-less optical frequency comb generator 3.5 External modulation-based approach

3.5.1 Intensity modulator-based approach 3.5.2 Phase modulator-based approach

4. Injection locking based on external modulation

53

4.1 Concept and setup

4.2 Laboratory implementation 4.2.1 UHF setup

4.2.2 X-band setup

5. Injection locking using a mode locked laser

67

5.1 Concept and setup

5.2 Laboratory implementation and results 5.2.1 UHF setup

5.2.2 X-band setup

6. Conclusions

75

List of Figures

Chapter 1

1.1 Elements involved in a radar transmission and reception process. 1.2 Block diagram of superheterodyne receiver

1.3 Pulsed signal waveform with its parameters

1.4 Directional beam antenna over a surface at range R 1.5 Classification of an EM wave considering its frequency

1.6 Concept scheme of (a) Phased Array, (b) Multistatic and (c) MIMO radar

1.7 Backscatter as a function of the azimuth

Chapter 2

2.1 Scheme of principle of a microwave photonics system 2.2 Electromagnetic spectrum

2.3 Scheme of principle of a semiconductor laser

2.4 Mach-Zehnder modulator’s architecture scheme. PM: Phase Modulator. 2.5 Mach-Zehnder modulator’s response. Red line: power response. Blue

line: amplitude response.

2.6 General erbium-doped fiber configuration, showing bidirectional pumping.

2.7 Gain Curve of a Typical EDFA 2.8 Structure of a PIN photodetector

2.9 Block diagram of an Intensity Modulation and Direct Detection system. MZM: Mach-Zehnder Modulator

2.10 Scheme of a coherent Homodyne detection scheme. MZM: Mach- Zehnder Modulator, LO: Local Oscillator

2.11 Scheme of cavity modes generation. The blue curve represents the gain, whereas the green one is the attenuation. The light-grey arrows are the rejected modes, and the deep-grey arrows are the suppressed modes. The black arrow in the middle is the only sustained mode

2.12 Spectrum of a mode-locked laser (Tr is the pulse repetition time)

2.13 Block diagram for the generation of a microwave signal from a MLL 2.14 Block diagram of a photonics-based analog-to-digital converter

2.15 Conceptual scheme of a photonics-based transceiver

2.16 ROBORDER technical concept diagram in maritime operations. 2.17 ROBORDER technical concept diagram in land operations.

Chapter 3

3.1 Optical Mixing of two optical waves to generate a microwave signal. Continuous lines represent the optical path, dotted lines represent the electrical path.

3.2 Block diagram of an optical phase lock loop. Continuous lines represent the optical path, dotted lines represent the electrical path. The system into the dotted box is an electrical phase detector

3.3 Optical injection locking of two slave lasers. Master laser is directly FM modulated by an RF reference with its output injected into the two slave lasers. In this example the slave lasers are chosen with a free running

wavelength equal to +2nd_{-order and -2}nd_{-order sidebands from the output of}

master laser.

3.4 Scheme of principle of an IM-PM comb generator. MZM: Mach-Zehnder modulator; PM: Phase modulator.

3.5 Microwave signal generation based on external modulation using a Mach- Zehnder modulator and a wavelength-fixed optical filter. Continuous lines represent the optical path, dotted lines represent the electrical path

3.6 Microwave signal generation based on external modulation using an optical phase modulator and a Fabry-Perot Grating as an optical notch filter. Continuous lines represent the optical path, dotted lines represent the electrical path.

Chapter 4

4.1 Block diagram of the basic setup used for the Phase noise measures. MZM is the Mach-Zehnder Modulator, PC is polarization controller, PBS is

Polarization Beam Splitter, VOA is Variable Optical Attenuator, ESA is Electrical Spectrum Analyzer.

4.2 Mach-Zehnder Modulator output in the two operative modes: (a) is the carrier suppression mode, (b) is the quadrature mode.

4.3 Voltage/Attenuation Plot of employed Variable Optical Attenuator

4.4 Injection locking stability as a function of injection ratio and frequency detuning. Strong optical injection broadens stable locking range

4.5 Measured Locking Range for different master lasers.

4.6 Measured Phase Noise of the microwave reference fm = 500 MHz.

4.7 Measured Phase Noise with HP 8168E as master laser, Pinj = -28.5 dBm, at

4.8 Improved setup by balancing the direct and conditioning path. In this way synchronization, between the signal on the two paths, is achieved.

4.9 Measured Phase Noise after paths balancing. Also in this case Pinj = -25.5

dBm, at fm=500 MHz.

4.10 Further improved setup. An Erbium Doped Fiber Amplifier (EDFA) has been added before the splitter. This allow us to check the optical injected power, adjusting the injection ratio.

4.11 Measured Phase Noise at fm = 500 MHz, Pinj = -7.5 dBm, for different

detuning frequency ∆f

4.12 Measured Phase Noise at fm = 500 MHz, ∆f = ±500 kHz, for different

injected power Pinj.

4.13 Phase noise level achieved with the three different kind of master laser and comparison with the microwave reference phase noise at fm=500MHz.

4.14 Measured Phase Noise of the microwave reference fm = 10 GHz.

4.15 Measured Phase Noise of the system at fm = 10 GHz and Pinj = -7.5dBm.

4.16 Normalized Optical Spectrum at the output port of the circulator

4.17 Side modes suppression ratio considering different values of Injected power. Note that the shift between the input and the other measures is due to the fact that the measures have been carried out in different moments.

4.18 Phase Noise and SMSR summary.

Chapter 5

5.1 Block diagram of Mode Locking Laser setup. MLL is the mode locking laser used as Master Laser, the second block is an optical filter, PC is the

Polarization Controller, EDFA is an Erbium Doped Fiber Amplifier, WSS is Wavelength Selective Switch, PBS is Polarization Beam Splitter, SL1 and SL2 are the Slave Lasers, ESA is the Electric Spectrum Analyzer.

5.2 Measured Mode locking Laser phase noise at 400 MHz.

5.3 Optical spectrum of the signal at the output of the coupler. As it can be noted from the image, the two injected lines are spaced of exactly 400 MHz. 5.4 Electrical spectrum of the signal at the output of the photodetector. The

difference between the first maximum and the highest of the sidemodes gives the Side Mode Suppression ratio, that is 6dB

5.5 Phase Noise level of the 400 MHz RF signal compared with the reference 5.6 Optical spectrum of the signal at the output of the coupler. As it can be

noted from the image, the two injected lines are spaced of exactly 10.8 GHz. 5.7 Electrical spectrum of the signal at the output of the photodetector

5.8 Phase noise level of the X-band (10.8 GHz) signal compared with the reference.

Chapter 6

6.1 Summary of the phase noise level measured for an offset frequency equal to 10 kHz of the different devices employed. As it can be seen, when the carrier frequency (x-axis) get high, the RF performances and the external modulator based performances get worse because of electronic devices limits.

