GNSS Receiver Front-ends I: Signals, Noise And Distortions

DANISH GPS CENTER
GNSS Receiver Front-ends I:
Signals, Noise And Distortions
GPS Receiver Technology MM7
Darius Plaušinaitis
[email protected]
Based on original slides from Ragnar V. Reynisson
Agenda
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Receiver Basics
Description of electrical signals
Noise
Linearity/Distortion
Receiver Figures of Merit (FoM)
Summary
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Receiver Basics
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• The purpose of a receiver is to:
”Separate information from carrier
signal, keeping signal quality above
predetermined minimum”
Receiver (signal processing)
• A radio front-end lies between the antenna
and the baseband signal processing (digital or
analog)
Radio signal
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RF
Front-end
IF signal
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Signal
processing
Position
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Description Of Electrical Signals
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Signals
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• An RF signal is divided in two distinct parts:
– A carrier signal
– Modulation (Information)
• The carrier signal is a sine wave which
amplitude and frequency depends on the
system (standards & regulations)
• The modulation is a time-dependent variation
in signal phase, frequency and/or amplitude
which carries the actual information content in
the signal
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Signals
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• An ideal signal can be expressed in several
ways:
In-phase/Quadrature
Polar
Complex Envelope
Complex Envelope
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Signals
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• All three representations are equivalent
• The conversion between I/Q and A/P is written
as:
Polar  I/Q
I/Q  Polar
Complex envelope useful in representing the signal at baseband:
Modulation diagrams, signal constellations, etc.
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Different Ways to Visualize
Signals
Complex Envelope
0.5
jQ(t)
In-phase/Quadrature
1
I(t)
1
0
-1
0
0
0.2
0.4
0.2
0.4
0.6
0.8
1
0.6
0.8
1
0.8
1
1
-1
-1
Q(t)
-0.5
Polar
0.2
0.6
0.4
0.8
1
s(t)
a(t)
0.5
φ(t) [π rad]
1
0
-0.5
0
-1
0
t
Signal (ω = 50)
1
0.5
0
0
0
-1
0
1
0.5
0
I(t)
-0.5
1
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0.2
0.4
t
0.6
0.8
-1
0
1
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0.2
0.4
t
0.6
8
Amplitude/Power/Energy
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Instantaneous Power
Energy
Average Power
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What is dB (dBm, dBW)?
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• Decibel (dB) is a logarithmic unit of measurement that
expresses the magnitude of a physical quantity
relative to a specified or implied reference level
 P1
dB = 10 ⋅ log10 
 P2



• dB is dimensionless and is used for signal power
comparison e.g. signal amplification, attenuation or
signal to noise ratio
• Signal power is typically measured in dBW or dBm
 P 
dBW = 10 ⋅ log10 

1
W


 P 
dBm = 10 ⋅ log10 

 1mW 
dBW = dBm − 30
• dBV and dBµV are used for voltage amplitude levels
VdBV = 20 ⋅ log10 (V )
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 P
VdBµV = 20 ⋅ log10 
 1µV
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


