# On the Testing of Advanced Automotive Radar Sensors by Means of Target Simulators

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## Abstract

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## 1. Introduction

_{r}) and azimuths (Ψ) of targets in their view [4,5]. Detailed information on these sensors including realization in a single-chip technology can be found in [6]. In recent years, a significant effort has been made to develop advanced automotive sensors. Beyond ensuring higher levels of immunity against mutual interferences by using more complex modulations, the development is, above all, focused on reaching a substantially higher accuracy and resolution [7,8]. Both goals can be met using a wider modulation frequency band in the 77–81 GHz region, and more transmitting (TX) and receiving (RX) channels. As a result, modern AR sensors detect significantly more targets than common types. For example, as described in [2], common narrow-bandwidth, low-resolution sensors detect a nearby vehicle as a single target. However, the surface of any vehicle consists of areas with low reflectivity and areas with high reflectivity. That is why advanced, wide-band, high-resolution automotive sensors “see” any neighboring car in its view as a set of many targets, each corresponding to one high-reflecting area [7,9]. This is true for all other type of targets.

_{S}, ranging from 0.5 to 1 m. In TSCs, the signal from the tested sensor is received by the receiving antenna, delayed in time, shifted in frequency and amplified/attenuated. The time delay corresponds to the required range of the simulated target, and the frequency shift simulates the Doppler frequency shift resulting from the target´s radial velocity, while the amplitude of the transmitted signal corresponds to the target´s RCS and range. The processed signal is then sent back to the sensor. Such a sensor simulator setup can simulate a single target (or several targets at different ranges) at a single azimuth defined by the sensor’s TS transmitting antenna’s interconnecting line. Simulated target motions can occur at this line only. However, to simulate real traffic scenarios, it is necessary to generate a higher number of targets at more azimuths while the velocity vectors can also evince the azimuthal components (components in directions perpendicular to the sensor’s TX antenna’s interconnecting lines).

_{i}independent signal processing and transmitting module. The high number of installed array elements enables a high number of targets at arbitrary ranges and azimuths to be generated in parallel. Switching targets by ΔΨ from one azimuth to another simulates motions with the azimuthal velocity components. Despite having been published in 1987 as a tool for testing missile radars, up to now, this initial design and the realization of this type of testing setup have not yet matured. To accelerate its development, it is, above all, necessary to derive an acceptably simple and economically acceptable HW structure. This primarily concerns the most demanding and costly millimeter-wave and digital circuits. The following sections indicate that the required simplification can be derived from a detailed analysis of the sensor simulator setup in question. The same analysis is also beneficial for system programming, that means specific settings of all system circuits and parameters, which can enable the generation of the required complex radar pictures. Considering AR sensors alone, their structures, parameters, algorithms, applications, etc., can be found in a great number of references, some of which are mentioned within this text. This also concerns a detailed analysis of additive RF noise and the phase noise of FMCW sensors which can be found even in somewhat dated references [22,23]. Unfortunately, a detailed theoretical analysis of the AR sensor–target simulator setup under concern is lacking. This article aims to fill this gap.

## 2. Signal Level Analysis

_{T}) with its output antenna gain equal to G

_{RT}. The TS receiving antenna with gain (G

_{SR}) and TS transmitting antenna with gain (G

_{ST}) are situated at distances (R

_{S}) from the AR sensor. The gain (G

_{S}) depicts the overall TSC system gain, excluding the gains of the input and output antennas, while G

_{RT}stands for gain of the sensor’s receiving antenna.

