IR-SB-EX-0202[1]

SOFTWARE MODEL OF A RADAR RECEIVER

MASTER’S THESIS PROJECT

Roland Standert

Saab Bofors Dynamics AB, Sensors, Linköping Royal Institute of Technology, Signals-Sensors-Systems Department, Stockholm

Report number: IR-SB-EX-0202

February 2002

2 (47)

Abstract An integrated simulation environment of a radar receiver has been developed further to enable simulations of different target scenarios and show effects on detectability of targets when component parameters are changed. The model and its parts were implemented by Ericsson Microwave Systems AB, FOI and Linköping University. It is implemented in Agilent’s software Advanced Design System (ADS) combined with Matlab models of some parts in the radar model. A chirp pulse generator has been added to the model for simulation of target echoes and different presentations of the signal as well. Simulations have been made to verify the functionality of the model and how different parameters affect the result of a simulation. It is now possible to try out different parameter setups to enhance the functionality of the receiver and see effects on the presentation of the target echoes. En integrerad simuleringsmiljö av en radarmottagare har utvecklats ytterligare för att möjliggöra simuleringar av olika målscenarier och visa effekten på detekterbarheten för målen då systemparametrar ändras. Modellen och dess delar har utvecklats av Ericsson Microwave Systems AB, FOI och Linköpings tekniska högskola. Den är implementerad i Agilents mjukvara Advanced Design System (ADS) kombinerat med Matlab-modeller av några delar i radarmottagaren. En chirppulsgenerator har lagts till i modellen för simulering av målekon och även olika presentationer av signalen. Simuleringar har gjort för att verifiera funktionaliteten hos modellen och hur olika parametrar påverkar resultatet av en simulering. Det är nu möjligt att prova olika parameterinställningar för optimering av mottagarens prestanda och se effekter på presentationen av målekona.

3 (47)

Acknowledgements This Master of Science in Engineering thesis was conducted between September 2001 to February 2002 at Saab Bofors Dynamics AB, Sensors, Linköping, Sweden. I would like to thank my supervisors Ann-Marie Andersson at Saab Bofors Dynamics AB, Sensors, Linköping, Björn Völcker at the Signals-Sensors-Systems department of the Royal Institute of Technology, Stockholm and Andreas Gustafsson at FOI, Microwave Tech., Linköping for their support. Special thanks to Bertil Grelsson for learning the simulation model and giving much support. Also great thanks to Sune Axelsson for discussion of a possible pulse type for implementation and to every one else who answered my questions about radar.

4 (47)

Contents

1 INTRODUCTION ....................................................................................................................... 5

1.1 BACKGROUND AND PREVIOUS WORK ...................................................................................... 5 1.2 PROBLEM DEFINITION ............................................................................................................. 5 1.3 REPORT OUTLINE .................................................................................................................... 6

2 RADAR THEORY....................................................................................................................... 7

2.1 OVERVIEW OF LINEAR FM CHIRP WAVEFORM....................................................................... 7 2.2 I/Q DETECTION ....................................................................................................................... 9 2.3 I/Q ERRORS .......................................................................................................................... 11 2.4 RANGE/DOPPLER PROCESSING............................................................................................... 13 2.5 WINDOWING ......................................................................................................................... 14 2.6 NOISE AND THRESHOLD SETTING .......................................................................................... 14 2.7 SATURATION OF THE RECEIVER............................................................................................. 18

3 RECEIVER MODEL ................................................................................................................ 21

3.1 SIGNAL GENERATOR BLOCK WITH CHIRP PULSE PROGRAM ................................................... 21 3.2 RF STAGE ............................................................................................................................. 24 3.3 ADC ..................................................................................................................................... 24 3.4 DIGITAL FILTERS................................................................................................................... 25 3.5 SEPARATE PROGRAMS........................................................................................................... 25

4 SIMULATIONS......................................................................................................................... 26

4.1 MODEL VERIFICATIONS......................................................................................................... 26 4.1.1 Image frequency rejection for different target frequencies .......................................... 26 4.1.2 Average noise floor level vs. input power..................................................................... 26 4.1.3 Spurious signals ........................................................................................................... 26

4.2 PARAMETER CHANGES .......................................................................................................... 29 4.2.1 Simulations with 8 bit ADC.......................................................................................... 29

4.2.1.1 Effect of S21 (AMP1)............................................................................................ 29 4.2.1.2 Effect of NF (AMP1)............................................................................................. 30

4.2.2 Simulations with 12 bit ADC........................................................................................ 31 4.2.3 Effect of Maximal Rejection (MaxRej) in BPF2........................................................... 31 4.2.4 Effect of Maximal Rejection (MaxRej) in BPF1........................................................... 32 4.2.5 Effect of rejection parameters in the mixer (MIX)........................................................ 32

4.3 DOPPLER/RANGE SIMULATIONS ............................................................................................ 32 4.4 CELL AVERAGING CFAR ...................................................................................................... 33

5 CONCLUSIONS ........................................................................................................................ 35

5.1 MODEL LIMITATIONS ............................................................................................................ 36 5.2 FUTURE WORK ...................................................................................................................... 36

REFERENCES ............................................................................................................................. 37

ABBREVIATIONS....................................................................................................................... 38

APPENDICES............................................................................................................................... 39

A SIMULATION PARAMETER VALUES .......................................................................................... 39 A.1 Simulations with 8 and 12 bit ADC................................................................................. 39 A.2 Spurious signals simulations........................................................................................... 39 A.3 Phase imbalance simulations.......................................................................................... 40

B MODEL SCREENSHOTS AND NEW SIMULATION PARAMETERS................................................... 41 C SEPARATE PROGRAMS ............................................................................................................. 46 D MIXER PARAMETERS............................................................................................................... 47

5 (47)

1 Introduction 1.1 Background and previous work Radar On a Chip (ROAC) is part of the Smart Sensors project, financed by the Swedish Foundation for Strategic Research. Smart Sensors is a co-operation between Linköping University, FOI in Linköping, ACREO, Ericsson and Saab Bofors Dynamics AB. The main objective of this project is to find efficient and low cost on-chip receiver implementation strategies. The proposed receiver is an X-band two-chip receiver with one single mixer stage. A software model of the receiver based on Advanced Design System (ADS) from Agilent Technologies and Matlab from The MathWorks Inc has been developed by Ericsson Microwave Systems AB, FOI and Linköping University. The model simulates both analog and digital signals in the same simulation. The radio frequency (RF) part is modeled using ADS components and the analog-to-digital converter and digital parts are modeled in Matlab. 1.2 Problem definition A radar receiver consists of several different parts. There is an analogue part where the signal from the target is filtered, frequency transformed and converted from analog to digital. In the digital part further filtering and signal processing is performed. If changes are made in a part of the receiver those changes may be good or bad for the over all performance of the system. If a part is improved, the improvement may not give correspondingly better performance for the over all system and there will only be an unwanted increase in cost. The aim of this thesis work was to develop the model further to be able to evaluate changes in the performance and demands on particular components of the receiver when different parameters are changed within the receiver. Suitable input signals and radar parameters for evaluation and optimization of performance were to be defined. The model should be able to show the effect of those parameter changes and be easy to use. An interesting functionality is to simulate different target scenarios to see how well the echoes can be resolved in a range spectrum for different simulation parameter setups. With the help of Matlab a new pulse type, chirp pulse, for generation of simulated target echoes and different presentations of the signal in the receiver were implemented. The receiver simulation parameters affect the performance of the receiver in different ways. The effect of some of these parameters has been studied and simulations for verification of the model were made.

