Digital Modulation. Kate Ching-Ju Lin ( 林靖茹 ) Academia Sinica

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1 Digital Modulation Kate Ching-Ju Lin ( 林靖茹 ) Academia Sinica

2 Map bits to signals Modulation TX bit stream x(t) modula7on signal s(t) wireless channel

Map signals to bits Demodulation TX RX bit stream x(t) 1 0 1 1

3 Map signals to bits Demodulation TX RX bit stream x(t) modula7on demodula7on signal s(t) wireless channel

4 Data rate Bits per second Considerations Bandwidth requirement MHz Power efficiency t s(t) 2 Bit error rate Related to SNR (E b /N 0 ) Hardware cost

5 Sinusoid with Phase Shift Sinusoidal carrier with center frequency f c s(t) = cos(2πf c t) Sinusoid with phase shift s(t) = cos(2πf c t+φ)

6 Sinusoid with Phase Shift Sinusoidal carrier with center frequency f c s(t) = cos(2πf c t) Sinusoid with phase shift s(t) = cos(2πf c t+φ) = cos(φ)cos(2πf c t)-sin(φ)sin(2πf c t)

7 Sinusoid with Phase Shift Sinusoidal carrier with center frequency f c s(t) = cos(2πf c t) Sinusoid with phase shift s(t) = cos(2πf c t+φ) = cos(φ)cos(2πf c t)-sin(φ)sin(2πf c t) = s I *cos(2πf c t) s Q *sin(2πf c t)

8 Sinusoid with Phase Shift Sinusoidal carrier with center frequency f c s(t) = cos(2πf c t) Sinusoid with phase shift s(t) = cos(2πf c t+φ) = cos(φ)cos(2πf c t)-sin(φ)sin(2πf c t) = s I *cos(2πf c t) s Q *sin(2πf c t)

9 Sinusoid with Phase Shift Sinusoidal carrier with center frequency f c s(t) = cos(2πf c t) Sinusoid with phase shift s(t) = cos(2πf c t+φ) = cos(φ)cos(2πf c t)-sin(φ)sin(2πf c t) = s I *cos(2πf c t) s Q *sin(2πf c t) = s I *cos(2πf c t) s Q *cos(2πf c t+π/2) s I and s Q are in-phase and quadrature components of the signal s(t), respectively

10 Modulator

11 Demodulator

12 Constellations cos(2πf c t+φ) = cos(φ)cos(2πf c t)-sin(φ)sin(2πf c t) = s I *cos(2πf c t) s Q *sin(2πf c t) Constellation point on I-Q plane (s I,s Q ) = (cos(φ), sin(φ)) φ=0 Q φ=π/4 Q φ=π/2 Q φ=π Q I I I I Delay in )me domain = Phase shi1 in frequency domain = Rota)on in I- Q plane

13 Types of Modulation s(t) = Acos(2πf c t+φ) Amplitude ASK: Amplitude Shift Keying Frequency FSK: Frequency Shift Keying Phase M-PSK: Phase Shift Keying Amplitude + Phase M-QAM: Quadrature Amplitude Modulation

14 Amplitude Shift Keying (PSK) Represent samples using different amplitudes 1 à A=1, 0 à A=0 TX RX bit stream s(t) modula7on demodula7on signal s(t)

15 PSK Pros Easy to implement Energy efficient Low bandwidth requirement Cons Low data rate bit-rate = baud rate 1 baud 1 second High error probability Hard to pick a right threshold

16 Types of Modulation s(t) = Acos(2πf c t+φ) Amplitude ASK: Amplitude Shift Keying Frequency FSK: Frequency Shift Keying Phase M-PSK: Phase Shift Keying Amplitude + Phase M-QAM: Quadrature Amplitude Modulation

f=f 1, 0 à f=f 2 TX RX bit stream s(t) 1 0

17 Frequency Shift Keying (FSK) Represent samples using different frequencies 1 à f=f 1, 0 à f=f 2 TX RX bit stream s(t) modula7on demodula7on signal s(t)

18 Pros Easy to implement FSK Better noise immunity than ASK Cons Low data rate Bit-rate = baud rate Require higher bandwidth BW(min) = N b + N b

19 Types of Modulation s(t) = Acos(2πf c t+φ) Amplitude ASK: Amplitude Shift Keying Frequency FSK: Frequency Shift Keying Phase M-PSK: Phase Shift Keying Amplitude + Phase M-QAM: Quadrature Amplitude Modulation