_{R}) obtained through the TS can be expressed as

_{R}) can be compared with power which corresponds to the AR detecting a real target (P

_{Rt}) with the RCS (σ) situated at a range (R

_{t}), see Figure 3. This power can be evaluated using the standard radar equation

_{S}) can be derived as

_{S}corresponds to the gain of the overall TS circuits which provide a constant RCS of the simulated target. This gain includes the gains of all millimeter-wave circuits, intermediate frequency (IF) circuits, base-band (BB) circuits and, with care, the digital circuits used and the signal processing applied. It is one of the most important parameters for TS design. When designing TS output circuitry, the output TS power (P

_{ST}) can be useful:

_{SR}is the power received by the AR. In specific programming steps described more closely in Section 7, the solution of Equations (1) and (2), with respect to the RCS, can be necessary, and the resulting formula can be expressed as

## 3. Additive RF Noise Analysis

_{Rt}) corresponding to a real target must also be evaluated, see Figure 3. Consequently, it must be determined how the TS influences the AR sensor noise behavior. The SNR

_{Rt}is related to the input of the AR sensor receiver and can be expressed using the formula

^{−23}J/K represents the Boltzmann constant, while B equals the noise bandwidth. This bandwidth depends upon the sensor type and signal processing applied, e.g., during the evaluation of range in common FMCW sensors, it equals a width of one FFT (Fast Fourier Transform) bin. In Equation (6), P

_{Rt}stands for the AR input signal power received through a reflection from a real target and this power can be evaluated using Equation (2). T

_{0}= 290 K is a standard thermodynamic temperature. Noise power (N

_{aR}) added by the AR, and related to the input of its receiver, is a function of the AR sensor noise figure (F

_{R}), and is defined by the formula

_{0}, for the purposes of the RF noise analysis, these signal paths can be modeled using matched attenuators showing overall attenuations L

_{1}and L

_{2}, see Figure 1. Considering the AR sensor–TS signal path, L

_{1}attenuation can be expressed as

_{2}attenuator models the TS–AR sensor signal path and its value can be calculated using the following relation:

_{1}and L

_{2}equal kT

_{0}B, and this relation describes a logical phenomenon that, from a noise generation point of view, any well-matched attenuator with high loss will behave like a matched load. The noise figure of the TSC equals F

_{S}, while its gain (G

_{S}) is described by Equation (3). Noise added by the TS related to its input can be evaluated as

_{RS}) related to the AR sensor input, and corresponding to an artificial target simulated by the TS, can be evaluated using

_{Smax}) is, or the added noise power (N

_{aSmax}) which degrades the SNR

_{RS}, with respect to the SNR

_{Rt}, by a still acceptable degree. This can be evaluated using the relation

_{RF}stands for the coefficient of the allowed SNR

_{Rt}drop by additive RF noise, e.g., K

_{RF}= 0.5 for the –3 dB drop considered. If the TS shows the same RCS as the real target, hence P

_{RS}= P

_{Rt}, the maximum possible noise (N

_{aSmax}) added by the TS, and related to the input of TSC, can be expressed using Equations (12) and (6) as

_{Smax}) TSC noise figure can be evaluated as

_{RS}(K

_{RF}= 1), the highest TSC noise figure equals F

_{Smax}= 1, but quickly increases when even a slight (tenths of dB) SNR

_{RS}degradation is allowed.

_{Smax}are perhaps even surprisingly higher than can be expected from the low range of R

_{S}. The high obtained values of F

_{Smax}are naturally advantageous and they can lead to simpler than usual millimeter-wave down-converting structures. On the other hand, the TS cannot be fully passive, and amplifiers must be used at suitable system positions. That is why their noise figures must be considered and the noise figure of the whole TSC carefully evaluated.

## 4. Phase Noise Influence

_{0}± B

_{R}/2 into the intermediate frequency band f

_{IF}± B

_{R}/2. The frequency band B

_{R}equals the AR sensor’s modulation bandwidth. In the IF frequency band, all signal processing steps necessary for the target simulator operation are performed. Consequently, the processed signal is converted back to the AR sensor frequency band using the up-converter consisting of the MIX2 millimeter-wave mixer and the LO1 local oscillator. Since the same LO1 is used for both the down- and up-conversions, the process is coherent and precise output frequencies can be reached. The power amplifier PA is needed if an output power (P

_{ST}) exceeding approximately −10 dBm is required, which is nearly always true in the communication field.

