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The User Segment
Receiver Design (Module 5)
The User Segment consists of the receivers,
processors, and antennas that allow land,
sea, or airborne operators to receive the GPS
satellite broadcasts and compute their precise
position, velocity and time.
1
Basic Structure of a GPS Receiver
Antenna
RF front-end
Position
calculation
A/D converter
Receiver channel
Analog signal
Digital signal
2
History
• More than 25 years have passed since the introduction of first
commercial GPS receiver.
• First receivers were based on analog signal processing, only using
microprocessors for application calculations. Analog means
receivers were large and consumed a lot of power.
• When GPS Phase II satellites were launched in 1989, all analog
signal processing was replaced by microprocessors and integrated
circuits.
• The modern standard GPS receivers are based on applications
specific integrated circuits (ASICs) for signal processing and fast
microprocessors for application calculations. An ASIC cannot be
reprogrammed like the microprocessor but is effective.
3
Generic GPS Receiver
RF stage
Antenna
LO
Reference
oscillator
BPF
M2
BPF
AMP
M1
AMP
Amp
BPF
A/D
Conv
LO
Frequency
synthesizer
Digitized IF signal
Clocks
Code acquisition/tracking
Carrier acquisition/tracking
External inputs
Navigation processing
including Kalman filtering
Navigation outputs
(position, velocity, time,
Fault, detection/isolation)
4
The Antenna
• Basic antenna: The most basic antenna is called "a quarter wave
vertical", it is a quarter wavelength long and is a vertical radiator.
Typical examples of this type would be seen installed on motor
vehicles for two way communications. Technically the most basic
antenna is an "isotropic radiator". This is a mythical antenna which
radiates in all directions as does the light from a lamp bulb. It is the
standard antenna.
• Depending upon how the antenna is orientated physically
determines its polarization. An antenna erected vertically is said to
be "vertically polarized" while an antenna erected horizontally is said
to be "horizontally polarized". Other specialized antennas exist with
"cross polarization", having both vertical and horizontal components
and can have "circular polarization".
5
Radio Theory
• In a theoretical antenna called an isotropic antenna, radio waves are
transmitted equally in all directions.
• Power density from an antenna can be measured as milliwatts (mW)
per centimeter squared, or mw/cm2.
• In practice, no antenna works like an isotropic antenna, because no
antenna gives a perfectly spherical transmission pattern.
• In radio theory, we use mW, watts, or kilowatts; however, the
numbers can get rather big and unmanageable, and so many
engineers convert watts or mW into logarithmic references. If you
work in mW, the expression is dBm. If you work in watts, the
expression is dBW. With kilowatts, the expression is dBK.
• The notation dB is for decibel. As a stand-alone notation, it is a ratio
of gain, which can be added or subtracted to any referenced
number.
6
Types of Antennas
•
•
•
•
•
•
•
•
•
•
•
The quarter wave vertical antenna
Half wave dipole antenna (used for GPS)
The folded dipole antenna
The Yagi antenna
UHF Yagi antenna
Loop antennas
Slot antennas
Helical antennas (used for GPS)
Microstrip antennas (used for GPS)
Dish antennas
Array antennas
7
Antenna Selection
• A major selection criteria of antennas is the antenna gain.
• In antenna design, gain is the logarithm of the ratio of the intensity
of an antenna’s radiation pattern in the direction of strongest
radiation to that of a reference antenna. If the reference antenna is
an isotropic antenna, the gain is often expressed in units of dBi
(decibels over isotropic).
• Different antenna designs render different gain factors. A singleelement antenna may render a gain of 6 dB, whereas a microwave
antenna may render a gain of 12 dB. A parabolic antenna could
render a gain of over 60 dB.
8
Selection Criteria for GPS Antenna
• GPS antenna is designed for use in the GPS.
• Gain versus elevation: High gain for angles above a specified
elevation angle.
• Interference rejection: The antenna should reject signals in
different frequency bands.
• Multipath rejection: The antenna should reject multipath signals as
effective as possible. Usually such signals arrive to the antenna as a
result of reflection from the ground.
• Physical properties: The antenna should have a size, shape, and
material that makes it suitable to its environment.
9
Best Type of GPS Antenna
• Questions are put to us almost daily as to which is the "best" type of
GPS antenna. The answer is: there is no best type of antenna for
all GPS applications.
• The most popular type for consumer model receivers is the Quad
Helix style. This style has several advantages and several
disadvantages.
• The most popular alternative is the Patch antenna. It too has
advantages and disadvantages. Other GPS antenna configurations
include:
•
•
•
•
•
Spiral
Helices
Microstrip (one form is the "patch" antenna.)
Planar rings (aka "choke ring")