Abstract

In the last few years, Multistatic radar systems have been extremely investigated. Such systems are better known as Multiple Input Multiple Output (MIMO) radars, since the same concept of MIMO telecommunication systems is employed. The basic idea is to exploit the advantages of Multiple Input Multiple Output systems in order to improve the performances of a radar system. In fact, enhancing the number of employed antennas, and positioning them in a proper way, increases the performances and the degrees of freedom of the system. In particular, MIMO Radars with widely separated antennas achieve the so called super-resolution, allowing improvements of the detection and imaging capability with respect to a single antenna-based (or antenna array) radar system. Since RAW datas from the RF front-ends have to be delivered in a central processing unit, it involves low loss and high capacity links between the CPU and the RF front end.

Multispectral radar image processing is highly desirable in order to enhance the classification capability of an imaging radar system. This process is achievable if multiband radar is employed. In order to effectively perform an effective multispectral processing, high stable clock signal has to be distributed to all the system nodes, ensuring the coherence between all the radar signals.

As known, electronic devices are characterized by limited bandwidth and lossy links that avoids to achieve the features just discussed (multiband and low loss distribution respectively). A solution for these problems could be represented by photonics technologies applied to microwaves. In the last few years, the research field of microwave photonics has been suggesting the possibility of exploiting the huge bandwidth and flexibility of photonics in order to generate RF signals that cover the frequency range from a few megahertz up to several tens of gigahertz. Several functions currently performed by electronic devices can be realized using photonics, overtaking all the limitations of electronic based systems. These functionalities are: up-and-down conversion, signal distribution, beamforming, filtering, local oscillators.

In recent years, the first photonics based radar system has been designed and realized by the CNIT’s photonics team. Such device exploits a multifrequency laser as optical clock, replacing the electronic ones, for generating multiple tunable radar signals intrinsically coherent each other and for receiving their echoes, avoiding noisy radio-frequency up-and downconversion and guaranteeing both the software-defined approach and high resolution. Its performance exceeds state-of-the-art electronics at carrier frequencies above two gigahertz.

An other fundamental feature of photonics-based radar systems is that all the signals can be delivered using the optical fibers. Such optical medium are characterized by extremely low losses (∼0,3 dB/km) allowing long distance links with low loss and no coherence degradation. This feature enables the possibility to realize a radar network where the RF signals are converted in optical domain and travels through the optical fiber (Radio over Fiber concept) from the network nodes (RF

This work is inserted in an European project named ROBORDER, that foresee the realization of a complex sensor network that includes a multiband MIMO radar. This last unit will be characterized by a photonics-based core where photonics is used for up and down conversion, and widely separated antenna connected to each other employing optical fibers.

The objective of this thesis is the design and implementation of a highly stable multifrequency optical clock to be used as local oscillator of the multiband MIMO radar. This single optical clock should replace the different RF clocks required in the radar network working at different RFs. To this purpose, different techniques have been evaluated, based on Mode-locking laser, Phase Lock Loop and Injection Locking, looking for a trade off between the complexity of the system and flexibility in terms of carrier frequency generation. Two different architectures have been developed and tested. Both of them are based on injection locking technique and are particularly suitable for applications where flexibility in terms of carrier frequency is required (for example multiband radar systems).

The first solution consists in a photonic-based multifrequency RF oscillator that still require an external microwave reference signal. While the second architecture is an all optical solution.

In this work, the two architectures are analyzed, implemented and compared to identify the better solution in the different scenarios.

All the experiments reported in this thesis have been carried out in the Photonic Network and Technologies National Laboratory (PNTLab) of National Inter-university Consortium for Telecommunications (CNIT) with the collaboration of the Institute of Communication, Information and Perception Technologies (TeCIP) of Sant’Anna School of Advanced Studies (SSSA).

Preface

RADAR (RAdio Detection And Ranging) technique is undergoing continuous revolution since its invention. In the past, radar purposes were limited just to the detection and ranging of a target; developing tracking algorithm, an other fundamental issue was to track the target and predict its future position. In the last decades, the concept of radar imaging has been developed in order to obtain a 2D (or 3D) radar high resolution image allowing target classification. However, Radar systems have evolved a lot since World War II (WWII). It went from a largely military detection system into a complex three-dimensional imaging tool, with applications in many different areas, from commercial aviation to fundamental research in the earth and planetary sciences.

Nowadays, radar systems must be able to provide a more and more amount of information about the environment around them. To this purpose, different Carrier Frequency are exploited to highlight different spectral characteristics of the same scenario.

Multi-band radar is the solution to these requirements. However, actual electronic technologies do not allow a full digital software defined radio system due to the high frequencies of employed RF signals and, for these reasons, analog stages are used to perform up and downconversions into the bandwidth of interest [1]. Such processes usually employ analog mixers, amplifiers and filters, which are source of noise and suffer from electromagnetic interferences, causing degradation in terms of sensitivity and dynamic range. In addition, the use of electronic ADCs represents a major problem regarding the signal bandwidth, since its precision drops with increasing input bandwidth and sampling speed [2], [3], [4]. Indeed, electronic subsystems can guarantee high performance over a given bandwidth but as the frequency increases the performance get dramatically worse [4], [5], [6]. Furthermore, the distribution of RF signals is prohibitive in the electrical domain due to high losses of RF lines, as coaxial cables [7].

The answer to these issues is the Microwave Photonics. This is an interdisciplinary area that studies the interaction between microwave and optical signals, for applications such as broadband wireless access networks, sensor networks, radar, satellite communications, instrumentation, and warfare systems [7].

The aim of this research field is to use photonics technologies to overcome the major issues of electronic systems. Its major functions are: generation, processing,

control and distribution of microwave and millimeter-wave signals [7] using photonics technologies.

Summing up the main features of microwave photonics,

- Photonics enable the generation of high quality microwave (or mm-wave) signals on an extremely wide range of carrier frequency and with high phase stability. Furthermore, performances does not depend on the selected carrier frequency, overtaking the bandwidth limitations of electronic devices;

- Fast analog-to-digital conversion can be achieved using photonics technologies, thanks to the reduced timing jitter of optical sources [7], [3]. The photonic- based ADC guarantees a large input bandwidth, high sampling rates with extremely low jitter, a fully digital approach, independence from the RF carrier frequency and the capacity of simultaneously receive multiple signals [8], [3], [9], [10], [11].