_{mem}) (practically unachievable) of the TS, the resulting phase noise influences equal zero. The concerned frequency fluctuations are eliminated in the down- and immediate up-conversions, generally described as

_{mem}) consists of a latency of both the analog and digital TS circuits, and an intentionally set delay simulating a round-trip of the radar signal to the target and back. The utilized LO signal includes a phase noise described by random phase fluctuations (φ(t)). Due to the multiplicative nature of phase noise, i.e., phase noise power is always directly proportional to a power of the deterministic signal, the following analysis neglects signal amplitudes. Hence, the complex LO signal can be expressed as

_{mem}) and up-conversion, the signal (s

_{TX}) transmitted back from the TS to the AR sensor can be described as

_{0}(τ

_{mem}) represents a general constant phase shift, while Δφ(t

_{,}τ

_{mem}) describes time-dependent random phase fluctuations:

_{mem}) of the entire chain generating an artificial target at the required distance. A voltage transfer function (H (Δf)) of the circuit equals the Fourier transform of Equation (23):

_{b}) corresponding to the FMCW principles to be described. Based on Equation (24), the power transfer function can be expressed as

_{LO}(Δf).

_{Δφ}(Δf)) at the up-converter’s output can be evaluated as

_{Δφ}(Δ f ) evaluated for the PLL phase noise specified in Figure 7 can be seen in Figure 8.

_{b}). For this purpose, before being processed by the FFT, the IF or BB signals at the outputs of radar receivers are sampled by suitable ADCs throughout almost an entire duration of frequency chirps (T

_{sw}). The corresponding noise bandwidth B usually equals 1/T

_{sw}, and determines the resolution in a spectrum [26]. The phase noise power in the digitized IF or BB signal can be evaluated as

_{2}– f

_{1}= B. For the target range evaluation, the bin containing the beat frequency (f

_{b}) is decisive; the influences of phase noise in other bins are unimportant.

_{Δφ}(Δf) plot in a common B = 12.5 kHz-wide FFT window, including the beat frequency (f

_{b}) at Δf = 0, leads to very low values of N

_{PN}, resulting in negligible effects of TS phase noise on the AR sensor’s overall noise behavior. This situation can significantly differ if a simulation of multiple targets is required.

## 5. Simulation of Multiple Targets

_{ti}) of the i-th target measured by the FMCW sensor can be evaluated from the detected i-th beat frequency (f

_{bi}) as

_{0}is the speed of light. In this equation, B

_{R}represents the FMCW radar modulation bandwidth (chirp bandwidth), while T

_{sw}stands for the chirp duration. The total phase noise power (N

_{PNi}) degrading the beat signal of the i-th simulated target takes into account the PSD of its own phase noise and the phase noise of M–1 neighboring targets simulated at the same sensor simulator’s TX connecting line. The phase noise power (N

_{PNi}) can be calculated as a summation of the phase noise powers of Equation (28) from of all the individual targets in a B spectrum frequency bin width as

_{bi}positions, the maxima of the PSD of the phase noise of the neighboring targets fall at the beat frequency of the middle target. According to Figure 8, the PSD maxima occur around the frequency offset Δf =f

_{bc}= 100 kHz, and by using Equation (29), the critical distance (ΔR

_{tc}) between the simulated targets can be evaluated as

_{Δφ}(Δf) strongly depend upon the phase noise properties of the microwave frequency source used. Modern LOs are based on the PLL structure which, within a bandwidth of its low-frequency loop, reduces the PSD of the phase noise around the carrier to an approximately constant value (${\mathcal{L}}_{\mathrm{P}}$) shaped into a so-called pedestal ([26,27]). In an example presented in Figure 7, only the right end of this phase noise pedestal determines the maxima of the function S

_{Δφ}(Δf), and therefore the critical beat frequency (f

_{bc}) and the critical distance (ΔR

_{tc}) between the two targets, respectively.

