Low sidelobe level radar techniques using Golay based coded sequences

Research ArticleEstimation of Sidelobe Level Variations ofPhased Codes in Presence of Random Interference forBistatic Wideband Noise Radar

Ana Vazquez Alejos1 Muhammad Dawood2 and Habeeb Ur-Rahman Mohammed3

1 The Signal Theory and Communication Department University of Vigo 36310 Vigo Spain2The Klipsch School of Electrical and Computer Engineering New Mexico State University Las Cruces NM 88001 USA3 Texas Instruments Inc Dallas TX 75243 USA

Correspondence should be addressed to Ana Vazquez Alejos analejosuvigoes

Received 22 July 2014 Accepted 3 November 2014

Academic Editor Yong Bae Park

Copyright copy Ana Vazquez Alejos et alThis is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

We discuss the importance of using the sidelobe level of the cross-correlation function as a criterion to implement a noise radarbased on the transmission of wideband binarywaveformsTheoretical expressions are introduced for the parameters Peak-SidelobeSecondary-Sidelobe and Integrated-Sidelobe levels for both Golay and pseudorandom binary sequences in presence of additivewhite Gaussian noise relating the sequence length119872 to the spectral power 119873

0of the interfering noise These expressions offer a

valuable method for adaptive radar waveform design in order to determine sequence requirements which allow facing the noisepresent in the frequency band of interest We also show a comparison of the ambiguity functions for Golay and PRBS sequencesto analyze their performance in terms of Doppler and range accuracy We describe a practical implementation of a pseudonoisewaveform-based bistatic radar with reduced sidelobe level due to the use of Golay codes in combination with single side bandmodulation and operation at UHF band Experimental measurements were performed in actual scenarios for ranging test of singleand double targets Linear polarizations were combinedwith different length sequences to determine their influence on the sounderperformance under field test conditions

1 Introduction

Radar data consisting of returns from several objects mightresult easily corrupted [1ndash4] because of the presence of noiseand interferences scattered signal components and frequ-ency dispersion [5ndash7] due to the random nature of the prop-agation medium As a result of those impairment propaga-tions the target detection process is further complicated dueto the problem of weak signals which carry informationabout subtle changes that are buried in the sidelobes of stron-ger reflections

At present widely used noise radar systems operatewith either very short pulses or linear frequency modulatedwaveforms and are based on eithermono- or bistatic configu-rations [8]These systems suffer fromhaving strong sidelobesthereby masking weaker returns from subtle changes andmaking it difficult to detect those variations due to a targetpresence

In order to overcome the sidelobe problem various cod-ing techniques have been proposed with different degrees ofsuccess in [1ndash4]One such technique is based on the transmis-sion of pseudonoise (PN) waveforms such as pseudorandombinary sequences (PRBS) and the system using them isknown as noise radar [9ndash14] Although PRBS are considereda good option in terms of their autocorrelation functionthese sequences are not optimal if sidelobe level is taken intoaccount This problem can be overcome if the transmittingprocess is composed of codes showing good autocorrelationproperties mainly estimated in terms of sidelobe level ampli-tude This is the case of the complementary binary series ofsequences known as Golay series [9ndash14]

Golay complementary codes are a pair of equal lengthsequences that have the property of canceling the sidelobeswhen the autocorrelation functions corresponding to eachsequence are algebraically added As a consequence of this

Hindawi Publishing CorporationInternational Journal of Antennas and PropagationArticle ID 297823

2 International Journal of Antennas and Propagation

addition the correlation peak is double to the one corre-sponding to the PRBS case thereby providing a significantenhancement in the output signal-to-noise ratio Also oncethe individual autocorrelation functions are added they pro-vide zero sidelobesThese improvements are important whendealing with large attenuation andor with stronger side-lobes as is generally the case of subsurface through-wall orthrough-dispersive media detections or in applications thatrequire the use of large frequency bandwidth

Due to a priori knowledge of the real-time cross-correlation function (CCF) properties of the transmittedbinary sequences an adaptive-on-transmit (AT) system canbe derived for wideband radar systems using the informationgiven by the Peak-Sidelobe (PSL) Secondary-Sidelobe (SSL)and Integrated-Sidelobe (ISL) as a design criterion

Thismeans that we can know the theoretical value of PSLSSL and ISL parameters at any instant for the transmittedcode besides the generating conditions of the transmittedcodes could be changed to improve the sidelobe values underthe detection of a certain noise level presence By adapting thesidelobe properties of the transmittedwaveform tominimumlevels the overall performance of the system will achieveenhanced performance features to face anomalous or extremeoperation conditions [15ndash18]

In this paper we introduce a formal analysis of thesidelobe level trend for the phase codes PRBS and also forthe complementary phase codes namedGolay seriesThe ISLSSL and PSL parameters from their CCFs have been param-eterized as functions of code length and interfering whiteGaussian random noise power

Additionally to the sidelobe issue the noise radar tech-nique presents some implementation requirements that oftenturn these systems into technical- or cost-unaffordable soun-ders At the transmitter end high bit rates and large sequencelengths are needed to achieve large amplitude and spatial res-olution respectively This feature implies an analogue-digitalconversion stage of great bandwidth and large amplituderesolution at the receiver end if a digital implementation isselected to build the sounder This SDR (software definedradio) architecture may not be always easy to achieve and itusually results in very costly hardware

In this paper we introduce a solution to the problemcaused by a large bandwidth requirement based on the useof single side band transmission that offers a double benefitfirstly only half bandwidth will be required at the analogue-digital conversion stage of the receiver end which will sim-plify the hardware and reduce costs secondly the travelingwaveform will be exposed to less noise (interferences) levelsan especially important feature if the frequency band is radioelectrically polluted as the UHF band case

Section 2 presents software simulations to illustrate acomparison of the robustness of PRBS and Golay sequencesagainst noise interferences Theoretical expressions arederived for PSL SSL and ISL terms for both Golay and PRBScases Section 3 briefly describes the hardware implementa-tion of the prototype system followed by the experimentalresults in Section 4 Experimental measurements were car-ried out to perform ranging tests for single and double targetidentification for both sequences demonstrating the viability

of a phase code based noise radar in the UHF band Theinfluences of the sequence length as well as the linear polar-ization used have been analyzed in order to determine thebehavior of this radar sounder under field test conditionsFinally conclusions are offered in Section 5

2 Noise Radar Techniques Based onPhase Coded Binary Sequences

Thenoisemodulated radar technique offers a large number ofadvantagesmainly due to its robustness to interferences [8 1819] and the wideband version received importance especiallyin the last decades [13 14 17ndash19] Nevertheless until not longago it was very difficult to find practical implementationsof these systems One of the main problems with them isthat they show detection ambiguity zones and the presenceof sidelobes that can mask weak reflections [8] Anotherkey element of the noise radar technique is the waveformgeneration that is mostly based on the transmission of awideband signal that usually consists of monopulsed trans-missions

Other implementations of the wideband random noisetechnique use waveforms based on pseudorandom binarysequences with maximum length also named PRBS sequ-ences with length119872 given in bits or chirps This technique[8] offers great advantages regarding high resolution of targetsas well as its great immunity to detection in hostile surroun-dings as well as in presence of natural or man-made causedinterferences

Nevertheless the radar technique by transmission ofPRBS sequences presents a limitation in the offered dynamicrange which goes bound to length 119872 of the transmittedsequence [12 13] Thus detecting weaker echoes is difficultwhich may be confused with noise in some cases due to thelarge attenuation undergone by the propagated signal Inaddition PRBS sequences present a serious problem of largepower sidelobes presence [10] which worsens the problem offalse echoes detection that is usual in radar applications

The sidelobe amplitude level is directly proportional tolength 119872 of the sequence so that if the length is increasedwith the purpose of increasing the dynamic range the side-lobe amplitude level will be increased in counterpart How-ever by increasing the length of the transmitted sequencethe speed of target detection is decreased thus limiting theresponse speed of the radar device

In this paper we considered a solution to the problemproduced by increasing the length119872 of the transmitted PRBSsequence by considering the use of Golay series [9ndash11] whichlead to a twofold dynamic range with respect to the onecorresponding to a PRBS sequence with the same length119872This allows the use of smaller length sequences to increase thetarget detection speed This feature compensates the needof transmitting two sequences in the Golay case that wouldincrease the time needed for measurement

In Section 21 the capabilities of PRBS and Golaysequences are measured in terms of PSL SSL and ISLlevels The effect of noise is presented in Section 22 Thiscomparison also shows better understanding of advantages

International Journal of Antennas and Propagation 3

provided by reduced sidelobe levels The results indicatewhich parameters of these binary sequences used in noiseradar can be easily adapted depending on the operationrequirements according to the idea of an AT system

21 Theoretical Expressions PSL SSL and ISL The theoret-ical expressions have been derived for PSL SSL and ISLparameters definition sequence length 119872 and the noise1198730statisticsmean 120583

119873and variance120590

119873 for unitary amplitude

level of the pulses plusmn1 V The theoretical definition of thesidelobe level parameters for a signal 119904(119905) is given by

PSL = max 119877119878(120591) minusmax 119877

119878(120591)

= 119877119878(120591 = 0) minusmax 119877

119878(120591 = 0)

SSL = max 119877119878 (120591 = 0)

ISL = intinfin

minusinfin

119877119878 (120591 = 0)

(1)

For the Golay case the pair of sequences composing thecode 119892(119905) are denoted as 119892

119886(119905) and 119892

119887(119905) with 0 le 119905 le 119872 sdot 119879

119888

As we explained above each of them has been added with thesame noise signal 119899(119905) and later correlated with the originalsequence These operations can be expressed according to(2)ndash(4) where otimes indicates correlation

119877119892119899(120591) = [(119892

119886(119905) + 119899 (119905)) otimes 119892

119886(119905 minus 120591)]

+ [(119892119887 (119905) + 119899 (119905)) otimes 119892119887 (119905 minus 120591)]