6 (47)

1.3 Report outline Chapter two presents the theory about how the radar works with the newly implemented chirp waveform (see also chapter three) and other radar theory that connects to implemented programs and presentation plots. Chapter three describes the model structure with its parts and a more mathematical description of the chirp pulse implementation. Chapter four presents the simulations for verification of the model and effects of changes in the simulation parameters. Chapter five presents the conclusions. References and appendices are attached after chapter five. The appendices includes parameter settings for the presented simulations in chapter four, model screenshots and new simulation parameters, description of separate programs and mixer parameters.

7 (47)

2 Radar theory The radar was first developed for detection of objects at a great distance and range measurement with the help of electromagnetic waves. The word radar means radio detection and ranging. When the radar transmits a pulse, some of the pulse energy will hit a target and echo back to the radar. The time, T, it takes for the pulse to travel to the target and back gives the range to the target. With 8103c ⋅= m/s, the range, R, in meters is

2

cTR = (2.1)

where the factor 2 comes from the two-way propagation of the pulse. The pulses are sent one after an other in a pulse train. To get an unambiguous range measurement the pulse echo from one transmitted pulse must be received by the radar before the next pulse is transmitted. Then the radar will be able to know which pulse that caused the echo and measure the right propagation time. If an echo would arrive after the transmission of the next pulse it would appear to be at a much shorter range than it actually is. The maximal range at which a pulse can reflect and come back before the next pulse is sent is the maximal unambiguous range in meters

r

u f2cR = (2.2)

where rf is the pulse repetition frequency (PRF) in Hertz. This is only the main principle of how a radar measures the distance to a target. For further reading, see e.g. reference [5] or [2]. 2.1 Overview of Linear FM Chirp Waveform The pulse generator program produces a sawtooth FMCW (Frequency Modulated Continuous Wave). The chirp wave form is used in high resolution radars for small-target detection and target recognition. For a more mathematical description see chapter 3.1. The radio frequency is increased at a constant rate from the carrier frequency fc to fff cH ∆+= where f∆ is the sweep bandwidth, see figure 2-1, where Tm is the modulation period. This type of modulated waveform gets its bandwidth from the modulation and not the pulse width as for a waveform with rectangular pulses. The chirp waveform bandwidth is given by the sweep bandwidth f∆ . With this waveform it is possible to have wide bandwidths, giving good range resolution, and wide pulse widths, giving a higher average radiated power and thus a higher probability of detection. For example, a sweep bandwidth

MHz150f =∆ gives a range resolution of

( )s/m103cm1f2

cR 8⋅==∆

=∆ (2.3)

8 (47)

time

fc

fH

0 Tm 2Tm

freq

uenc

y

Figure 2-1. The linear modulation is continued for a period, Tm, at least several times as long as the roundtrip transit time for the most distant target so that a large part of the sweep is used having the constant frequency difference fb, called beat frequency. This instantaneous frequency difference between the transmitted and received signal results from the received pulse being delayed a time tr proportional to the target range, see figure 2-2. The beat frequency is calculated as

]Hz[cT

fR2fm

b∆

= (2.4)

== rtcR2 round trip propagation time

where f∆ is the sweep bandwidth, Tm the modulation period and R the distance in meters to the target. The distance, R, to the target can be obtained from (2.4)

f2fcT

R bm

∆= (2.5)

When the target is moving with a constant speed vt it will cause a doppler frequency, fd, that will change the frequency difference between the transmit and echo signal, figure 2-3. More about this in chapter 2.2, I/Q Detection.

transmitted received transmitted received

fb

tr tr

fb-fd

Left: Figure 2-2.

Right: Figure 2-3.

9 (47)

2.2 I/Q Detection The incoming signal to the radar is a real valued sinusoid with amplitude A and phase Φ . To extract the information from the signal it is split into its in-phase, I, and quadrature, Q, components. They are both real signals but in the signal processing the I component is considered as the real part and the Q component as the imaginary part. In a common radar the analog signal is demodulated as in figure 2-4 and then digitized with two analog-to-digital converters.

900

phaseshift

)tf2cos( 0π

)tf2sin( 0π

Low-passfilter

Low-passfilter

Real-vauedinput signal

s(t)

In-phasecomponent

Quadraturecomponent

Figure 2-4. Analog quadrature demodulator. The I and Q components are related as ( )Φ= cosAI (2.6) ( )Φ= sinAQ From this, the signal magnitude and phase can be calculated, see (2.7) below. The vector representation is shown in figure 2-5. 22 QIA += (2.7) ( )IQarctan=Φ

I

Q

A

Φ

Figure 2-5. Vector representation of I and Q components.

10 (47)

The phase of the received signal is proportional to the range to the target as

c

Rf4R4 0T

π=

λπ

=Φ (2.8)

=ΦT total two-way phase from radar to target =R range to target =0f transmit frequency When the target is moving, its radial velocity, vr, can be measured from the phase shift. The radial velocity is the velocity component directed toward or away from the radar. The phase changes with target range as

ddrT f2v4

dtdR4

dtd

ω=π=λπ

=λπ

=Φ (2.9)

==cvf2

f r0d doppler frequency (2.10)

The doppler shift can be described as for every half wavelength that a target’s range changes, the frequency phase of the received echo advances by the equivalent of one whole cycle per second. When two targets are at the same position relative to the radar but are moving with different velocities they can be separated by measuring their respective doppler frequencies. Just as the sweep bandwidth sets the range resolution the doppler resolution is set by the time over which signal data is gathered. This time is called the look time or integration time. It is equal to the number of pulses, N, multiplied by the modulation time, mT , for a pulse; mlt TNT ⋅= . To resolve two targets the doppler frequencies must differ by at least one cycle over the time of observation. The doppler resolution, df∆ , in Hertz or the corresponding velocity resolution, v∆ , in meters per second is

]Hz[T1f

ltd =∆ (2.11)

]s/m[T2

vlt

λ=∆ (2.12)

=λ the radar’s wavelength As an example, two flying objects have doppler frequencies 20 000 Hz and 19 950 Hz respectively. They are flying at the same range, azimuth and elevation to the radar. The doppler frequency difference which has to be resolved is 50 Hz. Equation (2.11) gives the required look time which is 1/50 seconds. During this time the 20 000 Hz frequency undergoes 400 cycles and the 19 950 Hz frequency 399 cycles. Hence, there is a one cycle difference. There will always be a trade off between achieving good ranging and range resolution at the same time as good doppler extraction and doppler resolution. To get good ranging the target should not move much during the time of data gathering so the look-time should be short but to get good doppler resolution the look-time should be long.

11 (47)

2.3 I/Q Errors The receiver model for Radar On a Chip uses digital filters for the IQ-split but in a radar not using digital filters the I/Q detector can introduce errors that limit dynamic range and create false targets at image frequencies. In the ADS model there are two parameters making it possible to simulate these errors. They are gain imbalance and phase imbalance between the I and Q channels and are set in the QAM-block. The consequence of gain imbalance is that the I signal and the Q signal will have different amplitudes. Ideally the Q channel should lag 90 degrees in phase after the I channel but if phase imbalance is present this will not be the case. If any of these imbalances are introduced in the system there will be interfering peaks at the image frequency (which is as far below the sample rate as the real target signal is above zero) in the range spectrum. This is shown in figure 2-7. The image rejection (IR) can be calculated for different values of the gain and phase imbalances. The image rejection of a I/Q detector is given by [10].

