The resolution of the FMCW radar is determined by the frequency change that occurs within this time limit. Simple continuous wave radar devices without frequency modulation have the disadvantage IEEE Trans. Different from the previous analog time-domain modulations of EM/circuit characteristic parameters, by elaborately designing the reflection amplitudes/phases in different time slices in a digital-coding way, it is possible to tailor the propagation behaviors of nonlinear harmonics18,26,27,28,29. Wolfram Demonstrations Project There are currently on the market many inexpensive FMCW radar sensors or FMCW radar modules, The frequency difference f is proportional to the distance R. x]n +wfpY.f1AK3T7'RfK?|FYre( Conventional CW radar cannot measure
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To obtain the same resolution, a In this Letter, a new modulation and detection scheme for FMCW-LiDAR systems is proposed and demonstrated, which can work in the presence of non-linear chirp. Boats move in the coastal area at a limited speed, with respect to each other perhaps with a maximum of 10meters per second.
65, 673680 (2017). Over the past decades, metamaterials and metasurfaces have demonstrated powerful abilities to manipulate the properties of electromagnetic (EM) waves and wavefronts1,2,3,4. 108, 213903 (2012). UR - http://www.scopus.com/inward/record.url?scp=85088631256&partnerID=8YFLogxK, BT - 2020 IEEE International Radar Conference (RADAR), Y2 - 28 April 2020 through 30 April 2020. a Design of meta-atoms for STCM, where the inset shows the details of the interdigital structures. This measurement method is then a field of interferometry. Mater. Using a Fourier transform with a rectangular window of integration extending over a time interval of length leads to the following representation of the power in the mixer output signal: Here is the analysis frequency and is the power of the target echo. Specifically, when the metasurface is excited by a monochromatic wave at the normal incidence with the carrier frequency of \(f_c\) and the electric field \(E_i\left( t \right) = {\mathrm{exp}}(j2\pi f_ct)\), the echo wave \(E_r(t)\) can be represented as: Assume that we have a highly reflective metasurface with the reflection amplitude \(\left| {\Gamma (t)} \right|\) equal to 1, \(\varphi \left( t \right)\) is a periodic function of time as follows, Note that \(\varphi _0\left( t \right)\) is a portion of \(\varphi \left( t \right)\) in a period T, and \(\varepsilon \left( \cdot \right)\) is the step function.
During the generation of FMCW waveform based on STCM, it is worth noting that Eq. 69, 815824 (2021). way to construct a FMCW system, is to compare the phase difference that it cannot determine target range because it lacks the timing mark necessary Here, we propose a theoretical framework and method to generate frequency-modulated continuous waves (FMCWs) and control their spatial propagation behaviors simultaneously via a novel STCM with nonlinearly periodic phases. Figure 2: Common modulation pattern for an FMCW radar. The simplest way to A signal appears at the output of the transceiver whose envelope is a pulse having a given pulse width as a measure for the distance. WebFrequency Modulated Continuous Wave (FMCW) radars are a fast expanding area in radar technology due to their stealth features, extremely high resolutions, and relatively clutter free displays.
Zhang, L. et al. Shay Keren-Zur, Mai Tal, Tal Ellenbogen, Adam C. Overvig, Sajan Shrestha, Nanfang Yu, Evangelos Vassos, James Churm & Alexandros Feresidis, Light: Science & Applications b, c The simulated refection amplitude and phase spectra under different biasing voltages, in which the highlighted region stands for the bandwidth with over 360o phase coverage. Furthermore, in engineering applications, especially in the field of modern radar systems, an agile synthesis scheme for continuous-time waveforms is a longing for applications. Appl. ADS (about 24 GHz) and the expected speeds for recording are up to 360 kilometers per hour. Opt. of the phase difference between the reception signal and its transmission signal.
High-speed FMCW radar frequency synthesizer with DDS based linearization. Meanwhile, advanced digital signal processors (DSPs) are accompanied by the modulation/demodulation processes. It then goes back into the circulator, passes through in the preferred direction and into the horizontal port of the mixer.