= 119892119886(119905) otimes 119892

119886(119905 minus 120591) + 119892

119887(119905) otimes 119892

119887(119905 minus 120591)

+ 119899 (119905) otimes 119892119886(119905 minus 120591) + 119899 (119905) otimes 119892

119887(119905 minus 120591)

(2)

119877119892119899(120591) = 119877

119892119886

(120591) + 119877119892119887

(120591) + 119877119892119886119899(120591) + 119877

119892119887119899(120591)

= 119877119892(120591) + 119877

119892119886119899(120591) + 119877

119892119887119899(120591)

(3)

119877119892119899(120591) =

2119872 + 119877119892119886119899(0) + 119877

119892119887119899(0) 120591 = 0

119877119892119886119899(120591) + 119877

119892119887119899(120591) 120591 = 0

(4)

Taking into account (2)-(3) (1) can be written for theGolay case as follows

PSL = max 119877119892119899 (120591) minusmax 119877

119892119899 (120591)

= 119877119892119899(120591 = 0) minusmax 119877

119892119899(120591 = 0)

= 2119872 minusmax 119877119892119899(120591 = 0)

= 2119872 minusmax 119877119892119886119899 (120591 = 0) + 119877119892

119887119899 (120591 = 0)

SSL = max 119877119892119899(120591 = 0)

= max 119877119892119886119899 (120591 = 0) + 119877119892

119887119899 (120591 = 0)

ISL = intinfin

minusinfin

119877119892119899(120591 = 0)

(5)

The discrete CCFs 119877119892119886119899[119896] and 119877

119892119887119899[119896] are given by the

following expressions

119877119892119886119899 [119896] =

119872

sum

119898=1

119886119898sdot 119899lowast

119898+119896lt1

119872

119872

sum

119898=1

1003816100381610038161003816119886119898 sdot 119899lowast

119898+119896

1003816100381610038161003816

2

lt1

119872

119872

sum

119898=1

10038161003816100381610038161198861198981003816100381610038161003816

2sdot10038161003816100381610038161198991198981003816100381610038161003816

2=1

119872sdot 119872 sdot (119873

0minus 120583119873)

(6)

119877119892119886119899 [119896] lt

1

119872sdot 119872 sdot

119872

sum

119898=1

10038161003816100381610038161198991198981003816100381610038161003816

2asymp 119899 minus var (119899) (7)

From (7) we infer that the cross-correlation between asequence of the pair and random noise is not dependent onindex 119896 Finally we reach the following expressions (8) forPSL SSL and ISL involving119872 and119873

0

PSL [dB]

=

10 sdot log10(2119872) 119873

0le 6 minus 10 sdot log

10(119872)

10 sdot log10(2119872) minus 2 sdot [6 minus 10 sdot log

10(119872) minus 119873

0]

6 minus 10 sdot log10(119872) le 1198730 le 47 dBW

0 1198730ge 47 dBW

SSL [dB] = 1198730 minus 120583119873

ISL [dB] =1198730

2

(8)

For the PRBS case only one sequence composes the codeand it is denoted as 119901(119905) with 0 le 119905 le 119872 sdot 119879

119888 The same noise

signal 119899(119905) is added and the resulting noisy signal is correlatedwith the original sequenceThese operations can be expressedaccording to (9) where otimes indicates correlation

119877119901119899(120591) = [(119901 (119905) + 119899 (119905)) otimes 119901 (119905 minus 120591)]

= 119901 (119905) otimes 119901 (119905 minus 120591) + 119899 (119905) otimes 119901 (119905 minus 120591)

119877119901119899 (120591) = 119877119901 (120591) + 119877119899119901 (120591)

119877119901119899 (120591) =

119872 + 119877119899119901(0) 120591 = 0

119877119899119901(120591) 120591 = 0

(9)

Taking into account (8) (1) can be written for the PRBS caseas follows

PSL = max 119877119901(120591) minusmax 119877

119899119901(120591)

= 119877119901 (120591 = 0) minusmax 119877

119899119901 (120591 = 0)

= 119872 minusmax 119877119899119901(120591 = 0)

SSL = max 119877119899119901 (120591 = 0)

ISL = intinfin

minusinfin

119877119899119901(120591 = 0)

(10)


Finally we reach the following expressions

PSL [dB]

=

10 sdot log10(119872) 119873


10(119872)


10(119872) minus 119873

0]


0 1198730ge 47 dBW

SSL [dB]

=

10 sdot log10(radic3

2sdot 119872)


10(119872)

minus10 sdot log10(119872) + [6 minus 10 sdot log

10(119872) minus 119873

0]


0 1198730ge 47 dBW

ISL [dB] =1198730

2minus 10 sdot log

10(2119872)

(11)

The first observation to be inferred when comparingPSLSSLISL expressions for both types of codes is that thePSL for the Golay case is not influenced by the AWGN asmuch as for the PRBS case Moreover the SSL in the Golaycase depends only on the noise parameters whereas it alsodepends on the inherent autocorrelation noise in the PRBScase Sowe conclude that an irreducible noise is present in theACF for a PRBS sequence the so-called code noise [18] Thesame trend is observed for the ISL parameter

22 Robustness against Sidelobe Presence Software simula-tions using MATLAB have been performed to illustrate therobustness of PRBS and Golay sequences against noiseinterferences For this purpose two 4096-bit-length Golaysequences and one 8192-length PRBS sequence with ampli-tude level of plusmn1 V and chip period 119879

119888= 1 s were gener-

ated using software [14ndash16] Additive white Gaussian noise(AWGN) was added to each sequence with power level 119873

0

within the range [minus100 +100] dBW The added noise has thesame bit rate as sequences used thus offering identicalbandwidth conditions

Cross-correlation functions between noisy and originalsequences were obtained Later PSL SSL and ISL levels weremeasured without performing any average that would aim toreduce the added noise From the plots shown in Figure 1 thefollowing conclusions can be inferred

(i) For1198730larger than 3 dB PSL levels in Golay and PRBS

are the same(ii) SSL level in Golay sequences is almost 50 dB down

compared to that in PRBS(iii) As the 119873

0ratio increases the SSL level difference

between Golay and PRBS sequence decreases(iv) ISL level in the Golay case is almost 50 dB lesser than

the ISL level for PRBS

0 10 20 30 40 50

0

20

40

60

80

PSL PRBS 8192ISL PRBS 8192SSL PRBS 8192

PSL Golay 4096ISL Golay 4096SSL Golay 4096

minus20

minus40

minus60

minus80

minus100minus50 minus40 minus30 minus20 minus10

(dB)

EbN0 (dB)

Figure 1 PSL SSL and ISL comparison for 4096-Golay and 8192-PRBS sequences

(v) As the 1198730ratio increases the ISL level difference

between the Golay and PRBS sequences decreases

(vi) For 1198730equals 16 dB PSL level is zero At this point

the AWGN power is larger than the sequence powerso the noise masks the signal This fact would corre-spond to a negative signal-to-noise ratio region

If cross-correlation functions are averaged to obtain anoise effect reduction the plots in Figure 2 are obtainedAmong other differences we can notice that when the case ofzero noise is considered for the SSL curve in the Golay casethe cross-correlation sidelobes are always cancelled regard-less of the noise level and then the SSL value is constant andis only determined by the sequence length

23 Ambiguity Functions Comparison The ambiguity func-tion for the complementary codes has been derived followingthe simplified method based on combining multiple rangecuts [17 19ndash21] According to this method the formal expres-sion for the ambiguity function of a complementary codewaveform is given by

1003816100381610038161003816120594 (120591 119891119889)1003816100381610038161003816

=

10038161003816100381610038161003816100381610038161003816

int

infin

minusinfin

119904 (119905) sdot 119904lowast(119905 minus 120591) sdot 119890

1198952120587119891119889119905119889119905

10038161003816100381610038161003816100381610038161003816

=

10038161003816100381610038161003816100381610038161003816

int

infin

minusinfin

119904119886 (119905) sdot 119904

lowast

119886(119905 minus 120591) sdot 119890

1198952120587119891119889119905119889119905

+ int

infin

minusinfin

119904119887(119905) sdot 119904lowast

119887(119905 minus 120591) sdot 119890

1198952120587119891119889119905119889119905

10038161003816100381610038161003816100381610038161003816

(12)


0 10 20 30 40 50

0

20

40

60

80



minus20

minus40

minus60


(dB)

EbN0 (dB)

Figure 2 PSL SSL and ISL comparison for 4096-Golay and 8192-PRBS sequences with averaged CCFs

The above expression turns into (13) if Parsevalrsquos theorem isapplied

1003816100381610038161003816120594 (120591 119891119889)1003816100381610038161003816

=

10038161003816100381610038161003816100381610038161003816

int

infin

minusinfin

119878lowast(119891) sdot 119878 (119891 minus 119891

119889) sdot 119890minus1198952120587119891120591

119889119891

10038161003816100381610038161003816100381610038161003816

=

10038161003816100381610038161003816100381610038161003816

int

infin

minusinfin

119878lowast

119886(119891) sdot 119878

119886(119891 minus 119891

119889) sdot 1198901198952120587119891120591

119889119891

+ int

infin

minusinfin

119878lowast

119887(119891) sdot 119878

119887(119891 minus 119891

119889) sdot 119890minus1198952120587119891120591

119889119891

10038161003816100381610038161003816100381610038161003816

(13)

Equation (13) can be implemented in MATLAB devel-oping the ambiguity function as a sequence of range cutsMoreover a simpler expression to be implemented can bederived from an arrangement of (12) which can be seen asa correlation of two functions

1003816100381610038161003816120594 (120591 119891119889)1003816100381610038161003816 =

10038161003816100381610038161003816100381610038161003816

int

infin

minusinfin


1198952120587119891119889120591119889119905

10038161003816100381610038161003816100381610038161003816

=10038161003816100381610038161003816[119904 (120591) sdot 119890

1198952120587119891119889120591] otimes 119904 (120591)

10038161003816100381610038161003816

(14)