Φ++Φ−+

−=)cos(g2g1)cos(g2g1log10IR 2

2

10 (2.13)

−

= 20dBG

10g where g is the gain imbalance (G is the gain imbalance in decibels) and Φ the phase imbalance in radians. The ideal image rejection according to (2.13) vs. gain imbalance for different phase imbalances is shown in figure 2-6.

0 1 2 3 4 5 6 7 8 9 100

5

10

15

20

25

30

35

40

45

50

Gain imbalance [dB]

Image rejection [dB]

0.1 deg

1 deg

2 deg

5 deg

10 deg

20 deg

40 deg

Figure 2-6. Image rejection vs. gain imbalance

for different phase imbalances. Figure 2-7 illustrates how the peak at the image frequency caused by phase imbalance affects the presentation. For the simulation a phase imbalance of five degrees was introduced. Other parameter values are listed in appendix A.3. The signal was weighted with a Hanning window. The image rejection, 27 dB, agrees

12 (47)

well with the theoretical result, see figure 2-6 for a five degree phase imbalance. Similar results are shown with a gain imbalance in the system.

0 5 10 15 20 25 30 35 40-140

-120

-100

-80

-60

-40

-20

0

Output power [dBm]

Frequency [MHz]

27 dB Target

Image

Figure 2-7. Range spectrum showing effect of 5-deg phase imbalance.

Another way of checking the imbalances is to plot 22 QI + which should have a constant amplitude. A time history representation of the received vector is done by tracing the locus of the vector tip as it rotates as shown in figure 2-8, [4]. The gain imbalance results in an elliptical vector plot. The compression in height or sideways is dependent on the relative gain between I-channel and Q-channel. Nonorthogonality, phase imbalance, results in an ellipse turned from a major axis and compressed similar to the case with gain imbalance. There can also be a DC offset causing a displacement of the vector from the origin.

Figure 2-8. Locus plot (I vs. Q) of ideal target vector and the effects of I/Q errors.

13 (47)

2.4 Range/doppler processing The last presentation in the model is a range spectrum or a doppler/range spectrum which is done by taking the fast Fourier transform (FFT) of the signal. Depending on the range resolution and distance between target and reference point the peak in the spectrum indicating the target will show up in a certain range bin. Which one can easily be calculated as follows. The range resolution, R∆ , is given by (2.1). If the difference in range between target, 1R , and reference point, refR , is

ref1 RRr −= the peak will fall into range bin number Rr ∆ . For example with m1R =∆ and m20r = the bin number is 20.

When simulating a moving target, a number, K, of pulses are generated and stored in a matrix with the first pulse in column one and the second pulse in column two and so on, each pulse consisting of N samples. This results in a matrix of size

KN × . Taking the FFT on each column gives the range coefficients. Then the matrix is transposed and the FFT is taken on each column again, calculating the doppler coefficients, [11]. Figure 2-9 shows the matrix with pulse samples k,np . This process is only done when pulse code is set to 501 (chirp pulse) and the number of pulses 1> . To get a non-ambiguous doppler processing the doppler frequency may not be higher than half the modulation frequency.

FFT

FFTFFT

FFT

FFT

FFT

p0,1

pN-1,1

p0,2

pN-1,2 pN-1,3 pN-1,4

......

...

p0,3 p0,4...

...... ... ...

... ...

pN-1,K

p0,K......

Figure 2-9. Range/doppler matrix. With a modulation frequency mm T1f = Hertz and K number of pulses each doppler bin will be Kff md =∆ Hertz wide. If the doppler frequency is df the peak will fall into doppler bin number dd ff ∆ . For example, kHz100fm = and

50K = pulses gives 2fd =∆ kHz per doppler bin. If the target speed is 300 m/s and the carrier frequency of the signal is 10 GHz, equation (2.10) gives the doppler frequency to be 20fd = kHz and this results in a peak in doppler bin number 10.

14 (47)

2.5 Windowing The spectrum for the pulses is sinc shaped and shows the sidelobes on each side of the peak. To increase the ratio between the peak and first sidelobe the signal is weighted, also called windowed. There are different windows each affecting the signal more or less. The window used in the model is a Hanning window (or Hann window) that gives 32 dB peak sidelobe ratio. Another effect on the pulse is that it is widened by a factor of 1.62 when using a Hanning window [4]. This can affect the resolution in range. The mathematical description of the Hanning window is

( )

π

=Nksinkw 2 (2.14)

( ) =kw the window value =k 0 to N-1 =N number of points in the signal/window 2.6 Noise and threshold setting Thermal noise sets a limit on the sensitivity of the receiver. It is modeled in the receiver as random white Gaussian, normally distributed. The thermal noise power generated by a receiver of bandwidth Bn is n0BkTN = (2.15) where 290T0 = K is the standard noise temperature and k = Boltzmann’s constant = 231038.1 −⋅ Joule / Kelvin. The power spectral density =0kT –174 dBm/Hz. The minimum detectable signal, minS , is the smallest echo signal that successfully can be received. It is expressed as dBmindBndBndBm0dBmmin, ])NS[()F()B()kT(S +++= (2.16) where nF is the receiver noise figure and min)NS( is the minimum signal-to-noise ratio necessary for detection for a given system requirement. The bandwidth nB used in (2.15) is the equivalent noise bandwidth over which the measurement is made. It is defined as

( )

( ) 20

2

nfH2

dffHB

∫∞

∞−= (2.17)

( )fH = frequency response of the filter through which the noise passes. ( )0fH = peak response of the filter.

15 (47)

The equivalent noise bandwidth is illustrated, as in [13], in figure 2-10.

H(f0)

Bn Figure 2-10. Equivalent noise bandwidth of a lowpass filter, as in [13].

When white Gaussian noise only is passed through a narrowband intermediate frequency (IF) filter the probability density function, pdf, of the envelope is the Rayleigh pdf

( ) 2

2

2v

2n evvp σ−

σ= (2.18)

where v is the noise voltage envelope and 2σ is the variance of the noise. This gives the probability of false alarm for a single signal echo as

∫∞

σ−

σ−

=σ

=t

2

2t

2

2

v

2v

2v

2fa edvevP (2.19)

It is the probability that the noise voltage envelope exceeds a voltage threshold,

tv , which is a predetermined voltage level. Figure 2-11 shows the Rayleigh probability density and figure 2-12 the noise probability, faP . When the voltage envelope exceeds the threshold the radar considers it to be a target detection. faP needs to be small to get a small average time between crossings of the threshold by the noise voltage envelope. This time is the false alarm time, faT , given as

2

2t

2v

nfa e

B1T σ= (2.20)

16 (47)

0 1 2 3 4 5 6 7 810-14

10-12

10-10

10-8

10-6

10-4

10-2

100

Noise probability

Voltage

Left: Figure 2-11. Rayleigh pdf. Right: Figure 2-12. Noise probability.

When a sine-wave signal with amplitude A and noise is input into the receiver simultaneously the probability density function of the output envelope is called Ricean, [2].

( )( )

σσ= σ

+−

202

Av

2snvAIevvp 2

22

(2.21)

where ( )K0I is the modified Bessel function of zero order. Equation (2.18) comes from (2.21) when there is no signal present, i.e. 0A = . The probability of detection, dP , is the probability that the envelope, v, will exceed the threshold level when a signal is present. It is given by

( )dvvpPtv

snd ∫∞

= (2.22)

It is not needed to solve (2.22). Specifying a false alarm time and a probability of detection for a radar system the designer can compute the probability of false alarm and then determine the required signal-to-noise ratio for a single hit from figure 2-13, scanned from [5].