- Advanced kind of operations, such as all-optical microwave signal processing, photonics true-time delay, beamforming and radio-over-fiber systems can be realized using microwave photonics [7], [12], [13], [14].

- Thanks to the optical fibers coherent signal distribution between different radar system becomes very easy. State-of-the-art optical fibers present an extremely broad bandwidth and low loss, which benefits the microwave or mm-wave signals distribution [7].

This thesis is framed in an European Project named ROBORDER. The aim of this project is to realize a complex sensor network for border surveillance that enclose a radar network with a photonic-based core. The purpose of this work is to design and realize a coherent multifrequency oscillator, based on photonics technologies, that generate different carrier frequency. Different possibilities have been evaluated:

- Mode locked laser (MLL) - Phase lock loop

- Optical injection locking

Using a MLL to generate RF signals presents some disadvantage since the optical filter bandwidth must be smaller than the MLL’s repetition rate, this require narrow optical filters that are really difficult to realize. This problem is strictly related to the frequency flexibility, in fact, using a MLL, the RF signal’s carrier frequency must be an integer multiple of the pulse repetition rate. As a solution to these problems, the injection locking can be exploited as a way to filter a MLL output in order to carry out two lines that can be beaten into a photodetector to generate a RF signal. This process allow to achieve a continuous tunability of the RF signals and avoid the need of optical narrow bandwidth filters.

A state of the art research have been conducted in order to design the best setup. Two different architectures have been implemented and tested. Different sets of

measures have been carried out in order to evaluate the performances of the chosen setups. The measures have been particularly focused on the Phase Noise level, that give us information about the signal’s coherence level.

This work is organized as follows:

Chapter 1 deals with the concept of radar and MIMO radar. It presents state of

the art in radar systems and shows which are the most promising feature of photonics in radar systems.

Chapter 2 deeply describes the employment of photonics technologies in radar

system analyzing the state of the art and the main exploited functionalities. An example of fully photonics-based radar system and radar network are reported.

Chapter 3 illustrates different kinds of multifrequency optical-based oscillators

evaluating all the pro and cons for each architecture.

Chapter 4 reports the first implemented architecture describing the concept, the

motivations of such architecture and all the results carried out during the trials. Different carrier frequencies have been generated in order to highlight performance improvements or worsening.

Chapter 5 reports the other implemented architecture and it is organized like the

previous chapter.

Conclusions will draw a summary of the whole thesis, fixing the results and

Chapter 1

Distributed Radar Systems

1.1 Radar architecture

RADAR (RAdio Detection And Ranging) is a telecommunication system that uses electromagnetic waves in order to transmit and receive radiofrequency signals towards a region of interest. A typical radar architecture is reported in Figure 1.1. In such architecture it is possible to recognize the main elements involved in a radar transmission and reception process. The main macro-blocks are transmitter, antenna, receiver and a signal processor unit.

Figure 1.1 : Elements involved in a radar transmission and reception process. Radar system can be classified in many different ways. Considering the antenna subsystem, radar can be divided in:

-

Monostatic, that employs one antenna for both signal’s transmission and reception

-

_{Multistatic, that employs one antenna for signal’s transmission and one antenna}

for signal’s reception.

Considering the picture above, a monostatic radar configuration is reported.

The transmitter is responsible for generating the EM waves, which is converted and irradiated by the antenna subsystem. In the most simple case, the transmitter consists of a waveform generator, a power amplifier and a circulator. Different

kind of amplifier can be employed, such as Klystron, Traveling Wave Tube (TWT), cross-field amplifiers or solid state devices [1].

1.1.1 Radar Front-End

The antenna works as a transducer converting the EM wave in an electrical signal and vice versa. It is responsible for the transmission and reception of the radio signal. The target can be detected only if it is located within the antenna field of view, which is defined as the angular region that the main beam can scan. In order to scan a larger area, the antenna can be steered mechanically or electronically, depending on the required scanning speed [1]. Antenna sizes are inversely proportional to the carrier frequency. This last parameter is strictly related to the radar purpose.

A circulator is typically employed in order to separate transmitter and receiver in a monostatic configuration. This device provides isolation to protect the receiver form high power signals coming from the transmitter. During its propagation, the EM wave illuminates both the interest area, but also unwanted surfaces present in the sight area. This unwanted backscattering phenomenon is called clutter. So, when the signal come back to the receiving antenna, a sum of useful signal and clutter is received.

In the receiver chain, the signal is separated from interferences sources, such as white noise, amplified using a low noise amplifier (LNA) and downconverted in order to be detected [1]. Considering the Friis formula:

(1.1) The reason why the first conditioning block has to be characterized by low noise (LNA) is that receiver’s noise figure Ftotal hardly depends on the first

block’s noise figure.

1.1.2 Radar Transceiver

Modern radars’ receiving chain is composed as follows. The echo signal, captured from the antenna, is coupled to the mixer through the duplexer. In some configurations, the Sensitivity Time Control (STC) is employed to reduce the power that reach the receiver, in order to protect the receiver itself from saturation, and providing enhanced dynamic range. After that, the EM signal is amplified by a low-noise amplifier (LNA) and filtered by a band-pass filter to cut the out-of-band frequency components. A mixer is used to convert the signal from RF to an intermediate frequency (IF), in a process called downconversion, making use of a local oscillator (LO). The IF amplifier boosts the receiver signal and maximizes the output signal-to-noise ratio, which is a Ftotal= F1+ F2_G− 1 1 + F3− 1 G1G2 + F4− 1 G1G2G3 + . . . + Fn− 1 G1G2. . . Gn−1

matched filter’s function. This feature helps to maximize the detectability of the signal [1].

Posteriorly, another IF filter for rejecting the unwanted intermodulation products outgoing from the mixer is employed. After this, detection is performed, and the signal is sent to an ADC. Here, the signal is digitized and then a DSP unit is responsible for signal processing [1]. The detector is responsible for removing the carrier from the modulated signal in order to make the data available to be analyzed by the DSP [5].

The receiving process analyzed above is called “Superheterodyne”. A block diagram of such receiver is reported in Figure 1.2.

Figure 1.2: Block diagram of superheterodyne receiver .

The most important feature is that different IF can be applied changing the local oscillator’s frequency. If a fixed frequency local oscillator (LO) is employed, the same process is called “heterodyne”. The superheterodyne feature allows to employ the same receiver with different carrier frequencies (Multi-band receiver). The received signal suffers from varied noise sources. These noises can appear in different forms: internal and external electronic noise, reflection from unwanted surfaces, the so called clutter, unintentional external EM waves coming from other electronic sources, called electromagnetic interference, and finally intentional jam- ming in the form of noise or false targets.