The autocorrelation of complementary codes is achievedby adding two individual autocorrelation functions so theterm 119904(120591) sdot 1198901198952120587119891119889120591 otimes 119904(120591) can be expressed as a composition ofthe correlation corresponding to each sequence of the pair

120594 (120591 119891119889) = [119904

119886 (120591) sdot 1198901198952120587119891119889120591] otimes 119904119886 (120591)

+ [119904119887(120591) sdot 119890

1198952120587119891119889120591] otimes 119904119887(120591)

(15)

In the Fourier domain (15) turns into (16) if we applyParsevalrsquos theorem as in (13)

119865 120594 (120591 119891119889) = 119865 [119904

119886(120591) sdot 119890

1198952120587119891119889120591] otimes 119904119886(120591)

+ 119865 [119904119887(120591) sdot 119890

1198952120587119891119889120591] otimes 119904119887(120591)

(16)

If we evaluate both Fourier transforms in (16) for adiscrete interval of frequency values 119891

119889= 119891119896 and then we

apply an IFFT and a modulus operator we obtain the ambi-guity function corresponding to the complementary codes bythe method of range cuts A comparison has been performedfor the ambiguity functions corresponding to PRBS andGolay codes A sequence length of119872 = 31was chosen for thePRBS case and119872 = 32 for the Golay case with pulse ampli-tude of plusmn1 V and an oversampling factor equal to 100 Theoutcomes are plotted in Figures 3 and 4 respectively

Generally we can observe a better performance in rangeestimation and Doppler tolerance for the Golay code in thecontour plots In the |120594(120591 119891

119889= 0)| cuts we observe a null

presence of sidelobes for the Golay case that agrees with theautocorrelation properties of these codes In the PRBSsequence larger sidelobe values are present

In the following section we describe a practical imple-mentation of the Golay-based noise radar Additionally somedetails of the measurement procedure and signal processingare analyzed

3 Measurement System

The proposed wideband noise radar consists of the transmis-sion of a binary sequence either PRBS orGolayThe sequenceis digitally generated with the desired length and binary rateand modulated for transmission A single side band trans-mission has been applied in order to reduce the bandwidthrequirement in the analogue-digital conversion stage and itis accomplished by using the transmitting antenna as a filterIn the reception and later processing the phase componenthas been also considered and not only the envelope of thereceived signal [22] For this purpose a superheterodynedetection is carried out by means of a zero baseband down-conversion combined with a 119868119876 demodulation A completeblock diagram of the system can be seen in Figure 5

A software tool was developed in Labview to configureand control the PN generator and the oscilloscope henceensuring the correct data acquisition and recordingThis toolensures the impulse response snapshot to be measured ina short enough time in order for the channel response toremain essentially constant during acquisition

The resultant measurement system is a wideband radiochannel sounder in the time domain that uses the cross-corr-elation technique to obtain the complex impulsive responseestimate or ℎ(119905 120591) [23] From this function the range or dis-tance to a target can be extracted from the delay informationreported by the echoes detected in the CCF

31 Parameters of the Implemented Sounder The pulsepattern generator produced the binary Golay and PRBSsequences of 2119881pp amplitude with a maximum baseband


0

5

10

15

20

Del

ay

Del

ayFrequency

0 005 01

0

5

10

15

20 1

0 minus50 minus100 minus150 minus200

minus20

minus15

minus10

minus5

minus20

minus15

minus10

minus5

09

08

07

06

05

04

03

02

01minus01 minus005

|120594(120591 fd = 0)| (dB)

Figure 3 Ambiguity function for a 32-bit-length Golay code contour plot and |120594(120591 119891119889= 0)| cut

0

10

20

30

Del

ay

minus30

minus20

minus10

0

10

20

30

Del

ay

minus30

minus20

minus10

0 minus50 minus100 minus150

Frequency0 005 01minus01 minus005

1

09

08

07

06

05

04

03

02

01

|120594(120591 fd = 0)| (dB)

Figure 4 Ambiguity function for a 31-bit-length PRBS code contour plot and |120594(120591 119891119889= 0)| cut

frequency 119891119888of 250MHz resulting in a chip period of 4 ns

(1119891119888) As indicated in Figure 5 this binary code was mixed

with a frequency carrier 1198910of 500MHz which was also used

in the receiver end to demodulate the incoming signal so theoutput radio frequency (RF) band extended from 250MHz to750MHz The RF modulated signal boosted an amplifier toobtain an output power of +17 dBm and was transmitted viaa log periodic antenna operating from 500MHz Thus onlythe upper band of the modulated signal that is 500MHz to750MHz was transmitted The radiating elements consistedof one quad ridged horn antenna model WJ-8326-12 anda log antenna model AR7-19 also from Watking Johnson

arranging the first one in the receiver and the second onein the transmitter end All the frequency generators as wellas the sequence generator and the digital oscilloscope werephase synchronized by using a 10MHz rubidium oscillator asa reference clock

Once conditioned the received RF signal was fed to an119868119876 mixer to yield in-phase baseband (119868) and quadrature-phase (119876) components of the baseband downconvertedsignalThe analog to digital conversion of the 250MHz base-band 119868 and 119876 signals was made by an oscilloscope at a sam-pling rate of 1 GSamplesThat signal could later be resampledat higher or lower rates if needed The sounder design has a


Digital oscilloscopeBB

SplitterLO

Limiter

Splitter

RF

Splitter

Splitter

LNA1

f0

f0

f0

f0 BW

f0 BW

LIM1 SPL4

Mix2

Mix1

SPL3

I

Q

Mix3 AD

DC-BW2

DC-BW2LPF1

LPF2

PC

LNA3

fs = BWBPF2

BW2

BW2

Antennas

BPF1

SPL2 SPL1

10MHz

fcPA

BPSK

Pulse patterngenerator

Rubidiumoscillator

M = 213 = 8192

LNA2

2 way 0∘

2 way 90∘

3 way 0∘

fc = 250 MHzn = 13 bits

f0 = 500 MHzBW = 500 MHz

Figure 5 System block diagram

Table 1 System parameters

Parameter ValueRegister length (119898) in bits 13 11 10Code length119872

PRBS119872 = 2119898minus 1 8191 4095 2047

Golay119872 = 2119898 8192 4096 2048

Code rate or chip period 119879119888 4 ns 4 ns 4 nsDynamic range

PRBS 3913 dB 3613 dB 3313 dBGolay 4214 dB 3913 dB 3613 dB

Delay resolution Δ120591 8 ns 8 ns 8 nsMaximum delay 120591max

PRBS 32764 120583s 16380 120583s 8188120583sGolay 32768 120583s 16384 120583s 8192 120583s

Range resolution Δ119904 12m 12m 12mMaximum spatial 119904max

PRBS 98292m 4914m 24564mGolay 98304m 49152m 24576m

noise figure of 311 dB and dynamic range of 8084 dB at roomtemperature 290K In Table 1 we have summarized the mainfeatures of the salient systemTheparameters that indicate thedetection capability of the implemented sounder are listed inTable 2 [14 23]

4 Experimental Measurements

Field tests were performed for determining the range ordistance to a target firstly they were conducted under con-trolled conditions inside an anechoic chamber and later the

Table 2 Design system specifications

Parameter ValueCarrier Frequency 500MHzBaseband DC-250MHzFrequency range 500ndash750MHzNoise figure 311 dBReceiver output noise minus839 dBDynamic range 8084 dBSampling frequency 1 GSasTransmitting antenna gain 731 dBiReceiving antenna gain 5 dBi

Tx

Rx

Target

Range

Radar

Figure 6 Bistatic radar configuration for measurement setup

experiment was repeated in one outdoor scenario (top-roof)with different link ranges for single and double target detec-tion Orthogonal linear polarizations were used to analyze apossible influence of polarization on results Transmitterreceiver and target locations were chosen to provide line ofsight (LOS) A general schematic of the measurement setupused for the outdoor tests is given in Figure 6 It can be seenthat it corresponds to a classical bistatic radar configuration


Tx

Rx

L

h

Metallic target

b2

b2

120579r

120579i

Figure 7 Geometry setup for single target detection measurementFor ranges 1 and 2 119887 = 225m ℎ = 1422m 119871 = 144m and 120579

119894=

445∘ for range 3 119887 = 335m ℎ = 3107m 119871 = 376m and 120579

119894=

255∘

Rx

Tx

h d

L

TargetTargetnumber 1number 2

b2

b2

L998400

120579r

120579i

Figure 8 Geometry setup for double target detectionmeasurement119887 = 335m ℎ = 3107m 119871 = 311m 1198711015840 = 376m 120579

119894= 255

∘ and119889 = 65m

A single target detection experiment was conductedfirstly The geometry for this measurement setup is shownin Figure 7 Secondly a double target experiment was drivenaccording to the geometry shown in Figure 8 This secondtarget was also an aluminum plate with smaller dimensions0315m2

PRBS and Golay sequences were generated modulatedand later single side band transmitted in order to obtain aperformance comparison in terms of range estimation andPSL SSL and ISL values achieved The transmission is not incontinuous mode but it is armed with an external signal thatindicates when transmission starts once the sequence startsbeing transmitted by the programmable digital generator itstrigger output is activated further this signal triggers theacquisition in the oscilloscope

The two-way measured distance between transmittingand receiving antenna can be obtained according to twodifferent procedures Firstly bymeasuring the delay observedbetween the received signals with respect to the delay presentin a back-to-back connection The second one consists ofperforming a cross-correlation between the receiving signalsand an ideal version of the transmitted waveformThe outputof this cross-correlation is the impulsive response estimatethat contains the detected multipath components and the

0 100 200 300 400 500 600 700Sample

Am

plitu

de (V

)

BB output

1

08

06

04

02

0

minus02

minus04

minus06

minus08

minus1

Fs = 1GSampless

Back-to-back

Back-to-back delay = 445 samples

Propagation delay = 505 minus 445 samples

Figure 9 Propagation delay estimation for determining link rangein the anechoic chamber

excess delay value corresponding to each one of themFrom this relative delay value the two-way range can bederived adding the delay corresponding to the back-to-backconnection