17 (47)

Figure 2-13. Rice curves for single hit, non-fluctuating target. Scanned from [5]. The threshold makes it possible to discard interference echoes that otherwise would have been seen as target echoes due to their strength. Setting the threshold at a certain amplitude level implies that only echoes with amplitude higher than the threshold will be interpreted as a target echo. The threshold level can be set in different ways. The simplest is to have a fixed level as shown in figure 2-14. This technique may cause a weak echo near a strong echo not to be shown to the radar operator. Instead it would be better to have a threshold that adapts to the interference level similar to that in figure 2-15.

target echoes threshold

ampl

itude

time

target echoes threshold

ampl

itude

time Left: Figure 2-14.

Right: Figure 2-15. The threshold is set so that a relatively constant number of false alarms occur per unit of time. This adaptive threshold setting is also called constant false alarm rate detection (CFAR). There are a number of different CFAR methods to use. The

18 (47)

one that has been implemented for the ADS model is called cell-averaging CFAR. It is a function of range and takes place on a range bin basis, [5], se figure 2-16.

Figure 2-16.Cell-Averaging CFAR. The method of cell-averaging CFAR is to average the signal level in a few bins on each side of the bin being tested for a target. This average value is multiplied by a constant to get the threshold level. To see if a target echo is present in the center bin the signal level in that bin is compared to the threshold level. After each comparison the signals are shifted one bin and the process is repeated. The threshold level is established by

])n(V][1N

M[V12/N

12/N

THTH ∑

−

+−−= (2.23)

VTH = the detection threshold voltage MTH = the threshold multiplier (from figure 2-12) N = the number of cells, including the cell being tested V(n) = the voltage in cell n

2.7 Saturation of the receiver If too large signals are input into the receiver it will cause saturation of amplifiers and analog to digital converter (ADC). Simulations were made to study the effect of large signal input, see chapter 4.1.3. If the signal into the A/D converter is too strong the A/D converter cannot give a correct digital representation of the signal. This is called saturation. A worst case condition, from [4], is that a large (relative to the A/D maximum value) sinusoidal waveform results in saturation severe enough that only two values of the signal are produced. This produces harmonics of the original spectrum. If the original signal was

)Tt2cos(ASIN π= (2.24)

19 (47)

then the output is

...])

Tt14cos(191,0)

Tt10cos(127,0

)Tt6cos(212,0)

Tt2cos(637,0[{BSOUT

+π−π

+π−π= (2.25)

resulting in odd harmonics of the original spectrum. When strong signals are input to the receiver the amplifiers will saturate and give a non-linear amplification. If two targets are close together in range their signal frequencies, 1f and 2f in the receiver will also differ by a small amount. The effect of the saturation and the two frequencies together are intermodulation (IM) products at frequencies OUTf according to

sfrequencieinputfandffrequencyoutputf

wherefnfmf

21

OUT

21OUT

==

⋅+⋅=

(2.26)

m and n = integers (positive or negative) The order of an IM product is ( )nm + , e.g. third order IM products are

213order f2ff += , (m = 1, n = 2) and 213order ff2f += , (m = 2, n = 1) or (m = -1, n = 2), (m = 1, n = -2). An amplifier’s output power vs. input power is shown in figure 2-17, [1]. Its third order of intercept point (TOI) is the input power for which the gain curve and third order intermodulation product curve intercept. The gain of the amplifier has got a slope of two while the third order IM products has got a slope of three. One way of defining the dynamic range, DR, of the receiver is as in the text to figure 6-4 in [1], page 103. See figure 2-17 below. It is the difference between a high and a low signal level where the low level is the noise level at the output of the receiver. The noise is comprised of all unwanted spurious signals. The high signal level is the level at the output of the receiver that causes IM products of the third order at a level equal to the previous described noise level. If there are other spurious signals which are higher than the other products these reduces the dynamic range.

20 (47)

Input power [dBm]

Out

put p

ower

[dBm

]fun

damen

tal

(slop

e = ga

in)

3:rd

ord

er IM

pro

duct

(slo

pe =

3 ti

mes

gai

n)

TOI

noisefloor

DR

Figure 2-17. Illustration of third order intercept point.

21 (47)

3 Receiver model Figure 3-1 shows a schematic description of the model. The presentation blocks show the signal spectrum before and after the ADC, after the I/Q-split in the digital filters block and finally the range spectrum or doppler/range spectrum. A cutting from the ADS environment interface showing the model with its simulation parameters and newly added parameters can be found in appendix B.

Signalgenerator

RFstage ADC Digital

filters

Presentation

Presentation

PresentationPresentation

Figure 3-1. Schematic description of the radar receiver model. 3.1 Signal generator block with Chirp pulse program The signal generator block at the input to the RF block generates the type of signal chosen with the pulse-code-number parameter in the ADS interface. If this is set to 501 a received chirp pulse signal will be generated. This is the newly implemented waveform that can be used in the model. The chirp pulse generation is implemented as follows. The carrier frequency is 10 GHz (X band). A transmitter would generate the signal ( )]ttf2[j

transmit0Ae)t(s θ+π= (3.1)

The phase of stransmit(t) is ( ) ( )ttf2t 0 θ+π=Ψ where 0f is the carrier frequency and for a linear chirp pulse

( ) ∫∆π

=∆π=θt

0

2

mm

tT

fdxTxf2t

where f∆ is the sweep bandwidth and Tm the modulation period. The received signal will be a delayed version of the transmitted signal as ( ) ( ) ( ) ( )TtjTtf2j

transmitrec0BeTtsts −θ+−π=−= (3.2)

where T is the delay time proportional to target range R in meters and target speed v in meters per second radial to the radar as

( ) [ ]sc

vtR2T +=

22 (47)

The factor of two in the expression for T is because the signal has to travel both to the target and back again. In the model there is the possibility to simulate two targets at different ranges and at different speeds radial to the radar. It is easy to add extra targets in the model. The received echo signal from the first target can be written as ( ) ( ) ( )( ) ( )( )[ ]tsinjtcosBBets 11

tj1,rec

1 Ψ+Ψ== Ψ (3.3)

( ) ( ) ( )21

m101 Tt

TfTtf2t −

∆π+−π=Ψ

For the second target it is just the same and its real and imaginary components are added to the respective components of ( )ts 1rec , hence ( ) ( )( ) ( )( ) ( )( ) ( )( )[ ]tsinCtsinBjtcosCtcosBts 212112,rec Ψ+Ψ+Ψ+Ψ= (3.4)

( ) ( ) ( )22

m202 Tt

TfTtf2t −

∆π+−π=Ψ

To be able to detect targets in a pre-defined range interval the frequency of the received signal must lie within the receiver bandwidth. This is made possible by mixing the received signal with a reference signal that is delayed a time Tref similar to srec(t). The generated signal, sout(t), that is input into the RF stage will have a constant frequency. The expression for sout(t) is

( ) ( ) ( ) ( ) ( ) ( )[ ]2ref

2

mref0TtTt

Tfj

TTf2jreftransmit

*recout eeTtststs

−−−∆

π−π=−⋅= (3.5)

The reference delay time

( )[ ] [ ]sc

vtxR2Tref+−

=

is changed with target range R minus an offset x meters depending on which range interval that is of interest. Depending on R and x the interval may look like that in figure 3-2 where ( )xRR 1ref −= meters, 1R is the distance to the target and maxR is the range producing the maximal beat frequency, see equation (2.4) or (3.6) below, that is not filtered out by the receiver.

