Performance Evaluation of Wavelength Division Multiplexing Photonic Analogue-to-Digital Converters for High-Resolution Radar Systems

The performance of the wavelength division multiplexing (WDM) photonic analogue-to-digital converter (ADC) used for digitization of high-resolution radar systems is evaluated numerically by using the peak signal-to-noise ratio (SNR) metric. Two different WDM photonic ADC architectures are considered for the digitization of radar signals with 5 GHz of bandwidth (spatial resolution of 3 cm), in order to provide a comprehensive study of the compromises present when deploying radar signals with high-resolution: 1) a four-channel architecture with each channel employing an ADC with 5 GSamples/s, and 2) an eight-channel architecture with each channel employing an ADC with 2.5 GSamples/s. For peak powers of the pulsed source between 10 and 20 dBm and a distance between the radar antenna and the sensing object of 2.4 meters, peak SNR levels between 29 and 39 dB are achieved with the eight-channel architecture, which shows higher peak SNR levels when compared with the four-channel architecture. For the eight-channel architecture and for the same peak powers of the pulsed source, peak SNR levels between 11 and 16 dB are obtained when the distance increases to 13.5 meters. With this evaluation using the peak SNR, it is possible to assess the performance limits when choosing a specific radar range, while keeping the same resolution.


Introduction
Modern radar applications, such as driverless automobiles and unmanned aerial vehicles [1], require high-range, high sampling speed and high-resolution [2] [3] [4]. To achieve high-resolution in radar systems, a radar signal with large bandwidth is required [1]. However, the digitization of a high-bandwidth radar signal requires analogue-to-digital converters (ADCs) with high-speed and large-bandwidth, which are limited in terms of resolution and electronic timing jitter [5]. Thus, ADC operation is key in the radar performance [6].
Recently, radar systems have benefited considerably from the development of microwave photonic technology, and the existence of mode-locked lasers generating ultra-short pulses with reduced aperture jitter has opened the door for photonic ADCs [6] [7] [8] [9] [10]. A photonic ADC employs an ultra-stable mode-locked laser that provides an array of ultra-short optical pulses which define the sampling instants for the signal to be digitized [11]. At the output of the mode-locked laser, a high-speed electro-optic modulator samples the signal of interest, at the pace of the mode-locked laser [8] [11]. The optical signal containing the information of the signal of interest as an amplitude variation is then converted to electrical using a high-speed photodiode and quantized by an electronic ADC. This procedure ensures that all the timing issues are controlled by the mode-locked laser. This includes the sampling rate, which is controlled by the pulse repetition rate of the laser, and the timing jitter, which is ruled by the laser jitter [8] [11]. This solution does not reduce the rate of the electronic ADC as a single ADC is still responsible for the quantization of the signal at the photodiode output. An effective way to overcome this bottleneck is to employ a time-wavelength interleaving scheme [6] [7] that can relax the front-end bandwidth requirements. For example, a high-bandwidth photodiode and a high-sampling rate ADC can be replaced into a structure with different channels where each channel employs a lower-bandwidth and low-cost photodiode and an off-the-shelf low-speed ADC, removing the impact of comparator ambiguity which occurs with high-speed ADCs [5] [8] [11]. For instance, a single ADC with sampling rate of 20 GSamples/s can be replaced by a time-wavelength interleaved photonic ADC with 4 channels, where each channel employs an ADC with 5 GSamples/s. With a time-wavelength interleaved photonic ADC, the mode-locked laser, or pulsed source, which generates a signal with ultra-short pulses with a given repetition rate, is sliced in frequency into N different channels, forming narrower-band pulsed signals at different wavelengths. Adequate time-separation between the pulsed signals is then guaranteed using tunable delay lines, to form a time-wavelength interleaved sampling clock with N times greater repetition rate than the one of the original pulsed source. A high-speed electro-optic modulator is then used to modulate the RF signal onto the interleaved sampling clock. At the receiver side, the optical signal is demultiplexed into N channels, which are converted to the electrical domain using low-cost photodiodes. The electrical signals of the N channels are digitized by N low-sampling rate ADCs  [12]. However, in practical radar systems, wideband input signals are normally used [13]. In [13] and [14], a wideband radar signal with a frequency range of 8 -12 GHz is digitized using a time-wavelength interleaved photonic ADC. In this work, the time-wavelength interleaved photonic ADC is used to digitize a radar signal with large bandwidth (5 GHz) and small time width (200 ps) as RF input, which provides high-resolution (3 centimeters). The performance of the photonic ADC in this work is evaluated for different architectures and distances between the radar antenna and the sensing object in order to provide a comprehensive study of the compromises present when deploying radar signals with high-resolution. Additionally, the time-stretching operation is employed, which compresses the bandwidth of each channel, relaxing the front-end requirements [10] [15]. Time-stretching is achieved using two dispersive elements, one before optical modulation, to produce a chirped pulsed source, and another dispersive element (with higher length than the first dispersive element) to time-stretch the signal before conversion to the electrical domain [10].
