ANALOG (DE)MODULATION Amplitude Modulation with Large Carrier Amplitude Modulation with Suppressed Carrier Quadrature Modulation Injection to Intermediate Frequency idealized system Software Receiver Design Johnson/Sethares/Klein 1 / 17
Analog Up and Downconversion Focus The message symbols to reconstructed symbols portion of the PAM digital communication system Pulse shaping Message w(kt) { 3, 1, 1, 3} Analog upconversion Interferers Noise Analog conversion to IF T s Digital down- conversion Decision to baseband reconstructed message f m(kt ) { 3, 1, 1, 3} Carrier synchronization Having begun at the center of the system with linear channel corruption modelling, e.g. indicated in figure above by the additive interferers and noise, we now spread out on both sides of the channel to consider the analog upconversion and downconversion (to IF). Software Receiver Design Johnson/Sethares/Klein / 17
Amplitude Modulation with Large Carrier analog message signal: w(t) transmitted/modulated signal: v(t) = A c w(t)cos(πf c t)+a c cos(πf c t) w(t) v(t) A c cos ( f c t) Software Receiver Design Johnson/Sethares/Klein 3 / 17
Amplitude... Large Carrier (cont d) transmitted signal spectrum: From (A.33) and (A.18) V(f) = 1 A cw(f+f c )+ 1 A cw(f f c )+ 1 A cδ(f f c )+ 1 A cδ(f+f c ) W(f ) 1 B f (a) B V(f ) (A c /) (A c /) A c f c B f c f c B f c B f c f c B f (b) Software Receiver Design Johnson/Sethares/Klein / 17
Analog... Large Carrier (cont d) demodulation with envelope detector: If w(t) 1, envelope of v(t) matches w(t). Using a nonlinearity and LPF as envelope detector in AMlarge produces Amplitude (a) message signal Amplitude 1 1 (b) carrier Amplitude (c) modulated signal Amplitude.1..3. Seconds.5 (d) output of envelope detector main advantage: carrier phase and frequency synchronization not needed at receiver main disadvantage: power needed for large carrier does not reinforce message signal Software Receiver Design Johnson/Sethares/Klein 5 / 17.6.7.8
Amplitude Modulation with Suppressed Carrier analog message signal: w(t) transmitted/modulated signal: v(t) = A c w(t)cos(πf c t) transmitted signal spectrum: From (A.33) V(f) = 1 A cw(f +f c )+ 1 A cw(f f c ) ideal demodulation with synchronized mixing and LPF: m(t) = LPF{v(t)cos(πf c t)} = 1 A cw(t) main advantage: extra power not needed for added carrier main disadvantage: carrier phase and frequency synchronization needed at receiver Software Receiver Design Johnson/Sethares/Klein 6 / 17
Analog... Suppressed Carrier (cont d) Example: Perfect (delayed) recovery with perfect synchronization using AM Amplitude 3 1 1 (a) message signal Amplitude (b) message after modulation Amplitude 3 1 1 (c) demodulated signal Amplitude 3 1 1.1..3..5.6.7.8.9.1 (d) recovered message is a LPF applied to (c) Software Receiver Design Johnson/Sethares/Klein 7 / 17
Analog... Suppressed Carrier (cont d) Transmitter/Modulator and Unsynchronized Receiver/Demodulator w(t) v(t) A c cos(pf c t) (a) v(t) x(t) LPF m(t) cos(p(f c + g)t + f) (b) (a) modulator; (b) demodulator Software Receiver Design Johnson/Sethares/Klein 8 / 17
Analog... Suppressed Carrier (cont d) Unsynchronized Demodulation: Using (A.33) x(t) = v(t)cos(π(f c +γ)t+φ) X(f) = A [ c e jφ {W(f +f c (f c +γ)) +W(f f c (f c +γ))} +e jφ {W(f +f c +(f c +γ)) +W(f f c +(f c +γ))}] = A c [ e jφ W(f γ)+e jφ W(f f c γ) ] + e jφ W(f +f c +γ)+e jφ W(f +γ) Software Receiver Design Johnson/Sethares/Klein 9 / 17