Rref R1 Rmax0 [m]

range interval

Figure 3-2. Range interval. This receiver is designed for a signal bandwidth of 18 MHz, thus after down conversion into base band, echo signals with frequency 0 to 18 MHz will be

23 (47)

detected. This means that frequencies corresponding to a range of refR to ( )rR ref + meters will be visible in the range spectrum where a target at a distance

refR meters yields a frequency of 0 Hz and a target at a distance ( )rR ref + meters yields a frequency of 18 MHz. The beat frequency, (2.4), is

]Hz[cT

fR2fm

b∆

= (3.6)

As can be seen from this, the range interval in which targets can be detected is dependent on the bandwidth of the receiver, sweep bandwidth and modulation period. A doubling of f∆ in the example above enhances the range resolution with a factor of two, see (2.1), but will result in a range interval of half the length of the original interval. The constant frequency difference between the received pulse and the reference pulse, the beat frequency bf , is shown in figure 3-3 where T1 is the two way travel time back and forth to the target.

frequency reference signal

0 Tref T1

constant frequencydifference

Tm

f0+fsweep

f0

fb

time

received signal

Figure 3-3. Beat frequency. The range to the reference point shall be chosen so that 1ref RR − << sweepR∆ (3.7) 1R << sweepR∆

where [ ]m2

cTR msweep =∆

If this is fulfilled the part of the sweep that results in a constant frequency difference when mixed with the reference signal will be large, hence using much of the pulse energy. The small parts in the beginning and end of the sweep where the frequency difference is not constant will be decreased in energy with the help of a window, in this model a Hanning (Hann) window.

24 (47)

The signal from the signal generator block is the input signal to the RF block and will be of the form

( ) ( ) ( )

πΦ

+ω−ω=180

tsinVgtcostVAtV c2inc1inout

( ) ( ) ( )( ){ }tjQoutIoutout

cetjvtvRetV ω+=

( ) ( ) ( )

πΦ

−=180

sintVgtVAtv 2in1inIout

( ) ( )

πΦ

=180

costVgAtv 2inQout

=Φ phase imbalance

=g gain imbalace

3.2 RF stage Figure 3-4 shows a schematic description of the RF block. In the RF block the signal first passes an image rejection filter and an amplifier before it is down converted to intermediate frequency (IF) by the mixer. After that, the signal passes through another amplifier and an anti-alias filter (a surface acoustic wave (SAW) filter) before it is amplified again. There are many parameters for every component such as third order intercept point, S-parameters and noise figure for the amplifiers and mixer. For the filters the insertion loss and bandwidths can be set among other parameters. Important parameters that can be set for the mixer (MIX) are listed in appendix D.

BPF1 MIX AMP2 BPF2 AMP3AMP1

Figure 3-4. Schematic description of the RF stage. 3.3 ADC The analog to digital converter (ADC) in the model uses successive approximation. It is offset to work within –1 V and +1 V. For every sample it divides this interval, first into two and tests in which of these intervals the signal level is. Then it divides this subinterval into two and so on until the maximal number of subintervals is reached and the sample is quantized. The maximal number of subintervals is ( )12M − for an M-bit converter. Since the receiver front end uses only one mixer stage the intermediate frequency, IF, is much higher compared with a front end using more than one mixer stage. The input signal frequency to the ADC is 360 MHz. This is a very high frequency for the ADC to

25 (47)

sample and there are no A/D converters capable of handling such a high input frequency on the market today [8]. Instead of using a sampling frequency of twice the highest frequency component of the input signal according to the Nyquist theorem the ADC performs bandpass sampling. It samples with 160 MHz which results in that the time between samples is less than half the inverted value of the signal bandwidth. Frequency components of higher order are folded down to 40 MHz which is the output frequency of the ADC. The signal is decimated with a factor of six. In the simulations the number of bits and sampling jitter has been varied. The sampling jitter is uncertainty in sampling moment and is modeled as a random Gaussian addition to the phase of the signal [7]. 3.4 Digital filters The digital filter part, the digital down converter (DDC), in the ADS model splits the signal into its real and imaginary components, i.e. its I and Q components, performs decimation to reduce sampling rate and gives the baseband signal on the output port. This part is done in the I/Q detector in a real radar. The DDC stage description is based on [9]. In this radar receiver model the input sample rate of the DDC is 160 MHz and the signal bandwidth is 36 MHz. The output sampling rate is 40 MHz so the total decimation factor of the DDC is four. The DDC filter configuration is shown in figure 3-5. It is divided into two parts, the IQ-split stage and the decimation stage.

H1(z)

2

2

H2(z)

H2(z)

2

2

I

Q

Figure 3-5. The DDC filter configuration from [9].

Using a Hilbert transformer, filter H1(z), the signal is split into its I and Q components. In this stage the sample rate is reduced by a factor of two because every even sample is used in the I-channel and every odd sample is used in the Q-channel. The decimation stage, filter H2(z), performs a decimation by two for each channel. 3.5 Separate programs Some programs can be run separately after a simulation. This makes it possible to quickly plot spectras for different parameter values within the programs. These programs are listed in appendix C.

26 (47)

4 Simulations 4.1 Model verifications During the study of the model it was found that there were imbalances in the I/Q filters causing high peaks at image frequencies to appear in the range spectrum. The largest difference achievable between target amplitude and image peak amplitude was about 36 dB. The filters were modified by Henrik Ohlsson at Linköping University. When the new I/Q filters were tested separately in Matlab they showed no gain and/or phase imbalances at all. 4.1.1 Image frequency rejection for different target frequencies These simulations were done to verify that the new I/Q filters do not give changing image frequency rejection for different target frequencies as the previous filters did. The input signals are echoes from two targets, target 1 at a frequency near DC in the range spectrum and target 2 at varying frequencies. Target 2 was moved away from target 1 to see if the image rejection was affected by the frequency at which target 2 appeared. The simulations showed that the rejection is constant. 4.1.2 Average noise floor level vs. input power These simulations are just to see if the average thermal noise floor level is affected by the input power level. The calculations of the average level were done with the cell-averaging threshold program. The input power was varied from –25 dBm to –80 dBm but the noise floor level remained constant. 4.1.3 Spurious signals The harmonics caused by saturation of the ADC were investigated by simulating one target. Parameter values are listed in appendix A.2 (target two is not simulated, Target2_ON = 0). The harmonics of order five and nine are the first to appear in the range spectrum after the ADC. Order three and seven are very low in amplitude. This is for an input power of –11 dBm for the present settings in the model. Nothing except for the target is seen in the spectrum before the ADC. To see the behavior of the intermodulation (IM) products, two targets close in range were simulated. Other parameter values are listed in appendix A.2. The signal spectrum before the ADC shows IM-products with the third order as the strongest ones and decreasing amplitudes for higher orders. The ADC has got the same effect on the IM-products as on the harmonics in terms of increasing the amplitude of order five and nine the most while order three is almost unaffected. Figure 4-1 and 4-2 shows the signal spectrum (windowed with a Hann window) before and after the ADC respectively.

27 (47)

360 362 364 366 368 370 372 374 376 378 380-110

-100

-90

-80

-70

-60

-50

-40

-30

-20

-10

0

Frequency [MHz]

Pow

er [d

Bm

]

3:rd order IM products

5:th order IM products



Targets

Figure 4-1. Windowed signal spectrum before the ADC showing

IM products of orders 3, 5, 7 and 9.

