Reconfigurable Range-Doppler Processing and Range...

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Reconfigurable Range-Doppler Processing andRange Resolution Improvement for FMCW RadarSharef Neemat, Faruk Uysal, Senior Member, IEEE, Oleg Krasnov, and Alexander Yarovoy, Fellow, IEEE

Abstract—A reconfigurable range-Doppler processing methodfor FMCW radar is presented. By concatenating beat-frequencysignals from more than one sweep, a continuous beat-frequencysignal for the whole coherent processing interval (CPI) can becreated. As a result, continuous targets’ observation time isextended beyond that of a single chirp duration, leading torange resolution improvement. The created continuous beat-frequency signal can be split in the digital domain to any two-dimensional slow-time fast-time matrices with the same numberof elements as in the original signals, which offers a realization ofa software defined pulse/sweep repetition rate in Range-Dopplerprocessing. The signal concatenation is done in the Short-timeFourier Transform (STFT) domain, where beat-frequency slicesare extrapolated to compensate for the observation time lost inthe transient region between sweeps, then a phase correctionis applied to each frequency-slice as appropriate, followed byan Inverse STFT (ISTFT). The proposed technique is verifiedwith simulation and experiments with an FMCW radar forstable and moving target scenarios. We found that the methodallows for range resolution improvement without the transmissionof additional bandwidth, and allows for the ability to observedifferent resolution granularities in parallel from one CPI. Itadditionally allows the decoupling of the transmitted PRF fromthe Doppler processing PRF, permitting the facility to observedifferent unambiguous Doppler velocity intervals from one CPI,without compromising on the total CPI processing gain.

Index Terms—Beat-Frequency, Coherent Processing Interval(CPI), Frequency-Modulated Continuous-Wave (FMCW), RangeResolution, Unambiguous Doppler velocity.

I. INTRODUCTION

DERAMPING Frequency Modulated Continuous Wave(FMCW) radars operate by mixing a transmitted chirp

signal with received returns, and filtering the resulting beatsignal [1]. For a single point-target, the time delay between theprobing signal transmission and the scattered signal receptionwill result in a single-tone signal, known as a beat-frequency,whose frequency is proportional to that target’s range. Rangeis therefore defined by frequency. The scaling between beat-frequencies and range is defined by the transmitted bandwidth,and the signal observation time. A frequency estimation tech-nique like the Fourier Transform (FT) is typically used toseparate targets in range, by separating beat-frequency tonesin the frequency domain. The radar’s range resolution isdetermined by the transmitted bandwidth and the FT frequencyspectrum resolution. Legacy computer architectures used in

Manuscript received . ., .; revised . ., .. The first author acknowledges thesupport from KACST scientific institution.

The authors are with the Group of Microwave Sensing, Signals and Systems(MS3), Delft University of Technology, 2628CD Delft, The Netherlands(e-mail: [email protected]; [email protected]; [email protected];[email protected]).

FMCW radars are highly compatible with the FT for itsreduced computational requirements and predictable latency.The range resolution granularity defines the width of targets’range bins. In signal processing, the FT frequency resolution isdefined by the signal observation time [2]. Target velocities arecalculated from Doppler processing - also typically using theFT - across targets’ range bins from multiple sweeps [3]. Theradar Pulse/sweep Repetition Frequency (PRF) is therefore theDoppler sampling frequency. The time spent to gather multiplesweeps for range and Doppler processing is typically knownas a Coherent Processing Interval (CPI). Sweeps in a CPI aretypically arranged in a fast-time slow-time matrix, where fast-time is the time within a sweep, and slow-time is the timeacross multiple sweeps. The total processing gain in a CPIis contributed to the matrix’s 2-D FT processing gain. It istypical for radars to transmit at different PRF values, acrossmultiple CPIs to unambiguously determine targets’ ranges andvelocities, in what is known as staggered-PRF techniques [4].In FMCW, the observation time is limited by what is known asthe ’transient’ or ’fly-back’ region between frequency sweeps[5]. The received signal is typically only sampled after thetransient region, which causes discontinuities in received beat-frequencies (demarking the end of a received sweep), and putsa limit on the possibility of having a continuous observationtime.

The problem this paper offers a solution for is the existenceof the transient regions in received beat-frequency sweeps ina CPI, in the sense that:

1) The existence of the transient regions does not allowfor longer targets observations. If a method were tobe developed to extend the observation time by co-herently concatenating/processing beat-frequencies frommore than one sweep at a time, that would result in afiner radar range resolution.

2) Such a concatenation method, would give a tool to de-couple the Doppler processing PRF from the transmittedsignal PRF. This is in the sense that it becomes possibleto - in parallel and from one CPI - create differentlengths fast-time slow-time matrices, without compro-mising on the total processing gain in any of the createdmatrices. This would therefore allow the implementationof staggered-PRF velocity disambiguation techniques ina single CPI.

The solution proposed in this paper is to concatenate beat-frequency slices in the Short-time Fourier Transform (STFT)domain, by applying a phase correction to each frequencyslice as appropriate, followed by an Inverse STFT (ISTFT). A

This is the author's version of an article that has been published in this journal. Changes were made to this version by the publisher prior to publication.The final version of record is available at http://dx.doi.org/10.1109/JSEN.2019.2923053

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second optional realization of this solution is to first extrapo-late beat-frequency slices, to compensate for the observationtime lost in the transient region, then concatenate the slices asaforementioned.