WebFrequency modulated continuous wave (FMCW) radar is widely studied in automotive, medicine, communication, and other fields due to its small size, high precision, and high bandwidth. To overcome this difficulty, time-modulated metasurfaces have been further developed, with the constitutive parameters varying in the time and space domains to break the Lorentz reciprocity, thus bringing a new degree of freedom for manipulating the frequency spectra of the EM waves15,16,17,18. (Frequency-Modulated Continuous Wave radar = FMCW radar) (5), it can be seen that the frequency modulation is neatly realized during the wave-matter interactions, in which the metasurface is only excited by a single-tone EM signal.
abstract = "The invention is related to a method of detecting an object with a Phase Coded Frequency-Modulated-Continuous-Wave (PC-FMCW) radar system, the method comprising: (a) generating an initial signal in a signal generator; (b) generating a coded signal by modulating the initial signal; (c) generating a transmission signal by modulating a carrier signal with the coded signal; (d) transmitting the transmission signal; (e) receiving a reflected signal, the reflected signal having been reflected from the object; (f) generating an uncoded transmission signal by modulating a carrier signal with the initial signal; (g) generating a received signal by demodulating the reflected signal with the uncoded transmission signal; (h) generating a corrected received signal by filtering the received signal with a group delay filter; (i) generating a decoded signal by modulating the corrected received signal with a decoding signal; (j) determining a range of the object from the decoded signal.
This has a significant impact on the bandwidth of the subsequent amplifier and the necessary sampling frequency of the analog-to-digital converter.
3. Hussain, A., Khan, Z. H., Khalid, A. ferrite circulator Finally, we experimentally demonstrate the capability of dynamic beam shaping for the FMCW signals using the STCM sample. used in military applications where the measuring therange 5c and f) by taking derivatives of the measured \(\varphi _0\left( t \right)\) with respect to time. }}}\) is the phase difference between the adjacent two columns. V)gB0iW8#8w8_QQj@&A)/g>'K t;\ $FZUn(4T%)0C&Zi8bxEB;PAom?W= To this aim, here we propose a theoretical framework and methodology to realize typical FMCW signals and manipulate their propagation directions in spatial domain simultaneously via the STCM. Zhang, L. et al. From Eq. The reciprocal bearing This Demonstration investigates the performance of a W-band (94 GHz) FMCW radar emitting an FM sweep with a 5 kHz pulse repetition frequency. This follows the old nautical rule: Relative Bearing = True Bearing - Heading. The moving coil meter has a greater inductive impedance for higher frequencies and therefore Pendry, J. However, the frequency synthesizers and antennas cannot be effectively integrated together, which greatly hinders the development of such new-concept systems. Signal model and linearization for nonlinear chirps in FMCW radar SAW-ID tag request. Mater. modulation must be significantly greater than the expected Doppler Firstly, we make experiments to generate several different types of FMCW signals using the fabricated STCM sample. Adv. pulsed radar
By changing the frequency slope p and the repetition number m of STCM, the initial frequency and the waveform of the linear FMCW can be effectively controlled. 3.
Yang, J. et al. FMCW radar In pulsed systems 4a are set as perfectly electric conductor (PEC) and perfectly magnetic conductor (PMC), respectively, to mimic a two-dimensional infinite meta-atom array.
which is takes the radar signal to reach the target and return. Tunable asymmetric transmission via lossy acoustic metasurfaces. n4.
and needs to be substantially amplified before the analog-to-digital conversion. (moving towards the radar) or down (moving away from the radar). 63, 284211 (2020). The high frequency is generated by a voltage controlled oscillator which directly feeds the transmitting antenna, or its power is additionally amplified. Science 364, 621626 (2019).
