Download 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
•
•
•
•
•
•
2008
DANISH GPS CENTER
Receiver Basics
Description of electrical signals
Noise
Linearity/Distortion
Receiver Figures of Merit (FoM)
Summary
Danish GPS Center
2
Receiver Basics
DANISH GPS CENTER
• 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
2008
RF
Front-end
IF signal
Danish GPS Center
Signal
processing
Position
3
DANISH GPS CENTER
Description Of Electrical Signals
2008
Danish GPS Center
4
Signals
DANISH GPS CENTER
• 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
2008
Danish GPS Center
5
Signals
DANISH GPS CENTER
• An ideal signal can be expressed in several
ways:
In-phase/Quadrature
Polar
Complex Envelope
Complex Envelope
2008
Danish GPS Center
6
Signals
DANISH GPS CENTER
• 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.
2008
Danish GPS Center
7
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
2008
DANISH GPS CENTER
0.2
0.4
t
0.6
0.8
-1
0
1
Danish GPS Center
0.2
0.4
t
0.6
8
Amplitude/Power/Energy
DANISH GPS CENTER
Instantaneous Power
Energy
Average Power
2008
Danish GPS Center
9
What is dB (dBm, dBW)?
DANISH GPS CENTER
• 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 )
2008
 P
VdBµV = 20 ⋅ log10 
 1µV
Danish GPS Center



10
DANISH GPS CENTER
Signal Quality
2008
Danish GPS Center
11
Signal Quality
DANISH GPS CENTER
• 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
2008
Danish GPS Center
12
Signal Quality
DANISH GPS CENTER
• 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
2008
Danish GPS Center
13
Signal Quality
DANISH GPS CENTER
• 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
2008
Danish GPS Center
14
DANISH GPS CENTER
Noise
Noise sources, filtering, SNR
Physical Noise Sources
DANISH GPS CENTER
• Noise can be roughly grouped into:
– Externally generated noise
• Man-made noise
• Atmospheric noise
– Internally generated noise
•
•
•
•
2008
Termal noise (one of the biggest noise sources in GNSS)
Resistive/lossy circuits
Semiconductors
Quantization
Danish GPS Center
16
Noise Mathematical
Description
DANISH GPS CENTER
• 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:
2008
Danish GPS Center
17
Filtering\Components of Noise
DANISH GPS CENTER
Non-limited
LPF (5 MHz)
HPF (5 MHz)
BPF (5-10 MHz)
BPF (25-30 MHz)
2008
Danish GPS Center
18
Thermal Noise
DANISH GPS CENTER
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
2008
Danish GPS Center
19
Quantization Noise
DANISH GPS CENTER
Figures are taken from ”Global Positionig System, Theory and applications I”
2008
Danish GPS Center
20
Signal to Noise ratio (SNR)
DANISH GPS CENTER
• 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
2008
Danish GPS Center
21
DANISH GPS CENTER
Signal Distortions
Distortion
DANISH GPS CENTER
• 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
2008
Danish GPS Center
23
Distortion
DANISH GPS CENTER
• 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
2008
Danish GPS Center
24
Distortion: Non-linear Blocks
DANISH GPS CENTER
• 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
2008
Danish GPS Center
-1
-0.5
0
si
0.5
1
1.5
25
Non-linear Transfer Functions
DANISH GPS CENTER
• 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
2008
Danish GPS Center
26
Non-linear Transfer Functions
DANISH GPS CENTER
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
2008
Danish GPS Center
1
2
t [ns]
3
4
5
27
Non-linear Effects Are…
DANISH GPS CENTER
• 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
2008
Danish GPS Center
28
Example of a Distortion
DANISH GPS CENTER
A simple non-linear
Amplifier
1
so(t)
0.5
0
-0.5
-1
-1.5
2008
Danish GPS Center
-1
-0.5
0
si
0.5
1
1.5
29
Example of a Distortion
DANISH GPS CENTER
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
2008
0
-2
0
2
so(t)
• Three amplitude cases:
so(t)
2
0
-2
0
Danish GPS Center
30
Distortion: Frequency
Domain View
DANISH GPS CENTER
• 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.
2008
Danish GPS Center
31
Distortion: Frequency
Domain View
DANISH GPS CENTER
A=0.7
So [dBV]
0
-50
0
1
2
3
4
5
6
7
f [GHz]
2008
Danish GPS Center
32
Distortion: Frequency
Domain View
DANISH GPS CENTER
A=1.0
So [dBV]
0
-50
0
1
2
3
4
5
6
7
f [GHz]
2008
Danish GPS Center
33
Distortion: Harmonics
DANISH GPS CENTER
• 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:
2008
Danish GPS Center
34
DANISH GPS CENTER
Receiver Figures-of-Merit
Receiver Figures-of-Merit
•
•
•
•
2008
DANISH GPS CENTER
Gain
Sensitivity/Noise Figure
Intercept points (2nd and 3rd order)
Dynamic Range
Danish GPS Center
36
Gain
DANISH GPS CENTER
• 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
2008
Danish GPS Center
37
Sensitivity
DANISH GPS CENTER
• 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
2008
Danish GPS Center
38
Dynamic Range
DANISH GPS CENTER
• 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
2008
Danish GPS Center
39
Summary
DANISH GPS CENTER
• 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
2008
Danish GPS Center
40