40 42 44 46 48 50 52 54 56 58 60-110

-100

-90

-80

-70

-60

-50

-40

-30

-20

-10

0

Frequency [MHz]

Pow

er [d

Bm

]

3:rd order IM products Targets




Figure 4-2. Windowed signal spectrum after the ADC showing

IM products of orders 3, 5, 7 and 9. Also appearing in the range spectrum are mixing products in the vicinity of the target echo peaks. They are serious interfering peaks and can easily be interpreted as targets. These mixing products appear in the spectrum for lower input powers than the IM products. If two targets having the frequencies 1f and 2f respectively, equal in amplitude (and the amplitude is high enough to cause the receiver to saturate), are input into the receiver the produced mixing products will have frequencies according to

28 (47)

[ ][ ]

[ ]1n

HzfffHzfnffHzfnff

12

2n

1n

≥

−=∆

∆⋅+=∆⋅−=

+

−

(4.1)

Their amplitude decreases with increasing n. Figure 4-3 shows the amplitudes for the two targets and mixing products for n = ± 1 and n = ± 2 vs. input power. The mixing products for n = ± 2 has decreased in amplitude below the noise floor level for an input power somewhere between –20 dBm and –25 dBm.

-30 -25 -20 -15-80

-70

-60

-50

-40

-30

-20

-10

0

Output power [dBm]

Input power [dBm]

Mixing prod. n = +/-1Mixing prod. n = +/-2Target 1 Target 2

Figure 4-3. Amplitudes for the two targets and

mixing products for n = ± 1, ± 2 vs. input power. Figure 4-4 shows the range spectrum when two large signals are input into the receiver. Their input powers are –20 dBm respectively. See appendix A.2 for other parameters. It is easy to see how these peaks appears as false targets adjacent to the targets in the spectrum. This problem can be solved by an automatic gain control (AGC) which keeps the signal level within those specified to protect the receiver against saturation. In this simulation model however, this is not desirable since it would preclude the possibility to do large signal simulations to saturate the receiver. The mixing products first appears for an input power of about –30 dBm. For this input power the SNR is 75 dB and the ratio of the signal amplitude to the highest spurious (mixing product) amplitude, the spurious-free dynamic range [4], is 54 dB.

29 (47)

0 2 4 6 8 10 12 14 16 18-140

-120

-100

-80

-60

-40

-20

0

Output power [dBm]

Frequency [MHz]

Targets

Mixing productsfor n = +/- 1

Figure 4-4. Range spectrum showing targets and mixing products.

4.2 Parameter changes These simulations were made to study the effect of changes of different parameters within the receiver and how they effect the presentation of the received target echoes in the range spectrum, that is, how easily the targets can be resolved. The scenario is chosen to simulate echoes from two targets, a weak echo (target 2) nearby a strong echo (target 1). 4.2.1 Simulations with 8 bit ADC 4.2.1.1 Effect of S21 (AMP1) In the RF stage of a receiver the amplification of the first amplifier should be high and its noise factor (NF) low to get a low value of the total NF of the RF stage. In this model, the first amplifier, AMP1, is just before the mixer, see chapter 3.2. Parameter values for these simulations are listed in appendix A.1. AMP1:s amplification, S21, from port one to port two was changed in steps from 10 dB to 20 dB while NF = 3 dB for all values of S21. This increase in amplification causes the difference, tnD , between the second targets amplitude and the average thermal noise floor level (the signal-to-noise ratio (SNR) for target 2) to increase from 11 dB to 18 dB, consequently a high amplification in the first amplifier before the mixer is important to make it easy to resolve the weaker target echo when using an 8 bit ADC. The average thermal noise floor level, constantly around –78 dBm, was calculated with the cell-averaging threshold program. The difference in amplitude between target echo and noise floor is much greater than the difference,

peak,tnD , between target echo and the highest noise peak in the vicinity of the target or between the two targets. When tnD = 11 dB, peak,tnD may only be 4,5 dB, of course varying slightly from simulation to simulation due to the noise being

30 (47)

random. Figure 4-5 shows how the SNR for the weak target changes with the amplification, S21, in amplifier AMP1 before the mixer.

10 11 12 13 14 15 16 17 18 19 2010

11

12

13

14

15

16

17

18

19

20

Amplification, S21 [dB]

SNR [dB]

Figure 4-5. Effect of S21 in an 8 bit ADC receiver, NF=3dB.

4.2.1.2 Effect of NF (AMP1) The noise factor (NF) ideally equal to three was changed in steps from 3 dB to 21 dB while S21 = 20 dB for all values of NF. Not until NF reaches 21 dB there is an evident drop in tnD to 14,5 dB. When S21 = 10 dB the change in tnD is much smaller. Figure 4-6 shows how the SNR for the weak target changes with the noise factor, NF, in amplifier AMP1 before the mixer.

2 4 6 8 10 12 14 16 18 20 2210

11

12

13

14

15

16

17

18

19

20

Noise figure, NF [dB]

SNR [dB]

Figure 4-6. Effect of NF in an 8 bit ADC receiver, S21=20dB.

31 (47)

4.2.2 Simulations with 12 bit ADC The parameter S21 was changed as in the simulation above with an 8 bit ADC, while NF = 3 dB for all values of S21. For the receiver with a 12 bit ADC the difference tnD (the SNR) is much higher but almost constant during the simulations. tnD varies around 26 dB ( ± 1 dB, roughly) for all values of S21. With an increase in timing jitter in the ADC, still 12 bits, from 0,5 ps to 10 ps the average noise floor level is increased causing tnD to be almost constant around 19 dB. Figure 4-7 shows how the SNR for the weak target changes with the amplification, S21, in amplifier AMP1 before the mixer when there is a timing jitter of 10 ps and 0,5 ps.

10 11 12 13 14 15 16 17 18 19 2010

12

14

16

18

20

22

24

26

28

30

Amplification, S21 [dB]

SNR [dB]

12 bit ADC with jitter = 10 ps. 12 bit ADC with jitter = 0,5 ps.

Figure 4-7. Effect of S21 in a receiver with a 12 bit ADC which

has a timing jitter of 0,5 ps or 10 ps. 4.2.3 Effect of Maximal Rejection (MaxRej) in BPF2 The antialias filter, BPF2 (see figure 3-4 in chapter 3.2), is important for the image frequency rejection in the range spectrum. This image frequency is the same as discussed in chapter 2.3 about I/Q errors. The input power is first set so that the amplitudes of the image frequencies are of the same height as the highest noise peaks in the range spectrum. The receiver is not saturated. The parameter values are like in appendix A.2 except that RF_power_1 = RF_power_2 = -35 dBm and R2 = 200 m. For a maximal rejection (MaxRej) of 60 dB in the antialias filter, which is the standard value for all other simulations, the image frequency rejection is about 59 dB in the range spectrum. This can be regarded as a good value compared to what can be expected if phase or gain imbalance is present which also causes image frequency peaks in the spectrum, see plot 2-6 in chapter 2.3. When the maximal rejection is increased from 30 dB to 60 dB the image frequency rejection changes as in figure 4-8. Also, the peak at DC will be high and interfere significantly with echoes at low frequencies for low values of the maximal rejection.

32 (47)

30 35 40 45 50 55 6025

30

35

40

45

50

55

60

SAW filters Maximal Rejection [dB]

Image Rejection [dB]

Image rejection for target 1.Image rejection for target 2.

Figure 4-8. Image rejection vs. maximal rejection in BPF2.