_{sw}= 80 μs and B

_{R}= 600 MHz used in Section 6 lead to ΔR

_{tc}= 2 m which may be quite a realistic inter-target distance. In Figure 9, the simulated spectra of the IF or BB radar signal, with M = 3-detected targets with identical RCSs, are plotted. All considered targets share the same LO characterized by the PSD of its phase noise, as defined in Figure 7. The middle target is exactly 2 m from the outer targets, i.e., about 100 kHz on the frequency axis. The beat signal (S

_{IF2}) corresponding to the middle target at the distance R

_{t2}= 15 m is degraded by a phase noise originating from both outer beat signals. Considering the approximately constant values of S

_{Δφi}(Δf) in a frequency band B around f

_{bc}, the worst case phase noise power (N

_{PNw}) in the single FFT bin containing the middle beat frequency can be estimated as

_{R1}and P

_{R3}depict the powers of beat signals of the two outer targets, while S

_{Δφ1}(f

_{bc}) and S

_{Δφ3}(f

_{bc}) represent the maximal values of the PSD of the correlated phase noise according to Equation (29). Due to the generally small value of S

_{Δφ}for small frequency offsets (see Figure 8), the degradation of the beat signal of the middle target by its own phase noise is considered to be negligible. The above-described behavior is illustrated in Figure 9.

_{PN}) integrated in the B = 12.5 kHz windows, and related to three targets simulated at the ranges equal to 13, 15 and 17 m. The phase noise powers related to the individual beats were calculated using Equation (28) and the phase noise power corresponding to the phase noise floor was calculated using Equation (30). It can be clearly seen that the worst case phase noise power level corresponds to the 15-m-target, but significant phase noise levels are apparent even around both side targets. If R

_{t1,3}>> R

_{tc}, the received powers and the PSD of the correlated phase noise from both side targets are almost identical, and assuming an approximately constant value for ${\mathcal{L}}_{\mathrm{P}}$, another degree of simplification can be derived:

_{PNw}, corresponding to the 15-m-target, requirements placed on the target simulator LO phase noise qualities can be determined. Since no practical data on AR sensor phase noise are generally available, the influence of TS phase noise was related to the AR sensor’s additive RF noise properties, which can be estimated much more easily and much more precisely. As with the case of the additive RF noise analysis presented in Section 3, an allowed drop (K

_{PN}) of the SNR

_{Rt}of the detected beat signal occurs at the AR sensor’s input and this can be evaluated using the relation

_{PN}= 0.5 for a −3 dB drop, K

_{PN}= 0.1 for a −10 dB drop, etc., the SNR

_{RP}represents the signal-to-noise ratio of the power of the detected beat signal of the 15-m-target, with respect to the total influence of the additive RF noise power and worst case phase noise evaluated by Equation (30), and related to the input of the AR sensor’s receiver. From the FMCW sensor point of view, both additive RF noise and phase noise show similar behavior. Both noises are uncorrelated, increase the noise floor and vary the phase of the detected beat signals. That is why their total influence can be evaluated as the sum of the above stated noise powers:

_{PN}-times degrades the signal-to-noise ratio (SNR

_{Rt}) in a single B-wide FFT bin as

## 6. Application and Verification of Derived Formulas

_{SR}= G

_{ST}= 14 dB and AR sensor–TS distance equal to R

_{S}= 0.5 m. With respect to [6], all further calculations consider targets with an RCS σ = 1, 10 and 100 m

^{2}, and simulated target ranges of R

_{t}= 3, 10, 30 and 100 m. These values should sufficiently cover the requirements for MRR testing involving pedestrians, cars, trucks, traffic signs or guardrails.

_{SR}= –20.1 dBm behind the TS’s receiving antenna, while the calculated values of the TS system’s gain (G

_{S}) providing a constant RCS, as defined by Equation (3), are stated in Table 2. The values range from –60 dB to +20 dB which represents an 80 dB required dynamic range. In practice, this dynamic range can be significantly lower. Usually, AR sensors show relatively narrow antenna radiation patterns and large targets in near ranges are not fully illuminated. In addition, in near ranges, for proper target detection, it is not necessary to simulate targets with very high RCSs. Therefore, a G

_{smax}not higher than 0 dB and a dynamic range lower than 60 dB can be considered as satisfactory. This dynamic range can be easily realized, for example, by a combination of digitally controlled analog attenuators.

_{ST}) according to Equation (4), see Table 3.

_{Smax}equal to 0 dB and P

_{ST}equal to −20 dBm can easily be ensured. Further, for proper target detection at a 3-m-range, an RSC equal to 1 m

^{2}should be fully sufficient.