When digitizing radar signals with photonic ADCs, two of the main constraints are the very low signal power captured by the radar antenna, and the signal losses coming from its photonic structure. Therefore, electrical and optical amplifiers with large gain are required, leading to signal-to-noise ratio (SNR) degradation [15]. In this work, the performance of the time-wavelength interleaved photonic ADC, hereafter referred as wavelength division multiplexing (WDM) photonic (Ph)-ADC, is assessed by investigating the compromise between the peak SNR of the recovered samples of the radar signal and the distance between the radar antenna and the sensing object, for optical pulsed sources with different peak powers and WDM Ph-ADCs with different number of channels. With this evaluation, it is possible to assess the performance limits when choosing a specific radar range, while keeping the same resolution.
The paper is structured as follows. Section 2 presents and explains the WDM photonic ADC architecture and its parameters. The WDM photonic ADC architecture enables relaxing the sampling rate of ADCs required to digitize the radar signals employed in systems with high spatial resolution. Section 3 presents the performance results (obtained with the SNR metric) of the recovered samples of the radar signal when using the WDM photonic ADC architecture. The performance results are evaluated and discussed for two different architectures: 1) a four-channel architecture with each channel employing an ADC with 5 GSamples/s, and 2) an eight-channel architecture with each channel employing an ADC with 2.5 GSamples/s. Section 4 summarizes the main conclusion.

WDM Photonic ADC
In this section, the WDM Ph-ADC architecture is presented, and the parameters

WDM Photonic ADC Architecture
The WDM Ph-ADC architecture is described in this subsection. Figure 1(a) shows the WDM Ph-ADC architecture. Figure 1 Ph-ADC. In the illustration of Figure 1(b) it is assumed that the wideband spectrum of the pulsed source is much greater than the bandwidth of the WDM signal to ensure that the different wavelengths have similar power. An optical delay line (ODL 1 ) is introduced to ensure adequate time-separation between the pulsed signals of each WDM channel in order to sample the radar signal sequentially over time. The time delay from ODL 1 is given by where ∆ res = T rep /N is the time resolution of the digitized radar waveform, and n is the channel index ( 1, 2, , n N =  ). ODL 2 is used to compensate for the walk-off effect suffered by each WDM channel due to the propagation over the first single mode fiber (SMF) span (SMF 1 with length L 1 ) [3] (point A in Figure   1(a) and subfigure (1) in Figure 1(b)). The time delays introduced by ODL 2 (n) are equal to for N even, where D λ is the fibre dispersion parameter in ps/nm/km, L 1 is the first span length in km, and ∆λ is the AWG channel spacing in nm. AWG2 combines the pulsed signals of the different channels in a pulsed signal with consecutive pulses separated in wavelength. The signal at the AWG2 output is propagated along the SMF 1 span, which broadens the optical pulses and introduces walk-off between them (previously compensated by ODL 2 ) [3]. The signal after propagation along SMF 1 is a pulsed signal with a repetition period given by ∆ res . Afterwards, amplification is performed by an optical amplifier (OA 1 ) to compensate for the accumulated losses of the AWGs and the first SMF span. In the estimation of the noise introduced by the optical amplifiers, it is assumed that the amplified spontaneous emission (ASE) noise is modelled by a zero mean Gaussian noise with power spectral density (PSD) along one polarization direction (parallel or perpendicular) and along one signal component (in-phase or quadrature) given by where h is the Planck constant, ν is the central frequency of the optical signal spectrum, f n is the OA 1 noise figure and g o1 is the OA 1 gain.
