analog/digital communications primer - virginia tech communications primer for amateur radio joseph...

Analog/Digital Communications Primerfor Amateur Radio

Joseph D. Gaeddert

Virginia Polytechnic Institute & State University

March 19, 2013

Joseph D. Gaeddert Analog/Digital Communications Primer

# include <liquid / liquid.h>

// ...

int main() {

float kf = 0.1f; // modulation factor

liquid_freqdem_type type = LIQUID_FREQDEM_DELAYCONJ;

// create modulator/demodulator objects

freqmod fmod = freqmod_create(kf);

freqdem fdem = freqdem_create(kf, type);

float m; // input message

float complex s; // modulated signal

float y; // output/demodulated message

// repeat as necessary

{

// modulate signal

freqmod_modulate(fmod, m, &s);

// demodulate signal

freqdem_demodulate(fdem, s, &y);

}

// clean up objects

freqmod_destroy(fmod);

freqdem_destroy(fdem);

}


introduction

I about your presenter

I what we all should get from this presentation

I brief introduction to analog communications (AM/FM)

I brief introduction to digital communications

I software-defined radio

I why I joined in amateur radio


fourier transformdefinition

Time domainx(t)

FrequencydomainX (f )

X (f ) =∞∫−∞

x(t)e−j2πftdt

x(t) =∞∫−∞

X (f )e j2πftdf

I We can think of the Fourier Transform and the Inverse FourierTransform as the means for moving between the time andfrequency domains

I Note that no information is lost in the transformationI Both are equivalent representations of a signal


fourier transformexample: cos(2πf0t)

t

g(t)

f

G(f )

12δ(f + f0)

12δ(f + f0)

g(t) = cos(2πf0t) ⇔ G (f ) =1

2δ(f + f0) +

1

2δ(f − f0)

Notes: g(t) has even symmetry ∴ G (f ) is purely real.


analog communicationsintro to modulation

I In general time-varying modulation of a sinusoid can bewritten as

s(t) = A(t) cos(

2πfct + θ(t))

I fc is the nominal carrier frequencyI A(t) is the time-varying amplitudeI θ(t) is the time-varying phase

t

s(t), unmodulated carrier


amplitude modulationspectrum of double side-band transmitted carrier AM

t

m(t)

t

1 + kam(t)

t

s(t) = [1 + kam(t)] cos(2πfc t)

f

M(f )

f

δ(f ) + kaM(f )

f

S(f )

−fc fc


amplitude modulationdouble side-band transmitted carrier AM

t

m(t), message signal

t

s(t) = Ac [1 + kam(t)] cos(2πfc t)

f

S(f )

−fc fc


amplitude modulationdouble side-band suppressed carrier AM

t


t

s(t) = Acm(t) cos(2πfc t)

f

S(f ) = Ac2M(f + fc ) +

Ac2M(f − fc )

−fc fc


amplitude modulationsingle side-band AM

f

M(f ), message signal

f

S(f ), modulated messageBPF

−fc fc

f

S(f ), single side-band

−fc fc


frequency modulationintroduction

We can transmit information m(t) by varying the angle θi (t) of acarrier

Phase Modulation (PM)The phase of the carrier is varied

linearly with m(t)

θi (t) = 2πfct + kpm(t)

s(t) = Ac cos(2πfct + kpm(t))

Frequency Modulation (FM)The frequency of the carrier is varied linearly

with m(t)

fi (t) = fc + kfm(t)

θi (t) = 2πfct + 2πkf

t∫0

m(τ)dτ

s(t) = Ac cos

2πfct + 2πkf

t∫0

m(τ)dτ


frequency modulationamplitude vs. frequency modulation

t


t

s(t), DSB AM

t

s(t), FM


band-pass digitalbinary band-pass modulation

Three forms of signaling...

0 0 1 1 0 1 1 0 0 1Input Data

t

Amplitude-shift keying

t

Phase-shiftkeying

t

Frequency-shift keying


band-pass digitalM = 4 (2-bit) band-pass modulation

Extend binary to include more data...