The signal processor unit is responsible for detecting and extracting information about the environment from raw radar signals, as target, clutter and jamming [5]. Modern systems use DSP units, which have the advantage of being completely programmable. This feature allows the system to implement a vast range of functions in a single unit, while enhancing the overall radar performance [5].

1.2 Radar principle of operation

The basic idea in a radar system is that an EM wave is sent from the transmitter antenna. During its path, the EM wave illuminates a certain number of surfaces that back-scatter the incident energy. So, a portion of such energy, named echo, come back to the receiving antenna allowing the radar detection. Two different waveform can be employed in radar signal transmission: continuous wave (CW) or pulsed signal. The CW represents the configuration in which the transmitter is continuously transmitting the signal. For this reason when a continuous waveform is adopted, a multi static configuration is required.

In case of pulsed signals, differently, the transmitter sends the waveform in a finite time intervals. In this way both mono static and multi static configurations are allowed.

In the CW configuration the receiver is always operational, while in pulsed signal, the receiver is “on” when the transmitter is “off”, so the transmitted signal can be detected [5].

For pulsed signals, different parameters can be defined. These are highlighted in Figure 1.3.

Figure 1.3: Pulsed signal waveform with its parameters [5].

The time in which the signal is transmitted is called pulse width τ, usually measured in µs. During this time the receiver is isolated from the transmitter in order to protect its components from the high power signal. It is possible to define the blind distance as the circular area around the radar radius:

(1.2)

where c is the speed of light in free space and the one half is due to the go-back path. Target that are present in this area are not detectable since the receiver is “off” when the echoes come back.

During the interval in which the transmitter is not sending pulses, the receiver is turned on in order to allow the reception of the reflected echoes. The total time the radar is listening to the environment plus the time of one pulsed radar cycle time is called pulse repetition interval (PRI). The inverse of the PRI, is called pulse repetition frequency (PRF = 1/PRI), and represents the number of cycles the radar completes per second.

The range (distance) R to the target can be calculated according to the following equation [5]:

(1.3)

where c is the speed of light and ∆T is the time the E M wave takes to propagate to the target and return back from it [5].

_{The fraction of time that the transmitter is emitting the signal is known as} duty cycle (dt), and its related with the pulse width as [5]:

(1.4)

In pulsed waveforms, there is a maximum range in which a transmitted signal can be reflected and received before the next pulse is transmitted. This parameter depends on the PRI (PRF) and is called maximum unambiguous distance (Rua). It is given by

(1.5)

If the target’s distance is higher than Rua, ambiguities can occur since the

receiver can not identify if the echo is coming from the previous or from the last transmitted waveform. This range ambiguities can be avoided if all the targets of interest are confined within a PRI [5].

Another important parameter, related to the radar waveform, is the radar range resolution. It is defined as the smallest distance between two different targets that the radar can still distinguish between them. If, on the contrary, the distance between two targets is smaller than the range resolution, then the radar will not be able to identify the presence of both targets. The range resolution, ∆R is defined as [5]:

(1.6)

Radar system can be further classified considering the the detection processing it employs. They are divided in coherent and non-coherent. The substantially difference between these two categories consists of the detection outputs. In particular:

R = cΔT₂

dt= τ_PRI = τPRF

Rua = cPRI₂ = c_2PRF

-

Non-coherent system, can use only the amplitude information of the received signals;

-

Coherent system, can use both the amplitude and phase information.

In order to have a coherent system, the phase information has to be available at the receiver in order to apply a matched filtering to the received signal that contain also the phase information.

In coherent systems, the phase information provides information about target motion characteristics and the ability to perform tasks, such as moving target indication, Doppler processing, target imaging and space-time adaptive processing [5]. A highly stable source must be used to provide the references for both transmitter and LO frequencies.

1.3 Radar Equation

The radar equation (RE) is an expression that describes the received back-radiated power from the target that was influenced by sources of interference. Many sources of interference take place during a radar transmission.

The receiver thermal noise is the first significant interference that affect the signal. The ratio between the target signal and noise power is called signal-to-noise ratio (SNR). Furthermore, the signal can suffers interference from the unwanted sources of reflection from the environment, known as clutter. The ratio between the signal and clutter power in this case is called signal-to-clutter ratio (SCR). Generalizing, the ratio of the target signal to the total interfering signal is referred as signal-to-interference ratio (SIR) [5].

The radar equation gives the received power of the echo waves reflected from the target, other surfaces and volumetric clutter signal. There are several different forms of RE. Its importance is mostly related to the minimum power the received signal must have in order to detect a target (radar system’s Sensitivity), or the maximum range, given a certain power, in order to detected a target (Rmax) [5].

_{The radiated power density, Q}i, given in watts per square meter from a

radiating omnidirectional radiating antenna at a distance R, is given by [5]:

(1.7)

where Pt is the total peak power applied to the antenna, divided by the surface

area of a sphere, whose radius is given by R. The denominator represents the free space attenuation for EM waves radiated by an isotropic source. However, real systems mainly use directional antennas instead of an isotropic beam pattern. The power density, in this case, increases by the antenna gain, G, which is directly proportional to the directivity, as shown in Figure 1.4. [5]. Gt

is the transmit antenna gain and the new equation considering a directional beam pattern is given by:

(1.8)

Figure 1.4: Directional beam antenna over a surface at range R [5].

Then, the signal transmitted from a radiating antenna is directed to a real target. The echo signal from the desired surface is scattered over many directions. Only a little part of it will return to the radar (radar echo). The power reflected by the target back to the antenna, Prefl is given by the

product of the incident power density (Qi) by the target radar cross section

(RCS). This last parameter is defined as the effective area intercepting an amount of incident power, which produces a level of reflected power at the radar that is equal to that from the target. Mathematically [5]:

(1.9)

where σ is the RCS. Considering Eq. 1.9, the power density received back at the radar (Qr ) is [5]:

(1.10)

Q_i= _4πRPtGt₂

Prefl = Qiσ = P_4πRtGtσ₂

Furthermore, the receiver antenna area must be considered. The power received (Pr ) by a receiving antenna, with an effective area of Ae, can be mathematically

described as the power density at the antenna times the effective area of the antenna [5]:

(1.11)

Considering that the receiver antenna gain (Gr ) is related to its effective area

as [5]:

(1.12)

and substituting in Eq. 1.11, the final expression of the received power, Pr , is

[5]:

(1.13)

where Pt is the peak transmitted power expressed in watts, Gt and Gr are the

transmission and reception gains, respectively, λ is the carrier wavelength expressed in meters, σ is the target mean RCS expressed in square meters, and R is the range from the antenna to the target expressed in meters [5]. In the case of mono static radar systems, in which the system uses the same antenna for both transmission and reception, the gain from the transmit and receive antennas (Gt and Gr ) are the same, so [5]:

(1.14)

The expression cited above (Eq. 1.13) is derived without considering any sources of noise. However, there are many sources of random noise that influences the received signal. Below 1 GHz cosmic noise is a significant contributor to the total noise. Beyond 1 GHz, it is not a big issue, and its effect is reduced by the antenna sidelobe gain [5].