The signal at the OA 1 output feeds the electro-optic modulator (EOM), which modulates the optical pulses by the high-resolution radar signal to be sampled (point C in Figure 1(a) and subfigure (3) in Figure 1(b)). The EOM is described by a linear input-output characteristic. This model is valid when the modulation depth of the electrical signal driving the EOM is sufficiently small to ensure linear operation. For spatial resolutions of the order of a few centimetres, radar bandwidths of the order of a few GHz are required. The spatial resolution of a radar signal, ∆d, is related with the radar bandwidth B r . This relation is given by , where c is the speed of light in a vacuum. For instance, a radar signal with a 5 GHz bandwidth leads to a spatial resolution of 3 cm [3].
The number of samples along the radar pulse width, N s , is related with ∆ res by where ⋅     corresponds to the operation of approximation to the nearest lowest integer. The radar signal is emitted by the radar antenna in order to "sense" the distance of the objects in the surrounding environment (few meters range). The where P out is the output power of the radar signal sent by the antenna in dBm, P in is the radar received power in dBm, d is the distance between the antenna and the sensing object and f 0 is the central frequency of the radar signal. The received radar signal (with average power P in ) is then amplified by an electrical amplifier (EA 1 ) and filtered by a Gaussian-shape low-pass filter (LPF 1 ) (point B in Figure   1(a) and subfigure (2) in Figure 1(b)). The EA 1 -generated electrical noise is modelled as zero mean additive Gaussian noise with a two-sided PSD given by where k B is the Boltzmann constant (k B = 1.38 × 10 −23 J•K −1 ), T is the temperature in Kelvin, R L is the load resistance, f e is the EA 1 noise figure and g e is the voltage gain of the electrical amplifier EA 1 .
After electro-optic modulation, a second SMF span (SMF 2 ), with the same dispersion parameter as SMF 1 but with length L 2 (L 2 > L 1 ), broadens even more the optical pulses causing time-stretching [15]. The time-stretching operation compresses the spectrum at the receiver-side and is regulated by the stretching factor M = 1 + (L 2 /L 1 ) [15]. Then, the optical signal is amplified by the optical amplifier OA 2 , which compensates for the EOM losses and the losses of the second SMF span. The optical signal at the OA 2 output is demultiplexed by AWG3 to photodetect individually each channel. For the photodetection operation, PIN-photodetectors (PDs) are employed to convert the intensity fluctuations of the optical pulses to electrical current. The photodetected signals of each channel are then amplified (EA 2 amplifiers) and filtered by a Gaussian-shape low-pass filter (LPF 2 filters) with bandwidth equal to half of the repetition rate of the pulsed source (LPF 2 emulates the bandwidth of each ADC, which should be half of the ADC sampling rate). The EA 2 -generated current noise is modelled as an additive Gaussian thermal noise with two-sided PSD given by where f r is the EA 2 noise figure and g r is the voltage gain of the electrical amplifier EA 2 . An electrical delay line (EDL 1 ) is introduced to compensate for the walk-off effect suffered by each WDM channel due to the propagation over the second SMF span [3]. EDL 1 (n) adds time delays equal to  Figure 1(b)), which are responsible for the digitization of the waveforms of each channel (point E in Figure 1(a) and subfigure (5) in Figure 1(b)). These ADCs have to be adequately synchronized by a trigger signal in order to sample the pulsed signals in the peak of each pulse [3]. The trigger associated with the sampling process of each ADC is obtained directly from the pulsed source signal, which has been previously photodetected. To en-  Figure 1(a) and subfigure (6) in Figure 1(b)), that receives and combines the digital signals of the different ADCs.