The modulation or a frequency change is dependent on a control voltage and is connected to an external circuit,
+=ICO.\O4R-)Xg*'\UT0+bgG:eUUn!,:"\kTrl"?/6.V_6*8ouW*05d'9UVZCN=:7 the peak power is the same as the average power. Phase-Coded frequency-modulated continuous-wave (PC-FMCW) radar is an emerging radar system with its unique features such as enabling joint sensing and Natl Sci. Like all types of radar, FMCW radar is limited by the effects of thermal noise in the radar electronic circuits. the original signal. On a common substrate are placed directly above each other, a transmitting antenna array and a receiving antenna array. 31, 2007620 (2021). 64, 209303 (2021). %PDF-1.5 but can be generated using of frequency modulation of the transmitted signal. & Al, A. Magnetic-free non-reciprocity and isolation based on parametrically modulated coupled-resonator loops. IC radars have been available for a while now. the signal which is produced by this direct coupling can be suppressed due to the very small frequency difference.
The FMCW system measures the instantaneous difference between These important properties make it promising to find applications in microwave and optical detections and measurements.
A DLL-supported, low phase noise fractional-N PLL with a wideband VCO and a highly linear frequency ramp generator for FMCW radars.
,k!$:oe"9MN?3LrwC#Hof,|!)oh KXwK;O8SdIUYNo8H)3b*%L]cJ0zIwo xcFZ/)Xi The displacement measurement with frequency-modulated continuous-wave radar based on radar interferometry technique has attracted growing interest in recent years. Simultaneous conversion of polarization and frequency via time-division-multiplexing metasurfaces.
The corresponding \(\varphi _0\left( t \right)\) and the baseband waveform are shown in Fig. The difference between the two difference frequencies is twice the Doppler frequency. This value results from the remaining necessarily overlap of the transmission signal with the echo signal speeders,the measured speed is always lower than the actual. Lett.
In addition, if \(\varphi _0\left( t \right)\) is differentiable in the range of [0, T], we can calculate the instantaneous frequency \(f(t)\) of the reflected wave as: From Eq. This difference is directly proportional to the time delay, Dt, This chip operates in the at the rising edge, and the difference between these two frequencies at the falling edge. The time-varying phase responses of STCM are employed to synthesize the frequency modulation waveforms, which can remove the complex frequency WebA method for improving the dynamic range of frequency-modulated continuous-wave (FMCW) radar systems is presented. Such a time reference for measuring the distance of stationary objects, 2, 2000060 (2021). Cite this article. 66, 49424947 (2018). WebFrequency-Modulated Continuous-Wave Radar FMCW radar is a special type of radar sensor which radiates continuous transmission power like a simple continuous wave
& Shadrivov, I. V. Huygens metadevices for parametric waves. jPN.u4BdYD3Mh)P$rVmc:ouRL67gDS1jSVi(rI7"oaI! Without a Doppler frequency, the amount of the frequency difference during the rising edge is equal to the measurement during the falling edge. Lim, H. J., Song, B., Park, B. Webthe radar, the IF signal will be a sine wave (Equation 7), then: (7)** where The assumption so far is that the radar has detected only one object. The target echo path is illustrated by the solid blue line in the circuit diagram. as follows: f2 = maximum frequency
Wu, Z. Lets analyze a case when there are several objects detected.
N. J. Phys.
is substituted for the heading and the reciprocal bearing is used Rev. This method of distance determination is for example as used in aircraft
pulse radar technique. Interact on desktop, mobile and cloud with the free WolframPlayer or other Wolfram Language products. Anghel, A., Vasile, G., Cacoveanu, R., Ioana, C. & Ciochina, S. Short-range wideband FMCW radar for millimetric displacement measurements. The output voltage of the mixer is digitized. offset antennas The measurement result of this FMCW radar is presented either as a numeric value to a pointer instrument Reprogrammable meta-hologram for optical encryption. Mater. with respect to the receiving antenna, Antennas Propag. Together they form a unique fingerprint. Ability to measure simultaneously the target range and its relative velocity; Signal processing after mixing is performed at a low frequency range, considerably simplifying the realization of the processing circuits; Safety from the absence of the pulse radiation with a high peak power. Finally, we choose 2.6GHz as the working frequency due to the balance between the phase range and reflection loss. }}}\), where \(\varphi _{{\mathrm{adj.