Analog... Suppressed Carrier (cont d) Unsynchronized Demodulation (cont d): If no frequency offset (γ = ), then with (A.) X(f) = A c Thus, [ ] (e jφ +e jφ )W(f) +e jφ W(f f c )+e jφ W(f +f c ) [ ] e jφ W(f f c )+e jφ W(f +f c ) = A c W(f)cos(φ)+ A c m(t) = LPF{x(t)} = A c w(t)cos(φ) Recovered signal is attenuated relative to perfectly synchronized demodulation. As φ approaches π/, recovered signal vanishes. Software Receiver Design Johnson/Sethares/Klein 1 / 17
Analog... Suppressed Carrier (cont d) Unsynchronized Demodulation (cont d): If no carrier offset (φ = ), X(f) = A c [W(f γ)+w(f f c γ) +W(f +f c +γ)+w(f +γ)] Thus, with m(t) = LPF{x(t)} M(f) = A c [W(f γ)+w(f +γ)] Using (A.33) m(t) = Ac w(t)cos(πγt). Recovered signal is low-frequency amplitude modulated relative to perfectly synchronized demodulation; periodically (every 1/γ sec) it vanishes. M(f) W(f g) A c W(f g) f Software Receiver Design Johnson/Sethares/Klein 11 / 17
Quadrature Modulation For a baseband message spectrum covering a chunk of positive frequencies B Hz wide, AM with suppressed carrier (aka double sideband or DSB) uses a B wide chunk of positive frequencies W(f ) 1 B (a) S(f ) B f 1/ f c B f c f c B f c B f c f c B (b) f Software Receiver Design Johnson/Sethares/Klein 1 / 17
Quadrature Modulation (cont d) To recover this lost bandwidth, consider transmitting two messages simultaneously one modulated by a cosine and the other by a sine v(t) = m 1 (t)cos(πf c t) m (t)sin(πf c t)] and demodulating using a cosine and a sine mixer each with LPF cos(pf c t) Transmitter Receiver cos(pf c t) m 1 (t) x 1 (t) LPF s 1 (t) m (t) x (t) LPF s (t) sin(pf c t) sin(pf c t) Software Receiver Design Johnson/Sethares/Klein 13 / 17
Quadrature Modulation (cont d) Evaluating receiver outputs: x 1 (t) = v(t) cos(πf c t) = m 1 (t) cos (πf c t) m (t) sin(πf c t) cos(πf c t) = m 1(t) (1+cos(πf c t)) m (t) (sin(πf c t)) s 1 (t) = LPF{x 1 (t)} = m 1(t) x (t) = v(t) sin(πf c t) = m 1 (t) cos(πf c t) sin(πf c t) m (t) sin (πf c t) = m 1(t) sin(πf c t) m (t) (1 cos(πf c t)) s (t) = LPF{x (t)} = m (t) If receiver mixers are not exactly 9 out of phase, cross-interference occurs. Software Receiver Design Johnson/Sethares/Klein 1 / 17
Injection to Intermediate Frequency Analog downconversion to an intermediate frequency can be accomplished by a mixer with a frequency above the carrier (called high-side injection) or below (called low-side injection) transmitted signal: v(t) = w(t)cos(πf c t) V(f) = W(f +f c )+W(f f c ) received signal: r(t) = v(t)+n(t) where n(t) includes various interferers mixing to IF: x(t) = r(t)cos(πf I t) downconverted spectrum: using (A.33) X(f) = V(f +f I )+V(f f I )+N(f +f I )+N(f f I ) = W(f +f c f I )+W(f f c f I )+W(f +f c +f I ) +W(f f c +f I )+N(f +f I )+N(f f I ) Software Receiver Design Johnson/Sethares/Klein 15 / 17
Injection... Frequency (cont d) Example: message spectrum W(f) positive frequencies khz carrier frequency f c = 85 khz intermediate frequency target 55 khz low-side injection frequency f I satisfies 55 f c f I = f I = 395 khz high-side injection frequency f I satisfies 55+f c f I = f I = 135 khz narrowband interferers at ±15 and ±178 khz Software Receiver Design Johnson/Sethares/Klein 16 / 17
Injection... Frequency (cont d) Example (cont d) (a) received IF, (b) low-side injection, (c) high-side injection V(f ) 178 85 15 15 85 178 f (khz) (a) X(f ) f (khz) 175 1385 15 55 9 9 55 15 1385 175 5 5 (b) X(f ) 385 156 11 1 55 55 1 11 156 385 f (khz) 75 75 (c) Both high and low side injection end up in this example with unwanted narrowband interferences in passband need for pre-mixer BPF NEXT... We examine sampling and an adaptive implementation of accompanying gain controller. Software Receiver Design Johnson/Sethares/Klein 17 / 17