4.2.4 Effect of Maximal Rejection (MaxRej) in BPF1 The band pass filter, BPF1 (see figure 3-4 in chapter 3.2), before the mixer is for rejection of image frequencies before the mixer. Its standard maximal rejection is 20 dB. An increase to 60 dB does not result in much difference at all in the range spectrum from that of the 20 dB rejection simulation. 4.2.5 Effect of rejection parameters in the mixer (MIX) Simulations show that the parameter LO_rej2 needs to be high. It is the local oscillator signal to output port rejection in dB. A lowering of its value increases the amplitude of the DC component in the range spectrum. The other parameter LO_rej1 which is the local oscillator signal to input port rejection in dB does not give any effect on the range spectrum. This is as it should be because there is no implementation of reception of reradiated power in the model, see appendix D about the parameter LO_rej1. The input to output port rejection, RF_Rej, in decibels does not effect the simulations when changed. 4.3 Doppler/range simulations With pulse code 501 for chirp pulse chosen it is possible to simulate targets having a velocity radial to the radar and get a range/doppler plot. Figure 4-9 is an example plot showing a simulation of two targets at equal distance from the radar but with velocities differing slightly more than the velocity resolution given by (2.12) The peak in zero range/doppler bin may be a result of LO leakage in the mixer. Simulating with N = 50 pulses each having a modulation period

s2,3Tm µ= gives a look time ms16,0TNT mlt =⋅= . This results in a doppler resolution of

33 (47)

Hz6250T1f

ltd ==∆ (4.2)

or a corresponding velocity resolution of

s/m75,93T2

vlt

=λ

=∆ (4.3)

The targets has got the velocities 1000 m/s and 1120 m/s respectively and the simulation results in the plot shown in figure 4-9.

Figure 4-9. Range/doppler plot.

4.4 Cell averaging CFAR With the separate Matlab program “cfar.m”, see appendix C, the user can set a threshold level in the range plot according to what is described in chapter 2.6. An indication (black stars) is added in the spectrum to show where the signal level is higher than the threshold level and the radar will interpret it as a target detection. Some examples are presented below. The behavior of the threshold is determined by the number of bins for averaging and the multiplication factor, MTH, that controls the threshold level. Figure 4-10 and 4-11 shows two targets around 5 MHz in a range spectrum with a threshold set as described below. The stars at 0 Hz and 40 MHz are due to a peak at DC. In figure 2-13, chapter 2.6, it can be seen that a probability of detection equal to 99,5 % and a threshold multiplication factor resulting in a probability of false alarm equal to 1210− (calculated with (2.19)) requires a minimum SNR of 17 dB. The signal level must then be higher than the average noise floor level within the cell-averaging interval plus 17 dB. The weak echo has got a SNR of 25 dB, i.e. it will be interpreted as a target detection. If the number of bins for averaging is too high a weak echo besides a strong will be masked by the threshold as seen in figure 4-11.

34 (47)

0 5 10 15 20 25 30 35 40-130

-120

-110

-100

-90

-80

-70

-60

-50

-40

Amplitude [dBm]

Frequency [MHz]

Signal-above-threshold indication

Threshold

0 5 10 15 20 25 30 35 40-130

-120

-110

-100

-90

-80

-70

-60

-50

-40

Amplitude [dBm]

Frequency [MHz]

Signal-above-threshold indication

Threshold

Left: Figure 4-10. 35 bins for averaging, MTH = 7,434.

Right: Figure 4-11. 99 bins for averaging, MTH = 7,434. For targets further apart it is possible to average over more bins. The threshold for figure 4-12 is set for a probability of false alarm equal to 1010− (calculated with (2.19)). With a probability of detection specified to be equal to 98,5% this requires a minimum SNR of 16 dB. The SNR for the weak echo in figure 4-12 is 21 dB. Figure 4-13 shows an other example but with only one target echo (just above 5 MHz).

0 5 10 15 20 25 30 35 40-130

-120

-110

-100

-90

-80

-70

-60

Amplitude [dBm]

Frequency [MHz]

Signal-above-threshold indication Threshold

0 5 10 15 20 25 30 35 40-130

-120

-110

-100

-90

-80

-70

-60

Amplitude [dBm]

Frequency [MHz]

Signal-above-threshold indication Threshold

Left: Figure 4-12. 99 bins for averaging, MTH = 6,786.

Right: Figure 4-13. 99 bins for averaging, MTH = 7,434.

35 (47)

5 Conclusions A chirp pulse generator has been implemented for simulation of target echoes and different presentations of the signal are added to the model. Simulations have been made to verify the functionality of the model and how different parameters affect the result of a simulation. It is now possible to try out different parameter setups to enhance the functionality of the receiver and see effects on the presentation of the target echoes. For large input signals, harmonics, intermodulation and mixing products are generated in the model. The signal spectrum before the analog to digital converter (ADC) shows intermodulation products with the third order as the strongest ones and decreasing amplitudes for higher orders as should be. When intermodulation products are passed through the ADC, the products of order five and nine are amplified. Also the harmonics (caused by saturation of the ADC) of order five and nine have got the highest amplitudes. This has not been investigated further due to lack of time and since it is not part of this work. One very important parameter is the number of bits in the ADC. The resolution improves with increasing number of bits. For example, the average thermal noise floor level was increased from about –96 dBm to around –78 dBm when the number of bits was changed from 12 to 8 in the simulations studying the effect of S21 and noise factor, NF, in the amplifier before the mixer. The same simulations show that an increase in timing jitter in the ADC from 0,5 ps to 10 ps causes the noise floor to rise from –96 dBm to about –87 dBm when a 12 bit ADC was used. For a radar receiver with only 8 bit ADC the amplification before the mixer, changed with parameter S21 in AMP1, is important for the resolution. A higher amplification (from 10 dB to 20 dB) increases the SNR for the weak target (target number two in the simulations) from 11 dB to 18 dB. For the receiver with a 12 bit ADC the SNR varies around 26 dB ( ± 1 dB, roughly) when varying S21 from 10 dB to 20 dB. A comparison with a 12 bit ADC shows that it is essential to have an ADC with as many bits as possible enabling a good representation of all signal levels to get a higher resolution. The maximal rejection of the filters in the RF block was changed and the maximal rejection of the antialias filter, BPF2, effected the simulations the most. A low rejection in this filter resulted in low image frequency rejection in the range spectrum and high DC peak amplitude. An other parameter that also affects the amplitude of the DC peak in the range spectrum is the rejection of local oscillator signal to output port, LO_rej2, in the mixer. It is now possible to simulate one or two targets having different radial velocities to the radar and get a range-doppler-bin plot. With the cell-averaging CFAR program it is possible to set a threshold level in a range spectrum after a simulation.

36 (47)

5.1 Model limitations The model can generate phase noise (implemented in previous work) but due to the long simulation times for simulations with multiple pulses it is almost impossible to see the effect of phase noise in doppler simulations. Also the doppler simulation itself, without any phase noise added, takes quite a long time. To get many samples for the range spectrum (after a total decimation of 24 times) the PRI_length (a model parameter) has to be set quite high which extends the simulation time. 5.2 Future work It is possible to add measurement data files for e.g. an amplifier into ADS and use this amplifier instead of a model from the ADS component library. The future user may change all parameter values for other simulations and add further functionality’s to the model.

37 (47)

References [1] Börje Andersson, Hans Bergdal, Rolf Gustavsson, Peter Nagy, Fredrik

Oscarsson, “Signalspaningsteknik del 1, Grunder samt radiosignalspaning”, FOA 75 Institutionen för Telekrigsystem, Sammanställt av Hans Bergdal, FOA 75, Linköping juli 1998 / april 1999.

[2] Merrill I. Skolnik. “Introduction to radar systems, second edition”.