Different sequence lengths have been used for the Golaycase it was always chosen a sequence with half the length thanthe one corresponding to PRBS codeThis allows performinga comparison in the same conditions of dynamic range levelbut it also compensates for the need of a doublemeasurementtime due to transmitting two sequences in theGolay caseThemeasurement procedure has been firstly used for an 8192-length PRBS sequence followed by a 4096-length Golay codeThen it was repeated for a 4096-PRBS with a 2048-Golaycode

41 Anechoic Chamber A simple range test was performedin order to ensure a proper functioning of the sounder Thisexperiment consisted of placing the transmitter and receiverantennas in opposite sides of the anechoic chamber facingeach other and with a separation distance of 868m Theheight of the transmitter and receiver antenna was 15mExperiments were performed when both the antennas werecopolarized that is horizontal (HH) and vertical (VV)polarization

The two-way measured distance between transmittingand receiving antenna was 1736m Figure 9 shows the recei-ved signal when the system is connected back-to-back andthe received 119868119876 signals when the anechoic chamber setupis utilized The measured delay due to the anechoic chamberlength was 60445 samples which gives a time delay of60 nsec for a sampling frequency of 1 GSas Thus a round-trip delay of 18mwas calculated representing an error of 18for both polarization cases


42 Single Target We selected a wide rectangular terraceplaced on a building roofwithin theNMSUCampus to ensureopen field propagation and quasistatic conditions Threecombinations of transmitter receiver and target locationswere considered The transmitter-receiver set stayed in thesame position on the terrace 119887 meters apart whereas thetargetwas placed in two different locations Later the distancebetween the transmitter-receiver sets was increased from225m to 335m

These three situations created three different range linksThe two-way distance between the sounder and the targetwas about 288 42 and 752 meters for the three ranges Theheight of the transmitter and receiver antenna was the samefor all the cases 18mThe target was an aluminum plate withdimensions 126m2

43 Double Target Taking as a base the third configurationused in the single target experiment corresponding to a two-way range of 752 meters a second metallic laminate wasplaced in front of the previous target This second target wasseparated by 65m from the first one as depicted in Figure 8and their dimensions were smaller 025 sdot 126 = 0315m2

From the first echo delay we will infer the two-waydistance travelled from the transmitter to the receiver viareflection on the second target (smaller) whereas the secondecho is related to the range of the first target (larger)

5 Experimental Results

The received signals were offline processed by estimating thecross-correlation of the recorded signal with an ideal versionof the transmitted waveform The results for both PRBS andGolay sequences were obtained and the comparison betweenthem was done in terms of range accuracy estimation anddetected sidelobe level presence Tables 3 and 4 summarizeresults achieved for the PSL SSL and ISL level derived fromfield measurements Large values of radio interferences havebeen detected along the field test due to the pollution presentin the UHF band in which the experiments were conducted

The values corresponding to the anechoic chamber werereduced to simple link range estimation As we indicated inabove Section 41 a round-trip link was calculated with anerror of 18 for both polarization cases The value of thistest was to demonstrate the proper functioning of the radarsounder

For the outdoor experimental tests it can be observed thatwith larger code lengths the values for PSL SSL and ISLalso tend to increase Some coherence loss can be appreciatedin these results for both polarizations that are due to thelarge level interferences found in the UHF bandThese inter-ferences degrade the correlation functions as indicated inFigures 1 and 2 and as explained in Section 21 Furthermorefor the longest range link ground reflection can be the mainreason for the correlation distortion

The experiments were driven in actual open field con-ditions so the calculated sidelobe levels integrated in thePSL SSL and ISL parameters do not only correspond to theinherent sidelobe level of the code but also correspond to

Table 3 Results for PSL SSL and ISL parametersmdashPRBS case

Sequence transmitted PRBS119872 (sequence length) 4096 8192Link range [m] 288m 42m 752m 288m 42m 752mPSL [dB]Vertical 495 0034 286 449 06 143Horizontal 293 212 349 214 151 368

SSL [dB]Vertical 3883 4093 3858 4191 4392 4270Horizontal 3883 3987 3573 4200 4308 3710

ISL [dB]Vertical 2298 2264 2179 241 2384 2296Horizontal 2473 2337 2367 2545 2477 2678

Table 4 Results for PSL SSL and ISL parametersmdashGolay case

Sequence transmitted Golay119872 (sequence length) 2048 4096Link range [m] 288m 42m 752m 288m 42m 752mPSL [dB]Vertical 702 356 665 730 492 486Horizontal 504 339 673 452 325 670



actual multipath components By enlarging the range link wechanged the environment conditions so new elements couldappear in the area illuminated by the radar that is a widerfield of view Only free-scatterer environments could ensurethat all the integrated values really corresponded to sidelobespresence

Despite these facts a general trend is clearly detectedAccording to results shown in Tables 3 and 4 Golay offersan overall better performance in terms of sidelobe problemreaching values up to 432 dB larger for PSL (119872 = 4096 42mrange vertical polarization) 467 dB less for the ISL parame-ter (119872 = 4096 42m range vertical polarization) and 378 dBless in the ISL (119872 = 4096 42m range horizontal polariza-tion)

It was determined that range estimation worked withmore accuracy for the Golay case whereas PRBS reaches arelative error of 21 for the 288m range and the combina-tion 8192-PRBS with 4096-Golay in both polarization casesThis result agrees with the lower PSL level calculated from thecorresponding acquired snapshots which offered a differenceof 274 dB for the same parameter in the Golay case

Based on the outcomes the polarization influence onsidelobe detection shows lower PSL and larger SSLISL levelsfor the vertical case for ranges 1 and 2 In the range estimationas per Tables 5 and 6 the polarization has provided similarresults in the single target case but outcomes seem to bemore


Table 5 Range estimation resultsmdashsingle target case

Sequence transmitted Golay PRBS119872 (sequence length) 4096 8192Link range [m] 288 42 752 288 42 752Link range [ns] 96 140 25067 96 140 25067Measured delay [ns]

Vertical 97 141 25167 94 138 25467Horizontal 97 142 25167 94 138 25467

Estimated range [m]Vertical 291 423 755 282 414 764Horizontal 291 426 755 282 414 764

Relative error []Vertical 104 071 04 21 143 16Horizontal 104 143 04 21 143 16

Table 6 Range estimation resultsmdashdouble target case

Code transmitted PRBS Golay119872 (sequence length) 4096 8192 2048 4096 8192Measured delay (ns)

Horizontal 42 40 44 44 42Vertical 42 42 44 44 44

Relative error ()Horizontal 296 758 166 166 296Vertical 296 296 166 166 166

accurate for the vertical polarization in the double targetresults on the other hand the horizontal polarization reachesa range estimation relative error of 754 for the combination8192-PRBS with 4096-Golay

6 Conclusions

A bistatic radar system operating in the UHF band accordingto the wideband noise principle was built for experimentalranging tests Theoretical simulations were conducted todemonstrate the influence of noise on a wideband noise radarperformance while using PRBS or Golay codes Robustnessagainst noise was theoretically determined in terms of PSLSSL and ISL values

A simplification is presented for the ambiguity functionsof complementary code based waveform According to theexpression reached for Golay a comparison between Golayand PRBS sequences was obtained The results indicate abetter performance in Doppler and range accuracy for thecomplementary codes as shown in the contour plots of theambiguity functionThe outcomes also indicate a good agree-ment with the autocorrelation properties of the respectivecodes especially in the |120594(120591 119891

119889= 0)| cuts

Field tests were driven on the roof top of Thomasand Brown building at NMSU Different ranges have beensuccessfully determined not only for single but also fordouble target experiments Results for both PRBS and Golaysequences were obtained and the comparison between themwas done in terms of range estimation and values for PSL

SSL and ISL parameters Our experimental tests indicatedthat the Golay codes seem to offer lower sidelobe level thanPRBS sequences even when a ratio 2 1 is observed in thelength selection of the involved sequences

Generally speakingwe have shown improvement of noiseradar system performance by using Golay-based sequencesover PRBS in four terms SSL and ISL levels reduction betterdynamic range better range estimation andminimized side-lobe masking problem observed on the PSL parameter valuetendency These results are important in the context of alargely radio polluted band in actual open field conditionsThis opens the door to future work a method that improvesthe wideband noise radar performance in noisy conditionsshould be developed

An adaptive-on-transmit (AT) system can be derived forwideband radar systems using the information given by thePSL SSL and ISL as a design criterion The minimal out-of-band sidelobe (OBS) level has been pointed out as an addi-tional criterion to choose the correct transmitting waveform[18 19]

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

The authors dedicate this paper to the memory of theirrespected professor Dr Russell Paul Jedlicka demised onMarch 11 2008 The authors thank the funding and supportof Klipsch School of Electrical and Computer EngineeringNewMexico StateUniversity and theXunta deGalicia (GrantEMR2012238)

References

[1] B L Lewis and J Kretschmer ldquoA new class of polyphasepulse compression codes and techniquesrdquo IEEE Transactions onAerospace andElectronic Systems vol 17 no 3 pp 364ndash372 1981

[2] B L Lewis and F F Kretschmer Jr ldquoLinear frequency modul-ation derived polyphase pulse compression codes and tech-niquesrdquo IEEE Transactions on Aerospace and Electronics Sys-tems vol 18 no 5 1981

[3] W K Lee H D Griffiths and L Vinagre ldquoDevelopments inradar waveform designrdquo in Proceedings of the 12th InternationalConference on Microwaves and Radar (MIKON rsquo98) vol 4 pp56ndash76 May 1998

[4] W K Lee H D Griffiths and R Benjamin ldquoIntegrated sidelobeenergy reduction technique using optimal polyphase codesrdquoElectronics Letters vol 35 no 24 pp 2090ndash2091 1999

[5] A V Alejos and M Dawood ldquoEstimation of power extinctionfactor in presence of brillouin precursor formation throughdispersive mediardquo Journal of Electromagnetic Waves and Appli-cations vol 25 no 4 pp 455ndash465 2011

