easy sdr experimentation with gnu radio - · pdf filetransforms, fourier, dft/fft sine wave...
TRANSCRIPT
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Easy SDR Experimentationwith
GNU Radio
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Introduction to DSP(and some GNU Radio)
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About Me
● EE, Independent Consultant
– Hardware, Software, Security
– Cellular, FPGA, GNSS, ...● DAGR – Denver Area GNU Radio meet-up
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Purpose
● Get you into SDR!
● Cover the basics of SDR to get you started
● Not – Comprehensive coverage
● Not – “How To Do X”
● Some examples to make it real
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Audience
● Well, you... duh!
● Radio fundamentals
● Algebra, Trigonometry (just a little!)
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Software Defined Radio (SDR)
● What is it?
● “Software”?
– Implies generalized hardware, reconfigurable for a specific purpose
– E.g. Computer / Software● But really… “Digital”
– Convert an analog signal to digital data
– Process in the digital realm, rather than analog● Digital Signal Processing (DSP)
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Analog Receiver Evolution
Frequency Selectivity
Detector
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Analog Receiver Evolution
Gain!
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Analog Receiver Evolution
Frequency Conversion
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Analog Receiver Evolution
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Digital Conversion
ADC DSP DAC
DSP
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SDR Evolution
DSP
● Super-Heterodyne– Demod filtering, processing– Detector/Demodulator– Additional final IF filtering
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SDR Evolution
DSP
DSP ● Sub-sampling● Zero-IF / Direct-Conversion
– I/Q, Quadrature
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SDR Evolution
DSP
DSP
DSP ● Direct Sampling, the final frontier
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Why?
● Flexibility!
● Avoid analog component imperfections
– Tolerances, Non-linearity, etc.
– The math doesn’t change● Greater performance – e.g. very sharp filters
● Sometimes cost
● Things you just wouldn’t do in analog (OFDM)
● Moore’s Law...
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Why for Amateurs?
● Flexibility
● Performance
● Advanced modulations
● Digital modes
● Experimentation!
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Basic DSP Concepts
● Signals
● Time ↔ Frequency Domains
● Filtering
● Sampling
● Sample Rate Conversion
● I/Q, Quadrature, Analytic Signals
● Frequency Conversion
● De/modulation
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Signal
● Sinusoids
● Unit Circle, Trigonometry
● sin(θ)=opp/hyp, cos(θ)=adj/hyp
● If r=hyp=1 and adj=x, opp=y
– y=sin(θ), x=cos(θ)● Frequency is speed around circle
– Hz (cycles/sec) = 2*pi (rad/sec)
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Time ↔ Frequency Domains
● Different ways of looking at a signal
● Transforms, Fourier, DFT/FFT
● Sine wave →”spike”
● Square wave → Odd harmonics
● Pulse → Sinc... sin(x)/x
● Negative frequency
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Filtering
● Change frequency response
– and/or phase● Filtering = convolution
● Convolution and multiplication are time-frequency pairs
● FIR/IIR
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● Sampling
– Discrete time● Quantization
– Discrete value
Sampling
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● Nyquist frequency (½ fs)
● Spectral Folding
– Aliasing
– Inversion
– Sub-sampling
Sampling
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Sample Rate Conversion
● Decimation
● Interpolation
● Aliasing / Filtering
(Pause before I/Q)
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I/Q Sampling
● In-phase and Quadrature-phase
● AKA Quadrature, Analytic Signal
● Complex Numbers
● VERY common in DSP/SDR
● Very common area of newcomer confusion
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SSB → I/Q
● Single sideband modulation and IQ sampling are very similar
● Use SSB to understand IQ
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What is SSB?
● A derivative of Amplitude Modulation (AM)
● To understand SSB, first understand AM
● Before AM, understand “modulation”
Here we go...
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Modulation
All about altering the properties of a sinusoid.
“Carrier Wave”
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Amplitude
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Frequency
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Phase
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Modulation - Basic Types
Carrier & Modulation Signal → AM, FM, PM
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Modulation - Math
The modulation function:
Amplitude Frequency Phase
→ “something(t)” means it may change with time
More concisely:
s (t )=am( t)cos (( f c+ f m( t))t+ pm( t))
s=am cos(( f c+ f m)t+ pm)
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AM Modulation
The “universal” modulation function:
s=am cos(( f c+ f m)t+ pm)
We are only interested in modulating amplitude, so the frequency and phase components drop out.
sam=am cos( f c t)
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AM Waveform
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Recall the AM function:
The modulation signal vm is in the range 0 to 1, where 0 yields zero signal output, and 1 yields 100% carrier amplitude.
We want to test our modulation with a sinusoid input so we need to scale and shift it so it is in the range 0 to 1.