20 BPSK Represent samples using different phases 1 à φ=0, 0 à φ=π TX RX bit stream s(t) modula7on demodula7on signal s(t)

21 Constellation Points for BPSK 1 à φ=0 0 à φ=π cos(2πf c t+0) = cos(0)cos(2πf c t)-sin(0)sin(2πf c t) = s I *cos(2πf c t) s Q *sin(2πf c t) cos(2πf c t+π) = cos(π)cos(2πf c t)-sin(π)sin(2πf c t) = s I *cos(2πf c t) s Q *sin(2πf c t) φ=0 Q φ=π Q I I (s I,s Q ) = (1, 0) 1 à 1+0i (s I,s Q ) = (- 1, 0) 0 à - 1+0i

22 Demodulate BPSK Map to the closest constellation point 0 Q 1 n 0 s =a+bi n 1 s=1+0i I n 1 = s - (1+0i), n 0 = s - (- 1+0i) Since n 1 < n 0, map s to (1+0i) = 1

23 Decoding error Demodulate BPSK 0 Q 1 s =a+bi s=1+0i I Incorrectly map s to (- 1+0) = 0

24 SNR vs. BPSK BER Q s = a+bi n I SNR = s' 2 2 n = s' 2 s' s = 2 SNR db =10log 10 (SNR) " Bit error rate: P b = Q$ # a + bi (a + bi) (1+ 0i) 2 E b N 0 % ' & 2

25 Quadrature PSK (QPSK) Use 2 degrees of freedom in I-Q plane Represent two bits as a constellation point Rotate the constellations by π/2 Double the bit-rate No free lunch: Higher error probability (Why?) Q I 11 10

26 Quadrature PSK (QPSK) Maximum power is bounded Amplitude of each point should still be 1 Q Bits Symbols = 1/ 2(1+1i) 00 1/ 2+1/ 2i I 01-1/ 2+1/ 2i 10 1/ 2-1/ 2i 11-1/ 2-1/ 2i

27 Higher BER in QPSK For a particular error n, the symbol could be decoded correctly in BPSK, but not in QPSK Why? Each sample only gets half power. Q 0 1 x1 x0 Q n 1 I I n in BPSK 1/ 2 In QPSK! Bit error rate: P b = 2Q# " 2E b N 0 $ ( &* % 1 1 ) 2 Q 2E b N 0 + -,

28 Types of Modulation s(t) = Acos(2πf c t+φ) Amplitude ASK: Amplitude Shift Keying Frequency FSK: Frequency Shift Keying Phase M-PSK: Phase Shift Keying Amplitude + Phase M-QAM: Quadrature Amplitude Modulation

29 Quadrature Amplitude Modulation Change both amplitude and phase s(t)=acos(2πf c t+φ) Q Bits Symbols a a I 1000 s 1 =3a+3ai 1001 s 2 =3a+ai 1100 s 3 =a+3ai s 4 =a+ai QAM 1010 expected power: E! 2 s # " i $ =1 64-QAM: 64 constellation points, each with 8 bits

30 BER Comparison ~3dB Require extra 3dB to ensure P b =0.001

31 Modulation in a 6 mb/s: BPSK + ½ code rate 9 mb/s: BPSK + ¾ code rate 12 mb/s: QPSK + ½ code rate 18 mb/s: QPSK + ¾ code rate 24 mb/s: 16-QAM + ½ code rate 36 mb/s: 16-QAM + ¾ code rate 48 mb/s: 64-QAM + ⅔ code rate 54 mb/s: 64-QAM + ¾ code rate FEC (forward error correction) k/n: k-bits useful information among n-bits of data Decodable if any k bits among n transmitted bits are correct

32 Bit-Rate Selection throughput r = (1-PER r,snr ) * r = (1-BER r,snr ) N *r r* = arg max throughput r

33 Bit-Rate Selection best rate Adapt bit-rate to dynamic RSSI

Wireless Communication

Wireless Communication Systems @CS.NCTU Lecture 2: Modulation and Demodulation Reference: Chap. 5 in Goldsmith s book Instructor: Kate Ching-Ju Lin ( 林靖茹 ) 1 Modulation From Wikipedia: The process of varying