00 01 11 10 01 01 11 10 00 11Input Data

t


t

Phase-shiftkeying

t



M-ary level modulationM-ary amplitude-shift keying (ASK)

00 01 11 10 01 01 11 10 00 11Input Data

t

t


s(t) =

0 symbol 00

0.4 · Ac sin (2πfct) symbol 01



I Similar to on-off keying

I Spectrum contains a linecomponent at f = fc

I Does not need coherent detector


M-ary level modulation2-level amplitude-shift keying (2-ASK)


M-ary level modulation4-level amplitude-shift keying (4-ASK)


M-ary level modulationM-ary phase-shift keying (PSK)

00 01 11 10 01 01 11 10 00 11Input Data

t

t

Phase-shiftkeying

s(t) =

+Ac sin (2πfct) symbol 00

+Ac cos (2πfct) symbol 01

−Ac sin (2πfct) symbol 10

−Ac cos (2πfct) symbol 11

I Similar to analog QAM

I Spectrum contains no linecomponents

I Does need coherent detector


M-ary level modulationM-ary phase-shift keying (PSK)

I In general, M-ary PSK signals can be written as

s(t) =

√2

Tscos(2πfct + θm)

where

θm =2π

M(m − 1) m = 0, 1, 2, · · · ,M − 1

real

imag

01 M = 2

real

imag

0001

10

11

M = 4

real

imag

000001

010

011

100101

110 111

M = 8


M-ary level modulation2-level phase-shift keying (2-PSK)


M-ary level modulation4-level phase-shift keying (4-PSK)


M-ary level modulationM-ary quadrature amplitude modulation (M-QAM)

I In general we may arbitrarily modulate both amplitude and phase:

s(t) = am

√2

Tscos(2πfct) + bm

√2

Tssin(2πfct) 0 ≤ t < Ts

I

Q

0000

0001

0011

0010

0100

0101

0111

0110

1100

1101

1111

1110

1000

1001

1011

1010

16-QAM

I

Q 64-QAM


M-ary level modulation64 quadrature amplitude modulation (64-QAM)

I

Q

000000

000001

000010

000011

000110

000101

000110

000111

001000

001001

001010

001011

001110

001101

001110

001111

010000

010001

010010

010011

010110

010101

010110

010111

011000

011001

011010

011011

011110

011101

011110

011111

110000

110001

110010

110011

110110

110101

110110

110111

101000

101001

101010

101011

101110

101101

101110

101111

110000

110001

110010

110011

110110

110101

110110

110111

111000

111001

111010

111011

111110

111101

111110

111111

64-QAM


Digital Communications16-QAM, High SNR

16-QAM

Qu

ad

ratu

re

In-phase

I In-phase (cosine), quadrature(sine)

I Each of 16 symbols represents 4unique bit sequences (16 = 24)

I High ratio of signal energy tonoise energy (SNR)

I Low probability of error (good!)


Digital Communications16-QAM, Low SNR

16-QAM

Qu

ad

ratu

re

In-phase

I SNR degrades

I Received sample points notconfined to within their bins

I Probability of error increases(bad!)


Digital CommunicationsQPSK, Low SNR

QPSK

Qu

ad

ratu

re

In-phase

I Fall back to lower modulationscheme

I Each of 4 symbols representsonly 2 unique bit sequences(4 = 22)

I Probability of error againreduced

I ...but at the expense of lowerdata rate


M-ary level modulationM-ary frequency-shift keying (FSK)

00 01 11 10 01 01 11 10 00 11Input Data

t

t


s(t) =

Ac cos (2πf0t) symbol 00




I Similar to analog FM

I Spectrum contains linecomponents at f = f0, f1, f2, f3

I Unlike ASK and PSK, FSKincreases bandwidth


M-ary level modulation2-level frequency-shift keying (2-FSK)


M-ary level modulation4-level frequency-shift keying (4-FSK)


software-defined radioswhat is SDR?

traditional radio designsoftware radio design

float mod_index = 0.1f; // modulation index

int sc = 1; // suppress carrier?

liquid_modem_amtype type = LIQUID_MODEM_AM_DSB;

// create/initialize automatic gain control

agc_rrrf agc = agc_rrrf_create();

// create AM demodulator object

ampmodem demod = ampmodem_create(mod_index,type,sc);

// run demodulator

while (devices.rf.data_availble()) {

// pull input sample and apply gain control

agc_rrrf_execute(agc, devices.rf.data(), &y);

// demodulate signal

float y;

ampmodem_demodulate(demod, x, &y);

// push demodulated output to sound out device

devices.sound.push(y);