A great source of noise rises from the thermally random electron motion in the receiver circuits, known as receiver thermal noise. The signal from a target must exceed the noise signal for a reliable detection and in some cases even by a significant value. This noise source is uniformly distributed over all radar frequencies, for this reason is called “white” noise. The thermal noise power (Pn)

in the radar receiver is given by [5], [15].

(1.15) Pr = QrAe= P_(4π)tGt₂A_Reσ₄ G_r = 4π A_λ2e Pr = PtGtGrλ 2_σ (4π)3_R4 P_r = P_(4π)tG2₃λ_R2σ₄ P = kT B = kT FB

where k is the Boltzmann constant, T0 is the standard temperature (290

°K), Ts is the system noise temperature (Ts = T0F ), B is the instantaneous

receiver bandwidth in Hz and F is the noise figure of the receiver subsystem [5], [15]. As Eq. 1.15 shows, the noise power is proportional to the receiver bandwidth. The optimal bandwidth depends on the specific shape of the receiver filter characteristics [5] and in practice is usually calculated as 1/τ . The signal-to-noise ratio (SNR) can be calculated as the received target signal power Pr divided by the noise power Pn [5]:

(1.16)

Generalizing, the radar performance is determined by the signal-to-interference ratio, which considers all interference sources. The SIR is represented as [5]:

(1.17)

where S is the received target signal, N is the receiver thermal noise, C is the clutter noise and J is the jamming noise [5].

1.4 Radio-Frequencies and Radar applications

Considering the carrier frequency, an RF signal can be classified in a certain radar band. Figure 1.5 shows the IEEE assignment. Each frequency band possesses its own characteristics, which make each of them suitable for different applications.

Figure 1.5: Classification of an EM wave considering its frequency.

The High Frequency (HF) band, which covers frequencies from 3 to 30 MHz, was mainly adopted during the World War II [1]. The many disadvantages of this frequency band are the large antenna size, high natural ambient noise level and narrow bandwidths. This characteristics makes it unattractive for most modern applications. Nevertheless, over-the-horizon detection of aircrafts

SNR = _PPr

n =

PtGtGrλ2σ

(4π)3_R4_kT0FB

employs the HF region, since the observation of large areas are not practical with conventional microwave radars [1].

The Very High Frequency (VHF) band covers frequencies from 30 to 300 MHz. This band was employed in the majority of the early radars in the 1930s. The disadvantages of this band are quite the same of those for the HF band. On the other hand, the components required are cheap and easy to assembly, especially compared to microwave frequencies. The VHF band can find applications in lower-cost radars and for long-range radars such as those for the detection of satellites [1].

Ultra High Frequency (UHF) band covers frequencies from 300 to 1000 MHz. It can be suitable for applications as long-range surveillance radar, especially for extraterrestrial targets such as spacecraft and ballistic missiles, and it can also be used for airborne early warning. Also in this case, there are disadvantages similar to VHF and HF, but the external noise is much less, and beamwidths are narrower with respect to the HF and VHF [1].

Frequencies ranging from 1 to 2 GHz belong to the L-band. In this band the external noise is low and it is possible to obtain high power with narrow beamwidth antennas. Applications include land-based long-range air surveillance radars, military 3D radars and long-range radars that must detect extraterrestrial targets [1].

The S-band covers frequencies from 2 to 4 GHz. The long range capability is more difficult to achieve at these frequencies and also moving target indication is less suitable at this band compared to lower bands. Rain’s attenuation can greatly reduce the operative range of these radars. The suitable applications for S-band radars are long-range weather radars, medium-range air surveillance applications, military 3D and height finding radars [1].

Frequencies from 4 to 8 GHz compose the C-band. This band is a compromise between S and X-bands. The C-band radars find applications as long-range precision instrumentation radars used for the accurate tracking of missiles, multifunction phased array air defense radars and for medium-range weather radars [1].

X-band covers the frequency range from 8 to 12.5 GHz. In this frequency band, long range capability is a drawback. Rain and weather conditions dramatically affect this band. However, X-band radars are generally of practical size and are thus of interest for mobile and relatively light weight applications. The large bandwidth make this frequencies suitable for high-resolution radars. Narrow beamwidths can also be obtained with relatively small-size antennas. These radars find applications in military weapon control (tracking) radar and for commercial applications. Moreover, it can be suitable for shipboard navigation and piloting, weather avoidance, Doppler navigation, and for police speed meter [1].

Frequencies from 12.5 to 40 GHz belong to the K-band. This band is divided in three sub-bands called Ku, K and Ka. The choice of subdividing

the K-band was based on the fact that the center of the native K-band was too close to the water-vapor absorption frequency. Advantages of these bands are the wide bandwidths they can provide, and also the narrow beamwidths achievable using small apertures. On the other hand, operative range limitations due to rain clutter and attenuation occur at higher frequencies [1]. _{Above 40 GHz until 300GHz the so-called millimeter (mm)wave-lengths band} is defined. Applications around 60 GHz are precluded due to the high attenuation caused by the atmospheric oxygen. This zone is further subdivided into letter bands in the IEEE standard. This carrier frequencies are particularly suitable where no atmosphere is present, such as for spatial application. It might also be considered for short-range applications within the atmosphere where the short range lead to low total attenuation that can be tolerated [1].

1.5 MIMO Radar systems with widely separated antennas

The basic idea in MIMO radar is to extend the advantages achievable in MIMO communication system to radar application. This concept have become very popular in the last few years. MIMO stands for Multiple Input Multiple Output, term used in telecommunications to describe systems with more than one input and more than one Output. MIMO systems can be divided in different sub-categories:

- SISO: Single Input Single Output - MISO: Multiple Input Single Output - SIMO: Single Input Multiple Output - MIMO: Multiple Input Multiple Output

The classification of MIMO systems depends on the system’s topology, in particular on the number of transmitting and receiving elements. In communications, the key property that made MIMO such a successful concept has been the ability to substitute the spatial dimension for the bandwidth resource. Narrowband MIMO communication systems perform like wideband systems without MIMO.