Other multipath-resistant designs.
10
GPS Antennas: Microstrip Antennas
L
xf
W
yf
Example of Calculated values
Antenna width (W): 5.74 cm
Antenna length (L): 4.49 cm
Feedpoint (yf): 2.87 cm
Feedpoint (xf): 1.09 cm
Center frequency: 1575 MHz
Diëlectric constant (Er): 4.5
Dielectric thickness (h): 1.6 mm
Feed point
11
GPS Antennas: Helix Antennas
12
GPS Antennas: Dipole Antennas
http://www.arrl.org/tis/info/pdf/0210036.pdf
13
RF Front End
• The RF front end is the block that prepare the analog signal for
sampling in the A/D converter. Practically, it is one-chip system to
interface GPS antenna to GPS microcontroller. The front end
contains two functionalities:
• Signal Conditioning
– Remove interfering signal components by using band pass filter.
– The other functionality is to amplify the receiving signal.
• Down Conversion
– Signal is down converted from 1575.42 MHz to an intermediate
frequency (IF) that is a couple of MHz.
– The conversion is carried out by mixer mixing the input signal
with that of local oscillator.
14
Basic Structure of a GPS Receiver RF Front-end
Antenna
Signal
Mixer
IF
Filter
Filter
Amplifier
Local oscillator
Signal conditioning
Down conversion
15
GPS RF Front-End IC
16
Down-Converting RF Signal to IF Signal
Fourier transform of the LO signal
Fourier transform of the input signal at RF
Mixing the above two signal
Resulting signal at IF after low-pass filtering
17
Image Frequencies
18
Signal to Noise Ratio
• Very important aspect of receiver design is the signal-to-noise ratio
(SNR) in the receiver IF bandwidth.
• Typical GPS receiver bandwidths range from 2 MHz to 20 MHz.
• Dominant type of noise is the thermal noise in the first RF amplifier
stage of the receiver front end.
• SNR is defined as the ratio of signal power to noise power in the IF
bandwidth or the difference of these powers when expressed in
decibles.
N  kTe B
k  1.3806 10  23 J/K
B is the bandwidth in Hz
Te is the effective noise temperatu re in degrees Kelvin.
The effective noise temperatu re is a function of sky noise,
antenna noise temperatu re, linec losses, receiver noise
temperatur e, and ambient te mperature.
19
Amplifiers
• Amplifiers are used to increase the voltage or power amplitude of
signals. They have many applications.
• Audio voltage amplifiers boost the amplitude of signals between the
frequency range 20 Hz to 20 KHz. This is the range of human
hearing. They are often used as PRE-AMPLIFIERS before the main
amplifier.
• Audio power amplifiers provide the power necessary to drive
loudspeakers. They also amplify a frequency range from 20 Hz to 20
KHz.
• Intermediate frequency (IF) amplifiers are used in radio receivers.
High frequency radio signals are changed to the lower intermediate
frequency by a frequency changer circuit.
20
• Radio frequency (RF) amplifiers amplify a selected band of
frequencies. RF extend from about 30 KHz up to several thousand
MHz. The band of frequencies is selected by a bandpass filter or a
tuning circuit.
• Wide band amplifiers are designed to amplify a very wide band of
frequencies, say from a few Hz up to several hundred MHz.
• Video amplifiers are used in television cameras, receivers, VCRs,
etc. The bandwidth extends from DC up to about 6 MHz.
• Directly coupled amplifiers have no coupling capacitors between
stages so that they are able to amplify DC signals.
• Differential amplifiers have two inputs and amplify the difference
between the two input voltages. If both inputs are the same then
there is no output from the amplifier.If there is an interfering signal
then it will be picked up by both inputs and will not be amplified.
21
Operational Amplifier
• Operational amplifier is an amplifier whose output voltage is
proportional to the negative of its input voltage and that boosts
the amplitude of an input signal, many times, i.e., has a very
high gain.High-gain amplifiers.
• They were developed to be used in synthesizing mathematical
operations in early analog computers, hence their name.
• Typified by the series 741 (The integrated circuit contains 8-pin
mini-DIP, 20 transistors and 11 resistors).
• Used for amplifications, as switches, as filters, as rectifiers, and
in digital circuits.
• Take advantage of large open-loop gain.
• It is usually connected so that part of the output is fed back to
the input.
• Can be used with positive feedback to produce oscillation.
22
The 741 Op-Amp Circuit
23
Operational Amplifier Model Symbols and Circuit Diagram
Figure 8.4
24
The Ideal and Real Op-Amp
•
•
•
•
•
•
•
Ideal Amplifier:
Two Inputs:
– Inverting.
– Non-inverting.
Vo = A (V+ - V-)
Gain A is large ().
Vo = 0, when V+ = VInfinite input resistance,
which produces no currents
at the inputs.
The output resistance is
zero, so it does not affect the
output of the amplifier by
loading.
The gain A is independent of
the frequency.
Real Amplifier:
• Gain (105 - 109).
• Input resistance
– 106 for BJTs
– 109 - 1012
• Output resistance: 100-1000
.
25
A Voltage Amplifier
Simple Voltage Amplifier Model
Figure 8.2,
8.3
Rin
RL
vin 
vS ; vL  Avin
RS  Rin
Rout  RL