Previous work on the topic is scarce, in the sense that amethod doesn’t exist where such a method:

• is applicable to deramping processing (as opposed tomatched filtering),

• only relies on the FT (as opposed to more computa-tionally intensive or iterative frequency estimation algo-rithms),

• does not improve the range resolution by stitches sweepsfrom multiple discontinuous bands, and therefore techni-cally requiring more overall system bandwidth,

• does not require target detection as a prerequisite,• is applicable to extended-targets.

Techniques that work by coherently processing data postrange-Doppler may not be suitable for wide-band systemswhere range migration causes targets’ energy to be spreadacross multiple range-Doppler bins. An interesting methodfor doubling the range resolution without increasing the band-width can be found in [6]. Their method is restricted to theradar’s intermediate frequency being an integer multiple ofthe transmitted bandwidth, and to being operable only with areal Double-Side-Band (DSB) deramping receiver. Bandwidthextrapolation techniques like in [7], [8] and [9] use predictiontechniques to synthetically extrapolate the data to improve theresolution. There usually is a practical limit to how much willextrapolated data really represent target returns as associatedwith their Radar-Cross-Section (RCS). The work in [10] useswaveform diversity to decouple the Doppler cycle from thePRF, but does not address range resolution improvement.We proposed the extrapolation and linking of parts of beat-frequencies - within the same sweep - in the STFT domainfor the purpose of interference mitigation in [11].

The difference from previous techniques and the novelty inthis work is highlighted in:

1) The first ever method for deramping FMCW radarsweeps coherent concatenation in the STFT domain.

2) The method allows for range resolution improvementwithout transmitting additional bandwidth.

3) The method offers the ability to observe different rangeresolution granularities in parallel from one CPI.

4) The method offers the ability to - in parallel - generatedifferent size fast-time slow-time matrices, and decou-ples the transmitted PRF from the Doppler processingPRF, without compromising on the total CPI process-ing gain. This offers the ability to observer differentunambiguous Doppler velocity intervals - to performstaggered PRF velocity-disambiguation techniques forexample - in one CPI.

5) The method does not require target(s) detection as aprerequisite.

LPF

Transmitter

front-end

Receiver

front-end

Waveform

Generator

ADC ProcessorRange-

Doppler

Maps

(a)

Sweep

Frequency

Time

Transmitted

Received

B

bf

2 /r r c

oT

sTmax Transient

region

Time

Beat frequency

after derampingAmplitude

oT

eB

Sweep 1 Sweep 2

1x 2x

(b)

Fig. 1. (a) Deramping FMCW radar simplified block diagram. (b) Derampingoperational overview, highlighting beat-frequency signals and the transientregion.

II. THEORY

A. Deramping FMCW Radar Range Resolution

A deramping FMCW radar - as in Fig. 1(a) - transmitsbandwidth B over a sweep time Ts and observes a target atrange r. The radar’s Pulse Repetition Interval (PRI) is Ts. Theobservation time (ADC sampling interval) To = (Ts−τmax),where τmax the maximum transient time [5], which is selectedbased the desired system maximum range of interest. The anti-aliasing Low Pass Filter (LPF) defines τmax. The observationtime To is less than Ts because it is limited by the transienttime region from the previous sweep. ADC sampling of thereceived signal typically begins after τmax. The received beatsignal from a point target can be expressed as

Sr(t) = A0rec (t/To) cos(2πfbt+ ϕ0) (1)

for −To/2 < t < To/2, where A0 is the received amplitude,fb the target beat-frequency, ϕ0 an arbitrary initial phase. Asdepicted in Fig. 1(b), the target range is defined as

r =fbToc

2Be(2)

where c is the speed of light and Be the effective bandwidth.The effective bandwidth is related to the transmitted on by

Be = B

(ToTs

). (3)





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-3 dB line

1T

1eT T

bf

1

FT rec cost

tT

2 12T T

Frequency

2

FT rec cost

tT

2T

2eT T

Fig. 2. Simplified sinc function spectral bandwidth illustration for signalswith different durations. When coherently concatenating two sweeps, the sincfunction 3 dB width will reduce.

which also expresses the degradation in the transmitted band-width due to the reduced observation time. From (2), the targetbeat-frequency is therefore

fb =2Ber

Toc. (4)

Spectral estimation techniques such as the FT are typicallyused to estimate the target frequency, and therefore its range.

It is well known from FT signal processing that for a signalas in (1), the FT will result in an impulse function - assumingthat fb is on a frequency grid point - and a sinc function,and that the frequency spectrum resolution is defined by the3 dB width of that sinc function centered at fb [4]. The 3 dBwidth of the sinc function in the frequency domain is inverselyproportional to the signal integration time Te [2] as

∆f =1

Te. (5)

This concept is depicted in Fig. 2. In FMCW radar, rangeresolution is proportional to the frequency spectrum resolution,and is defined by the 3 dB width of the sinc function centeredat fb. From (2), (4) and (5), for two targets r1 and r2 tobe separable in the frequency domain, they need to meet therequirement

2Ber1

Toc− 2Ber2

Toc≥ 1

Te(6)

which can be simplified to

r1 − r2 = ∆R =c(

2BTo

)Te. (7)

It should be noted that in typical FMCW processing, To = Te,yielding

∆R =c

2Be(8)

which is the classical form of FMCW range resolution. Butas seen in (7), if there were a way to increase the integrationtime, it would be possible to improve the range resolution.