1.5.1 Phased-Array, multistatic or MIMO radar?

Phased-array radars with digital beamforming at the receiver have the ability to steer multiple, simultaneous beams. Adaptive array radars process the signals received at the array elements in order to optimize some performance figure of merit, signal-to-interference ratio. In airborne and other applications, the detection of moving targets and their discrimination against the background clutter are of great interest; this led to the development of array radars with

space-time adaptive processing (STAP). Phased-arrays with multiple transmit elements are capable of cohering and steering the transmitted energy. Elements of phased-array radars are typically co-located, both at the transmitter and receiver ends. [16]

Multiple radars suitably placed may be configured to operate in multistatic mode. Typically, a multistatic radar is a system that networks multiple, independent radars. Each radar performs a significant amount of local processing. The output of the local processing may be delivered to a central processor through a communication link. This mean that individual radars of a multistatic system perform local detection decisions, delivering to the central processor just elaborated data. This inevitably lead to a loss of information during the process of data fusion, since non raw data are used to perform it [16].

The purpose of MIMO radar is to define a radar system that employs multiple transmit waveforms and have the ability to process signals received at multiple receive antennas jointly without information loss. Elements of MIMO radar transmit independent waveforms. A MIMO radar may be configured with its antennas co-located or widely distributed over an area. This kind of system has more degrees of freedom than systems with a single transmit antenna. These additional degrees of freedom support flexible time-energy management modes, lead to improved angular resolution, and improved parameter estimation. With widely separated antennas, MIMO radar has the ability to improve radar performance by exploiting RCS diversity, handle slow moving targets by exploiting Doppler estimates from multiple directions, and support high resolution target localization. Figure 1.6 tries to sum up the differences between Phased-Arrays, Multistatic radar configuration and MIMO radar, emphasizing the different kind of architectures. A phased array is a particular antenna configuration for single radar system; a multi static configuration is realized with n independent radar system and a post-processing data fusion. Whereas a MIMO radar is realized employing widely separated antenna that are capable of coherent detection and raw data fusion for multispectral image processing.

Figure 1.6: Concept scheme of (a) Phased Array, (b) Multistatic and (c) MIMO radar

1.5.2 MIMO communication systems and MIMO radars

MIMO systems have led to a revolution in wireless communications. Some publications (for example [20]) indicate that one can exploit similar ideas in radar, suggesting interesting cross-fertilization of ideas between MIMO communications and MIMO radar [17]. For quite some time, it has been understood that radar targets provide a rich scattering environment leading large target RCS fluctuations, as illustrated in Figure 1.7 [16].

Figure 1.7: Backscatter as a function of the azimuth [16].

Such targets display essentially independent scattering returns when radiated from sufficiently different directions. The premise of MIMO radar with widely separated antennas is that angular spread (RCS variations as a function of aspect) can be exploited to improve radar performance in a variety of ways [16].

The parallel to MIMO communication is recognized in the similar roles that the transmission medium (channel) and target play in respectively, communication and radar. In other words, the target serves as the “channel” in the radar problem. For example, combining echoes resulting from independent illuminations yields a Diversity Gain similar to the diversity gain obtained in the communication problem over fading channels, when the data is transmitted through independent channels. In radar, the idea is that any individual look at the target might have a small amplitude return with a significant probability, but by increasing the number of looks, the probability that all the echoes have small amplitude returns can be made arbitrarily small. Sometimes, the nomenclature “statistical” has been used for MIMO radars that exploit a target’s spatial diversity [19].

Diversity gain is only one of two key gains that MIMO communications can provide. The other gain is called Spatial Multiplexing. Spatial multiplexing in MIMO communications expresses the “ability to use the transmit and receive

antennas to set up a multidimensional space for signaling”. Then, it is possible to form uncoupled, parallel channels that enable the rate of communication to grow in direct proportion to the number of such channels (Throughput increase). Similarly, in MIMO radar, a multidimensional signal space is created when the returns from multiple scatterers or targets combine to generate a rich backscatter. With proper design, transmit-receive paths can be separated and exploited for improving radar performance.

In radar systems, bandwidth plays an important role. Frequency diversity (multiband receivers) has been applied to decorrelate RCS response of complex targets, and high resolution location estimation is possible with wideband waveform.

By exploiting the spatial dimension, MIMO radar with widely separated antennas may overcome bandwidth limitations and support high resolution target localization. At the same time, this kind of radar system has the challenge of time and/or phase synchronizing distributed systems, and needs to deal with ambiguities stemming from the large separation between sensors.

1.6 Applications and issues of current radar technologies

There are many different types of radar systems, according to the application they are realized for. Several remote sensing applications can be performed considering the basic radar functions, such as ground-penetrating applications, long-range over-the-horizon search systems, precision tracking systems, intrusion detecting radar, etc [1].

One of the most common type of radars systems is the search radar. This type of radar is used for surveillance, to maintain awareness of selected traffic within a selected area, such as an airport terminal area or an air route [21].

Surveillance radars, however, provide also target tracking, while a search radar can provide only a warning or a one-time designation of a target for acquisition by a tracker [21]. Often, these two functions (searching and tracking) are performed by two different radar systems due to the distinct parameters requirements. In fact, search process is realized pointing the antenna in a given direction, or a mechanically scanning a given volume, with the purpose of detect potential targets [5]; in case of tracking, system signal must reach long ranges, since it measures the target position as a function of time [5]. When there are limitations regarding the power or space available for the hardware implementation, search and track functions can be performed by a single system.

_{Search radar systems can be divided in two-dimensional (2D) and three-} dimensional (3D) search radars. A 2D search radar employs mainly a “fan” beam shaped antenna to perform the search or surveillance of a bounded volume [5], [21]. The antenna pattern is represented by a wide aperture horizontally and narrower vertically, which results in a narrow azimuth beamwidth and a wide elevation beamwidth [5]. A 2D search radar provides information about the

target position in range and azimuth, but the elevation and height information is not reliable, due to the wide elevation bandwidth [5]. On the other hand, 3D search radars can provide accurate range, azimuth and elevation data. It uses a pencil beam shaped antenna, which scans in both azimuth and elevation planes and eliminates the constraint in the vertical dimension, providing coverage of the full-range elevation sector [21].

These kind of radar systems are usually employed on ships, for surveillance or combat systems. In air defense applications, the system usually performs the following functions: detect, track and identify airborne threats [5].