Rin
RL 
vS ; vin  vS ; vL  Avin
vL   A
 RS  Rin Rout  RL 
26
Basic Operational Amplifiers
• Noninverting amplifier means the output voltage increases when
the input voltage increases. But there is usually a voltage gain. The
gain formula for a noninverting amplifier is feedback resistance plus
input resistance divided by input resistance.
• Inverting amplifier means the output voltage decreases when the
input voltage increases. The gain formula is feedback resistance
divided by input resistance.
• An important difference is the input impedance or current. The
noninverting amplifier has very high input impedance, and
consequently very low input current, because the signal goes
directly to the input. But for the inverting amplifier the input
impedance is the input resistor. When there is 1V input through the
1K resistor, the input current is 1mA.
27
vo
Av 
vs
Inverting Amplifier
is  i F  iin
vS  v 
vout  v 
is 
; iF 
; iin  0
Rs
RF
is  i F ; iin  0; v   v 
Figur
vs
vout
vout
vout e 8.5



Rs Av Rs
RF
Av RF
RF
vout  
vs
Rs
vs
vs
is 
; Ri 
 Rs
Rs
is
28
Design Example: Design an inverting amplifier with a closed loop
voltage of Av = -5. Assume the op-amp is driven by a sinusoidal soorce,
vs = 0.1 sin t volts, which has a source resistance of Rs = 1 k and
which supply a maximum current of 5 A. Assume that the frequency is
low.
vs
is 
( Rs in this example means two resistances : Rs  R1  Rsr .
Rs
Rsr represents the source resistance. Therefore is 
vs
Rsr  R1
v s (max)
0.1
If is (max)  5A, then we write R1 (min)  Rsr 

 20 kΩ

6
is (max)
5  10
 R2
R1 should be 19 k and Av 
 5.
Rsr  R1
Accordingly R2  5( Rsr  R1 )  5  20  100 k
29
Noninverting Amplifier
Voltage Follower
Figu
re
8.8,
8.9
v s
vs  vout vout
RF

;
 1
Rs
RF
vs
Rs
vS  vout
30
Design Example: Design a noninverting amplifier with a closed
loop gain of Av = 5. The output voltage is limited to -10 V  vo  +10
V and the maximum current in any resistor is limited to 50 A
Answer: R1 = 40 k, R2 = 160 k
31
Amplifier with a T-Network
i2
vx
R2
R4
i1
vs
R1
0
0
+
i3
R3
i4
vo
R
v x  0  i2 R2  vs ( 2 )
R1
v x v x v x  vo
i2  i4  i3 ;