B. Range Resolution Improvement

The method proposed in Section III increases the integrationtime in (5) and (7) by coherently concatenating d sweeps, andtherefore improving the range resolution. The improved rangeresolution is expressed as follows

∆Rd =c(

2Be

To

)dTe

=c

2Bed(9)

where d is the concatenation factor as well as the rangeresolution improvement factor. It should be noted that themore coherently concatenated sweeps, the finer ∆Rd becomes,and therefore the larger the observed range migration is formoving targets. Range migration is sometimes a desirablephenomenon, where it is exploited for better performanceof some detection algorithms [12]. If range migration is notdesirable for certain applications, it can be corrected usingalgorithms like in [13] and [14]. The value of d shouldtherefore become a radar system parameter. We will show inSection II-C and Section III that different size slow-time fast-time matrices can be created in parallel from a single CPI, byprocessing for different values of d.

C. Reconfigurable Range-Doppler Processing

In classical FMCW radar processing, a CPI of a certainduration is selected as a system parameter. Received sweeps inthe CPI are typically stored in a 2-D matrix (commonly namedthe fast-time slow-time matrix), after which, a 2-D FT isperformed on that matrix to produce range-Doppler maps. Thetotal processing gain in the CPI is the pulse compression gain- also known as the time-bandwidth product (BT) - multipliedby the number of sweeps in the CPI. Operationally, to maintainthis processing gain, the total number of samples stored in aCPI is typically kept the same when changing the PRF, anda tradeoff is made between the unambiguous range and theunambiguous Doppler velocity interval. This is in the sensethat more sweeps of shorter durations are received in HighPRF (HPRF) mode, and less sweeps of longer duration in lowPRF mode. If the radar operates in a HPRF mode, differentunambiguous Doppler velocity intervals can be created bysimply discarding every other sweep(s) in the fast-time slow-time matrix, but that would result in a total processing gainloss. The unambiguous velocity interval is related to the PRFas

vu = ±λ · PRF

4(10)





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TABLE IFLEXIBLE CPI PROCESSING RANGE RESOLUTION IMPROVEMENT VS MAXIMUM UNAMBIGUOUS DOPPLER VELOCITY TRADEOFF EXAMPLE.

ASSUMPTIONS ARE: TRANSMITTED PRF = 2KHZ, Ts = 500 µS, To = 400 µS, N = 64 SWEEPS IN THE CPI, CPI LENGTH = 32000 µS, Be = 32 MHZ,WAVELENGTH λ = 0.0905 M. NOTE THAT WHEN d = 1, THIS IS THE CASE FOR CONVENTIONAL PROCESSING.

ConcatenationFactor d

Range ProcessingGainGr = BeTod

Range Resolution∆Rd = c

2Bed(m)

N CPI DopplerProcessing Gain

Total CPI Processing Gain= Range Processing Gain xN CPI Doppler ProcessingGain

Processing PRF(kHz)

MaximumUnambiguousDoppler Velocityvu = ±λ·PRF

4(m/s)

1 12800 4.68 64 819200 2 45.252 25600 2.34 32 819200 1 22.624 51200 1.17 16 819200 0.5 11.31. . . . . . .. . . . . . .

64 819200 0.07 1 819200 Notapplicable.

Not applicable.Only a rangeprofile is available.

1x

: Number of samplesk

k 2x Nx

1d

1xk 3x 1Nx

2xk 4x Nx

2d

1xk 5x 3Nx

2xk 6x 2Nx

4d

Range FFT

Doppler FFT

Range FFT

Doppler FFT

3xk 7x 1Nx

4xk 8x Nx

: Beat frequencies sweepx

: Number of sweeps

in the CPIN

Range FFT

Doppler FFT

1x

d kRange FFT

d N

: Concatenation factord

+Proposed

Processing

Method

Standard

Processing

+Proposed

Processing

Method

+Proposed

Processing

Method

Fig. 3. Reconfigurable range-Doppler processing permutations of fast-timeslow-time received sweeps. The total CPI processing gain is maintained.Depending on the number of sweeps concatenated, there is a tradeoff betweenrange resolution and the maximum unambiguous Doppler velocity interval.Note that when d = N , only a range profile is provided because the matrixis then one dimensional.

where λ is the radar wavelength. We propose the creation ofdifferent lengths fast-time slow-time matrices by operating theradar in a HPRF mode, and concatenating sweeps for differentvalues of d in parallel. This will allow the creation of different’processing’ PRF values from the operational HPRF, whilemaintaining the total processing gain. The created different

processing PRF values will allow for the evaluation of multipleunambiguous Doppler velocity intervals, and multiple rangeresolution granularities, from the same CPI. The processingPRF can be expressed as

PRFd =PRF

d. (11)

This reconfigurable processing concept is illustrated in Fig. 3,where as the number of concatenated sweeps increase, theunambiguous Doppler velocity intervals is reduced, but allsamples are still used and therefore the processing gain ismaintained.