_{ST}= −20 dBm is considered. In near ranges, the values correspond well to the expected reduced RCS values. In far ranges, these achievable target RCSs are, with many dB to spare, sufficient for the simulation of all practical traffic scenarios.

_{Rt}values, defined by Equation (6), correspond to the AR sensor detecting real targets, and are referred to the input of its receiver. Calculated results are presented in Table 5. The noise bandwidth equals B = 1/T

_{sw}= 12.5 kHz, which relates to standard FMCW radar chirp rates and signal processing. As a threshold for a reliable target detection, an SNR

_{Rtmin}= 10 dB, defined in [6], was considered. This threshold corresponds to a target with an RCS equal to 20 m

^{2}at a 100-m range, which corresponds well with the expected MRR capabilities.

_{S}). The relation in Equation (16) enables the maximum F

_{S}values (F

_{Smax}) to provide a K

_{RF}-times degradation of the SNR

_{RS}, with respect to the SNR

_{Rt}values, to be calculated. Table 6 includes the calculated F

_{Smax}values corresponding to a mere 1 dB signal-to-noise ratio drop (K

_{RF}≈ 0.794). Assuming the fully passive millimeter-wave down-converter structure, according to Figure 4 with the LNA and PA left out, and IF LNA at the input of the following IF circuits, the noise figure (F

_{S}) can easily attain approximately 20 dB (5 dB input filter loss, 13 dB conversion loss, 2 dB IF LNA noise figure). As can be deduced from Table 6, the allowed noise figures are, mostly, many tens of dB higher. Moreover, according to Table 5, the SNR

_{Rt}values at low ranges are so high that even the concerned 1 dB drop cannot noticeably influence target detection. These parameters generally allow the TSs to be designed and realized in a relatively simple way by utilizing components with higher losses and noise figures, antennas with lower gains, etc.

_{PN}-times degradation of the SNR

_{Rt}, which is a signal-to-noise ratio corresponding to a real target in the defined ranges. Table 7 shows the results of Equation (36) for the allowed degradation of the SNR

_{Rt}equal to 1 dB, i.e., K

_{PN}= 10

^{−1/10}≈ 0.794. The evaluation assumes f

_{bc}= 100 kHz, which corresponds to a mutual critical distance between two neighboring targets R

_{tc}= 2 m. In the R

_{t}= 3 m and 10 m lines, the condition R

_{t}>> R

_{tc}does not hold and certain deviations can be expected.

_{Smax}included in Table 6. In the given 76–81 GHz frequency band, the common phase noise PSD pedestal values of ${\mathcal{L}}_{\mathrm{Pb}}$ of the available LOs range from −65 to −70 dBc/Hz. This explains why Table 7 indicates potential problems, especially in the 10 m and 3 m lines where relatively high PSD ratios are required. However, even at 30 m, the concerned values of the SNR

_{Rt}are, according to Table 5, so high that a 1 dB drop cannot represent any substantial degradation of the sensor’s detection capabilities. What is more, the evaluated values of ${\mathcal{L}}_{\mathrm{Pb}}$ corresponding to the decisive R

_{t}= 100 m range can easily be met, even by relatively “dirty” LOs.

_{0}B is the TS receiving antenna. Both mixers in TS are considered as noiseless and the overall TS noise figure (F

_{S}) is assigned to the A7 amplifier. This amplifier, with variable gain (G

_{S}), also ensures the simulation of an artificial target with an appropriate RCS in accordance with Equation (3). The influence of free-space losses between the AR sensor and TS are included in the AR sensor’s and TS’s receiving antennas. The time delay between the transmitted and the received signal, resulting in an appropriate beat frequency in the radar receiver, is ensured by RFDELAY blocks including free-space (FS) delays on the distance (R

_{S}) as well. The total noise contribution of the radar to the received signals is introduced by the A14 amplifier with a noise figure (F

_{R}) and 0 dB gain.