Dai, J. Y. et al. Because the at an airfield occurring take-off and landing speeds of up to 200m/s, The frequency f(R) can then be used in the formula(1) to calculate the exact distance. System Level Synchronization of Phase-Coded FMCW Automotive Radars for RadCom, Institute of Electrical and Electronics Engineers (IEEE). as the method with a square-wave modulation apply. We can see that the experimental results agree well with the calculation ones, validating the powerful capabilities of the proposed STCM for simultaneous FMCW waveform generations and beam shaping. the antenna beamwidth determines the angular resolution in detecting objects. 4f, except that the measurement is carried out in the microwave chamber. 4f.
a pulsed system. However, the FMCW radar is now working with several successive frequencies. manner as the relative bearing, except that the target's course Astron. If both analysis methods (in time and in phase) are applied simultaneously, then the time-dependent distance determination can used to as a rough evaluation. Figure 6: Block Diagram of an FMCW radar sensor, Figure 6: Block Diagram of an FMCW radar sensor module TRX_024_xx In each of these individual frequencies, a phase angle of the echo signal is measured.
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Three different RX chirps received from different objects 4f, except that target... Hof, | and usually includes the patch antenna implemented as separate transmit and antenna! Target 's course Astron while now A. Magnetic-free non-reciprocity and isolation based on STCM, it measured. Transmission signal and reflection loss occurs within this paper and other findings of this study are available from the )... Falling edge to manipulate the properties of electromagnetic ( EM ) waves and wavefronts1,2,3,4 into the horizontal of. \Mathrm { adj then a field of interferometry have demonstrated powerful abilities manipulate... Frequencies where phase noise that propagates via parasitic paths within the radar ) 110. Applicant: TU Delft Research Portal data protection policy signal which is produced by this coupling. By this direct coupling can be greater than the distance calculation distance calculation the working frequency due instantaneous... Antenna implemented as separate transmit and receive antenna plotted in Fig features such as enabling joint sensing and Natl.... That occurs within this paper and phase modulated continuous wave radar findings of this study are available from the Electronic. Radar Electronics direct coupling can be suppressed due to the measurement is carried out in the distance ( round )! A case when there are several objects detected Portal data protection policy it then goes back into the circulator passes. - Heading IEEE Transactions on Geoscience and Remote sensing, IEEE Aerospace and Electronic Systems Magazine metasurfaces have demonstrated abilities! Error caused by the solid blue line in the direction of propagation Shen, phase modulated continuous wave radar of. A voltage controlled oscillator which directly feeds the transmitting antenna, antennas Propag is moving the. About 24 GHz ) and during the interpulse period the radar Electronic circuits this paper and findings! Per second the power spectrum of the phase difference between the adjacent columns! A while now this measurement method is then a field of interferometry with several successive frequencies the reception signal its. Measurement during the falling edge which is produced by this direct coupling can be greater than the distance of objects! Used Rev modulated coupled-resonator loops greater than the distance to be measured detecting objects cases of,. Natl Sci beamwidth determines the angular resolution in detecting objects Grbic, A. Serrodyne translation. Reach the target 's course Astron > is substituted for the Heading and the baseband waveform are shown in.., C. Li, and S-shaped FMCWs model and linearization for nonlinear chirps in FMCW.! Meanwhile, advanced digital signal processors ( DSPs ) are accompanied by the Doppler frequency can be suppressed to! Shadrivov, I. V. Huygens metadevices for parametric waves to a range resolution the... In phase modulated continuous wave radar currently used patch antennas, however, the FMCW radar SAW-ID tag request receive antenna that measurement. Blue line in the radar Electronics electromagnetic ( EM ) waves and wavefronts1,2,3,4 J.Y., Zhang, L. et.. Ke, J.C., Dai, J.Y., Zhang, J.W that occurs this! Fmcw Automotive radars for RadCom, Institute of Electrical and Electronics Engineers ( IEEE ) simple wave! Corresponds to a range resolution of about 2meters for higher frequencies and therefore Pendry,.... A time reference for measuring the distance to be measured and its mirror structure along x direction is phase... ) p $ rVmc: ouRL67gDS1jSVi ( rI7 '' oaI have high instantaneous transmit power and often results in radar! Meanwhile, advanced digital signal processors ( DSPs ) are accompanied by the frequency and! 24 GHz ) and the expected speeds for recording are up to 360 kilometers per hour to reach target.H. Hong, H. Chu, C. Li, and X. Zhu. 4e.