A calculated example is furthermore given in Table I. Itcan be seen that when d = 2 for instance, the processingPRF becomes 1 kHz, which is half the transmitted PRF of2 kHz, but the range resolution is improved by a factor oftwo from 4.68 m to 2.34 m. All while maintaining the sametotal processing gain of 819200 in both cases because of notdiscarding any samples.

D. Reconfigurable Range-Doppler Processing Limitations

The limitations for improving the range resolution by coher-ently concatenating multiple sweeps are system non-linearities- in the transmitter and receiver - and concatenation errors.Because of non-linearities, even a point-target will have acertain 3 dB spectral width, dictated by the radar’s non-linearities [15]. Any concatenation errors may also result ingrating-lobes or spectral width widening.

III. METHOD: SWEEPS CONCATENATION WITHTRANSIENT REGION EXTRAPOLATION

In the time-frequency domain, beat-frequency slices are firstextrapolated to cover the transient region between sweeps, andthen coherently concatenated using a phase-shift operation, asdepicted in Fig. 4. The steps are:

1) Store digitally sampled beat-frequencies for sweepsfrom the output of the deramping receiver. A sweepcan be expressed as xn[k], where n is the sweepnumber, and 2 ≤ n ≤ N . The number of sweeps ina conventional Coherent Processing Interval (CPI) isN , and N ∈ N, and N denotes the set of all natural





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Frequency

Time

Transmitted

Received

Transient

Region

Time

Beat

frequency

after

deramping

Amplitude

.…..

Time

Frequency

2S

1S N

S

1x

1

B

(a) Conventional Processing:

rsT

2x Nx

2 N

Extrapolate

CPI

1x 2x Nx

Proposed

processing in the

STFT domain:

Sweeps

concatenation with

extrapolation

Time

1E

2E

NER

frames

Beat

Frequency-SliceFrequency

Time

Frequency

BForm phase

matched

matrix

Frequency

Time

ISTFT

Time

Amplitude

Time

Amplitude

1x

(b) Concatenation factor

d= 2

Time

Frequency

Time

Frequency

Time

Amplitude

Time

Amplitude

Nx

(c) Concatenation factor

d= 4

1x

2x

Nx

1 1,...,(2 )(2 )

Y LY L

E = B

(d) Concatenation factor

d= N

1x

1x

Time

Time

Amplitude

ISTFT

1x

1x

2x

1E

Frequency

Time

2 (2 ) 1,...,(4 )(2 )

Y L LY L

E = B

2E

1E

1 1,...,(4 )(4 )

Y LY L

E = B

2 (4 ) 1,...,(8 )(4 )

Y L LY L

E = B

ISTFT

Frequency

1E

1 1,...,( )( )

Y N LY N L

E = B

2E

Fig. 4. Examples for reconfigurable CPI processing with transient region frames extrapolation. Different values of the concatenation factor d are shown forsweep concatenation.

numbers. The time domain sample index in a sweep isk , where k = 1,...,K, and K = fsTo. The samplingfrequency is fs.

2) Take sweeps to the time-frequency domain by applyingan STFT, where a sweep can be expressed in matrixform as

Sn[l, y] =

W2 −1∑

q=−W2

x[q]w[q − l∆h]e−i2πqy/W

Y×L

(12)with Y rows and L columns, where l is the STFTframe index, l = 1,...,L, and L = 1+b(k −W)/∆h)c.The analysis window length is W . The STFT hopsize is ∆h, and b·c denotes the floor operation. Thefrequency-slice index in the STFT frequency grid isy, where y = 0,...,Y , and Y is the maximum beat-frequency index. The analysis window (for instance,Hamming) is w.

3) Using the Burg algorithm [16], estimate in-phaseand quadrature (IQ) Linear Prediction (LP) coeffi-cients [a]Y×o in matrix form for amplitudes of eachfrequency-slice y in each of the N sweeps. The pre-diction filter order is o, and o should be between 2 andbL/3c.

4) Extrapolate R frames for each y frequency-slice, for each of the N sweeps. Note thatR = 1 + b((τrfs) − W) / ∆h)c, and theextrapolated frames can be written as

Ay[r] =

[o∑i=1

ay,iSy,i

]1×R

(13)

where r = 1,...,R. After extrapolating for all yfrequency-slices, an extrapolated sweep can then bewritten as

En =[

An Sn]Y×L (14)





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where L = L+R. Note that If the radar is to operatewith long delays between sweeps (similarly to pulse-Doppler radar), steps 3 and 4 can be skipped becauseof the extrapolation quality degradation.

5) Form concatenated sweeps in matrix-form in the STFTdomain as:

B =[ E1 E2 ◦C2 . . . EN ◦CN ]Y×(N ·L)

(15)the E matrices are of the form as in (14), ’◦’ denotesthe Hadamard product. The phase matching term C hasL identical columns, and is defined as

Ci =

ei∆ϕi(f0) · · · ei∆ϕi(f0)

......

...

ei∆ϕi(fY ) · · · ei∆ϕi(fY )

Y×L

(16)

where

∆ϕi(fy) = (ϕi−1,L(fy)−ϕi,1(fy))+(2πfyth). (17)

Here fy is the frequency value at frequency-slice indexy, and the hop time th = ∆h/fs. The phase matchingis illustrated in Fig. 5.