A different concept is exploited in Over-the-Horizon (OTH) radar systems. They have been developed to detect ballistic missile activity at extremely long range (several thousand of miles), during the Cold War [5]. The basic idea is to employ ionospheric refraction phenomenon to allow the detection of the targets around the earth [5].

_{Multifunctional radars use electronically scanning antennas, which employs} phased array antenna technology [21]. In case of search and tracking functions, it exploits a single beam to scan and allocates typically half of its time to perform volume search [21]. The use of phased array systems allow the radar to perform interleaved multiple functions, using a single radar system. The beamwidths used are usually those available from the full aperture and chosen considering factors such as tracking accuracy [21].

There are many other types of radars within military applications, such as ballistic missile defense, radar seekers and fire control, instrumentation/tracking test range, tracking, fire control and missile support, artillery locating, and target identification radars [5].

Commercial radar systems, on the other hand, are used for different applications. For example, process control radars are used to measure the levels of fluid in enclosed tanks or determine the dryness of a product [5]. Other types of commercial radar systems include wake vortex detection radars, police speed measuring radars, ground penetrating radars, radar altimeters, etc [5].

_{Two-dimensional radar systems are also used in commercial applications for} airport surveillance. They scan 360 degree in azimuth through a mechanically steered antenna, while using a wide beamwidth to provide elevation coverage [5]. This kind of system can detect and track many commercial and general aviation planes simultaneously [5].

_{Commercial maritime radar systems are also available and can provide} information about shorelines, channel buoys and marine traffic above the water surface [5]. This kind of systems typically employ a narrow azimuth beam and a relatively wider elevation beam [5].

_{Radar sensors can also give information about the weather, as reflectivity of} rain precipitation, wind speeds, measure of turbulence, etc. The latter two are possible to be implemented with modern radars system that employs Doppler techniques [5]. It can also help to detect wind shear and tornadoes.

Furthermore, the polarization information of the echo signal, in more recent systems, also enables to discriminate between rain and hail [5].

Topographic mapping is a task performed by space-based radar systems. They operate from satellites in the low Earth orbit (typically ≈ 770 km of altitude). In order to provide high resolution information of the area under analysis, SAR techniques are used to obtain suitable range and cross-range resolution [5]. Interferometry is a technique usually employed for this kind of applications. Additionally, ground-based SAR systems use interferometry for providing deformation maps of delimited areas. It can be employed for monitoring large structures, as buildings, bridges and dams [22], and for measuring small displacements to prevent natural hazards, as earthquakes and landslides, subsidence, ice motion, etc [23].

_{Automotive applications also employ radar sensors. It can be used for collision} avoidance, with the radar installed in the vehicle, or for detecting road objects for unmanned vehicle applications, or driving assistance. These are short-range radar systems that can employ an electronically scanned antenna and typically work in the millimeter waveband [5].

_{The challenge on next generation RADAR (radio detection and ranging)} system is to make them very flexible in order to adapt to variable environments, with higher carrier frequencies in order to reduce the size of the antenna and with larger bandwidth for increase resolution.

The digital microwave components (synthesizers and analog-to-digital-converters) suffer from limited bandwidth with high noise at increasing frequencies. For this reason, fully digital radar system can work up to only a few GHz since noisy analogue up- and down-conversions are necessary for higher frequencies [20]. The main issues in conventional radar systems can be sum up as follows:

- Limited bandwidth of electronic components; - Performances frequency dependent;

- Noisy Analogue up-and-down conversions.

Furthermore, considering the MIMO radar concept, high capacity links are required in order to deliver raw data from the widely separated antenna to the radar core. As known RF links as coaxial cables suffers high attenuation for increasing frequency. For this reason they are not suitable for this MIMO radar link. As described in the next chapter, microwave photonics technologies can represent the solution to these issues.

Chapter 2

Microwave Photonics in Radar Systems

In this Chapter a theoretical background on all the photonics technologies employed during the experiments carried out during this thesis work is provided. Particular emphasis is given to the research field of Microwave photonics and the devices employed for the realization of the architectures exploited in the next chapters.

Microwave photonics is an interdisciplinary area that studies the interaction between microwave and optical signals, for applications such as broadband wireless access networks, sensor networks, radar, satellite communications, instrumentation, and warfare systems. In the last few years, there has been an increasing effort in researching new microwave photonics techniques for different applications.

A microwave photonics system uses the advantages of photonics technologies to provide functions in microwave systems that are very complex or even impossible to carry out directly in the RF domain. First, it performs an electrical-to-optical (E/O) conversion of the input electrical signal, then processes the signal in the optical domain, and finally realizes an optical-to-electrical (O/E) reconversion as output of the system (Figure 2.1)

In general, the topics covered by microwave photonics include photonics generation of microwave and mm-wave signals, photonics processing of microwave and mm-wave signals, optically controlled phased array antennas, radio-over-fiber systems, and photonics analog-to-digital conversion.

Figure 2.1: Scheme of principle of a microwave photonics system.

Electricalin

E/O Processing E/O

Optical

Electricalout

2.1 Microwave photonics devices

In this paragraph, all the devices used during the experiments are briefly illustrated. In this way the advantages of using photonics in RF application will be clear.

Photonics is the optics branch that investigate how to control the propagation of single photons that compose the light. It is possible to study the light as an electromagnetic wave made up of particles named “photons”. In Figure 2.2 the electromagnetic spectrum is reported; wavelength of interest for photonics applications are from 1.7 um to 0.8 um (highlighted in the figure).

Figure 2.2: Electromagnetic spectrum

In particular, we can identify three different intervals named “windows”. The difference between these windows is due to the attenuation of the optical fiber, the most common medium used for optical application. This attenuation depends on the wavelength of the light beam. Different parameters are responsible for this attenuation such as production defects and physical phenomenon.

2.1.1 Semiconductor laser

A LASER (Light Emission by Stimulated Emission of Radiation) is a device that emits light through a process of optical amplification based on the stimulated emission of electromagnetic radiation. A laser is different from all the others light sources, since it emits light coherently (Spatial Coherence). This feature allows a laser to emit light in a really narrow spatial beam, reaching high power spatial density and enabling applications such as laser cutting and lithography. An other important feature is the “temporal coherence”, which allows lasers to emit light with a very narrow spectrum.

A laser cavity consists of a gain medium, and an optical resonator (composed by a reflector and an optical coupler) that provides optical feedback (Figure 2.3) [24]. The gain medium is a semiconductor material, with properties that allow stimulated emission condition is verified. Light of a specific wavelength that passes through the gain medium is amplified. The laser pumping energy is typically supplied as an electric current or as light at a different wavelength.