R2 R4
R3
Combing the above equations we get
v
R
R
R
Av  o   2 (1  3  3 )
32
vs
R1
R4 R2
Design Example: An op-amp with a T-network is to be used as a preamplifier
for a microphone. The maximum microphone output voltage is 12 mV (rms)
and the microphone has an output resistance of 1 k. The op-amp circuit is to
be designed such that the maximum output voltage is 1.2 V (rms). The input
amplifier resistance should be fairly large but all resistance values should be
less than 500 k.
1. 2
 100
0.012
R
R
Av   2 (1  3 ) 
R1
R4
Av 
R3
R1
R
R
If we choose 2  3  8
R1 R1
R
R
 100  8(1  3 )  8; 3  10 .5
R4
R4
We should include the value of the source resistance in the calculatio n
If we set R1  49 k and Rsr  1 k then the total resistance ( R1 effective ) will be 50 k
R2  R3  400 k and R 4  38 .1 k
33
A Single Difference or Differential Amplifier
vout
R2
v2  v1 

R1
R2
vout 
v Id
R1
Figure
8.10
R2
Ad 
R1
34
Instrumentation Amplifier
Input (a) and output (b) stages
of Instrumentation amplifier
Figure
8.14,
8.15
vout
RF  2 R2 
1 

AV 

v1  v2
R 
R1 
35
Op-amp Differentiator
dvS (t )
vout (t )   RF CS
dt
Figure 8.35
36
Design Example. Design a difference amplifier with a
specified gain and minimum differential input resistance.
Design the circuit such that the differential gain is 30
and the minimum differential input resistance is Ri = 50
k
Ri  2 R1  50 kΩ
R1  R3  25 k
R2
Since the differenti al gain is
 30,
R1
we must have R2  R4  750 kΩ
37
Design Example: Calculate the common-mode rejection ratio of a
differential amplifier. Consider the difference amplifier shown in
page 2. Let R2/R1 = 10 and R4/R3 = 11. Determine CMRR (dB)
vo  vo1  vo2
 R4 


R
R
3 v  ( R 2 ) v
vo  (1  2 )
I1
R4  I 2
R1 
R1
1

R
3


11
vo  (1  10 )(
)v I 2  (10 )v I1  10 .0833 v I 2  10 v I1
1  11
vd
vd
v I1  v I 2
vd  v I 2  v I1; vcm 
; v I1  vcm 
; v 2  vcm 
2
2
2
v
v
vo  10 .0833 (vcm  d )  10 (vcm  d )
2
2
vo  10 .042 vd  0.0833 vcm ; vo  Ad vd  Acm vcm
Ad  10 .042 ; Acm  0.0833
 10.042 
CMRR(dB)  20log 10 
  41 .6 dB
0.0833