6) Select a concatenation factor d which indicates thedesired number of sweeps to be concatenated in theCPI, where d ∈ Q, and Q denotes the set of all rationalnumbers. The concatenated sweep number is N , whereN = N/d, and N ∈ N.

7) Form concatenated sweeps in matrix-form in the STFTdomain as

Em = [BY×((m−1)·d·L)+1),...,(m·d·L)]Y×(d·L) (18)

where m is the sweep number after concatenation,m = 1,...,N .

8) Perform an Inverse STFT (ISTFT) to form the newconcatenated beat-frequency sweeps as

¯xm = ISTFT(Em). (19)

The concatenated sweep ¯xm will be of length d · (k +(fsτr)).

9) Perform again from step 6 onwards in parallel fordifferent values of d to create multiple fast-time slow-time matrices from the same CPI.

IV. SIMULATION RESULTS FOR PROPOSED METHOD

To evaluate the reconfigurable range-Doppler and rangeresolution improvement method, a simulation and processingscenario for five point-targets is setup using the parametersin Table II and illustrated in Fig. 6. On the one hand, thesimulation compares 2-D FT results for the standard case witha PRF of 1 kHz (Fig. 6(a)), the creation of a second Dopplervelocity ambiguity interval by manually discarding every othersweep from the CPI resulting in a Doppler sampling PRFof 500 Hz (Fig. 6(b)), and the creation of a third intervalby manually using one sweep from every four sweeps fromthe CPI resulting in a Doppler sampling PRF of 250 Hz(Fig. 6(c)). On the other hand this is compared with the

Sweep 1

Frame

Number

Frequency

Yf

0f

yf

1,L

2,1

12L Sweep 2

12

Sweep Number,Frame Number

2 1, 2,1( ) ( ( ) ( ))

(2 )

y L y y

y h

f f f

f t

L

2 ( )yi fe

Fig. 5. Depiction of phase matching in the STFT domain after transient regionframes extrapolation, as discussed is Section III.

Range FFT

Doppler FFT

Simulation setup

for cases (d) and (e):

1x 3x 1Nx

2x 4x Nx

Range FFT

Doppler FFT

1x 5x 3Nx

2x 6x 2Nx

3x 7x 1Nx

4x 8x Nx

Range FFT

Doppler FFT

Range FFT

Doppler FFT

Simulation setup

for cases (b) and (c) :

1x Nx2x

1x Nx3x

Range FFT

Doppler FFT

1x 5x

250 Hz uv 5.5 m/s

PRF =

1 kHz uv 22.1 m/s

500 Hz uv 11 m/s

500 Hz uv 11 m/s

4d 250 Hz uv 5.5 m/s

Nx

Simulation setup

for case (a)

PRFd

PRFd

PRF

PRF

2d

Fig. 6. Simulation setup for the results presented in Fig. 7, where cases (a)to (e) correspond to Fig. 7 sub-figure labels.

proposed processing with d = 2 (Fig. 6(d)) and d = 4 (Fig. 6(e))to create the same velocity ambiguity intervals, but withimproving the range resolution. Hamming windowing is usedfor both the range and Doppler processing. The simulationresults are presented in Fig. 7. Target G1 wraps around theunambiguous velocity intervals as expected, as it can be seenat a velocity of around -9 m/s in Fig. 7(b) and (d), and ataround 3 m/s in Fig. 7(c) and (e). Targets G2 and G3 have avelocity which is always within the ambiguity intervals, andtherefore do not fold. Since targets G2 and G3 are spaced 1.5





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TABLE IISIMULATION AND EXPERIMENT SETUP PARAMETERS.

Simulated Targets’ SpecificationsTarget

Number Range (m) Velocity (m/s)

G1 348.28 13.85G2 362.98 1.38G3 364.45 1.38G4 379.14 0G5 380.61 0

CPI ParametersParameter Value Unit

Simulation ExperimentsWaveform Linear sawtooth n/a

PRF 1 2 KHzTs 1000 500 µsTo 950 450 µs

N CPI 64 sweepsCPI length 0.064 0.033 s

Be 49.5 R-1: 38R-2: 19 MHz

wavelengthλ

0.0905 m

Extrapolation ParametersParameter Value Unit

Simulation ExperimentsWindowlengthW

8192 6144 samples

Hopsize∆h

8 3 samples

Extrapolationfilter order

o120 coefficients

Flexible Range-Doppler Processing

ConcatenationFactor

RangeResolution∆Rd (m)

MaximumUnambiguous

DopplerVelocityvu (m/s)

Simulation Experiments Simulation Experimentsd = 1

(standard) 3.02 R-1: 3.74R-2: 7.49 ± 22.1 ± 44.4

d = 2 1.46 R-1: n/aR-2: 3.60 ± 11 ± 22.16

d = 4 0.73 n/a ± 5.5 ± 11.08

meters apart, they are only distinguishable when processingwith d = 4, because the improved range resolution is then0.73 m, as seen in Fig. 7(e). This resolvability is also the casefor targets G4 and G5 which are at zero velocity.

