1 1.1 1.2 Fourier 1.3 1.4 1.5 Fourier 1.6 1.6.1 1.6.2 1.7 1.7.1 (cumulative distribution function cdf) 1.7.2 1.8 1.9 1.10 dB 1.11 1.11.1 1.11.2 1.11.3

2 2.1 2.2 2.2.1 2.2.2 2.2.3 2.3 2.3.1 2.4 bit 2.4.1 Gray 2.5 2.6 2.6.1

3 3.1 3.2 Nyquist 3.3 3.4 3.5 3.5.1 3.6 3.6.1

4 4.1 (ASK) 4.1.1 ASK 4.1.2 4.1.3 4.1.4 ASK 4.1.5 4.2 (FSK) 4.2.1 FSK 4.2.2 FSK 4.2.3 FSK 4.2.4 FSK 4.2.5 FSK 4.2.6 FSK 4.3 (PSK) 4.3.1 PSK 4.3.2 PSK 4.3.3 PSK 4.3.4 PSK 4.3.5 PSK 4.3.6 PSK 4.3.7 PSK 4.4

5 5.1 ( ASK) 5.1.1 ASK 5.2 ( FSK) 5.2.1 5.2.2 FSK 5.2.3 FSK 5.3 ( PSK) 5.3.1 QPSK 5.3.2 QPSK 5.3.3 QPSK 5.3.4 QPSK (DQPSK) 5.3.5 /4QPSK 5.3.6 OQPSK 5.3.7 PSK 5.3.8 PSK 5.4 QAM 5.4.1 QAM 5.4.2 QAM 5.4.3 QAM 5.4.4 QAM PSK 5.4.5 Gray 5.4.6 Shannon

1

1.1

: . , , , . . , . Fourier ( ) Fourier ( ).

1.2 Fourier

Fourier , x(t)=x(t+T), T , :

x(t) : cn : 0, n bn :

an bn :

qn an bn :

1.3

(spectrum) . , , . 11. . sinc(n/) .

f=n/T, . f Fourier . 11 (f0=1/T), 11 Fourier , f=1/T =2p f.

11. Fourier . : . : :

,

.

, Fourier : . =T/2 : : : Fourier . : : Fourier . (: dc ).

1.4

.

sinc bit . ( .)

, , , .. , (raised cosine frequency response). Fourier .

1.5 Fourier

. x(t) Fourier, :

Fourier, :

. : Fourier (t|) : : .

Fourier 12.

12. Fourier. 13 Fourier .

1

sinc

13. Fourier . : Fourier , Fourier dirac (). : dirac t0

, 1, A=1.

, Fourier :

, : [1]

dirac

.

1.6

. , (carrier) .

1.6.1 () , : 1,0,1,0, , . , . , .

1.6.2 , , . (vector modulator).

12. . , , : 0.1dB . dB, , ; : , .

cos(ot) sin(ot) A cos(ct) (A+dA) sin(ct) (inphase) : (quadrature) : A cos(ct) cos(ot) = [cos(c+o)t + cos(co)t] 20 log(A+dA) 20 log(A) = 0.1 = 1.0115 20 log dA = 0.011579A. + = A cos(c+o)t + =A cos(c+o)t + = cos(c+o)t + cos(c+o)t cos(co)t cos(co)t [cos(c+o)t cos(co)t] = cos(c+o)t cos(co)t : = : 10log = 10log = 22.4dB. : 5 . , d, , ; (: (amplitude ratio) , 525:1 27dB). cos(c+o)t + cos(c+o) t cos(co)t + cos(co)t + cos(co)t cos(c+o)t = A cos(co)t + cos(co)t cos(co)t [ cos(co)t cos(c+o)t] cos(c+o)t cos(co)t = cos(co)t = : = 0.1 [ cos(co)t cos(c+o)t]

1.7

. i (=i) , .

1.7.1 (cumulative distribution function cdf) Px (x=x i) x xi. Fx (x i)=P x (x xi), x xi. :

: 0, l F (x ) x i l l l

Fx ( Fx (

) = 1, ) = 0, Fx (x 2) x1 x2.

Fx (x 1)

1.7.2 H (probability density function pdf) p : ,

1.7.2.1. : , 2 . :

Q(z) : , Q 13. , :

13. Q. Q (complementary error function erfc), : Q() 14, , .

14. Q.

1.8

, N(f), 15. 15. . (f)= Watts/Hz . , (Additive White Gaussian Noise AWGN). AWGN BW . ,

1.9

: : :

1.10

dB

, , , , , . , . ,

dB. P dB Pref. , 1mW P=1W=1000mW, 30dBmW. 1W, P=1W, 0dBW. , : , 1V V1=1V=1,000,000V, 120dBV. 1mV, V1=1V=1,000mV, 60dBV. dB . , PS PN, : PS =1W PN=1pW, S/N=60dB. , :

1.11

1.11.1 , , y(t) x(t) , . [] ( ) []. , x(tt0), y(tt0). x(t) y(t) h(t)H(f) 1.11.2 . (forcing function) Dirac. , y(t)=h(t) x(t)=(t). .

: t. , : t0, nt=, : .

1.11.3 Fourier , : H(f)= [h(t)] (transfer function) (frequency response) . , Fourier, h(t) H(f). : |H(f)| [2] q(f) . |H(f)| . , h(t) ,

2

2.1

, , :n n n

( , , ). . .

2.2

. . 1 0, 2 .

2.2.1 . ( ; ) , 21.

21. . , . , .

2.2.2

, . ( ; ) . =2n (n=2) bit (00 , 01 , 10 , 11 ).

22. . , . . . , . , .

2.2.3 : n .n

/ , (, ) .

2.3

(information transfer rate): (bit) [bits/sec]. (baud rate): [symbols/sec baud]. ( bandwidth efficiency): [bits/sec/Hz]. ( ) .

2.3.1 n bit : = 2n, . () 23.

23. . :n

( C). , ( ), . ( .)

n

:n

, . . / .

n n

2.4 bit

bit , bit. (>2) . , . bit .

2.4.1 Gray Gray bit, bit. , bit k bit , .

2.5

, . , 24 0 Hz B Hz.

24. . (channel passband) Hz , , TS . () 2 log 2M bits, Hz :

2.6

, / . (signal power S to noise power N ratio) . Shannon Hartley: ShannonHartley S/N C, . , AWGN .

2.6.1 S=E b C, Eb bit (Watts/bit). =0 , 0 (Watts/Hz). ShannonHartley :

Eb/0 bit . ShannonHartley , 25.

25. ShannonHartley.

3

Fourier . . , 31.

31. .

3.1

(intersymbol interference). 32.

32. . . , , , (irreducible error rate).

3.2 Nyquist

, . ( , ) Nyquist, . Nyquist fs =1/2Ts ( 33).

33. Nyquist. Nyquist, , ( 34).

34. Nyquist. , ( 35). .

35. Nyquist. , , Nyquist . modem , . (adaptive equalizers) Nyquist. modem 9.6kbps , .

3.3

. . , . , . 36.

36. . . 37 , .

37. . 38.

38. .

3.4

Nyquist. , ( ) . . : 39.

39. . 0 1, 0 , 1 Nyquist. , . 310.

310. . : 100s. , =0.33; bits; : 1/10106 100,000 symbols/sec. 3 bit , bit 300,000 bits/sec. Nyquist . . (finite impulse responseFIR) .

3.5

. (zerocrossing).

311. .

, =1. , TS/2 ( 312) . TS/2 , . 1 0, .

3.5.1 =1 . , . , . 312.

312. . TS/2 . , . dc , .

3.6

. .

313. . . , .

. , AWGN , :

314. . , , : SNR 0 AWGN. Nyquist [3] , , . ,

3.6.1 () bits (Bit Error RatioBER) [ BER bits ] . AWGN V0 0 V1 1, :

315. AWGN. : 1 0 0 1 :

, . 1 Q, (1)=Q, (0)=1Q, . 0 1 , Q=0.5 :

0 1. . PE :

3.6.1.1.BER NRZ

V1=V, V0=0. , b i t . , (3.8) PE BER :

3.6.1.2.BER

V1=V, V0=V. H b i t . , (3.8) PE BER :

316 PE ES/N0 . . , E /N =10dB, P =103 P =106 . S 0 E E

316. BER .

3.6.1.3.BER PE BER :

317. BER 2, 4 8 . 317 PE Eb/N0 2, 4 8 . Eb=S/k, k bit .

: modem 2 8 , PE PE =1x10 4. (: x=3.85, Eb/No=51.878 17.15dB, x=3.72, E b/No=6.92 8.4 dB, 17.158.4=8.75dB)

4

0 Hz (bandpass signalling). . , / (carrier).

41. .

4.1 (ASK)

(Amplitude Shift KeyingASK). . ASK , ONOFF (OnOff KeyingOOK).

42. .

. ASK 1bit/s/Hz, .

4.1.1 ASK ASK . , , :

43. .

4.1.2 ASK, (envelope) . , , 44.

44. ASK. (quadrature) 45 .

45. . , . : (t).

4.1.3 (coherent detector) . 46.

46. . : (phase coherent) , ( =0), (t) .

4.1.4 ASK . (phase locked loopPLL), 47.

47. ASK. : ) (voltage controlled oscillatorVCO) , ) , ) . PLL . / , / VCO, . VCO .

4.1.5 ( ) ASK. ASK , ( 0) ( 1). , . ASK 48.

48. ASK . ASK . ON ( 1) =60, 49.

49. .

, ,

,

. , ,

. ,

. . ASK : , ASK bit :

.

BER Eb/No ASK 410.

410. ASK.

4.2 (FSK)

(Frequency Shift Keying FSK) , , . FSK , . FSK , .

4.2.1 FSK FSK , . . FSK (VCO). , . FSK FSK (Conntinuous Phase FSK, CPFSK).

411. FSK.

4.2.2 FSK FSK . FSK ASK FSK . 412 FSK. 412. FSK. FSK , Fourier. , CPFSK, , FSK . FSK , . FSK Sunde Minimum Shift Keying (MSK), . FSK Sunde, , . . MSK, , .

413. Sunde FSK MSK. MSK QPSK (Quadrature Phase Shift Keying), . MSK FSK, .. FSK Sunde. MSK ( ). , (Gaussian filter) MSK, Gaussian Minimum Shift Keying ( GMSK), . 414 GMSK.

414. GMSK. GMSK 2 GSM ( Global Standard for Mobile) . , 2 , GMSK.

4.2.3 FSK FSK , , .

415. FSK. ASK, . , ASK, FSK.

4.2.4 FSK FSK ASK, . ASK, . ,

. FSK Sunde FSK 1.5 2 ASK PSK .

416. FSK.

4.2.5 FSK FSK 417. bit ASK, . . FSK bit

417. bit FSK.

4.2.6 FSK FSK : l FSK ( ) .l

FSK . FSK Doppler.

FSK : FSK ASK PSK. bit FSK PSK.

4.3 (PSK)

(Phase Shift Keying PSK) .

, PSK (coherent PSK). PSK (Binary PSK, BPSK) 0 180. ( ) . (Differentially Coherent PSK).

418.

419. . BPSK ASK, . , BPSK ASK + + 0 ASK. FSK , . , .

4.3.1 PSK PSK 420. , , . .

420. PSK. PSK . PSK. . PSK (RRC). , , PSK.

421. PSK. modem, .

4.3.2 PSK PSK . , . ASK, , cos(). Eb/No cos 2(). . 90, .

422. PSK.

4.3.3 PSK 0, , .

423. PSK. BPSK, 0 180 modulo 2, . . , . , .

424. PSK. (=2 PSK), , modulo 2. , , . PSK, . PLL . , , () (phase jitter) . Costa. Costa ( Costas loop), . Costas (PLLs) VCO . PSK modulo 2 2 Costas . Costas : l .l

PLL, .

Costas .

4.3.4 PSK PSK (DPSK) , DEPSK, , . PSK DPSK DEPSK, . " " .

425. PSK. PSK DPSK modem ( 4800 bps). DPSK, , PSK, DPSK , , .

4.3.5 PSK (binary) (ASK, FSK PSK) , , . , modem, , , .

426. .

4.3.6 PSK PSK (antipodal signalling), .

427. PSK.

4.3.7 PSK PSK DPSK 428. PSK , bit PSK PSK, . , 2bits/s/Hz , 1/bit/s/Hz PSK, ASK FSK. 2bits/s/Hz, . , QPSK, PSK , BPSK! QPSK BER Eb/N0. . DPSK .

428. bit PSK.

4.4

429 . PSK , FSK ASK.

429. . Eb/N0 1bit/s/Hz ShannonHartley, Eb/N0=0dB, modem . , , ShannonHartley. .

5

, ( FSK, ). . (ary) , , (QAM), , .

51. .

5.1 ( ASK)

ASK ASK , , , . ASK , ASK.

52. ASK.

5.1.1 ASK (symbol sets) ASK, , . ASK . ASK , ASK .

53. ASK.

5.2 ( FSK)

ASK , FSK , FSK . , , . FSK modem Shannon / 1.6dB.

b

54. FSK. FSK , FSK. , , , FSK (BFSK). FSK , , .

5.2.1 i(t) j (t) ( ), :

FSK :

m=1, 2, 3, , , . , i(t) j (t), , , . , .

55. . , , . , , S/N , . FSK , .

5.2.2 FSK FSK ( ), , . , . b/ ShannonHartley 1.6dB .

56. FSK.

5.2.3 FSK FSK :

. 57, FSK, .

57. FSK.

5.3 ( PSK)

FSK , . , , , . PSK , . , .

58. (QPSK). PSK , 0, 90, 180 270, (quadrature) 90 . PSK (Quadrature Phase Shift Keying, QPSK). QPSK BPSK , BPSK.

5.3.1 QPSK QPSK . BPSK . , bit . . .

59: Offset QPSK. 45 BPSK.

5.3.2 QPSK QPSK 90 2 (modulo 2). , .

510: QPSK .

5.3.3 QPSK BPSK bit QPSK BPSK. , , , (crosstalk) . , QPSK BPSK . , QPSK BPSK , QPSK BPSK. QPSK, 2 bit , bit Gray. , bit QPSK , , : bit QPSK, 511.

511. QPSK.

5.3.4 QPSK (DQPSK) BPSK, QPSK. ,

, .., (preambles) , . QPSK, . DPSK BPSK . DQPSK QPSK. , DQPSK QPSK, . . DQPSK .

5.3.5 /4QPSK QPSK, 4 /4 . , . 512 /4QPSK.

512. /4QPSK. , RF , modem /4QPSK QPSK. 513 /4QPSK .

513. /4QPSK QPSK.

5.3.6 OQPSKH OQPSK ( Offset QPSK) , . QPSK. , . 514 /4QPSK

.

514. OQPSK QPSK. , /4QPSK OQPSK QPSK, .

5.3.7 PSK 515 QPSK ( ) MSK. . MSK QPSK, MSK . MSK (.. 2 GSM.)

515. QPSK MSK. QPSK , , , . , MSK, .

5.3.8 PSK PSK , , . , >4 , . PSK :

bit 516. .

516. PSK.

5.4 QAM

, , . APK (Amplitude and Phase Keying) QAM (Quadrature Amplitude Modulation), . 16 APK QAM, 517.

517. 16APK 16QAM.

5.4.1 QAM QAM QPSK, ( 90) , + . , 3, 16 , .

518. 16QAM. ASK. ASK .

5.4.2 QAM QAM , QPSK, . 519 QAM, QPSK . .

519. 16QAM. , .

5.4.3 QAM QAM, : : 520.

520. QAM. , bit QAM, :

5.4.4 QAM PSK QAM PSK, . 16QAM 16PSK 16 QAM 3. P P=V2/Z, V Z , 4 :

, , 1/16 , : 16PSK : , 16QAM 2, =1.62.

, . 16 ,

.

16PSK 22.5 :

521. 16QAM 16PSK . , , 16QAM

16PSK, 16QAM bit 16PSK Eb/N0. , 522, QAM PSK .

522. QAM PSK.

5.4.5 Gray Gray, bit ( ) bit, , 523.

523. 16QAM Gray.

5.4.6 Shannon Shannon.

524. Shannon.

, Shannon, 4dB. Shannon, , . FEC ( Forward Error Correction) block (.. ReedSolomon ) (.. Viterbi ). , (.. Trellis Coded Modulation TCM) 6dB, Shannon.

[1]. Bateman, A., Digital Communications Design for the Real World, Prentice Hall, 1998. [2]. Haykin, S., Communication Systems, 7 th Edition, John Wiley & Sons, 2000. [3]. Proakis, J. G. and Salehi, M., Digital Communications, 5 th Edition, McGraw Hill Higher Education, 2008. [4]. Schwartz, M., Information, Transmission, Modulation and Noise, McGraw Hill, 1990. [5]. Papatsoris, A. D., Digital Communications, Course Notes, Department of Electronics, University of York, U.K., 1999. [1] dirac. [2] Fourier. [3] Schwartz, M., Information, Transmission, Modulation and Noise, McGrawHill, 1990.