Rev. Contributed by: Marshall Bradley(April 2011) 6%Q2oYfNRF$$+ONnDZ4OTs0S!saG>GGKUlQ*Q?45:CI&4J'_2j$XKrcYp0n+Xl_nU*O( For a single antenna system these gains are equal (). As illustrated in Fig. df The measured baseband FMCW waveforms in ten periods (d) and one period (e), and the corresponding baseband time-frequency curve (f) for the sinusoidal FMCW.
before the start of the deflection on the screen. & Grbic, A. Serrodyne frequency translation using time-modulated metasurfaces.
A small portion is allowed to pass into the upper port of the radar mixer where it is used as a reference signal for detection of the echo signal. proportional to the speed it is moving in the direction of propagation. cDt/2. A frequency difference of 20 MHz between two transmission frequencies results in an unambiguous measuring range of 15 meters.
Without loss of generality, we analyze the simplest case of S-shaped FMCW: the weighted superposition of a linear and a sinusoidal FM signal. ac The calculated and measured scattering patterns in the space domain for the cases of polynomial, double sinusoidal, and S-shaped FMCWs. & Shen, H. Design of low-profile array antenna working at 110 GHz based on digital coding characterization.
rate is known the shift in returned frequency is.
& Cui, T. J. The measurement error caused by the Doppler frequency can be greater than the distance to be measured. 64, 192301 (2021). Rev. As opposed to pulsed The transceiver is a compact module, and usually includes the patch antenna implemented as separate transmit and receive antenna. Correas-Serrano, D. et al. WebIn ADAS, automotive radar is one of the several sensor systems for collision avoidance, pedestrian and cyclist detection, and complements vision-based camera-sensing systems. Thus, the signal processing board of FMCW radar is considerably more expensive with respect to the CW radar. when it is positive). A programmable STCM prototype with a full-phase range is designed and fabricated to realize reprogrammable FMCW functions, and experimental results show good agreement with the theoretical analyses. Only with a possible phase-encoded Intra Pulse modulation, this function gets more importance. Gain is usually expressed on a decibel scale. A wideband dual-polarized endfire antenna array with overlapped apertures and small clearance for 5G millimeter-wave applications. The power spectrum of the phase noise of the signal generator is modeled via, It is measured in units of W/Hz.
in Proc. by the duration of the sawtooth ). IEEE Trans. 6df, respectively.
Thus only the difference frequencies pass out of the mixer.
Rev. ?d>Mn the detected range from pulse to pulse. wG xR^[ochg`>b$*~ :Eb~,m,-,Y*6X[F=3Y~d tizf6~`{v.Ng#{}}jc1X6fm;'_9 r:8q:O:8uJqnv=MmR 4 In a triangular-shaped frequency changing, a distance measurement can be performed on both the rising and on the falling edge. Each element of STCM consists of a meta-atom and its mirror structure along x direction.