V. EXPERIMENTAL VERIFICATION

A. Experimental Setup

The reconfigurable processing and range resolution im-provement method is demonstrated experimentally using theDelft University of Technology (TU Delft) PARSAX FMCWradar [17] shown in Fig. 8(a). The radar is mounted on theroof of the electrical engineering, mathematics and computerscience (EEMCS) building at the TU Delft. It operates in S-band (3.1315 GHz) and uses an Intermediate Frequency (IF)of 125 MHz. A simplified PARSAX block diagram is depictedin Fig. 9 along with the experimental setup. On every receiverchannel, transmitted and received signals are sampled at IFusing a pair of Analog-to-Digital Converters (ADCs) on anInnovative Integrations X5-400M Xilinx Virtex5SX95T FPGAcard. The ADCs are 14-bit devices with sampling rates up to400 Mega Samples per Second (MSPS). Deramping Single-Sideband (SSB) signal processing is performed digitally on the

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(e)

Fig. 7. Simulation Results for the scenario setup using the parameters inTable II and illustrated in Fig. 6. (a) Standard processing, PRF = 1 kHz.(b) Dropped sweeps to create PRF = 500 Hz. (c) Dropped sweeps to createPRF = 250 Hz. (d) Proposed processing with d = 2. (e) Proposed processingwith d = 4.

FPGAs. Beat-frequencies are transferred to a computer via thePCI-express bus for further processing. Experiments were con-ducted using the experiments-applicable configuration optionsshown in Table II. The transmitted waveform from the AWGchannel-1 was created by combining two frequency slopes ofbandwidths 40 MHz and 20 MHz respectively. Receivers R-1 and R-2 separate the received beat-frequencies from the40 MHz and 20 MHz respectively. Both receivers are SSBIQ ones, with the ability to reject either positive or negativefrequencies.

The aim here is to demonstrate that the range resolutionfrom processing the 20 MHz waveform can be improved tomatch that of the 40 MHz one, using the proposed methodwith a concatenation factor d = 2.

B. Experiment 1: A Stable TargetIn this experiment we observe an industrial factory chimney

as depicted in Fig. 8(a) and (b). The chimney is chosen asa stable target. The chimney is made up of multiple sub-chimneys.

C. Experiment 2: A Moving TargetIn this experiment, we observe an automobile on a quiet

road as depicted in Fig. 8(a) and (c). The automobile driving at





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Chimney

Road

Radar

(a)

(b)

Car

(c)

Fig. 8. (a) The PARSAX FMCW radar situated at the top of the TU Delftbuilding was used for the experiments. (b) Industrial chimney used as a stabletarget in the first experiment. (C) An automobile used as a moving target inthe second experiment.

a velocity of around 19 m/s (70 kmh) will be unambiguous forthe transmitted PRF of 2 kHz, and for when processing with aconcatenation factor d = 2, which will reduce the processingPRF to 1 kHz.

D. Results and Discussion

For the first experiment, the results are shown in Fig. 10.When processing the 20 MHz waveform with a concatenationfactor d = 2, the results closely match that of the 40 MHzwaveform. The sub-chimneys are resolvable, as can be seenin the disbalanced shape of the sinc-function in Fig. 10.This resolvability is confirmed by the measurement usingthe 40 MHz bandwidth waveform, in comparison with theproposed method being used on the 20 MHz waveform. Forthe second experiment, the results are shown in Fig. 11. Theautomobile appears to be of around 7 m in length in the40 MHz channel, which is expected due to the range resolutionbeing 3.74 m (as seen in Table II), FT leakage, and typicalautomobile lengths of around 4 m. In the 20 MHz channel,the automobile appears to be of around 14 m in length, whichis also expected due to the range resolution being 7.49 m.When processing with manually discarding every other sweepof the the 20 MHz channel, similarly to what was done inthe simulations section, the automobile appears to have thesame velocity but with a slight SNR loss and a slight velocitydisplacement due to the FT leakage. When processing the20 MHz waveform with a concatenation factor d = 2, theautomobile’s resolution closely match that of the 40 MHzwaveform, in range, velocity and SNR.

VI. CONCLUSION

A reconfigurable range-Doppler processing and range reso-lution improvement method for FMCW radar was presented.

ADC2

Filters

X5-400M

R-1

PCFPGA Card

ADC1

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Frequency

Time

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number

500μssT 450μsoT

40

MHz

20

MHz Time

Time

TransmitterADC1

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Ch 1

Ch 2

Ch 3

Ch 1

AWG

Ch 2

Ch 3

Fig. 9. Simplified PARSAX radar block diagram with the configuration usedfor experiments discussed is Section V. A waveform combining a 20 MHzand a 40 MHz sweeps is generated and combined by the Arbitrary WaveformGenerator (AWG). Both FPGA receivers R-1 and R-2 are SSB IQ ones, withthe ability to reject either positive or negative frequencies. The shaded areasdepict the receivers’ upper and lower LPF bounds.

1120 1140 1160 1180 1200 1220 1240

Range (m)

-5

0

5

10

15

20

25

30

35

40

45

50

Am

plitu

de (

dB)

40 MHz20 Mhz20 MHz d = 2

Fig. 10. Zero-Doppler cut zoom-in on the Chimney shown in Fig. 8 (a) and(b). The proposed processing of the 20 MHz channel - with a concatenationfactor d =2 - closely matches that of the 40 MHz channel. The sub-chimneysare resolvable, as can be seen in the disbalanced shape of the sinc-function.

