Modulation Evan Everett and Michael Wu ELEC 433 - Spring 2013

Modulation Evan Everett and Michael Wu ELEC 433 - Spring 2013 Questions from Lab 1? Modulation x(t) = A sin(ωt + φ) Carrier Data 10100 Modulation • Goal: overlay data onto carrier signal (sinusoid) • Sinusoids have two very accessible parameters • Modulate amplitude and phase Modulation Why not? 1) Interference avoidance 2) High freq → small antennas Data 10100 Modulation • Goal: overlay data onto carrier signal (sinusoid) • Sinusoids have two very accessible parameters • Modulate amplitude and phase Signal Representation: Phasor • Polar: Amplitude & Phase • Rectangular: “In-phase” (I) & “Quadrature” (Q) Am pl itu de π/2 Q Im[x] Phase π I Re[x] -π/2 x(t) = A sin(ωt + φ) x(t) = I cos(ωt) + Q sin(ωt) I = A sin(φ) Q = A cos(φ) Signal Representation • Rectangular (I,Q) form suggests a practical implementation I Q Im[x] cos(ωt) 10100 I Re[x] I cos(ωt) + Q sin(ωt) 90˚ sin(ωt) Q • Modulation = mapping data bits to (I,Q) values Digital Modulation [01] [10] [00] [11] • Maps bits to complex values (I/Q) (focus of the Lab 3) • Complex • Set •# modulated values are called “symbols” of symbols is called “constellation” or “alphabet” of symbols in constellation is “modulation order”, M • M-order constellation can encode bits per symbol Digital Modulation [01] [10] [00] [11] • Maps bits to complex values (I/Q) (focus of the Lab 2) • Complex • Set •# modulated values are called “symbols” of symbols is called “constellation” or “alphabet” of symbols in constellation is “modulation order”, M • M-order constellation can encode log2(M) bits per symbol Phase Shift Keying (PSK) • Encodes information only in phase BPSK (M =2) QPSK (M =4) 8-PSK (M =8) [000] [00] [10] [0] • Constant [01] [001] [11] [1] power envelope • Pros: no need to recover amplitude, no need for linear amplifier • Con: wastes amplitude dimension Quadrature Amplitude Modulation (QAM) • Encodes • information in both amplitude and phase (I,Q) Mì 4-QAM ã M grid 16-QAM Common in wideband systems: 64-QAM 802.11b 802.11g/n 802.11ac 16-QAM 64-QAM 256-QAM Bit-to-Symbol Mapping • Confusing • with neighbor is most likely error Best to minimize bit-difference between neighbors • Gray Coding • Neighboring symbols differ by only one bit • Extra performance at zero cost (this is rare!) Natural-coded QPSK [01] [10] [00] [11] Gray-coded QPSK [01] [11] [00] [10] Tradeoff: Rate vs Error Probability • By increasing modulation order, M, we get: • More data in same bandwidth :) • Lower noise tolerance (i.e higher error probability) :( • Therefore, SNR dictates feasible constellation size QPSK: bits/symbol Q I QPSK: bits/symbol Q I 16-QAM: bits/symbol Q I 64-QAM: bits/symbol Q I Bit error rate (BER) vs SNR per bit (Eb/N0) 1E+00 BPSK QPSK 8-PSK 16-QAM 64-QAM 1E-01 1E-02 BER 1E-03 1E-04 1E-05 1E-06 1E-07 1E-08 1E-09 10 12 Eb/N0 (dB) 14 16 18 ... Q I 16-QAM: bits/symbol Q I 64-QAM: bits/symbol Q I Bit error rate (BER) vs SNR per bit (Eb/N0) 1E+00 BPSK QPSK 8-PSK 16-QAM 64-QAM 1E-01 1E-02 BER 1E-03 1E-04 1E-05 1E-06 1E-07 1E-08 1E-09 10... Modulation (QAM) • Encodes • information in both amplitude and phase (I,Q) Mì 4-QAM ã M grid 16-QAM Common in wideband systems: 64-QAM 802.11b 802.11g/n 802.11ac 16-QAM 64-QAM 256-QAM Bit-to-Symbol... rare!) Natural-coded QPSK [01] [10] [00] [11] Gray-coded QPSK [01] [11] [00] [10] Tradeoff: Rate vs Error Probability • By increasing modulation order, M, we get: • More data in same bandwidth :)