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

DANISH GPS CENTER

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

2008 Danish GPS Center 2

DANISH GPS CENTERReceiver Basics

• A radio front-end lies between the antenna and the baseband signal processing (digital or analog)


”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 CENTER

Description Of Electrical Signals

2008 4Danish GPS Center

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


DANISH GPS CENTER


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:


Polar I/Q I/Q Polar

Complex envelope useful in representing the signal at baseband:

Modulation diagrams, signal constellations, etc.

DANISH GPS CENTER


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)

DANISH GPS CENTER


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


⋅=

2

110log10

PPdB

⋅=

WPdBW

1log10 10

⋅=

mWPdBm

1log10 10 30−= dBmdBW

( )VVdBV 10log20 ⋅=

⋅=

VPV VdB µµ 1

log20 10

DANISH GPS CENTER

Signal Quality

2008 11Danish GPS Center

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



• 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



• 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


DANISH GPS CENTER

NoiseNoise sources, filtering, SNR

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


DANISH GPS CENTER

Noise Mathematical Description

• Band-limited white noise is called ”colored”. For a noise bandwidth, ∆ω and center frequency ω0:


• White noise has the following characteristics

• Gaussian distribution • Flat power spectral density• Without memory (uncorrelated with previous

values)

DANISH GPS CENTER


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


2.046MHz≈ -130dBm

1575.42 (MHz)

-- GPS C/A

Freq

Power

≈ -111dBm(2MHz BW)

-- Noise floor

kTB P seThermalNoi =

DANISH GPS CENTERQuantization Noise


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


DANISH GPS CENTER

Signal Distortions

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


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


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)


-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


DANISH GPS CENTER


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)

DANISH GPS CENTER


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

DANISH GPS CENTER


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


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)

DANISH GPS CENTER

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.


DANISH GPS CENTER


Distortion: Frequency Domain View

A=0.7

1 2 3 4 5 60 7-50

0

f [GHz]

So [d

BV]

DANISH GPS CENTER


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:


DANISH GPS CENTER

Receiver Figures-of-Merit

DANISH GPS CENTERReceiver Figures-of-Merit

• Gain• Sensitivity/Noise Figure• Intercept points (2nd and 3rd order)• Dynamic Range


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


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


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


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


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

Documents

Transcript of GNSS Receiver Front-ends I: Signals, Noise And...