WDM Photonic ADC Parameters
Different combinations of number of channels and repetition rates of the pulsed source can be considered. in a WDM Ph-ADC architecture with 2 channels and employing ADCs with 10 GSamples/s. In this work, a radar bandwidth of 5 GHz is considered, which leads to a radar pulse width (equal to 1/B r ) of 200 ps. Additionally, it is assumed that ∆ res = 50 ps, which indicates that 4 samples along the radar pulse width of 200 ps can be recovered. With 4 channels, it is possible to recover one sample of the radar signal per channel. With 8 channels, there will be channels which will not capture samples inside the radar signal when ∆ res = 50 ps. If the number of channels is reduced to 2, each channel is responsible for recovering 2 samples of the radar signal. In this work, two different WDM Ph-ADC architectures are considered: 1) architecture A with f rep = 5 GHz and N = 4, which represents a good compromise between number of channels and ADC sampling rate, and 2) architecture B with f rep = 2.5 GHz and N = 8, which is less demanding in terms of ADC sampling rate but requires a higher number of WDM channels.
The WDM Ph-ADC employs a pulsed source with 5 GHz and 2.5 GHz repetition rate for architectures A and B, respectively, and the pulsed source has a −3 dB bandwidth of 2 nm, similar to the ones shown in [17] [18]. Each AWG has an insertion loss of 5 dB, a frequency response modelled by a Gaussian filter with

Methods, Performance Results and Discussion
In this section, the performance of the WDM Ph-ADCs used to digitize the high-resolution radar signal is evaluated using numerical simulation in MATLAB.
The SNR is considered as a metric for performance evaluation and is estimated  Table 1 shows the radar received power and the distance between the radar antenna and the sensing object as a function of the FSPL. The analysed configurations correspond to radar-object distances that do not exceed 13.5 meters. Figure 2 shows the optical spectra of the pulsed source and of the channels at the AWG1 output, for architectures A and B, respectively. Figure 2 shows that, due to the power attenuation induced by the non-ideal amplitude response of    shows that the power level is relatively low for both architectures. To compensate this, optical amplification is employed before electro-optic modulation. Figure 4 shows the radar pulse before and after low-pass filtering with a LPF 1 filter with −3 dB bandwidth of 10 GHz (the radar signal is null outside the interval shown in Figure 4). The radar pulse is centered at 49 ns and its width is 200 ps (between 48.9 and 49.1 ns).    Figure 6 shows the signal voltages at the ADC input, for different channels of both architectures. It shows clearly the time-spreading, together with the difference in amplitude between different channels, also attributed to the non-flat amplitude response of the pulsed source and the non-flat amplitude of the radar pulse at the EOM input. Figure 6 also shows that the spreading in time is stronger for architecture B. This is a consequence of the bandwidth of the low-pass filter LPF 2 , which is lower for architecture B.