}

// destroy objects

agc_crcf_destroy(agc);

ampmodem_destroy(demod);


software-defined radiosarbitrary linear constellations

-1.5

-1

-0.5

0

0.5

1

1.5

-1.5 -1 -0.5 0 0.5 1 1.5

Q

I

0000

0001

0010

0011

0100

0101

0110

0111

1000

1001

1010

1011

1100

1101

1110

1111

-1.5

-1

-0.5

0

0.5

1

1.5

-1.5 -1 -0.5 0 0.5 1 1.5

Q

I

00000

00001

00010

00011

00100

00101

00110

00111

01000

01001

01010

01011

01100

01101

01110

01111

10000

10001

10010

10011

10100

10101

10110

10111

11000

11001

11010

11011

11100

11101

11110

11111

-1.5

-1

-0.5

0

0.5

1

1.5

-1.5 -1 -0.5 0 0.5 1 1.5

Q

I

000000

000001

000010

000011

000100

000101

000110

000111

001000

001001

001010

001011

001100

001101

001110

001111

010000

010001

010010

010011

010100

010101

010110

010111

011000

011001

011010

011011

011100

011101

011110

011111

100000

100001

100010

100011

100100

100101

100110

100111

101000

101001

101010

101011

101100

101101

101110

101111

110000

110001

110010

110011

110100

110101

110110

110111

111000

111001

111010

111011

111100

111101

111110

111111

-1.5

-1

-0.5

0

0.5

1

1.5

-1.5 -1 -0.5 0 0.5 1 1.5

Q

I

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

-2 -1.5 -1 -0.5 0 0.5 1 1.5 2

Q

I

0 1 2 3

4

5

6

7

8

9

10

11

12

13 14 15 16 17 18 19 20 21 22 23 24 25

26

27

28293031

32

33

34

35

36

37383940

41

42

43

44

45

4647484950

51

52

53

54

55

56

57

58

59

60

61

62

63

-1.5

-1

-0.5

0

0.5

1

1.5

-1.5 -1 -0.5 0 0.5 1 1.5

Q

I

0000

0001

0010

0011

0100

0101

0110

0111

1000

1001

1010

1011

1100

1101

1110

1111


numerically-controlled oscillatorphase-locked loop

-1

0

1

0 50 100 150 200 250 300 350 400

real

Sample Index

inputnco

-1

0

1

0 50 100 150 200 250 300 350 400

imag

Sample Index

inputnco

-3

-2

-1

0

1

2

3

0 50 100 150 200 250 300 350 400

phase e

rror

[radia

ns]

Sample Index

# include <liquid / liquid.h>

//...

int main() {

// create tx/rx nco objects

nco_crcf nco_tx = nco_crcf_create(LIQUID_VCO);

nco_crcf nco_rx = nco_crcf_create(LIQUID_VCO);

// ... initialize objects ...

float complex * x;

unsigned int i;

// loop as necessary

{

// generate complex sinusoid

nco_crcf_cexpf(nco_tx, &x[i]);

// compute phase error

float dphi = nco_crcf_get_phase(nco_tx) -

nco_crcf_get_phase(nco_rx);

// update pll and nco objects

nco_crcf_pll_step(nco_rx, dphi);

nco_crcf_step(nco_tx);

nco_crcf_step(nco_rx);

}

// destry nco object

nco_crcf_destroy(nco_tx);

nco_crcf_destroy(nco_rx);

}


arbitrary filter designrecursive/non-recursive

-100

-80

-60

-40

-20

0

20

-0.4 -0.2 0 0.2 0.4

Pow

er S

pect

ral D

ensi

ty [d

B]

Normalized Frequency

-80

-70

-60

-50

-40

-30

-20

-10

0

0 0.1 0.2 0.3 0.4 0.5

Pow

er S

pect

ral D

ensi

ty [d

B]

Normalized Frequency

-120

-100

-80

-60

-40

-20

0

20

0 0.1 0.2 0.3 0.4 0.5

Pow

er

Spectr

al D

ensity [dB

]

-0.4

-0.2

0

0.2

0 0.0625 0.125

Normalized Frequency, ω/2π

G(ω)H(ω)

I arbitrary non-recursive filterdesign (Parks-McClellan)

I improved square-root Nyquistfilters

I recursive filter design:Butterworth, Chebyshev-I/II,elliptic, Bessel


high-level communications structuresmulticarrier: OFDM (ofdmflexframe)

time

S0 S0

...

S1 H0 H1

...

P0 P1

...

P(n-1)

header payload

frequency

−Fs 0 Fs

pilot subcarrierspectral nullguard band

I fully configurable (like with flexframe structure)

I additionally configurable subcarrier allocation

I capable of notching spectrum


high-level communications structuresmulticarrier: OFDM (ofdmflexframe), actual transmission


high-level communications structuresmulticarrier: OFDM (ofdmflexframe), actual reception


ResourcesJoseph D. Gaeddert

I email: [email protected]

I website: http://ganymede.ece.vt.edu

I project: http://github.com/jgaeddert/liquid-dsp


analog/digital communications primer - virginia tech communications primer for amateur radio joseph...

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