38
Op-amp Integrator
1
vout (t )  
RS CF
t
 vS (t )dt
Figure
8.30

39
Op-amp Differentiator
dvS (t )
vout (t )   RF CS
dt
Figure 8.35
40
Filters
• Electrical filters are like mechanical filters like the fuel filter or oil filter
in your car.
• Electrical filters may accomplish the same thing: removal of
contaminating signals but the physical action is different. In electrical
filters, we take advantage of the filter’s different responses at
different frequencies, and the fact that many signals that are
corrupted by noise have a signal and noise that have different
frequency content.
• Filters have different types:
– Low-pass filter that preferentially pass low frequency signals.
– High-pass filters that preferentially pass high frequency signals.
– Band-pass filters that preferentially pass signals with a strong
frequency component within a band of frequencies.
– Band-reject filters that preferentially reject signals in a certain
frequency band.
41
Op-amp Circuits Employing Complex Impedances
Vout
ZF
( j )  
VS
ZS
Figure
8.20
Vout
ZF
( j )  1 
VS
ZS
42
Active Low-Pass Filter
Figure 8.21,
8.23
Normalized Response of Active Low-pass Filter
43
Active High-Pass Filter
Figure
8.24,
8.25
Normalized Response of Active High-pass Filter
44
Active Band-Pass Filter
Figure
8.26,
8.27
Normalized Amplitude Response of Active Band-pass Filter
45
Filter Design
• Can we use a simple passive filter (i.e., only passive components
such as resistors, capacitors and inductors; no operational
amplifiers.
• The advantages of a passive filter are that it is quite simple to
design and implement. It also provides a simple single pole or two
pole filter whose electrical response can be easily calculated. For a
single pole low-pass filter, fc = 1 / (2  RC) the filter roll-off is 6 dB
per octave or 20 dB/decade. However, this filter does have some
noticeable drawbacks:
• It is very sensitive to the component value tolerances.
• For low frequencies, the values of R and C can be quite large,
leading to physically large components.
46
• A first or second-order filter may not give adequate roll-off.
• If gain is required in the circuit, it cannot be added to the filter itself.
• The filter may have a high output impedance. Since the resistor
value is large, to keep the capacitors with reasonable values, the
next stage device can see a significant source impedance.
• An op amp can be added at the output, but why add the op amp
here when it can be used to improve the filter’s performance in
addition to lowering the output impedance?
47
Two-Port Network
Vo ( s )
Transfer function T ( s ) 
Vi ( s)
Filter tra nsmis
sion T ( j )  T ( j ) e j ( )
Gain function G(  )  20 log T ( j )
Attenuation function A( )  20 log T ( j )
48
Transmission Characteristics
49
Specifications of the Transmission Characteristics
50
Transmission Characteristics for Band Pass Filter
51
Exercise 12.2: If the magnitude of passband transmission is to remain
constant to within 5%, and if the stopband transmission is to be
greater that 1% of the passband transmission, find Amax and Amin.
Amax  20 log 1.05  20 log 0.95  0.9 dB
Amin
1
 20 log(
)  40 dB
0.01
52
The Filter Transfer Function
T ( s) 
aM s
M
 AM 1s
M 1
 ..  a0
s N  bN 1s N 1  ..  b0
a M ( s  z1 )( s  z 2 )..( s  z M )
T ( s) 
( s  p1 )( s  p2 )..( s  p M )
53
Transmission Characteristics of Fifth Order Low Pass Fliter
54
Exercise 12.3: A second order filter has its poles at
s  (1 / 2)  j ( 3 / 2). The transmiss ion is zero at   2 rad/s
and is unity at DC. Find the transfer function.
(s  j2)(s - j2)
T(s)  k
(s  1/2  j 3 / 2)(s  1/2 - j 3 / 2)
k
( s 2  4)
k
( s 2  4)
s  s  1 / 4  3 / 4)
s2  s 1
T (0)  4k  1
k  1/ 4
2
1 s2  4
T ( s) 
4 s2  s 1
55
Digitization
• In modern GPS receivers digital signal processing is used to track
the GPS signal, make pseudorange and Doppler measurements,
and demodulate the 50-bps data stream.
• For this purpose the down-converted signal is sampled and digitized
by an analog-to-digital converter (ADC).
• Most low-cost receivers use 1-bit quantization of the digitized
samples. Accordingly, the receiver needs no automatic gain control
(AGC).
• However, typical-end receivers use anywhere from 1.5 bit to 3-bit
(eight level) sample quantization. The receiver needs AGC.
• Some military receivers use even more than 3-bit quantization.
56
Sampling a Signal on a Carrier Wave
The sampling rate should be at least
f s  2.f
f s  2. f max
f  2 MHz
1
f max  f IF  f
2
f max  f IF  1 MHz
57
Receiver Channels
The GPS signal processing takes places in different channels. Every
satellite visible to the antenna is allocated to its own channel, limited by a
maximum number of channels in the receiver.
Code tracking
Incoming
signal
Navigation data
extraction
Acquisition
Pseudorange
calculation
Carrier tracking
One receiver channel
58
Allocation of Channels
• Before allocating a channel to a satellite, the receiver must know
which satellites are visible. There are two common ways of finding
visible satellites:
• Warm start: The receiver combines information in the stored
almanac data and the last position calculated by the receiver. The
almanac data is used to calculate coarse positions of all satellites at
the present time. These positions are then combined with the
receiver position in an algorithm calculating which of the satellites