[6] A V Alejos M Dawood and L Medina ldquoExperimental dyna-mical evolution of the brillouin precursor for broadband wire-less communication through vegetationrdquo Progress in Electro-magnetics Research vol 111 pp 291ndash309 2011


[7] A V Alejos and M Dawood ldquoInformation retrieval and cross-correlation function analysis of random noise radar signalthrough dispersivemediardquo inRadar Sensor Technology XVI vol8361 of Proceedings of SPIE Baltimore Md USA April 2012

[8] M Dawood N Quraishi and A V Alejos ldquoSuper-resolutiondoppler estimation using UWB random noise signals andMUSICrdquo IEEE Transactions on Aerospace and Electronic Sys-tems vol 49 no 1 pp 325ndash340 2013

[9] M Golay ldquoComplementary seriesrdquo IEEE Transactions on Infor-mation Theory vol 24 pp 82ndash87 1961

[10] R Sivaswamy ldquoMultiphase complementary codesrdquo IEEE Trans-actions on Information Theory vol 24 no 5 pp 546ndash552 1978

[11] S Budisin ldquoGolay complementary sequences are superior to PNsequencesrdquo in Proceedings of the IEEE International Conferenceon Systems Engineering pp 101ndash104 September 1992

[12] D Daniels Ground Penetrating Radar Institution of Engineer-ing and Technology 2nd edition 2004

[13] R M Narayanan X Xu and J A Henning ldquoRadar pene-tration imaging using ultra-wideband (UWB) random noisewaveformsrdquo IEE Proceedings Radar Sonar and Navigation vol151 no 3 pp 143ndash148 2004

[14] A V Alejos M G Sanchez and I Cuinas ldquoImprovementof wideband radio channel swept time-delay cross-correlationsounders by using golay sequencesrdquo IEEE Transactions onVehicular Technology vol 56 no 1 pp 362ndash368 2007

[15] C-Y Chen C-H Wang and C-C Chao ldquoComplete com-plementary codes and generalized Reed-Muller codesrdquo IEEECommunications Letters vol 12 no 11 pp 849ndash851 2008

[16] F Fiedler J Jedwab and M G Parker ldquoA framework forthe construction of Golay sequencesrdquo IEEE Transactions onInformation Theory vol 54 no 7 pp 3114ndash3129 2008

[17] M Dawood and R M Narayanan ldquoGeneralised widebandambiguity function of a coherent ultrawideband random noiseradarrdquo IEE Proceedings Radar Sonar and Navigation vol 150no 5 pp 379ndash386 2003

[18] A V Alejos M Dawood and M G Sanchez ldquoExtendedoptimal filters for adaptive-on-transmit radar systems usingbinary codesrdquoProgress in Electromagnetics Research vol 130 pp41ndash46 2012

[19] N Levanon and E Mozeson Radar Signals JohnWiley amp SonsNew York NY USA 2000

[20] R Turyn ldquoAmbiguity functions of complementary seriesrdquo IEEETransactions on Information Theory vol II-8 pp 46ndash47 1963

[21] B RMahafzaRadar Systems Analysis andDesignUsingMatlabChapman and Hall CRC Boca Raton Fla USA 2005

[22] A V Alejos M Dawood M G Sanchez I C Gomez RJedlicka andHUMohammed ldquoRadar de penetracion en tierramediante transmision de formas de onda basadas en seriesde secuencias de fase complementariardquo Patent no P2007011812012

[23] P A Bello ldquoCharacterization of randomly time-variant linearchannelsrdquo IEEE Transactions on Communication Systems volCS-11 pp 360ndash393 1963

Submit your manuscripts athttpwwwhindawicom

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RoboticsJournal of



addition the correlation peak is double to the one corre-sponding to the PRBS case thereby providing a significantenhancement in the output signal-to-noise ratio Also oncethe individual autocorrelation functions are added they pro-vide zero sidelobesThese improvements are important whendealing with large attenuation andor with stronger side-lobes as is generally the case of subsurface through-wall orthrough-dispersive media detections or in applications thatrequire the use of large frequency bandwidth

Due to a priori knowledge of the real-time cross-correlation function (CCF) properties of the transmittedbinary sequences an adaptive-on-transmit (AT) system canbe derived for wideband radar systems using the informationgiven by the Peak-Sidelobe (PSL) Secondary-Sidelobe (SSL)and Integrated-Sidelobe (ISL) as a design criterion

Thismeans that we can know the theoretical value of PSLSSL and ISL parameters at any instant for the transmittedcode besides the generating conditions of the transmittedcodes could be changed to improve the sidelobe values underthe detection of a certain noise level presence By adapting thesidelobe properties of the transmittedwaveform tominimumlevels the overall performance of the system will achieveenhanced performance features to face anomalous or extremeoperation conditions [15ndash18]

In this paper we introduce a formal analysis of thesidelobe level trend for the phase codes PRBS and also forthe complementary phase codes namedGolay seriesThe ISLSSL and PSL parameters from their CCFs have been param-eterized as functions of code length and interfering whiteGaussian random noise power

Additionally to the sidelobe issue the noise radar tech-nique presents some implementation requirements that oftenturn these systems into technical- or cost-unaffordable soun-ders At the transmitter end high bit rates and large sequencelengths are needed to achieve large amplitude and spatial res-olution respectively This feature implies an analogue-digitalconversion stage of great bandwidth and large amplituderesolution at the receiver end if a digital implementation isselected to build the sounder This SDR (software definedradio) architecture may not be always easy to achieve and itusually results in very costly hardware

In this paper we introduce a solution to the problemcaused by a large bandwidth requirement based on the useof single side band transmission that offers a double benefitfirstly only half bandwidth will be required at the analogue-digital conversion stage of the receiver end which will sim-plify the hardware and reduce costs secondly the travelingwaveform will be exposed to less noise (interferences) levelsan especially important feature if the frequency band is radioelectrically polluted as the UHF band case

Section 2 presents software simulations to illustrate acomparison of the robustness of PRBS and Golay sequencesagainst noise interferences Theoretical expressions arederived for PSL SSL and ISL terms for both Golay and PRBScases Section 3 briefly describes the hardware implementa-tion of the prototype system followed by the experimentalresults in Section 4 Experimental measurements were car-ried out to perform ranging tests for single and double targetidentification for both sequences demonstrating the viability

of a phase code based noise radar in the UHF band Theinfluences of the sequence length as well as the linear polar-ization used have been analyzed in order to determine thebehavior of this radar sounder under field test conditionsFinally conclusions are offered in Section 5

2 Noise Radar Techniques Based onPhase Coded Binary Sequences

Thenoisemodulated radar technique offers a large number ofadvantagesmainly due to its robustness to interferences [8 1819] and the wideband version received importance especiallyin the last decades [13 14 17ndash19] Nevertheless until not longago it was very difficult to find practical implementationsof these systems One of the main problems with them isthat they show detection ambiguity zones and the presenceof sidelobes that can mask weak reflections [8] Anotherkey element of the noise radar technique is the waveformgeneration that is mostly based on the transmission of awideband signal that usually consists of monopulsed trans-missions

Other implementations of the wideband random noisetechnique use waveforms based on pseudorandom binarysequences with maximum length also named PRBS sequ-ences with length119872 given in bits or chirps This technique[8] offers great advantages regarding high resolution of targetsas well as its great immunity to detection in hostile surroun-dings as well as in presence of natural or man-made causedinterferences

Nevertheless the radar technique by transmission ofPRBS sequences presents a limitation in the offered dynamicrange which goes bound to length 119872 of the transmittedsequence [12 13] Thus detecting weaker echoes is difficultwhich may be confused with noise in some cases due to thelarge attenuation undergone by the propagated signal Inaddition PRBS sequences present a serious problem of largepower sidelobes presence [10] which worsens the problem offalse echoes detection that is usual in radar applications

The sidelobe amplitude level is directly proportional tolength 119872 of the sequence so that if the length is increasedwith the purpose of increasing the dynamic range the side-lobe amplitude level will be increased in counterpart How-ever by increasing the length of the transmitted sequencethe speed of target detection is decreased thus limiting theresponse speed of the radar device

In this paper we considered a solution to the problemproduced by increasing the length119872 of the transmitted PRBSsequence by considering the use of Golay series [9ndash11] whichlead to a twofold dynamic range with respect to the onecorresponding to a PRBS sequence with the same length119872This allows the use of smaller length sequences to increase thetarget detection speed This feature compensates the needof transmitting two sequences in the Golay case that wouldincrease the time needed for measurement

In Section 21 the capabilities of PRBS and Golaysequences are measured in terms of PSL SSL and ISLlevels The effect of noise is presented in Section 22 Thiscomparison also shows better understanding of advantages







PSL = max 119877119878(120591) minusmax 119877

119878(120591)

= 119877119878(120591 = 0) minusmax 119877

119878(120591 = 0)

SSL = max 119877119878 (120591 = 0)

ISL = intinfin

minusinfin

119877119878 (120591 = 0)

(1)


119886(119905) and 119892

119887(119905) with 0 le 119905 le 119872 sdot 119879

119888


119877119892119899(120591) = [(119892

119886(119905) + 119899 (119905)) otimes 119892

119886(119905 minus 120591)]

+ [(119892119887 (119905) + 119899 (119905)) otimes 119892119887 (119905 minus 120591)]

= 119892119886(119905) otimes 119892

119886(119905 minus 120591) + 119892

119887(119905) otimes 119892

119887(119905 minus 120591)


119887(119905 minus 120591)

(2)

119877119892119899(120591) = 119877

119892119886

(120591) + 119877119892119887

(120591) + 119877119892119886119899(120591) + 119877

119892119887119899(120591)

= 119877119892(120591) + 119877

119892119886119899(120591) + 119877

119892119887119899(120591)

(3)