_{t}= 30 m and an RCS σ = 10 m

^{2}. The P

_{Rt}= −90.2 dBm power of the beat signal is in accordance with Equation (2), while the plotted noise floors correspond to the allowed SNR

_{Rt}drops (K

_{RF}) equal to 0, 3 and 10 dB. To mimic the sampling of the beat signal during the duration of the chirp, the noise bandwidth of the simulation was set to B = 1/T

_{sw}= 12.5 kHz. From Equation (12), the signal-to-noise ratios (SNR

_{RS}) at the radar receiver corresponding to the considered values of K

_{RF}are equal to 27.8, 24.8 and 17.8 dB. Figure 12 also includes noise levels (N

_{RS}) calculated according to Equation (11), and the agreement with the simulated values is very good.

_{sw}= 12.5 kHz are caused by periodic discontinuities in beat signals at the start of every frequency chirp. Aside from these spikes, very good agreement between Equation (27) and the VSS simulation is clearly observed.

^{2}at distances 13, 15, and 17 m. The concerned targets produce beat signals with frequencies (f

_{b}) equal to 650, 750 and 850 kHz and powers (P

_{Rt}) equal to −65.6, −68.1 and −70.3 dBm. The phase noise parameters of the LO signal are shown in Figure 7. To produce a spectrum with higher resolution, the simulation was performed with a noise bandwidth equal to B = 1.25 kHz. To reduce side lobes, the Hann window was applied to the time domain signals before the FFT processing. In addition, to smooth the noise floor, 10 individual spectrum realizations were averaged. During the first simulation (marked as “noiseless”), all noise sources were turned off, whereas during the next simulation (“PN”), only the phase noise of an LO was introduced. The spectrum in Figure 14 should correspond to that in Figure 9, with the only difference being that the noise floor is about 10 dB less because of the ten-times narrower noise bandwidth used, as mentioned, to obtain a higher resolution. Considering this 10 dB shift, the agreement between Figure 9 and Figure 14 is very good.

## 7. Optimized HW Structure, System Programming

_{Smax}values derived in Section 3 and evaluated in Section 6, the millimeter-wave LNA (MMIC chip, chip capacitors, non-trivial power supply, together with approximately 15 wire-bonds) can be eliminated. Secondly, taking into account the simulator output power (P

_{ST}) values derived in Section 2 and evaluated in Section 6, the power amplifier (PA) can also usually be omitted. The resulting down- and up-converters consist only of chip MMIC mixers and planar filters (see Figure 15).

_{S}) is set according to Equation (3), the sensor detects the target at any range as a target with a constant RCS. This is an advantageous, but not necessarily mandatory, setting. In near ranges, from the radar sensor point of view, even slightly lower signal levels are still strong enough and ensure perfect detection. That is why, in this case, practically set values of G

_{S}can be, without any difficulties, lower than those defined by Equation (3). Lower values of Gs also mean a lower system gain is required and minor intermodulation problems, even in the case of M, in parallel simulated targets can occur. An effective RCS value, corresponding to this modified setting, can be evaluated using Equation (5) and the procedure can check if such an RCS still ensures a reliable target detection. The time delay of the i-th artificial target should be set according to

_{L}describes the total latency of the simulator circuits, including the latency of both the analog and digital circuits. The Doppler frequency shift corresponding to a target’s radial velocity can be evaluated as

_{i}describes the instantaneous velocity of the i-th simulated target, ${\overrightarrow{v}}_{0i}$ represents its unity velocity vector, while ${\overrightarrow{\mathsf{\Psi}}}_{0i}$ stands for its unity azimuth vector defined by the AR sensor simulator’s TX antenna’s interconnecting line. In the digital domain, the Doppler frequency shift can be easily performed by multiplying the received and time-shifted signal by a complex exponential.

## 8. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

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**Figure 2.**Testing setup based on an array of transmitting modules. The TS receiving antenna is situated anywhere in view of the AR sensor.

**Figure 5.**(

**a**) Simplified schematic of TS used for the LO phase noise propagation analysis. (

**b**) Equivalent circuit of the LO phase noise propagation.

**Figure 6.**Transfer function of phase noise in TS and various target ranges. The function is plotted in the logarithmic frequency scale and positive values of Δf.