Semiconductor lasers’ applications are extremely widespread, including areas like optical data transmission, optical data storage, metrology, spectroscopy, material processing, etc., due to their compactness, performance, and cost. A wide range of wavelengths are available, covering much of the visible, near-infrared and mid-infrared spectral region. Most devices also allow for wavelength tuning, for example acting on the driving current that pumps the gain medium or the device temperature.

Figure 2.3: Scheme of principle of a semiconductor laser [24].

2.1.2 Mach-Zehnder Modulator

In the early optical communications era, the most common way for modulating an optical signal consisted in directly modulating the driving current of the laser source [25]. This approach presented mainly two drawbacks: first of all, the produced signal was often affected by an undesired frequency chirp and, secondly, the obtained dynamic range is usually not suitable for state-of-the-art microwave photonics applications [26]. The frequency chirp is a high unwanted effect since it spread the optical power over a larger range of frequency, decreasing the level of coherence.

Electro-optic modulators, on the other hand, are fundamental devices in optical communications, since they allow to modulate light more efficiently than with direct modulation. One of the most important Electro-optic modulators is the Zehnder modulator (MZM). Its name is due to its structure, based on the Mach-Zehnder interferometer. Such device is typically realized in Lithium Niobate (LiNbO3) that present particular features regarding to the refractive index. The

principle of operations of this device is based on the Pockels cells. This structures are characterized by an efficient linear electro-optic effect, that lead to medium’s refractive index variation that effectively changes the propagation velocity of light, thus influencing the signal’s phase [27].

The conceptual structure of a MZM is reported in Figure 2.4, as an optical path equally split in two arms, with a phase modulator (PM) on each (or, in some cases, only on one) branch. The two paths then recombine again and, acting on the individual refractive index of each arm, the output signals exhibit an amplitude modulation.

The phase variation, introduced by the PM, can be expressed as a linear function of the applied voltage:

Electric field

Light Output Reflector

(2.1) where Vπ is the half-wave voltage, i.e. the minimum necessary voltage to obtain a

π‑shift of the field phase in the PM.

Figure 2.4 Mach-Zehnder modulator’s architecture scheme. PM: Phase Modulator. Considering the optical field at the input of the MZM like:

(2.2)

Considering that there is a phase modulator on each branch driven by two voltages V1(t) and V2(t), the optical field, after equal splitting, independent phase

modulation on the two paths, and equal coupling, can be written as:

(2.3)

From Eq. 2.3 is possible obtain the amplitude response (Eq. 2.4) and the power response (Eq. 2.5) of a MZM:

(2.4)

(2.5)

Defining V(t)=V1(t)-V2(t) the trends of these two responses are reported in Figure 2.5. φ(υ) = φ0− π V_V π Eopt(t) = E0⋅ ejω0t Eout(t) = E₂0 ⋅ ejω0t⋅ [e−jπ V1(t) Vπ _{+ e}−jπV2(t)Vπ ] T_E(t) = cos [π V2(t) − V1(t) 2Vπ ]e −jπV1(t) − V2(t)_2Vπ TP(t) = cos2_[π V2(t) − V_2V 1(t) π ]

Figure 2.5 Mach-Zehnder modulator’s response. Red line: power response. Blue line: amplitude response.

2.1.3 Optical Amplifiers

Optical amplifiers are devices responsible for boost the optical signal. The function of all the optical amplifier is the same, what change is the task they are performing. For this reason they can be divided in different subcategories such as booster, pre-amplifier, non-regenerative repeater. As known, the presence of a amplifier in a system lead to a worse performance in terms of noise. This fact is true also for optical amplifiers, but for this device it is not a critical factor. Different kind of amplifiers have been developed during the years, exploiting different technologies, such as optical fiber amplifiers and semiconductor optical amplifier (SOA). However we are interested in optical amplifiers, in particular in erbium-doped fiber amplifiers, called EDFA. The conceptual architecture of an EDFA is reported in Figure 2.6.

Figure 2.6: General erbium-doped fiber configuration, showing bidirectional pumping. Erbium doped fiber Wavelength selective coupler Isolator _Isolator

The typical configuration consist of the doped fiber positioned between polarization-independent optical isolators. Different kind of configuration are possible, such as forward, backward, or bidirectional pumping. It depends on the wavelength selective coupler employed to couple the pump light with the input optical signal. To achieve the highest gain, the length is chosen so that the fiber is transparent to the signal at the point of minimum pump power. Isolators maintain unidirectional light propagation so that, for example, backscattered or reflected light from further down the link cannot reenter the amplifier and cause gain quenching, noise enhancement, or possibly lasing [24].

A typical gain curve of an EDFA is reported in Figure 2.7 [24].

Figure 2.7: Gain Curve of a Typical EDFA

2.1.4 Photodetectors

Other key devices in optical systems are the photodetectors that have the purpose to convert the light in an electrical signal by exploiting the absorption mechanism. In general it is a transducer, because it produces at its output a current, called photocurrent, that is proportional to the optical input power.

The photodiode is based on a p-n junction, composed by a p-doped and a n-doped semiconductor region, between two electrodes, as shown in Fig. 2.8.

This kind of photodetectors are referred to as p-i-n photodiodes, where "p" and "n" refer to the material different doping, whereas "i" stands for the middle "intrinsic" layer, which is created primarily to increase the bandwidth of the device (with respect to a simple p-n structure).

The electrical current that a photodiode yield is given by:

(2.6)

IP(t) = ηqP_{h f}in(t)

where the parameter R is the photodiode’s Responsivity and is measured in A W-1_.

As can be seen from Eq. 2.6 a linear relation between photocurrent and optical input power exists. For this reason the photodetector can be seen as a block that calculate the square absolute value of the electric field at the input.

Figure 2.8: Structure of a PIN photodetector.

The photodetector process can be implemented using different architectures. The first architecture historically employed was the optical direct detection. A direct detection receiver is characterized by a simple architecture, but low performances in terms of signal information. In fact, the direct detection process provide information only on signal amplitude. Phase or frequency information cannot be extracted from the optical carrier. For this reason, the direct detection is also called non-coherent detection [28]. Figure 2.9 report the Intensity Modulation and Direct Detection (IMDD) scheme:

Figure 2.9: Block diagram of an Intensity Modulation and Direct Detection system. MZM: Mach-Zehnder Modulator

The main advantage of such process is that the receiver sensitivity is independent from the carrier phase noise and the state of polarization of the incoming signal which are randomly fluctuating in real systems. On the other hand, they present

RFin

∿

Laser PD

MZM