gnss receiver front-ends i: signals, noise and...
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GNSS Receiver Front-ends I:Signals, Noise And DistortionsGPS Receiver Technology MM7Darius Plauš[email protected]
Based on original slides from Ragnar V. Reynisson
DANISH GPS CENTERAgenda
• Receiver Basics• Description of electrical signals• Noise• Linearity/Distortion• Receiver Figures of Merit (FoM)• Summary
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DANISH GPS CENTERReceiver Basics
• A radio front-end lies between the antenna and the baseband signal processing (digital or analog)
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”Separate information from carrier signal, keeping signal quality above
predetermined minimum”
• The purpose of a receiver is to:
RFFront-end
Signal processingIF signal
Radio signal Position
Receiver (signal processing)
DANISH GPS CENTERSignals
• 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
• An ideal signal can be expressed in several ways:
In-phase/Quadrature
Polar
Complex Envelope
Complex Envelope
DANISH GPS CENTERSignals
• All three representations are equivalent • The conversion between I/Q and A/P is written
as:
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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
0 0.2 0.4 0.6 0.8 1-1
0
1
I(t)
In-phase/Quadrature
0 0.2 0.4 0.6 0.8 1-1
0
1
t
Q(t)
-1 -0.5 0 0.5 1-1
-0.5
0
0.5
1Complex Envelope
I(t)
jQ(t)
0 0.2 0.4 0.6 0.8 10
0.5
1Polar
a(t)
0 0.2 0.4 0.6 0.8 1-1
0
1
t
φ (t)
[π ra
d]
0 0.2 0.4 0.6 0.8 1-1
-0.5
0
0.5
1Signal (ω = 50)
t
s(t)
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Amplitude/Power/Energy
Instantaneous Power
Average Power
Energy
DANISH GPS CENTERWhat is dB (dBm, dBW)?
• Decibel (dB) is a logarithmic unit of measurement that expresses the magnitude of a physical quantity relative to a specified or implied reference level
• 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
• dBV and dBµV are used for voltage amplitude levels
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⋅=
2
110log10
PPdB
⋅=
WPdBW
1log10 10
⋅=
mWPdBm
1log10 10 30−= dBmdBW
( )VVdBV 10log20 ⋅=
⋅=
VPV VdB µµ 1
log20 10
DANISH GPS CENTERSignal Quality
• 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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DANISH GPS CENTERSignal Quality
• 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 non-
linearity of active circuits– Non-linear I/V characteristics– Clipping
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DANISH GPS CENTERSignal Quality
• 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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DANISH GPS CENTERPhysical Noise Sources
• Noise can be roughly grouped into:– Externally generated noise
• Man-made noise• Atmospheric noise
– Internally generated noise• Termal noise (one of the biggest noise sources in GNSS)• Resistive/lossy circuits• Semiconductors• Quantization
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Noise Mathematical Description
• Band-limited white noise is called ”colored”. For a noise bandwidth, ∆ω and center frequency ω0:
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• White noise has the following characteristics
• Gaussian distribution • Flat power spectral density• Without memory (uncorrelated with previous
values)
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Filtering\Components of Noise
Non-limited
LPF (5 MHz)
HPF (5 MHz)
BPF (5-10 MHz)
BPF (25-30 MHz)
DANISH GPS CENTERThermal Noise
where:k - Boltzmann’s constant =
1.38e-23 J/°KT - absolute temperature in KB - equivalent noise bandwidth
in Hz
• 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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2.046MHz≈ -130dBm
1575.42 (MHz)
-- GPS C/A
Freq
Power
≈ -111dBm(2MHz BW)
-- Noise floor
kTB P seThermalNoi =
DANISH GPS CENTERQuantization Noise
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Figures are taken from ”Global Positionig System, Theory and applications I”
DANISH GPS CENTERSignal to Noise ratio (SNR)
• 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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DANISH GPS CENTERDistortion
• 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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DANISH GPS CENTERDistortion
• 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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DANISH GPS CENTERDistortion: Non-linear Blocks
• 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)
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-1.5 -1 -0.5 0 0.5 1 1.5-1
-0.5
0
0.5
1
si
s o
• 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
DANISH GPS CENTERNon-linear Transfer Functions
• 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
Non-linear input/output
relationship (e.g. amplifiers)
-1.5 -1 -0.5 0 0.5 1 1.5-1
-0.5
0
0.5
1
s i
s o
0 1 2 3 4 5-0.05
0
0.05
0.1
0.15
0.2
t [ns]
Gai
nTime-dependent transfer
characteristic (e.g. mixers)
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Non-linear Effects Are…
• 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
-1.5 -1 -0.5 0 0.5 1 1.5-1
-0.5
0
0.5
1
si
s o(t)
A simple non-linear Amplifier
DANISH GPS CENTERExample of a Distortion
• An input signal:
• Three amplitude cases:
• Red curve – output of a linear amplifier
• Blue curve – output of the non-linear amplifier from the previous slide
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0 1 2 3 4 5 6-1
0
1
so(
t)
0 1 2 3 4 5 6-2
0
2
so(
t)
0 1 2 3 4 5 6-2
0
2
t [ns]
so(
t)
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Distortion: Frequency Domain View• 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
A=0.7
1 2 3 4 5 60 7-50
0
f [GHz]
So [d
BV]
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Distortion: Frequency Domain View
1 2 3 4 5 60 7-50
0
f [GHz]
So [d
BV]
A=1.0
DANISH GPS CENTERDistortion: Harmonics
• 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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DANISH GPS CENTERReceiver Figures-of-Merit
• Gain• Sensitivity/Noise Figure• Intercept points (2nd and 3rd order)• Dynamic Range
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DANISH GPS CENTERGain
• 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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DANISH GPS CENTERSensitivity
• 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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DANISH GPS CENTERDynamic Range
• 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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DANISH GPS CENTERSummary
• 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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