McGraw-Hill book company. Copyright 1980, 1962 by McGraw-Hill, Inc. [3] Donald R. Wehner, “High Resolution Radar”, Artech House, 1987. [4] James A. Scheer and James L. Kurtz, “Coherent Radar Performance

Estimation”, Artech House, 1993. [5] B. Edde, “Radar: principles, technology, applications“, Englewood Cliffs,

New Jersey: PTR Prentice Hall. [6] George W. Stimson, “Introduction to Airborne Radar”, Hughes Aircraft

Company, El Segundo, California, 1983. [7] Andreas Gustafsson, Kalle Folkesson, Henrik Ohlsson, “A Simulation

Environment for Integrated Frequency and Time Domain Simulations of a Radar Receiver”, GigaHertz 2001 Symposium, Lund, Sweden, November 2001.

[8] Robert H. Walden, “Performance Trends for Analog-to-Digital

Converters”, HRL Laboratories, LLC, IEEE Communications Magazine, February 1999.

[9] Henrik Ohlsson, Håkan Johansson, Lars Wanhammar, ”Design of a

Digital Down Converter Using High Speed Digital Filters”, Department of Electrical Engineering, Linköping University, SE 581 83 Linköping, Sweden.

[10] Bert C. Hendersson, James A. Cook, “Image-reject and Single Sideband

Mixers”, Tech-notes, Watkins-Johnson Company, 1985. [11] Sune Axelsson, “DIGITAL RADAR: Range and Doppler Filtering in

Frequency Modulated Radar Using FFT-Processing”, Saab Missiles, 1995-01-11, Reg No: RD-R94:1006(I).

[12] Walter G. Carrara, Ron S. Goodman, Ronald M. Majewski, ”Spotlight

Synthetic Aperture Radar, Signal Processing Algorithms”, Appendix A, A Fast Algorithm for Digital Quadrature Demodulation, Artech House, 1995.

[13] John G. Proakis, Masoud Salehi, “Communication systems engineering”,

Prentice-Hall, Inc., 1994.

38 (47)

Abbreviations A/D Analog-to-Digital ADC Analog-to-Digital Converter ADS Advanced Design System AGC Automatic Gain Control CFAR Constant False Alarm Rate DC Direct Current DDC Digital Down Converter DR Dynamic Range FFT Fast Fourier Transform FMCW Frequency Modulated Continuous Wave I/Q In-phase/Quadrature phase IF Intermediate Frequency IM product Intermodulation product IR Image Rejection LO Local Oscillator NF Noise Figure pdf probability density function PRF Pulse Repetition Frequency PRI Pulse Repetition Interval QAM Quadrature Amplitude Modulation RF Radio Frequency SAW Surface Acoustic Wave SNR Signal-to-Noise Ratio TOI Third Order of Intercept

39 (47)

Appendices A Simulation parameter values A.1 Simulations with 8 and 12 bit ADC Chapter 4.2.1 and 4.2.2.

Parameter Value Unit Description

RF_power_1 -30 dBm Input power, target 1


R1 100 m Distance to target 1


Rref 80 m Distance to reference point

f∆ 300 MHz Sweep bandwidth for chirp pulse

PRI_length 24576 Must be a multiple of )64( ⋅

jitter 0,5 ps ADC timing jitter

A.2 Spurious signals simulations Chapter 4.1.3.








bits 12 no. Number of bits in the ADC

40 (47)

A.3 Phase imbalance simulations Chapter 2.3.








bits 12 no. Number of bits in the ADC

41 (47)

B Model screenshots and new simulation parameters Screenshots from the ADS environment showing, in order, the radar receiver model, main simulation parameters, RF block, ADC block and I/Q filters block are presented on the following pages. The new RF pulse type: • chirp pulse has pulse code number 501. The new simulation parameters added to the model for use with pulse code 501 are • RF_Power_1_dBm and RF_Power_2_dBm

Input power for target one and two respectively.

• Target2_ON If set equal to one, two echo signals will be generated for simulation.

• v_target_1 and v_target_2 Speed radial to the radar for target one and two respectively.

• Range1_m and Range2_m Range to target one and two respectively from the radar.

• Rref_m Range to reference point from the radar.

• Sweep_bandwidth_Hz Chirp pulse sweep bandwidth.

• Range_x_axis The x-axis scale for the range spectrum is changed by setting Range_x_axis equal to one of the following numbers. - If set to 1: x-axis in MHz above zero frequency (for baseband signal). - If set to 2: x-axis in range bins. - If set to 3: x-axis in meters from the radar.

• IQ_plots_ON If set equal to one, the following plots will be generated - I and Q signal in time. - 22 QI + with y-axis in dB and with a linear scale. - I vs. Q as showed in chapter 2.3 about I/Q errors.

42 (47)

Figure B-1. Model interface. New features are: Chirp pulse generator in block (I). New simulation

parameters, marked by a line, see also figure B-2. Presentation in block (IV), see figure B-5. Range and doppler/range spectra.

43 (47)

Figure B-2. Main simulation parameters. New ones marked by a line.

44 (47)

Figure B-3. RF block.

Figure B-4. ADC block.

45 (47)

Figure B-5. I/Q filters with presentations of the I and Q signals. See appendix B (and chapter 2.3)

for more information about the presentations.

46 (47)

C Separate programs The following program can be run before a simulation when choosing parameter values. • “values.m” is a program that makes it easier to choose simulation parameters

that works with the receiver model. The program can be found under …/radarmodell/matlab/.The program takes one argument. If this is

- “1” it calculates: beat frequency for each target, sweep length, range

resolution, maximal allowed doppler frequency for the chosen modulation frequency, doppler frequency for each target, Hz per doppler bin or doppler resolution, speed resolution in meters per second and in what range/doppler bin each target will show up.

- “2” it calculates: some examples of intermodulation (IM) products and

mixing products. - “3” it calculates: harmonics of order 3, 5, 7 and 9.

The following programs are run during a simulation. • With the program “attenuate.m” the signal amplitude can be decreased x dB

before input to the ADC if high signal power simulations are not to cause saturation of the ADC. This is set before a simulation. It is found under …/radarmodell/matlab/.

• The program “iq_test.m” is turned on or off with the simulation parameter IQ_plots_ON in the ADS interface, see appendix B.

The following programs can be run after a simulation. They each load a “.mat”-file produced during the simulation. • The range/doppler processing can be run with the program “plotdoppler.m”

found under …/radarmodell/matlab/. • The cell-averaging CFAR program “cfar.m” is only run as a separate program

after a simulation. In this program the user sets number of bins to average over, threshold factor and type of window function. This is found under …/radarmodell/matlab/.

47 (47)

D Mixer parameters A schematic figure of a mixer is shown in figure D-1.

Mixer

321RF in IF out

LO in

Figure D-1. Mixer. Important parameters, defined in [5], and their name in the model, that can be set for the mixer (MIX) in the RF stage are • Noise figure. Name in model: NF. • Conversion loss. Name in model: ConvGain = IFRF PP • Isolations

- L1-2 = P1/P2 = the loss from port 1 to 2. Important for multi-channel receivers to prevent signal leakage when there is a common local oscillator. Name in model: RF_rej.

- L3-1 = P3/P1 = the loss from port 3 to 1.

Prevents LO from leaking out port 1 and out the antenna, called reradiation. This clutters the spectrum and allows detection of the radar even if the transmitter is silent. Name in model: LO_rej1.


This is not important if the RF and IF bands are widely separated in frequency.


This is the least important of the isolations in that the LO is normally separated in frequency from the IF as to be filterable at the IF port. Name in model: LO_rej2.