**Figure 7.**Phase noise spectral density $\mathcal{L}\left(f\right)$ of a typical mmW LO source described as −65 dBc/[email protected] kHz, −75 dBc/[email protected] kHz and −115 dBc/[email protected] MHz. The half-width of the phase noise pedestal is 10

^{5}Hz.

**Figure 8.**Phase noise spectral density (S

_{Δφ}(Δf )) of the TS up-converted output signal for an LO source with $\mathcal{L}\left(f\right)$ shown in Figure 7. (

**a**) Plotted for the positive values of Δf in a log scale, frequency range 0–10 MHz. The marked frequency range is crucial when simulating more artificial targets at a single azimuth. (

**b**) For both the positive and negative frequencies of Δf in a linear frequency scale, at a frequency range of ±500 kHz.

**Figure 9.**(

**a**) MATLAB simulation of the power spectrum of received radar beat signals of three artificial targets at a single azimuth with a radar cross-sections (RCS) σ = 100 m

^{2}and distances of 13, 15 and 17 m (mutual critical distance equals 2 m). Applied noise bandwidth equals B = 12.5 kHz and all simulated targets share the same LO characterized by the power spectrum density (PSD) of its phase noise defined in Figure 7. The frequency-modulated continuous-wave (FMCW) radar parameters considered are defined in Section 6. (

**b**) Detail of the approximately calculated −125 dBm phase noise floor.

**Figure 10.**Measured spectrogram of received and down-converted signal from the MRR1 radar sensor with the external LO frequency set to 75.9 GHz. Transmitted chirps range from 76 to 76.5 GHz, while the active time of the chirp sweep is approximately 80 μs long.

**Figure 11.**AWR Visual System Simulator schematic used for the analysis of the FMCW radar with the TS simulating a single artificial target. The radar model consists of the chirp generator A1, mixer A13 and transmitting and receiving antennas A2 and A12. The radar–TS round-trip delay is simulated by blocks A3 and A11. The TS model consists of receiving and transmitting antennas A4 and A10, and down- and up-converting mixers A5 and A8, with the shared local oscillator A9. Range of a single target is set by delay block A6 and its RCS by amplifier A7.

**Figure 12.**Simulated and calculated spectra of BB radar signals with additive RF noise. The beat signal at frequency 1.5 MHz is caused by an artificial target set to a 30-m range and an RCS equal to 10 m

^{2}. The amplitude of the beat signal is constant independently of the TS’s noise figure. Values of K

_{RF}= 1, 0.5 and 0.1 correspond to TS’s noise figures F

_{S}= 0, 85 and 95 dB, respectively. The “theory” lines represent the theoretical additive noise floors evaluated according to Equation (14).

**Figure 13.**Simulation of phase noise at the radar BB output for targets at ranges of 3 and 100 m producing beat frequencies (f

_{b}) equal to 150 kHz and 5 MHz, respectively. The frequency axis of Δf

_{b}represents only the positive offset from the corresponding beat frequency. The spikes repeating every 1/Tsw = 12.5 kHz are caused by periodic discontinuities in beat signals at the start of every frequency chirp. The theoretical dependency of phase noise was computed using Equation (27).

**Figure 14.**Simulation of beat signals at the AR sensor’s receiver coming from three targets at distances of 13, 15 and 17 m with an RCS 100 m

^{2}. In the “noiseless” case, the AR and TS are considered to be noiseless, and the only factors worsening the detection of targets is a main lobe of the Hann window utilized in the FFT processing. The “PN” case introduces phase noise to the LO signal in TS according to Figure 7. Thanks to the summation of noise contributions from both side targets, the center target is degraded, as predicted in Figure 9.

**Figure 15.**Fabricated mmW down- and up-converter containing a built-in 14 dB horn antenna, MMIC balanced mixer, planar filters and LO and IF connectors.