should be visible.
• Cold start: The receiver does not rely on any stored information.
Instead it starts from scratch searching for satellites. The method of
searching is referred to as acquisition.
59
Acquisition
• The purpose of acquisition is first to identify if a certain satellite is
visible to the user or not. If the satellite is visible, the acquisition
must determine the following two properties of the signal:
– Frequency: The frequency of the signal from a specific satellite
can differ from its nominal value. Signals are affected by the
relative motion of the satellite causing a Doppler effect. The
Doppler frequency shift can in case of maximum velocity of the
satellite combined with a very high user velocity approach values
as high as 10 kHz.
– Code Phase: The code phase denotes the point in the current
data block where the C/A code begins. If a data block of 1 ms is
examined, the data includes an entire C/A code and thus one
beginning of a C/A code.
60
Acquiring a Satellite
• When acquiring a satellite k, the incoming signal is multiplied with
the local generated C/A code corresponding to the satellite k. The
cross-correlation between C/A codes for different satellites implies
that signals from other satellites are nearly removed by this
procedure. To avoid removing the desired signal, the locally
generated C/A code must be properly aligned in time, that is with the
correct code phase.
• After multiplication with the locally generated code, the signal must
be mixed with a locally generated carrier wave. This done to remove
the carrier wave of the received signal. To remove the carrier wave
from the signal, the frequency of the locally generated signal must
be close to the signal carrier frequency. The signal can change up to
± 10 kHz from the nominal frequency so different frequencies within
this area must be tested.
61
• To make sure that a satellite is visible, it is sufficient to search the
frequency in steps of 500 Hz resulting in 41 different frequencies in
case of fast moving receiver and 21 in case of a static receiver.
• After mixing with the locally generated carrier wave, all signal
components are squared and summed providing a numerical value.
• The acquisition procedure works as a search procedure. For each of
the different frequencies 1023 different code phases are tried.
• When all possibilities for code phase and frequency are tried, a
search for the maximum value is performed.
• If the maximum value exceeds a determined threshold, the satellite
is acquired with the corresponding frequency and phase shift.
62
Tracking
• The main purpose of tracking is to refine the coarse values of code
phase and frequency, and keep track of these as the signal
properties change over time.
• The accuracy of the final value of the code phase is connected to
the accuracy of the pseudorange calculated later on.
• The tracking contains two parts, code tracking and carrier
frequency/phase tracking.
– Code tracking: This is implemented as a delay lock loop (DLL)
where three local codes are generated and correlated with the
incoming signal.
– Carrier frequency/phase tracking: This tracking can be done
in two ways. Either by tracking the phase of the signal or by
tracking the frequency.
63
Navigation Data Extraction
• When the signals are properly tracked, the C/A code and the carrier
wave can be removed from the signal only leaving the navigation
data bits.
• The value of a data bit is found by integrating over a navigation bit
period of 20 ms.
• After reading about 30 s of data, the beginning of a sub-frame must
be found in order to find the time when the data was transmitted
from the satellite.
• When the time transmission is found, the ephemeris data for the
satellite must be decoded. This is later used to calculate the position
of the satellite at the time of transmission.
• Before making position calculation is necessary to calculate
pseudoranges based on the time of the transmission from the
satellite and the time of arrival at the receiver. The time of arrival is
based on the beginning of the sub-frame.
64
Position Calculation
The position is calculated from pseudoranges and satellite
positions found from ephemeris data.
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Receiver Design Choices
• Number of channels and sequencing rate: GPS receiver must
observe the signal from at least four satellites to obtain threedimensional position and velocity estimates. If the user altitude is
known, three satellites will suffice.
• Most modern GPS receivers have a sufficient number of channels to
permit one satellite to be continuously observed on each channel.
• In a single-channel receiver, all processing, such as acquisition,
data demodulation, and code and carrier tracking, is performed by a
single channel in which the signals from all observed satellites are
time shared.
• Although this reduces hardware complexity, the software required to
mange the time-sharing process can be quite complex.
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References
• Global Positioning Systems by MS Grewal, LR Weill, AP Andrews,
Wiley, 2001.
• Peter Rinder and Nicolaj Bertelsen, Design of a Single GPS
Software Receiver, Aalborg University 2004.
• The Internet.
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