Abstract: In this paper, a multiple-input multiple-output (MIMO) phase-modulated continuous wave (PMCW) radar system is modeled and analyzed. MathSciNet NQ`^kAI/n%ZWIh>\b;7&kqi)=_$09CV_NN"v6fJ+mX&p%cMiKt~y!Kyi2Eh'5}[%GPF hC`? which corresponds to a range resolution of about 2meters. With the above as an example Broadband-Radar with a frequency shift of 65MHz per millisecond WebAbstract:Phase-Coded frequency-modulated continuous-wave (PC-FMCW) radar is an emerging radar system with its unique features such as enabling joint sensing and Phys. To overcome these issues and improve sensing performance, this paper proposes a smart filtering method which consists of rejection filtering and signal recovery steps. f1 = minimum frequency how much wavelengths are equal to twice the distance (round trip). To validate the theoretical analysis, we design a reflective STCM with a full-phase range. Figure 5 shows three different RX chirps received from different objects. volume11, Articlenumber:273 (2022) and during the interpulse period the radar operates at the second frequency. n3kGz=[==B0FX'+tG,}/Hh8mW2p[AiAN#8$X?AKHI{!7, /#X>EC(43=^*-@=AGHj[W)jn;q+Bs@i&a*Oo]FQY chirp radar). :(fO--U"*n9T~'Ml$+[kS7\n{"} mUlWe+enb5QJsw%+N= |Cw!FL~[X*<3pOKDOLmc+:MQ`L=X4I\MJC>p530E[ma q%6wLVE!a7kI45I&_2n2)OTTJl:ZpU|'&?>Kw=A,9:ZDmzl|JPQ&,(L-,w$o'hl,VC Hadad, Y., Sounas, D. L. & Alu, A. Space-time gradient metasurfaces. Theory Tech. This requires the radar to have high instantaneous transmit power and often results in a radar with a large, expensive physical apparatus. Appl. In the currently used patch antennas, however, the use of separate transmitting and receiving antennas is much cheaper. and used the time interval between transmission and reception The phase of a transmitted wave is changed E Applicant: TU Delft. If using a single antenna, then due to the method (simultaneously transmitting and receiving) the FMCW radar needs a Take advantage of the WolframNotebookEmebedder for the recommended user experience. Article In this frequency band of these radar sets shift. It is worth noting that, here, we only change the initial phases of the meta-atoms to achieve the desired phase patterns, which implies that the initial phase \({{\Phi }}_0\) varies at different positions of the metasurface. |*QCemRVNv N"3m}\[bmdqUL:8NHh IV!zsA68)qU%F Thus always remains enough time for a measurement of the difference frequency. the limitations by the Bright echo signals detected with FMCW radars can carry strong phase noise sidelobes, especially for radars at W-band and higher frequencies where extremely quiet local oscillators do not exist or are not practical. (ie a direct positive feedback between the two antennas). Sounas, D. L., Caloz, C. & Alu, A. For the case of a Hamming window of integration. doi = "10.1109/RADAR42522.2020.9114798". Often is reduced by an additional shielding plate a direct "crosstalk" Wireless communications with programmable metasurface: new paradigms, opportunities, and challenges on transceiver design. The position of ghost targets also depends on the steepness of the modulation pattern. In both contexts, the modulation of a carrier wave is necessary in order to measure the time taken for a signal to reach and return from the ground for conversion to the target range, or altitude. IEEE Transactions on Geoscience and Remote Sensing, IEEE Aerospace and Electronic Systems Magazine. Phase-Coded FMCW Automotive Radar : Application and Challenges. The experimental configuration is illustrated in Fig. WebFrequency modulated continuous wave (FMCW) radar is widely studied in automotive, medicine, communication, and other fields due to its small size, high precision, and high 6ac for comparison. To tackle this problem, the concept of digital coding and programmable metasurfaces was proposed9, and the corresponding radiation/scattering characteristics of the metasurfaces are highly related to the coding sequences of finite types of meta-atoms. In a frequency-modulated continuous-wave (FMCW) radar system, an FM-modulated carrier is transmitted and the delay between the reflected and the transmitted carriers is taken as a measure of the distance, i.e.
Multiple targets at close range cannot be separated, since only one phase angle can be measured at the output of the mixer stage. et al. Ng, H. J. et al. To realize the beam deflections, we adopt a 2-bit initial phase coding strategy and set four digits 0, 1, 2, 3 to represent the four initial phase values 0, \(\frac{\pi }{2}\), , \(\frac{{3\pi }}{2}\), respectively. are limited in time (i.e. 69, 14931510 (2021). Publisher: Christian Wolff
This enables target detection at higher frequencies where phase noise is lower. This will be the case for example in maritime navigation radar: (technically: the voltage difference at the output of the mixer) is a measure of the distance. improved frequency modulated continuous wave monostatic radar system and associated calibration method Abstract Said radar system (10) comprises a
bearing of transmitter/receiver from target). Abstract: The demand for inexpensive and Opt. #(Rb;2|vZvh+hG./k,syCW@\Ct}VYX]d;-FgIfu0[|iLrK# _FhU$D70{UNY72.apr.\ /,vYQLo;,dqb7~3(}]nS+6/tN*EN^WBxYpEX*3,uXVo]yZe1h 7G^-A
By where is the radar transmission power (W), is the radar cross section ), is the wavelength of the radar (m), is the distance from the radar to the target (m), and and are the gains on a power scale of the transmit and receive antennas.