AM - Math
v am=vm cos (ωc t)
vm=12(cos (ωmt )+1)
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AM – Math 2
v am=vm cos (ωc t)
v am=12(cos (ωmt )+1)cos (ωc t )
vm=12(cos (ωmt )+1)
v am=12
cos (ωm t)cos (ωc t)+12
cos(ωc t)
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AM – Math 3
v am=12
cos (ωm)cos(ωc )+12
cos (ωc)
Use a trigonometric identity to separate the cosine product:
cos (A)cos (B)=12
cos (A−B)+12
cos (A+B)
v am=14
cos(ωc−ωm)+14
cos (ωc+ωm)+12
cos (ωc)
Lower Sideband Upper Sideband Carrier Component
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AM - Spectrum
Carrier Sidebands
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AM – Spectrum 2
Increased modulation signal frequency increases distance from carrier.
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Inching Toward SSB – AM/SC
AM wastes a lot of energy in the carrier component, can we fix that?
AM with Suppressed Carrier (SC)
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AM/SC - Spectrum
That is what it looks like, but how can we make it?
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Recall the AM function:
For AM, vm was in the range 0 to 1.
For SC, make the range +/- 1, just a regular sinusoid.
AM/SC - Math
v am=vm cos (ωc t)
vm=cos(ωm t)
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AM/SC – Math 2
v am=vm cos (ωc t)
v am=cos(ωm t)cos (ωc t)
vm=cos(ωm t)
v am=12
cos (ωc−ωm)+12
cos (ωc+ωm)
Lower Sideband Upper Sideband No Carrier Component!
cos (A)cos (B)=12
cos (A−B)+12
cos (A+B)
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AM/SC “breaks” AM
Wrong envelope! Carrier amplitude inversion!
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SC/SSB – Electronics
● Multiplying negative values
– One, two, and four quadrant● Switchers (Mixers)
– Diode Ring (Balanced Mixer)
– Transistor● Modulators (Multipliers)
– Logarithmic amplifiers (Gilbert Cell)
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Finally... AM/SSB
That is what it looks like, but how can we make it?
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AM/SSB - Math
cos (A)cos (B)=12
cos (A−B)+12
cos (A+B)
Remember the cosine product trig identity?
Here is another:
sin(A )sin (B)=12
cos(A−B)−12
cos (A+B)
Notice that minus sign?
cos(A)cos (B)+sin(A)sin (B)=cos(A−B)
Just the lower sideband!
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SSB – Time Domain
Just a sine wave?
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SSB – Time Domain 2
Carrier and SSB signal
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AM/SSB – Implementation
Simple output, but complicated input...
cos (A)cos (B)+sin(A)sin (B)=cos (A−B)
Recall that sin(x) = cos(x - 90°), so we just need a 90° phase shift of our carrier and modulating signal frequencies.
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Electronic SSB Modulator, Filtering
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This Might Look Familiar...
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Phase Quadrature
● Quadrature means 90 degrees
– Latin “Quadratura” - (making) a square● Sine and Cosine are in quadrature
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Quadrature – So what?
● Rotate a point around the unit circle
● Look at either the sine or cosine graph
– Can you tell rate of rotation (frequency)?● Yes.
– Can you tell the direction of the rotation?● No! (But you can if you see both sine and cosine)
● So quadrature allows frequency and direction
● E.g. “Negative Frequency”
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Quadrature Sensors
http://www.creative-robotics.com/quadrature-intro
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Real Signals
No difference between positive or negative frequencies.
Thus upper and lower sideband mirror images.
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IQ Signals Make You Smarter
I = In-phase → Cosine →Real
Q = Quadrature → Sine → Imaginary
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Why Complex Numbers?
● Why not just treat I and Q as two real values?
● In some ways IQ is like 2x sample rate, some ways not...
– 2x bandwidth, but still no “negative frequency”
– 90° offset is key, 2x would be 180°● Complex numbers represent the relationship between I&Q,
especially during operations; like multiplication.
● Beautiful Math... Euler's Formula:
e ix=cos x+i sin x
Complex Sinusoid
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SSB IQ
v ssb=vme iωc t
SSB is just a multiplication in the complex domain!
(As is any frequency translation)
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Radio Selection
● Transmit? Full duplex?
● Frequency Range
● Sampling Rate / Bandwidth
● ADC resolution
● On-board DSP – FPGA, CPU
● Connectivity
– USB2/3, Ethernet, PCIe, …●
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Some Radios...
● Realtek Dongles
● HackRF
● Ettus Research
● BladeRF
● LimeSDR
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Application Ideas
● Basic AM/FM modulation
– Multi-channel relay● Packet Radio
● Satellite
● Direction Finding
● RADAR
● Atmospheric/propagation monitoring, Ionosphere, etc.
● HAM IoT
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Demos
● GNU Radio
● Fosphor
– Tx spectrogram image● Simple AM/SSB/FM radio, CTCSS, trunking
– A CTCSS multi-channel full duplex relay● Digital Modes – OFDM
● Simultaneous Audio, Slow-scan video, data
● Digital audio
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