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Signal Quality
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Signal Quality
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• Signal Quality is a ”catch-all” term for
imperfections in the signal
– In digital system SQ is linked to Bit Error Ratio
(BER)
– In GNSS SQ is also linked to quality of position
measurements
• Several mechanisms affect signal quality:
– Noise
– Distortion
– Unwanted (interfering) signals
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Signal Quality
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• For microwave circuits, noise is
predominantly generated inside receiver
– Active circuits (noise from semiconductors)
– Passive circuits (filters, interconnections – lossy
circuits in general)
• Distortion is generated by inherent nonlinearity of active circuits
– Non-linear I/V characteristics
– Clipping
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Signal Quality
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• Strong unwanted signals interfere with signal
quality
– Drive active circuits (primarily amplifier) into
overload: Blocking
– Saturate analogue to digital converts (ADC)
– Third-order intermodulation effects can ”mix” two
out-of-band signals onto the wanted frequency
band: Impossible to filter out
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Noise
Noise sources, filtering, SNR
Physical Noise Sources
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• Noise can be roughly grouped into:
– Externally generated noise
• Man-made noise
• Atmospheric noise
– Internally generated noise
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Termal noise (one of the biggest noise sources in GNSS)
Resistive/lossy circuits
Semiconductors
Quantization
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Noise Mathematical
Description
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• White noise has the following characteristics
• Gaussian distribution
• Flat power spectral density
• Without memory (uncorrelated with previous
values)
• Band-limited white noise is called ”colored”. For a
noise bandwidth, ∆ω and center frequency ω0:
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Filtering\Components of Noise
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Non-limited
LPF (5 MHz)
HPF (5 MHz)
BPF (5-10 MHz)
BPF (25-30 MHz)
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Thermal Noise
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PThermalNoise = kTB
Power
where:
k - Boltzmann’s constant =
1.38e-23 J/°K
T - absolute temperature in K
B - equivalent noise bandwidth
in Hz
-- Noise floor
-- GPS C/A
≈ -111dBm
(2MHz BW)
≈ -130dBm
2.046MHz
1575.42 (MHz)
Freq
• Thermal noise for the GPS C/A signal:
– (1.38e–23)(290)(2e6) = 8.004e-15
• Thermal noise in dB:
– 10*log10(8.004e-15) = -140.97dBW ≈ -111dBm
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Quantization Noise
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Figures are taken from ”Global Positionig System, Theory and applications I”
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Signal to Noise ratio (SNR)
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• Signal to noise ratio is an important measure
of signal quality
• A high SNR implies a low error ratio for digital
modulation systems
• Minimum SNR requirement sets limit to
receiver sensitivity
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Signal Distortions
Distortion
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• While noise is critical for weak signals,
distortion sets the upper limit on receiver
performance
• This is because often strong (wanted and/or
interfering) signals cause distortions, but
there are also other kinds of distortions
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Distortion
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• Different distortion mechanisms include:
– Nonlinear transfer functions
– Clipping (signal amplitude exceeds hardware
limits)
• Distortions can occur also due to other
(interfering) signals
– Powerful, unwanted signals can block receiver by
driving non-linear circuits into compression
– An intermodulation product of two powerful
unwanted signals can cause interference in the
signal band  impossible to filter out
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Distortion: Non-linear Blocks
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• Active blocks in receiver
(amplifiers, mixers, active filters
etc.) have significant non-linear
behavior
• For linear blocks (amplifiers),
the effect is unwanted (but
practically unavoidable)
• For inherently non-linear blocks (mixers, etc),
a non-linear operation is needed while the
signal envelope should survive the process
with sufficiently low distortion
1
so
0.5
0
-0.5
-1
-1.5
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-1
-0.5
0
si
0.5
1
1.5
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Non-linear Transfer Functions
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• A linear transfer function is a function on the form:
• Which includes a change in amplitude and phase
shift/time delay
• A linear transfer function must satisfy the superposition
relation
• For a non-linear circuit, the output signal resulting from
two input signals cannot be determined by
superposition
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Non-linear Transfer Functions
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1
so
0.5
Non-linear input/output
0
relationship (e.g. amplifiers)
-0.5
-1
-1.5
-1
-0.5
0
0.5
1
1.5
0.2
si
0.15
characteristic (e.g. mixers)
0.1
Gain
Time-dependent transfer
0.05
0
-0.05
0
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1
2
t [ns]
3
4
5
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Non-linear Effects Are…
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• Complex to model  simple models for hand
calculations are rough guesses at best
• Difficult to calculate analytically  For most
RF receivers, the non-linear behavior of the
circuits is found via simulations
• On a system level, distortion effects are hard
to estimate without simulations
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Example of a Distortion
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A simple non-linear
Amplifier
1
so(t)
0.5
0
-0.5
-1
-1.5
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-1
-0.5
0
si
0.5
1
1.5
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Example of a Distortion
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1
so(t)
• An input signal:
0
-1
0
1
2
3
4
5
6
1
2
3
4
5
6
1
2
3
t [ns]
4
5
6
• Red curve – output of a
linear amplifier
• Blue curve – output of
the non-linear amplifier
from the previous slide
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0
-2
0
2
so(t)
• Three amplitude cases:
so(t)
2
0
-2
0
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Distortion: Frequency
Domain View
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• For RF circuits, time domain measurements can be
hard to perform or evaluate
• For transmitters, time-domain tests involving
modulated signals is possible
• Receiver distortion analysis is most often performed
in the frequency domain
• Next slide: A look at the output of the amplifier from
the previous example in the frequency domain
• The two largest tones (arrows) in the graphs are the
fundamental frequencies (850 MHz and 1 GHz). The
remainder of the spectrum is due to distortion.
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Distortion: Frequency
Domain View
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A=0.7
So [dBV]
0
-50
0
1
2
3
4
5
6
7
f [GHz]
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Distortion: Frequency
Domain View
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A=1.0
So [dBV]
0
-50
0
1
2
3
4
5
6
7
f [GHz]
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Distortion: Harmonics
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• Harmonics: Distortion in the signal can be seen in the
frequency domain as signal harmonics
• For multiple tones (sine waves), the non-linearity of
the block causes intermodulation:
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Receiver Figures-of-Merit
Receiver Figures-of-Merit
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Gain
Sensitivity/Noise Figure
Intercept points (2nd and 3rd order)
Dynamic Range
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Gain
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• Gain is a measure of power or amplitude
increase/decrease
• For RF circuits power gain is most frequently
used , as voltage levels can be hard to define
due to standing waves and reflected signals
• For integrated circuits, voltage gain is
sometimes used at RF and most often at
baseband
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Sensitivity
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• The quality of the signal at the lower end of the power
scale is dominated by signal-to-noise ratio (SNR)
• Receiver sensitivity is defined as the input signal
power level which results in minimum detectable SNR
at the demodulator
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Dynamic Range
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• The dynamic range of the receiver is the range
of input power levels that the receiver can be
used for without noise or distortion corrupting
the signal
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Summary
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• Radio receivers must deliver a received signal to the
signal processor while adding a minimum of noise
and distortion
• Noise can “burry” weak signals
• Distortion change received signals and/or create
unwanted additional signals
• Receiver/components figures of merit:
• Gain
• Intercept point
• Sensitivity
• Dynamic range
• Noise figure
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