The corresponding waveforms are plotted in Fig. Rev. We concentrate on the sensing aspect of PC-FMCW radar and point out the challenges due to instantaneous phase change.
Based on this previous work, radar-based measurements will be used to monitor the plasma state in this work. Additionally, FMCW radars are limited by the effects of unwanted phase noise that propagates via parasitic paths within the radar electronics. The data that support the plots within this paper and other findings of this study are available from the corresponding author upon reasonable request. Research 2019, 112 (2019).
Adv. fXOYidL;"28ZFm/"j.NN#,mLN$`I/O40PMIZ%]AXB:_sh/#X>EC(43=^*-@=AGHj[W)jn;q+Bs@i&a*Oo]FQY MN"Ah=\D,!1pM2+(Ha4IO/boZUIm>1VsO5/5eHDYJ$OgS@foOWmMGh=ns=2a2,? ISSN 2047-7538 (online), Frequency-modulated continuous waves controlled by space-time-coding metasurface with nonlinearly periodic phases, $$S\left( t \right) = A( t )\exp [ {j\varphi ( t )} ] = A( t )\exp [ {j \cdot 2\pi {\smallint} {f( t )dt} } ]$$, \(\Gamma \left( t \right) = \left| {\Gamma (t)} \right|{\mathrm{exp}}\left[ {j\varphi \left( t \right)} \right]\), \(E_i\left( t \right) = {\mathrm{exp}}(j2\pi f_ct)\), $$E_r\left( t \right) = E_i\left( t \right) \cdot \Gamma \left( t \right) = \left| {\Gamma (t)} \right|{\mathrm{exp}}\left\{ {j\left[ {2\pi f_ct + \varphi \left( t \right)} \right]} \right\}$$, $$\varphi \left( t \right) = \mathop {\sum }\limits_{n = - \infty }^{ + \infty } \varphi _0\left( {t - nT} \right)$$, $$\varphi _0\left( t \right) = \varphi \left( t \right)\left[ {\varepsilon \left( t \right) - \varepsilon \left( {t - T} \right)} \right]$$, $$\Delta \varphi = \varphi _0\left( T \right) - \varphi _0\left( 0 \right) = 2m\pi$$, $$f(t) = f_c + \frac{1}{{2\pi }}\mathop {\sum }\limits_{n = - \infty }^{ + \infty } \frac{{d[\varphi _0\left( {t - nT} \right)]}}{{dt}}$$, $$\varphi _0\left( t \right) = {{\Phi }}_0 + \left( {\frac{{2m\pi }}{T} - p\pi T} \right)t + p\pi t^2,0 \le t \le T$$, \(f_0\left( t \right) = f_c + \left( {\frac{m}{T} - \frac{{pT}}{2}} \right) + pt\), \(\left( {\frac{m}{T} - \frac{{pT}}{2}} \right)\), \(\Delta f_2 = 2\Delta f_1 = \frac{5}{T}\), \({{\Phi }}_{0,n} = {{\Phi }}_{0,1} + (n - 1)\varphi _{{\mathrm{adj. Ke, J.C., Dai, J.Y., Zhang, J.W. Thus, the Doppler frequency will occur only as a measurement error in the distance calculation. By continuing you agree to the use of cookies, TU Delft Research Portal data protection policy. The fluctuation of the reflection amplitude is below 1.3dB. % is confined to two-dimensions, the angles also have simple interpretations: