Analog/Digital Communications Primer

Transcription

1 for Amaeur Radio Virginia Polyechnic Insiue & Sae Universiy March 19, 2013

2 # include <liquid / liquid.h> //... in main() { floa kf = 0.1f; // modulaion facor liquid_freqdem_ype ype = LIQUID_FREQDEM_DELAYCONJ; // creae modulaor/demodulaor objecs freqmod fmod = freqmod_creae(kf); freqdem fdem = freqdem_creae(kf, ype); floa m; floa complex s; floa y; // inpu message // modulaed signal // oupu/demodulaed message // repea as necessary { // modulae signal freqmod_modulae(fmod, m, &s); } // demodulae signal freqdem_demodulae(fdem, s, &y); } // clean up objecs freqmod_desroy(fmod); freqdem_desroy(fdem);

3 inroducion abou your presener wha we all should ge from his presenaion brief inroducion o analog communicaions (AM/FM) brief inroducion o digial communicaions sofware-defined radio why I joined in amaeur radio

4 fourier ransform definiion X (f ) = x()e j2πf d Time domain x() Frequency domain X (f ) x() = X (f )e j2πf df We can hink of he Fourier Transform and he Inverse Fourier Transform as he means for moving beween he ime and frequency domains Noe ha no informaion is los in he ransformaion Boh are equivalen represenaions of a signal

5 fourier ransform example: cos(2πf 0) g() G(f ) 1 2 δ(f + f 0) 1 2 δ(f + f 0 ) f g() = cos(2πf 0 ) G(f ) = 1 2 δ(f + f 0) δ(f f 0) Noes: g() has even symmery G(f ) is purely real.

6 analog communicaions inro o modulaion In general ime-varying modulaion of a sinusoid can be wrien as ( ) s() = A() cos 2πf c + θ() fc is he nominal carrier frequency A() is he ime-varying ampliude θ() is he ime-varying phase s(), unmodulaed carrier

7 ampliude modulaion specrum of double side-band ransmied carrier AM m() M(f ) f

8 ampliude modulaion specrum of double side-band ransmied carrier AM m() M(f ) 1 + k am() δ(f ) + k am(f ) f f

9 ampliude modulaion specrum of double side-band ransmied carrier AM m() M(f ) 1 + k am() δ(f ) + k am(f ) f s() = [1 + k am()] cos(2πf c ) f S(f ) f c f c f

10 ampliude modulaion double side-band ransmied carrier AM m(), message signal s() = A c [1 + k am()] cos(2πf c ) S(f ) f c f c f

11 ampliude modulaion double side-band suppressed carrier AM m(), message signal s() = A c m() cos(2πf c ) S(f ) = Ac 2 Ac M(f + fc ) + M(f fc ) 2 f c f c f

12 ampliude modulaion single side-band AM M(f ), message signal f BPF S(f ), modulaed message f c f c f S(f ), single side-band f c f c f

13 frequency modulaion inroducion We can ransmi informaion m() by varying he angle θ i () of a carrier Phase Modulaion (PM) The phase of he carrier is varied linearly wih m() θ i () = 2πf c + k pm() s() = A c cos(2πf c + k pm()) Frequency Modulaion (FM) The frequency of he carrier is varied linearly wih m() f i () = f c + k f m() θ i () = 2πf c + 2πk f 0 m(τ)dτ s() = A c cos 2πf c + 2πk f 0 m(τ)dτ

14 frequency modulaion ampliude vs. frequency modulaion m(), message signal s(), DSB AM s(), FM

15 band-pass digial binary band-pass modulaion Three forms of signaling... Inpu Daa Ampliudeshif keying Phase-shif keying Frequencyshif keying

16 band-pass digial M = 4 (2-bi) band-pass modulaion Exend binary o include more daa... Inpu Daa Ampliudeshif keying Phase-shif keying Frequencyshif keying

17 M-ary level modulaion M-ary ampliude-shif keying (ASK) Inpu Daa Ampliudeshif keying 0 symbol A c sin (2πf c) symbol 01 s() = 0.8 A c sin (2πf c) symbol A c sin (2πf c) symbol 11 Similar o on-off keying Specrum conains a line componen a f = f c Does no need coheren deecor

18 M-ary level modulaion 2-level ampliude-shif keying (2-ASK)

19 M-ary level modulaion 4-level ampliude-shif keying (4-ASK)

20 M-ary level modulaion M-ary phase-shif keying (PSK) Inpu Daa Phase-shif keying +A c sin (2πf c) symbol 00 +A c cos (2πf c) symbol 01 s() = A c sin (2πf c) symbol 10 A c cos (2πf c) symbol 11 Similar o analog QAM Specrum conains no line componens Does need coheren deecor

21 M-ary level modulaion M-ary phase-shif keying (PSK) In general, M-ary PSK signals can be wrien as 2 s() = cos(2πf c + θ m) T s where θ m = 2π (m 1) m = 0, 1, 2,, M 1 M imag imag 10 imag M = 2 0 real 01 M = 4 00 real 001 M = real