119877119892119899(120591) =

2119872 + 119877119892119886119899(0) + 119877

119892119887119899(0) 120591 = 0

119877119892119886119899(120591) + 119877

119892119887119899(120591) 120591 = 0

(4)


PSL = max 119877119892119899 (120591) minusmax 119877

119892119899 (120591)

= 119877119892119899(120591 = 0) minusmax 119877

119892119899(120591 = 0)

= 2119872 minusmax 119877119892119899(120591 = 0)

= 2119872 minusmax 119877119892119886119899 (120591 = 0) + 119877119892

119887119899 (120591 = 0)

SSL = max 119877119892119899(120591 = 0)

= max 119877119892119886119899 (120591 = 0) + 119877119892

119887119899 (120591 = 0)

ISL = intinfin

minusinfin

119877119892119899(120591 = 0)

(5)


119892119887119899[119896] are given by the


119877119892119886119899 [119896] =

119872

sum

119898=1

119886119898sdot 119899lowast

119898+119896lt1

119872

119872

sum

119898=1

1003816100381610038161003816119886119898 sdot 119899lowast

119898+119896

1003816100381610038161003816

2

lt1

119872

119872

sum

119898=1

10038161003816100381610038161198861198981003816100381610038161003816

2sdot10038161003816100381610038161198991198981003816100381610038161003816

2=1

119872sdot 119872 sdot (119873

0minus 120583119873)

(6)

119877119892119886119899 [119896] lt

1

119872sdot 119872 sdot

119872

sum

119898=1

10038161003816100381610038161198991198981003816100381610038161003816

2asymp 119899 minus var (119899) (7)


0

PSL [dB]

=

10 sdot log10(2119872) 119873


10(119872)


10(119872) minus 119873

0]


0 1198730ge 47 dBW

SSL [dB] = 1198730 minus 120583119873

ISL [dB] =1198730

2

(8)




119877119901119899(120591) = [(119901 (119905) + 119899 (119905)) otimes 119901 (119905 minus 120591)]


119877119901119899 (120591) = 119877119901 (120591) + 119877119899119901 (120591)

119877119901119899 (120591) =

119872 + 119877119899119901(0) 120591 = 0

119877119899119901(120591) 120591 = 0

(9)


PSL = max 119877119901(120591) minusmax 119877

119899119901(120591)

= 119877119901 (120591 = 0) minusmax 119877

119899119901 (120591 = 0)

= 119872 minusmax 119877119899119901(120591 = 0)

SSL = max 119877119899119901 (120591 = 0)

ISL = intinfin

minusinfin

119877119899119901(120591 = 0)

(10)



PSL [dB]

=

10 sdot log10(119872) 119873


10(119872)


10(119872) minus 119873

0]


0 1198730ge 47 dBW

SSL [dB]

=


2sdot 119872)


10(119872)


10(119872) minus 119873

0]


0 1198730ge 47 dBW

ISL [dB] =1198730

2minus 10 sdot log

10(2119872)

(11)





0









0 10 20 30 40 50

0

20

40

60

80



minus20

minus40

minus60

minus80


(dB)

EbN0 (dB)








1003816100381610038161003816120594 (120591 119891119889)1003816100381610038161003816

=

10038161003816100381610038161003816100381610038161003816

int

infin

minusinfin


1198952120587119891119889119905119889119905

10038161003816100381610038161003816100381610038161003816

=

10038161003816100381610038161003816100381610038161003816

int

infin

minusinfin

119904119886 (119905) sdot 119904

lowast

119886(119905 minus 120591) sdot 119890

1198952120587119891119889119905119889119905

+ int

infin

minusinfin

119904119887(119905) sdot 119904lowast

119887(119905 minus 120591) sdot 119890

1198952120587119891119889119905119889119905

10038161003816100381610038161003816100381610038161003816

(12)


0 10 20 30 40 50

0

20

40

60

80



minus20

minus40

minus60


(dB)

EbN0 (dB)



1003816100381610038161003816120594 (120591 119891119889)1003816100381610038161003816

=

10038161003816100381610038161003816100381610038161003816

int

infin

minusinfin


119889) sdot 119890minus1198952120587119891120591

119889119891

10038161003816100381610038161003816100381610038161003816

=

10038161003816100381610038161003816100381610038161003816

int

infin

minusinfin

119878lowast

119886(119891) sdot 119878

119886(119891 minus 119891

119889) sdot 1198901198952120587119891120591

119889119891

+ int

infin

minusinfin

119878lowast

119887(119891) sdot 119878

119887(119891 minus 119891

119889) sdot 119890minus1198952120587119891120591

119889119891

10038161003816100381610038161003816100381610038161003816

(13)


1003816100381610038161003816120594 (120591 119891119889)1003816100381610038161003816 =

10038161003816100381610038161003816100381610038161003816

int

infin

minusinfin


1198952120587119891119889120591119889119905

10038161003816100381610038161003816100381610038161003816

=10038161003816100381610038161003816[119904 (120591) sdot 119890

1198952120587119891119889120591] otimes 119904 (120591)

10038161003816100381610038161003816

(14)


120594 (120591 119891119889) = [119904

119886 (120591) sdot 1198901198952120587119891119889120591] otimes 119904119886 (120591)

+ [119904119887(120591) sdot 119890

1198952120587119891119889120591] otimes 119904119887(120591)

(15)


119865 120594 (120591 119891119889) = 119865 [119904

119886(120591) sdot 119890

1198952120587119891119889120591] otimes 119904119886(120591)

+ 119865 [119904119887(120591) sdot 119890

1198952120587119891119889120591] otimes 119904119887(120591)

(16)


119889= 119891119896 and then we












0

5

10

15

20

Del

ay

Del

ayFrequency

0 005 01

0

5

10

15

20 1


minus20

minus15

minus10

minus5

minus20

minus15

minus10

minus5

09

08

07

06

05

04

03

02

01minus01 minus005

|120594(120591 fd = 0)| (dB)


0

10

20

30

Del

ay

minus30

minus20

minus10

0

10

20

30

Del

ay

minus30

minus20

minus10



1

09

08

07

06

05

04

03

02

01

|120594(120591 fd = 0)| (dB)










SplitterLO

Limiter

Splitter

RF

Splitter

Splitter

LNA1

f0

f0

f0

f0 BW

f0 BW

LIM1 SPL4

Mix2

Mix1

SPL3

I

Q

Mix3 AD

DC-BW2

DC-BW2LPF1

LPF2

PC

LNA3

fs = BWBPF2

BW2

BW2

Antennas

BPF1

SPL2 SPL1

10MHz

fcPA

BPSK


Rubidiumoscillator

M = 213 = 8192

LNA2

2 way 0∘

2 way 90∘

3 way 0∘


f0 = 500 MHzBW = 500 MHz




PRBS119872 = 2119898minus 1 8191 4095 2047

Golay119872 = 2119898 8192 4096 2048












Tx

Rx

Target

Range

Radar




Tx

Rx

L

h

Metallic target

b2

b2

120579r

120579i


119894=


119894=

255∘

Rx

Tx

h d

L


b2

b2

L998400

120579r

120579i


119894= 255

∘ and119889 = 65m




0 100 200 300 400 500 600 700Sample

Am

plitu

de (V

)

BB output

1

08

06

04

02

0

minus02

minus04

minus06

minus08

minus1

Fs = 1GSampless

Back-to-back









































6 Conclusions



119889= 0)| cuts







Acknowledgments


References


























VLSI Design



RotatingMachinery





Shock and Vibration



Advances in







Journal of





SensorsJournal of








Journal of










Volume 2014

RoboticsJournal of








PSL = max 119877119878(120591) minusmax 119877

119878(120591)

= 119877119878(120591 = 0) minusmax 119877

119878(120591 = 0)

SSL = max 119877119878 (120591 = 0)

ISL = intinfin

minusinfin

119877119878 (120591 = 0)

(1)


119886(119905) and 119892

119887(119905) with 0 le 119905 le 119872 sdot 119879

119888


119877119892119899(120591) = [(119892

119886(119905) + 119899 (119905)) otimes 119892

119886(119905 minus 120591)]

+ [(119892119887 (119905) + 119899 (119905)) otimes 119892119887 (119905 minus 120591)]

= 119892119886(119905) otimes 119892

119886(119905 minus 120591) + 119892

119887(119905) otimes 119892

119887(119905 minus 120591)


119887(119905 minus 120591)

(2)

119877119892119899(120591) = 119877

119892119886

(120591) + 119877119892119887

(120591) + 119877119892119886119899(120591) + 119877

119892119887119899(120591)

= 119877119892(120591) + 119877

119892119886119899(120591) + 119877

119892119887119899(120591)

(3)

119877119892119899(120591) =

2119872 + 119877119892119886119899(0) + 119877

119892119887119899(0) 120591 = 0

119877119892119886119899(120591) + 119877

119892119887119899(120591) 120591 = 0

(4)


PSL = max 119877119892119899 (120591) minusmax 119877

119892119899 (120591)

= 119877119892119899(120591 = 0) minusmax 119877

119892119899(120591 = 0)

= 2119872 minusmax 119877119892119899(120591 = 0)

= 2119872 minusmax 119877119892119886119899 (120591 = 0) + 119877119892

119887119899 (120591 = 0)

SSL = max 119877119892119899(120591 = 0)

= max 119877119892119886119899 (120591 = 0) + 119877119892

119887119899 (120591 = 0)

ISL = intinfin

minusinfin

119877119892119899(120591 = 0)

(5)


119892119887119899[119896] are given by the


119877119892119886119899 [119896] =

119872

sum

119898=1

119886119898sdot 119899lowast

119898+119896lt1

119872

119872

sum

119898=1

1003816100381610038161003816119886119898 sdot 119899lowast

119898+119896

1003816100381610038161003816

2

lt1

119872

119872

sum

119898=1

10038161003816100381610038161198861198981003816100381610038161003816

2sdot10038161003816100381610038161198991198981003816100381610038161003816

2=1

119872sdot 119872 sdot (119873

0minus 120583119873)

(6)