The problem which this paper offered a solution for wasthe existence of the transient regions in FMCW derampprocessing. This region does not allow for longer targetsobservations, and this limits the maximum range resolutionthat can be achieved. The solution proposed in this paper was





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-21 -20 -19 -18 -17 -16Velocity (m/s)

1119

1130

11341137

1149

Ra

ng

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m)

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1119

1129

1134

1138

1149

Ra

ng

e (

m)

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20

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(d)

Fig. 11. Range-Velocity results maps for the automobile in the experimentdescribed in Section. V-C. (a) As seen in the 40 MHz channel. (b) As seenin the 20 MHz channel. (c) Processing with manually discarding every othersweep of the 20 MHz channel. (d) Processing the 20 MHz waveform with aconcatenation factor d = 2, the automobile’s resolution closely match that ofthe 40 MHz waveform, in range, velocity and SNR.

to coherently concatenate beat-frequency slices in the STFTdomain, by applying a phase correction to each frequency sliceas appropriate, followed by an Inverse STFT (ISTFT). Themethod extends the observation time by using returns frommore than one sweep at a time, which resulted in a finer rangeresolution without the need to transmit additional bandwidth.The method also made it possible to decouple the Dopplerprocessing PRF from the transmitted signal PRF. This is inthe sense that it became possible to - in parallel and from oneCPI - create different lengths fast-time slow-time matrices,which allows the observation of different range resolutiongranularities, without compromising on the total processinggain in any of the created matrices. This therefore also allowsfor the observation of different unambiguous Doppler velocityintervals (to implement staggered-PRF velocity disambigua-tion techniques for example) in a single CPI.

ACKNOWLEDGMENT

The authors would also like to thank Fred van der Zwan forhis assistance with the measurements.

REFERENCES

[1] A. G. Stove, “Linear FMCW radar techniques,” IEE Proc. or Radar andSignal Process., 1992.

[2] J. D. M. W. N. B. Jones, Digital signal processing: principles, devices,and applications. P. Peregrinus Ltd. on behalf of the Institution ofElect. Engineers, 1990.

[3] D. E. Barrick, “FMCW radar signals and digital processing,” NOAATech. Rep. ERL 283-WPL 26, 1973.

[4] M. A. Richards, Fundamentals of Radar Signal Processing, SecondEdition. McGraw-Hill, 2014.

[5] E. D. Adler, E. A. Viveiros, T. Ton, J. L. Kurtz, and M. C. Bartlett,“Direct digital synthesis applications for radar development,” in Pro.Int. Radar conf., May 1995, pp. 224–226.

[6] Y. Li and S. O’Young, “Method of doubling range resolution withoutincreasing bandwidth in FMCW radar,” Elect. Lett., vol. 51, no. 12, pp.933–935, 2015.

[7] V. K. Nguyen and M. D. Turley, “Bandwidth extrapolation of LFMsignals for narrowband radar systems,” in 2013 Int. conf. on Radar,Sep. 2013, pp. 140–145.

[8] K. Suwa and M. Iwamoto, “A bandwidth extrapolation technique ofpolarimetric radar data and a recursive method of polarimetric linearprediction coefficient estimation,” in 2003 IEEE Int. Geosci. and RemoteSensing Symp. Proc. (IEEE Cat. No.03CH37477), vol. 7, July 2003, pp.4329–4331 vol.7.

[9] M. I. K. Suwa, “A two-dimensional bandwidth extrapolation techniquefor polarimetric synthetic aperture radar images,” IEEE Trans. onGeosci. and Remote Sensing, vol. 45, no. 1, pp. 45–54, Jan 2007.

[10] B. G. M. A. Lulu, “Phase matching of coincident pulses for range-doppler estimation of multiple targets,” IEEE Signal Process. Lett.,vol. 26, no. 1, pp. 199–203, Jan 2019.

[11] S. Neemat, O. Krasnov, and A. Yarovoy, “An interference mitigationtechnique for FMCW radar using beat-frequencies interpolation in theSTFT domain,” IEEE Trans. on Microwave Theory and Techniques, pp.1–14, 2018.

[12] N. Petrov, F. L. Chevalier, and A. G. Yarovoy, “Detection of range mi-grating targets in compound-gaussian clutter,” IEEE Trans. on Aerospaceand Elect. Systems, vol. 54, no. 1, pp. 37–50, Feb 2018.

[13] F. Uysal and N. Goodman, “The effect of moving target on range-dopplermap and backprojection algorithm for focusing,” in 2016 IEEE Radarconf. (RadarConf), May 2016, pp. 1–5.

[14] F. Uysal, “Comparison of range migration correction algorithms forrange-doppler processing,” J. of App. Remote Sensing, 2017.

[15] M. Jankiraman, Design of Multi-Frequency CW Radars. SciTech, 2007.[16] S. Kay, Modern Spectral Estimation: Theory and Application. Prentice

Hall, 1999.[17] O. A. Krasnov, L. P. Ligthart, Z. Li, G. Babur, Z. Wang, and F. van der

Zwan, “PARSAX: High-resolution doppler-polarimetric FMCW radarwith dual-orthogonal signals,” 18th Int. conf. on Microwave Radar andWireless Commun. (MIKON), 2010.