The power difference verified for different channels induces different performance among the WDM Ph-ADC channels. This performance can be quantified using the SNR per channel. The SNR is given by the ratio between the instantaneous signal power and the variance of the noise introduced by the Ph-ADC. When recovering the radar samples at the receiver side, we are most interested in the peak SNR (average power ratio between the peak of the instantaneous signal power and the noise variance at the same time instant), which gives the best performance level when recovering the radar samples [15]. For this reason, the SNR levels shown in this section correspond to the peak SNR levels.     shows that the channels with lower SNR are the first channel and third channels for architectures A and B, respectively. This is attributed mostly to the power attenuation induced by the pulsed source in these channels and reveals the importance of using optical pulsed sources with flattened shape. Figure 9 also shows that the peak SNR variation of the different channels does not exceed 4 dB and 3 dB for architectures A and B, respectively. The peak SNR variation is smaller for architecture B due to the smaller difference in power loss induced by the pulsed source. In each channel of interest, for both architectures, the SNR variation does not exceed 1.5 dB, for all considered gain combinations. Figure 9 also shows that, for all gain combinations, the peak SNRs are approximately 1.5 dB higher for architecture B, when comparing with architecture A. Since the non-flat amplitude response of the pulsed source induces less attenuation to the channels of interest of architecture B, the signal power at OA 2 output is higher for architecture B. This results in a small improvement in the overall SNR of the different channels of architecture B, when comparing with architecture A. Since the main interest is to obtain the highest peak SNR for a specific distance, in this work we define the peak SNR of interest as the highest peak SNR of the most limiting channel. Hereafter, this is referred as the worst-case scenario. For architecture A, the worst-case scenario is the highest peak SNR of the first channel. For architecture B, the worst-case scenario can be the highest peak SNR of the third or the sixth channel, as they present similar SNR values for some gain combinations. In the following analysis, the third channel is chosen as the worst-case scenario for architecture B. Additionally, the best-case scenario is also considered, which corresponds to the highest SNR levels for the third channel for architecture A, and to the highest SNR levels for the fifth channel for architecture B.  architectures. Figure 10 shows that the SNR decrease with increasing distance is stronger for higher peak powers of the pulsed source. For instance, for architecture A, with P p = 10 dBm, the SNR decreases approximately 16 dB when the distance increases from 2.4 to 13.5 meters. With P p = 20 dBm and for the same distance increase, the SNR decreases approximately 22 dB. Figure 10 also shows that, for a distance of 2.4 meters, peak SNR levels higher than 25 dB are achieved for both architectures. When the distance increases to 4.3 meters, peak SNRs higher than 20 dB are obtained. For a distance of 13.5 meters and for both scenarios, the peak SNR levels are substantially lower: for instance, the peak SNR for the worst-case scenario decreases to 9 dB for architecture A and to 11 dB for architecture B. Figure 10 also shows that the SNR variation between the worst-case and best-case scenarios, for the same peak power of the pulsed source and the same distance between the radar antenna and the sensing object, is higher for architecture A, when comparing with architecture B. This is a direct consequence of the non-flat amplitude response of the pulsed source, which induces higher power levels to the channels of interest of architecture B, when comparing with the power levels induced on the channels of architecture A. Figure 10 also shows that when comparing the worst-case and best-case scenarios for the considered peak powers of the pulsed source and for a distance of 2.4 m, the peak SNR varies between 25 and 38 dB for architecture A and between 29 and 39 dB for architecture B. When the distance increases to 13.5 m, the peak SNR varies between 9 and 15 dB for architecture A and between 11 and 16 dB for architecture B. In conclusion, architecture B provides higher peak SNR levels when compared with architecture A. Figure 10 also shows that the difference between both architectures does not exceed 4 dB, when considering the same peak powers of the pulsed source and the same scenario.

Conclusion
The performance of the WDM Ph-ADC system with 4 and 8 channels (employing ADCs with sampling rate of 5 GSamples/s and 2.5 GSamples/s, respectively) used for the digitization of high-resolution radar signals has been evaluated numerically by using the peak SNR metric. Results show that, when comparing the worst-case and best-case scenarios for the considered peak powers of the pulsed source and for a distance of 2.4 m, the peak SNR varies between 25 and 38 dB for architecture A and between 29 and 39 dB for architecture B. When the distance increases to 13.5 m, the peak SNR varies between 9 and 15 dB for architecture A and between 11 and 16 dB for architecture B. In conclusion, architecture B provides higher peak SNR levels when compared with architecture A, and the peak SNR difference between both architectures does not exceed 4 dB, when considering the same peak powers of the pulsed source and the same scenario. The SNR variation of both architectures can be reduced by choosing optical pulsed sources with more flattened spectrum or by leveling the different power levels induced by the optical pulsed source using optical attenuators for each channel.