MRR Parameter | Value |
---|---|

Start frequency of FMCW chirps | f_{c} =76 GHz |

Bandwidth of FMCW chirps | B_{R} = 500 MHz |

Sweep time FMCW chirps | T_{sw} = 80 µs |

Radar transmitted power | P_{T} = 10 dBm |

Radar transmitting antenna gain | G_{RT} = 20 dB |

Radar receiving antenna gain | G_{RR} = 10 dB |

Noise figure of radar receiver | F_{R} = 15 dB |

Sampling frequency of IF signal | f_{s} = 10 MHz |

**Table 2.**Calculated values of overall TS system gain (G

_{S}) (dB) necessary to simulate an artificial target with a constant RCS and specific ranges.

σ | 1 m^{2} | 10 m^{2} | 100 m^{2} | |
---|---|---|---|---|

R_{t} | ||||

3 m | 0.0 | 10.0 | 20.0 | |

10 m | −20.9 | −10.9 | −0.9 | |

30 m | −40.0 | −30.0 | −20.0 | |

100 m | −60.9 | −50.9 | −40.9 |

**Table 3.**Calculated values of the TS transmitted signal power (P

_{ST}) (dBm) necessary to simulate an artificial target with a constant RCS at specific ranges.

σ | 1 m^{2} | 10 m^{2} | 100 m^{2} | |
---|---|---|---|---|

R_{t} | ||||

3 m | −20.1 | −10.1 | −0.1 | |

10 m | −41.0 | −31.0 | −21.0 | |

30 m | −60.1 | −50.1 | −40.1 | |

100 m | −81.0 | −71.0 | −61.0 |

**Table 4.**Calculated values of an achievable RCS of targets at various ranges with a limited maximal TS output power equal to –20 dBm.

R_{t} (m) | 3 | 10 | 30 | 100 |
---|---|---|---|---|

σ (m^{2}) | 1.02 | 126 | 10,200 | 1,260,000 |

**Table 5.**Calculated values of the signal-to-noise ratio (SNR

_{Rt}) (dB) at the AR sensor receiver input for various RCS values and ranges considering real targets.

σ | 1 m^{2} | 10 m^{2} | 100 m^{2} | |
---|---|---|---|---|

R_{t} | ||||

3 m | 57.8 | 67.8 | 77.8 | |

10 m | 36.9 | 46.9 | 56.9 | |

30 m | 17.8 | 27.8 | 37.8 | |

100 m | −3.1 | 6.9 | 16.9 |

**Table 6.**Calculated values of maximal noise figures (F

_{Smax}) (dB) of TS circuits causing the degradation of the SNR

_{Rt}by 1 dB.

σ | 1 m^{2} | 10 m^{2} | 100 m^{2} | |
---|---|---|---|---|

R_{t} | ||||

3 m | 49.2 | 39.2 | 29.2 | |

10 m | 70.1 | 60.1 | 50.1 | |

30 m | 89.2 | 79.2 | 69.2 | |

100 m | 110.1 | 100.1 | 90.1 |

**Table 7.**Calculated values of the LO phase noise pedestal (${\mathcal{L}}_{\mathrm{Pb}}$) (dBc/Hz) causing degradation of the SNR

_{Rt}by 1 dB; the degradation relates to the middle target when generating three targets with identical RCSs and a critical R

_{tc}= 2 m distance.

σ | 1 m^{2} | 10 m^{2} | 100 m^{2} | |
---|---|---|---|---|

R_{t} | ||||

3 m | −68.9 | −78.9 | −88.9 | |

10 m | −59.0 | −69.0 | −79.0 | |

30 m | −49.6 | −59.6 | −69.6 | |

100 m | −39.1 | −49.1 | −59.1 |

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

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**MDPI and ACS Style**

Hudec, P.; Adler, V. On the Testing of Advanced Automotive Radar Sensors by Means of Target Simulators. *Sensors* **2020**, *20*, 2714.
https://doi.org/10.3390/s20092714

**AMA Style**

Hudec P, Adler V. On the Testing of Advanced Automotive Radar Sensors by Means of Target Simulators. *Sensors*. 2020; 20(9):2714.
https://doi.org/10.3390/s20092714

**Chicago/Turabian Style**

Hudec, Premysl, and Viktor Adler. 2020. "On the Testing of Advanced Automotive Radar Sensors by Means of Target Simulators" *Sensors* 20, no. 9: 2714.
https://doi.org/10.3390/s20092714