119877119892119886119899 [119896] lt

1

119872sdot 119872 sdot

119872

sum

119898=1

10038161003816100381610038161198991198981003816100381610038161003816

2asymp 119899 minus var (119899) (7)


0

PSL [dB]

=

10 sdot log10(2119872) 119873


10(119872)


10(119872) minus 119873

0]


0 1198730ge 47 dBW

SSL [dB] = 1198730 minus 120583119873

ISL [dB] =1198730

2

(8)




119877119901119899(120591) = [(119901 (119905) + 119899 (119905)) otimes 119901 (119905 minus 120591)]


119877119901119899 (120591) = 119877119901 (120591) + 119877119899119901 (120591)

119877119901119899 (120591) =

119872 + 119877119899119901(0) 120591 = 0

119877119899119901(120591) 120591 = 0

(9)


PSL = max 119877119901(120591) minusmax 119877

119899119901(120591)

= 119877119901 (120591 = 0) minusmax 119877

119899119901 (120591 = 0)

= 119872 minusmax 119877119899119901(120591 = 0)

SSL = max 119877119899119901 (120591 = 0)

ISL = intinfin

minusinfin

119877119899119901(120591 = 0)

(10)



PSL [dB]

=

10 sdot log10(119872) 119873


10(119872)


10(119872) minus 119873

0]


0 1198730ge 47 dBW

SSL [dB]

=


2sdot 119872)


10(119872)


10(119872) minus 119873

0]


0 1198730ge 47 dBW

ISL [dB] =1198730

2minus 10 sdot log

10(2119872)

(11)





0









0 10 20 30 40 50

0

20

40

60

80



minus20

minus40

minus60

minus80


(dB)

EbN0 (dB)








1003816100381610038161003816120594 (120591 119891119889)1003816100381610038161003816

=

10038161003816100381610038161003816100381610038161003816

int

infin

minusinfin


1198952120587119891119889119905119889119905

10038161003816100381610038161003816100381610038161003816

=

10038161003816100381610038161003816100381610038161003816

int

infin

minusinfin

119904119886 (119905) sdot 119904

lowast

119886(119905 minus 120591) sdot 119890

1198952120587119891119889119905119889119905

+ int

infin

minusinfin

119904119887(119905) sdot 119904lowast

119887(119905 minus 120591) sdot 119890

1198952120587119891119889119905119889119905

10038161003816100381610038161003816100381610038161003816

(12)


0 10 20 30 40 50

0

20

40

60

80



minus20

minus40

minus60


(dB)

EbN0 (dB)



1003816100381610038161003816120594 (120591 119891119889)1003816100381610038161003816

=

10038161003816100381610038161003816100381610038161003816

int

infin

minusinfin


119889) sdot 119890minus1198952120587119891120591

119889119891

10038161003816100381610038161003816100381610038161003816

=

10038161003816100381610038161003816100381610038161003816

int

infin

minusinfin

119878lowast

119886(119891) sdot 119878

119886(119891 minus 119891

119889) sdot 1198901198952120587119891120591

119889119891

+ int

infin

minusinfin

119878lowast

119887(119891) sdot 119878

119887(119891 minus 119891

119889) sdot 119890minus1198952120587119891120591

119889119891

10038161003816100381610038161003816100381610038161003816

(13)


1003816100381610038161003816120594 (120591 119891119889)1003816100381610038161003816 =

10038161003816100381610038161003816100381610038161003816

int

infin

minusinfin


1198952120587119891119889120591119889119905

10038161003816100381610038161003816100381610038161003816

=10038161003816100381610038161003816[119904 (120591) sdot 119890

1198952120587119891119889120591] otimes 119904 (120591)

10038161003816100381610038161003816

(14)


120594 (120591 119891119889) = [119904

119886 (120591) sdot 1198901198952120587119891119889120591] otimes 119904119886 (120591)

+ [119904119887(120591) sdot 119890

1198952120587119891119889120591] otimes 119904119887(120591)

(15)


119865 120594 (120591 119891119889) = 119865 [119904

119886(120591) sdot 119890

1198952120587119891119889120591] otimes 119904119886(120591)

+ 119865 [119904119887(120591) sdot 119890

1198952120587119891119889120591] otimes 119904119887(120591)

(16)


119889= 119891119896 and then we












0

5

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20

Del

ay

Del

ayFrequency

0 005 01

0

5

10

15

20 1


minus20

minus15

minus10

minus5

minus20

minus15

minus10

minus5

09

08

07

06

05

04

03

02

01minus01 minus005

|120594(120591 fd = 0)| (dB)


0

10

20

30

Del

ay

minus30

minus20

minus10

0

10

20

30

Del

ay

minus30

minus20

minus10



1

09

08

07

06

05

04

03

02

01

|120594(120591 fd = 0)| (dB)










SplitterLO

Limiter

Splitter

RF

Splitter

Splitter

LNA1

f0

f0

f0

f0 BW

f0 BW

LIM1 SPL4

Mix2

Mix1

SPL3

I

Q

Mix3 AD

DC-BW2

DC-BW2LPF1

LPF2

PC

LNA3

fs = BWBPF2

BW2

BW2

Antennas

BPF1

SPL2 SPL1

10MHz

fcPA

BPSK


Rubidiumoscillator

M = 213 = 8192

LNA2

2 way 0∘

2 way 90∘

3 way 0∘


f0 = 500 MHzBW = 500 MHz




PRBS119872 = 2119898minus 1 8191 4095 2047

Golay119872 = 2119898 8192 4096 2048












Tx

Rx

Target

Range

Radar




Tx

Rx

L

h

Metallic target

b2

b2

120579r

120579i


119894=


119894=

255∘

Rx

Tx

h d

L


b2

b2

L998400

120579r

120579i


119894= 255

∘ and119889 = 65m




0 100 200 300 400 500 600 700Sample

Am

plitu

de (V

)

BB output

1

08

06

04

02

0

minus02

minus04

minus06

minus08

minus1

Fs = 1GSampless

Back-to-back









































6 Conclusions



119889= 0)| cuts







Acknowledgments


References


























VLSI Design



RotatingMachinery





Shock and Vibration



Advances in







Journal of





SensorsJournal of








Journal of










Volume 2014

RoboticsJournal of




PSL [dB]

=

10 sdot log10(119872) 119873


10(119872)


10(119872) minus 119873

0]


0 1198730ge 47 dBW

SSL [dB]

=


2sdot 119872)


10(119872)


10(119872) minus 119873

0]


0 1198730ge 47 dBW

ISL [dB] =1198730

2minus 10 sdot log

10(2119872)

(11)





0









0 10 20 30 40 50

0

20

40

60

80



minus20

minus40

minus60

minus80


(dB)

EbN0 (dB)








1003816100381610038161003816120594 (120591 119891119889)1003816100381610038161003816

=

10038161003816100381610038161003816100381610038161003816

int

infin

minusinfin


1198952120587119891119889119905119889119905

10038161003816100381610038161003816100381610038161003816

=

10038161003816100381610038161003816100381610038161003816

int

infin

minusinfin

119904119886 (119905) sdot 119904

lowast

119886(119905 minus 120591) sdot 119890

1198952120587119891119889119905119889119905

+ int

infin

minusinfin

119904119887(119905) sdot 119904lowast

119887(119905 minus 120591) sdot 119890

1198952120587119891119889119905119889119905

10038161003816100381610038161003816100381610038161003816

(12)


0 10 20 30 40 50

0

20

40

60

80



minus20

minus40

minus60


(dB)

EbN0 (dB)



1003816100381610038161003816120594 (120591 119891119889)1003816100381610038161003816

=

10038161003816100381610038161003816100381610038161003816

int

infin

minusinfin


119889) sdot 119890minus1198952120587119891120591

119889119891

10038161003816100381610038161003816100381610038161003816

=

10038161003816100381610038161003816100381610038161003816

int

infin

minusinfin

119878lowast

119886(119891) sdot 119878

119886(119891 minus 119891

119889) sdot 1198901198952120587119891120591

119889119891

+ int

infin

minusinfin

119878lowast

119887(119891) sdot 119878

119887(119891 minus 119891

119889) sdot 119890minus1198952120587119891120591

119889119891

10038161003816100381610038161003816100381610038161003816

(13)


1003816100381610038161003816120594 (120591 119891119889)1003816100381610038161003816 =

10038161003816100381610038161003816100381610038161003816

int

infin

minusinfin


1198952120587119891119889120591119889119905

10038161003816100381610038161003816100381610038161003816

=10038161003816100381610038161003816[119904 (120591) sdot 119890

1198952120587119891119889120591] otimes 119904 (120591)

10038161003816100381610038161003816

(14)


120594 (120591 119891119889) = [119904

119886 (120591) sdot 1198901198952120587119891119889120591] otimes 119904119886 (120591)

+ [119904119887(120591) sdot 119890

1198952120587119891119889120591] otimes 119904119887(120591)

(15)


119865 120594 (120591 119891119889) = 119865 [119904

119886(120591) sdot 119890

1198952120587119891119889120591] otimes 119904119886(120591)

+ 119865 [119904119887(120591) sdot 119890

1198952120587119891119889120591] otimes 119904119887(120591)

(16)


119889= 119891119896 and then we












0

5

10

15

20

Del

ay

Del

ayFrequency

0 005 01

0

5

10

15

20 1


minus20

minus15

minus10

minus5

minus20

minus15

minus10

minus5

09

08

07

06

05

04

03

02

01minus01 minus005

|120594(120591 fd = 0)| (dB)


0

10

20

30

Del

ay

minus30

minus20

minus10

0

10

20

30

Del

ay

minus30

minus20

minus10



1

09

08

07

06

05

04

03

02

01

|120594(120591 fd = 0)| (dB)