22 M-ary level modulaion 2-level phase-shif keying (2-PSK)

23 M-ary level modulaion 4-level phase-shif keying (4-PSK)

24 M-ary level modulaion M-ary quadraure ampliude modulaion (M-QAM) In general we may arbirarily modulae boh ampliude and phase: s() = a m 2 T s cos(2πf c) + b m 2 T s sin(2πf c) 0 < T s Q 16-QAM Q 64-QAM I I

25 M-ary level modulaion 64 quadraure ampliude modulaion (64-QAM) Q 64-QAM I

26 Digial Communicaions 16-QAM, High SNR 16-QAM Quadraure In-phase (cosine), quadraure (sine) Each of 16 symbols represens 4 unique bi sequences (16 = 2 4 ) High raio of signal energy o noise energy (SNR) Low probabiliy of error (good!) In-phase

27 Digial Communicaions 16-QAM, Low SNR 16-QAM Quadraure SNR degrades Received sample poins no confined o wihin heir bins Probabiliy of error increases (bad!) In-phase

28 Digial Communicaions QPSK, Low SNR Quadraure QPSK In-phase Fall back o lower modulaion scheme Each of 4 symbols represens only 2 unique bi sequences (4 = 2 2 ) Probabiliy of error again reduced...bu a he expense of lower daa rae

29 M-ary level modulaion M-ary frequency-shif keying (FSK) Inpu Daa Frequencyshif keying A c cos (2πf 0) symbol 00 A c cos (2πf 1) symbol 01 s() = A c cos (2πf 2) symbol 10 A c cos (2πf 3) symbol 11 Similar o analog FM Specrum conains line componens a f = f 0, f 1, f 2, f 3 Unlike ASK and PSK, FSK increases bandwidh

30 M-ary level modulaion 2-level frequency-shif keying (2-FSK)

31 M-ary level modulaion 4-level frequency-shif keying (4-FSK)

32 sofware-defined radios wha is SDR? radiional radio design sofware radio design floa mod_index = 0.1f; // modulaion index in sc = 1; // suppress carrier? liquid_modem_amype ype = LIQUID_MODEM_AM_DSB; // creae/iniialize auomaic gain conrol agc_rrrf agc = agc_rrrf_creae(); // creae AM demodulaor objec ampmodem demod = ampmodem_creae(mod_index,ype,sc); // run demodulaor while (devices.rf.daa_availble()) { // pull inpu sample and apply gain conrol agc_rrrf_execue(agc, devices.rf.daa(), &y); // demodulae signal floa y; ampmodem_demodulae(demod, x, &y); } // push demodulaed oupu o sound ou device devices.sound.push(y); // desroy objecs agc_crcf_desroy(agc); ampmodem_desroy(demod);

33 sofware-defined radios arbirary linear consellaions Q Q Q I I I Q Q 0 Q I I I

34 numerically-conrolled oscillaor phase-locked loop real Sample Index inpu nco # include <liquid / liquid.h> //... in main() { // creae x/rx nco objecs nco_crcf nco_x = nco_crcf_creae(liquid_vco); nco_crcf nco_rx = nco_crcf_creae(liquid_vco); //... iniialize objecs... imag Sample Index inpu nco floa complex * x; unsigned in i; // loop as necessary { // generae complex sinusoid nco_crcf_cexpf(nco_x, &x[i]); // compue phase error floa dphi = nco_crcf_ge_phase(nco_x) - nco_crcf_ge_phase(nco_rx); phase error [radians] } // updae pll and nco objecs nco_crcf_pll_sep(nco_rx, dphi); nco_crcf_sep(nco_x); nco_crcf_sep(nco_rx); Sample Index } // desry nco objec nco_crcf_desroy(nco_x); nco_crcf_desroy(nco_rx);

35 arbirary filer design recursive/non-recursive Power Specral Densiy [db] Power Specral Densiy [db] G(ω) H(ω) Normalized Frequency Normalized Frequency, ω/2π Power Specral Densiy [db] Normalized Frequency arbirary non-recursive filer design (Parks-McClellan) improved square-roo Nyquis filers recursive filer design: Buerworh, Chebyshev-I/II, ellipic, Bessel

36 high-level communicaions srucures mulicarrier: OFDM (ofdmflexframe) header payload S0 S0... S1 H0 H1... P0 P1... P(n-1) ime guard band specral null pilo subcarrier Fs 0 Fs frequency fully configurable (like wih flexframe srucure) addiionally configurable subcarrier allocaion capable of noching specrum

37 high-level communicaions srucures mulicarrier: OFDM (ofdmflexframe), acual ransmission

38 high-level communicaions srucures mulicarrier: OFDM (ofdmflexframe), acual recepion

39 Resources websie: hp://ganymede.ece.v.edu projec: hp://gihub.com/jgaedder/liquid-dsp