Sharef Neemat received his B.S. in computer en-gineering from King Saud University (KSU) andhis M.Sc. in electrical engineering from the Uni-versity of Cape Town (UCT). His study focused onSecondary Surveillance Radar (SSR) IdentificationFriend or Foe (IFF). Before and after receiving hisM.Sc., he was involved in airborne radios work inthe form of design, development and test of FieldProgrammable Gate Array (FPGA)/Digital SignalProcessor (DSP) drivers and application layer SWfor radio housekeeping and scheduling. The DSP

designs and code were developed to comply with DO-178B level C (Soft-ware Considerations in Airborne Systems and Equipment Certification) andMISRA (Motor Industry Software Reliability Association C standard). Hewas furthermore responsible for system engineering/project management ofasset-tracking-systems’ development. The work had involved writing systemengineering management plans and requirements documentation for systemsand their sub-systems, complying with MIL-STD-490 and MIL-STD-491. Heis currently pursuing a Ph.D. degree at the Microwave Sensing, Signals andSystems (MS3) section of the Faculty of Electrical Engineering, Mathematics,and Computer Science (EEMCS) at Delft University of Technology, Delft, TheNetherlands.





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Faruk Uysal received his M.S and Ph.D. degreesin electrical engineering from New York University(NYU), NY, USA in 2010 and 2016 respectively.During his study, Dr. Uysal focused on signal sep-aration techniques for dynamic clutter mitigation.Between 2011 and 2014, he worked as a staffengineer at C&P Technologies, Inc., Closter, NJ,USA. He was a radar engineer with the AdvancedRadar Research Center (ARRC) at University of Ok-lahoma, Norman, OK, USA between 2014 and 2016,where he worked on the design and implementation

of various projects from Department of Defense (DoD) agencies. In September2016, he joined the Microwave Sensing, Signals and Systems (MS3) sectionof the Faculty of Electrical Engineering, Mathematics, and Computer Science(EEMCS) at Delft University of Technology as an Assistant Professor. Hiscurrent research interests include radar signal processing, waveform design,beamforming, radar image formation, clutter mitigation, cognitive radar anddistributed radar systems. Dr. Uysal is a senior member of the IEEE andcurrently serves as a reviewer for IEEE Transactions on Aerospace andElectronic Systems, IEEE Transactions on Geoscience and Remote Sensing(TGARS) and SPIE Journal of Applied Remote Sensing. Dr. Uysal is also anaffiliate member of Advanced Radar Research Center (ARRC) at Universityof Oklahoma.

Oleg Krasnov received the M.S. degree in radiophysics from Voronezh State University, Russia, in1982, and the Ph.D. degree in radiotechnique fromthe National Aerospace University “Kharkov Avia-tion Institute,” Ukraine, in 1994. In 1999 he joinedthe International Research Center for Telecommuni-cations and Radar (IRCTR), TU Delft. Since 2009he is a senior researcher at the Microwave Sensing,Signals and Systems (MS3) section of the Faculty ofElectrical Engineering, Mathematics, and ComputerScience (EEMCS) at Delft University of Technology,

and he became a Universitair Docent (Assistant Professor) there in 2012.His research interests include radar waveforms, signal and data processingalgorithms for polarimetric radars and distributed radar systems, multisensoratmospheric remote sensing, optimal resource management of adaptive radarsensors and distributed systems. Dr. Krasnov served as the Secretary of the9th European Radar Conference (EuRAD’12), Amsterdam, The Netherlands.

Alexander Yarovoy (F’15) received the Diplomadegree (Hons.) in radiophysics and electronics, Can-didate Phys. and Math. Sci. degree in radiophysics,and Doctor Phys. and Math. Sci. degree in radio-physics from Kharkov State University, Kharkov,Ukraine, in 1984, 1987, and 1994, respectively. In1987, he joined the Department of Radiophysics,Kharkov State University, as a Researcher, wherehe became a Professor in 1997. From 1994 to 1996,he was with the Technical University of Ilmenau,Ilmenau, Germany, as a Visiting Researcher. Since

1999, he has been with the Delft University of Technology, Delft, TheNetherlands. Since 2009, he has been the Chair of Microwave Sensing,Signals, and Systems. He has authored or co-authored over 250 scientificor technical papers and 14 book chapters, and holds 4 patents. His currentresearch interests include ultrawideband microwave technology and its appli-cations (particularly radars) and applied electromagnetics (particularly UWBantennas). Prof. Yarovoy was a co-recipient of the European Microwave WeekRadar Award for the paper that best advances the state of the art in radartechnology in 2001 (together with L. P. Ligthart and P. van Genderen) andin 2012 (together with T. Savelyev) and was also a co-recipient of the BestPaper Award of the Applied Computational Electromagnetic Society in 2010(together with D. Caratelli). He has served as a Guest Editor of five SpecialIssues for IEEE TRANSACTIONS and other journals. Since 2008, he hasbeen the Director of the European Microwave Association. Since 2011, hehas been an Associate Editor of the International Journal of Microwave andWireless Technologies. He has served as the Chair and TPC Chair of the fifthEuropean Radar Conference, Amsterdam, The Netherlands, as well as theSecretary of the first European Radar Conference, Amsterdam. He has alsoserved as the Co-Chair and TPC Chair of the 10th International Conferenceon Ground Penetrating Radar, Delft



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