SplitterLO

Limiter

Splitter

RF

Splitter

Splitter

LNA1

f0

f0

f0

f0 BW

f0 BW

LIM1 SPL4

Mix2

Mix1

SPL3

I

Q

Mix3 AD

DC-BW2

DC-BW2LPF1

LPF2

PC

LNA3

fs = BWBPF2

BW2

BW2

Antennas

BPF1

SPL2 SPL1

10MHz

fcPA

BPSK


Rubidiumoscillator

M = 213 = 8192

LNA2

2 way 0∘

2 way 90∘

3 way 0∘


f0 = 500 MHzBW = 500 MHz




PRBS119872 = 2119898minus 1 8191 4095 2047

Golay119872 = 2119898 8192 4096 2048












Tx

Rx

Target

Range

Radar




Tx

Rx

L

h

Metallic target

b2

b2

120579r

120579i


119894=


119894=

255∘

Rx

Tx

h d

L


b2

b2

L998400

120579r

120579i


119894= 255

∘ and119889 = 65m




0 100 200 300 400 500 600 700Sample

Am

plitu

de (V

)

BB output

1

08

06

04

02

0

minus02

minus04

minus06

minus08

minus1

Fs = 1GSampless

Back-to-back









































6 Conclusions



119889= 0)| cuts







Acknowledgments


References


























VLSI Design



RotatingMachinery





Shock and Vibration



Advances in







Journal of





SensorsJournal of








Journal of










Volume 2014

RoboticsJournal of



0 10 20 30 40 50

0

20

40

60

80



minus20

minus40

minus60


(dB)

EbN0 (dB)



1003816100381610038161003816120594 (120591 119891119889)1003816100381610038161003816

=

10038161003816100381610038161003816100381610038161003816

int

infin

minusinfin


119889) sdot 119890minus1198952120587119891120591

119889119891

10038161003816100381610038161003816100381610038161003816

=

10038161003816100381610038161003816100381610038161003816

int

infin

minusinfin

119878lowast

119886(119891) sdot 119878

119886(119891 minus 119891

119889) sdot 1198901198952120587119891120591

119889119891

+ int

infin

minusinfin

119878lowast

119887(119891) sdot 119878

119887(119891 minus 119891

119889) sdot 119890minus1198952120587119891120591

119889119891

10038161003816100381610038161003816100381610038161003816

(13)


1003816100381610038161003816120594 (120591 119891119889)1003816100381610038161003816 =

10038161003816100381610038161003816100381610038161003816

int

infin

minusinfin


1198952120587119891119889120591119889119905

10038161003816100381610038161003816100381610038161003816

=10038161003816100381610038161003816[119904 (120591) sdot 119890

1198952120587119891119889120591] otimes 119904 (120591)

10038161003816100381610038161003816

(14)


120594 (120591 119891119889) = [119904

119886 (120591) sdot 1198901198952120587119891119889120591] otimes 119904119886 (120591)

+ [119904119887(120591) sdot 119890

1198952120587119891119889120591] otimes 119904119887(120591)

(15)


119865 120594 (120591 119891119889) = 119865 [119904

119886(120591) sdot 119890

1198952120587119891119889120591] otimes 119904119886(120591)

+ 119865 [119904119887(120591) sdot 119890

1198952120587119891119889120591] otimes 119904119887(120591)

(16)


119889= 119891119896 and then we












0

5

10

15

20

Del

ay

Del

ayFrequency

0 005 01

0

5

10

15

20 1


minus20

minus15

minus10

minus5

minus20

minus15

minus10

minus5

09

08

07

06

05

04

03

02

01minus01 minus005

|120594(120591 fd = 0)| (dB)


0

10

20

30

Del

ay

minus30

minus20

minus10

0

10

20

30

Del

ay

minus30

minus20

minus10



1

09

08

07

06

05

04

03

02

01

|120594(120591 fd = 0)| (dB)










SplitterLO

Limiter

Splitter

RF

Splitter

Splitter

LNA1

f0

f0

f0

f0 BW

f0 BW

LIM1 SPL4

Mix2

Mix1

SPL3

I

Q

Mix3 AD

DC-BW2

DC-BW2LPF1

LPF2

PC

LNA3

fs = BWBPF2

BW2

BW2

Antennas

BPF1

SPL2 SPL1

10MHz

fcPA

BPSK


Rubidiumoscillator

M = 213 = 8192

LNA2

2 way 0∘

2 way 90∘

3 way 0∘


f0 = 500 MHzBW = 500 MHz




PRBS119872 = 2119898minus 1 8191 4095 2047

Golay119872 = 2119898 8192 4096 2048












Tx

Rx

Target

Range

Radar




Tx

Rx

L

h

Metallic target

b2

b2

120579r

120579i


119894=


119894=

255∘

Rx

Tx

h d

L


b2

b2

L998400

120579r

120579i


119894= 255

∘ and119889 = 65m




0 100 200 300 400 500 600 700Sample

Am

plitu

de (V

)

BB output

1

08

06

04

02

0

minus02

minus04

minus06

minus08

minus1

Fs = 1GSampless

Back-to-back









































6 Conclusions



119889= 0)| cuts







Acknowledgments


References


























VLSI Design



RotatingMachinery





Shock and Vibration



Advances in







Journal of





SensorsJournal of








Journal of










Volume 2014

RoboticsJournal of



0

5

10

15

20

Del

ay

Del

ayFrequency

0 005 01

0

5

10

15

20 1


minus20

minus15

minus10

minus5

minus20

minus15

minus10

minus5

09

08

07

06

05

04

03

02

01minus01 minus005

|120594(120591 fd = 0)| (dB)


0

10

20

30

Del

ay

minus30

minus20

minus10

0

10

20

30

Del

ay

minus30

minus20

minus10



1

09

08

07

06

05

04

03

02

01

|120594(120591 fd = 0)| (dB)










SplitterLO

Limiter

Splitter

RF

Splitter

Splitter

LNA1

f0

f0

f0

f0 BW

f0 BW

LIM1 SPL4

Mix2

Mix1

SPL3

I

Q

Mix3 AD

DC-BW2

DC-BW2LPF1

LPF2

PC

LNA3

fs = BWBPF2

BW2

BW2

Antennas

BPF1

SPL2 SPL1

10MHz

fcPA

BPSK


Rubidiumoscillator

M = 213 = 8192

LNA2

2 way 0∘

2 way 90∘

3 way 0∘


f0 = 500 MHzBW = 500 MHz




PRBS119872 = 2119898minus 1 8191 4095 2047

Golay119872 = 2119898 8192 4096 2048












Tx

Rx

Target

Range

Radar




Tx

Rx

L

h

Metallic target

b2

b2

120579r

120579i


119894=


119894=

255∘

Rx

Tx

h d

L


b2

b2

L998400

120579r

120579i


119894= 255

∘ and119889 = 65m




0 100 200 300 400 500 600 700Sample

Am

plitu

de (V

)

BB output

1

08

06

04

02

0

minus02

minus04

minus06

minus08

minus1

Fs = 1GSampless

Back-to-back









































6 Conclusions



119889= 0)| cuts







Acknowledgments


References


























VLSI Design



RotatingMachinery





Shock and Vibration



Advances in







Journal of





SensorsJournal of








Journal of










Volume 2014

RoboticsJournal of




SplitterLO

Limiter

Splitter

RF

Splitter

Splitter

LNA1

f0

f0

f0

f0 BW

f0 BW

LIM1 SPL4

Mix2

Mix1

SPL3

I

Q

Mix3 AD

DC-BW2

DC-BW2LPF1

LPF2

PC

LNA3

fs = BWBPF2

BW2

BW2

Antennas

BPF1

SPL2 SPL1

10MHz

fcPA

BPSK


Rubidiumoscillator

M = 213 = 8192

LNA2

2 way 0∘

2 way 90∘

3 way 0∘


f0 = 500 MHzBW = 500 MHz




PRBS119872 = 2119898minus 1 8191 4095 2047

Golay119872 = 2119898 8192 4096 2048












Tx

Rx

Target

Range

Radar




Tx

Rx

L

h

Metallic target

b2

b2

120579r

120579i


119894=


119894=

255∘

Rx

Tx

h d

L


b2

b2

L998400

120579r

120579i


119894= 255

∘ and119889 = 65m




0 100 200 300 400 500 600 700Sample

Am

plitu

de (V

)

BB output

1

08

06

04

02

0

minus02

minus04

minus06

minus08

minus1

Fs = 1GSampless

Back-to-back









































6 Conclusions



119889= 0)| cuts







Acknowledgments


References


























VLSI Design



RotatingMachinery





Shock and Vibration



Advances in







Journal of





SensorsJournal of








Journal of










Volume 2014

RoboticsJournal of



Tx

Rx

L

h

Metallic target

b2

b2

120579r

120579i


119894=


119894=

255∘

Rx

Tx

h d

L


b2

b2

L998400

120579r

120579i


119894= 255

∘ and119889 = 65m




0 100 200 300 400 500 600 700Sample

Am

plitu

de (V

)

BB output

1

08

06

04

02

0

minus02

minus04

minus06

minus08

minus1

Fs = 1GSampless

Back-to-back









































6 Conclusions



119889= 0)| cuts







Acknowledgments


References


























VLSI Design



RotatingMachinery





Shock and Vibration



Advances in







Journal of





SensorsJournal of








Journal of










Volume 2014

RoboticsJournal of



































6 Conclusions



119889= 0)| cuts







Acknowledgments


References


























VLSI Design



RotatingMachinery





Shock and Vibration



Advances in







Journal of





SensorsJournal of








Journal of










Volume 2014

RoboticsJournal of













6 Conclusions



119889= 0)| cuts







Acknowledgments


References


























VLSI Design



RotatingMachinery





Shock and Vibration



Advances in







Journal of





SensorsJournal of








Journal of










Volume 2014

RoboticsJournal of





















VLSI Design



RotatingMachinery





Shock and Vibration



Advances in







Journal of





SensorsJournal of








Journal of










Volume 2014

RoboticsJournal of



VLSI Design



RotatingMachinery





Shock and Vibration



Advances in







Journal of





SensorsJournal of








Journal of










Volume 2014

RoboticsJournal of


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Low sidelobe level radar techniques using Golay based coded sequences