Lecture 8 Demodulation Heterodyne Demodula- tion Output Sample Shot Noise in Output Lecture 8 Sample Sample Chapter 8 and 10 Statistic Shot Noise Limit Homodyne Demodula- tion One Signal Component Shot Noise Limit Two Signal Components Shot Noise for Direct Conversion 1 ECE243b Lightwave Communications - Spring 2019 Lecture 8
Direct to Baseband Demodulation Lecture 8 Demodulation Heterodyne Demodula- tion Output Sample Balanced photodetector shown in Figure ?? implements homodyne demodulation Shot Noise in Output of only one component of the baseband signal Sample Sample A separate different balanced photodetector based on a 90-degree hybrid coupler Statistic Shot Noise must be used to homodyne demodulate a lightwave waveform directly into a Limit complex-baseband electrical waveform Homodyne Demodula- tion Recall that the real part of the complex-baseband signal s I ( t ) is the One Signal cosine-modulated component of the waveform � s ( t ) Component Shot Noise Limit The imaginary part s Q ( t ) is the sine-modulated component of the waveform � s ( t ) Two Signal Components Shot Noise for Direct Conversion 2 ECE243b Lightwave Communications - Spring 2019 Lecture 8
Linear Lightwave Demodulation - component level Lecture 8 Demodulation Heterodyne Demodula- tion z 11 Output Electrical Signals Sample Photodetector Shot Noise + in Output Lightwave i I (t) z 12 Sample _ Signal Photodetector Sample Statistic s(t)=s I (t)+s Q (t) 90-degree Shot Noise hybrid coupler Limit z 21 Local Homodyne Photodetector Demodula- + oscillator i Q (t) tion z 22 s LO (t) _ One Signal Photodetector Component Shot Noise Limit Figure: A balanced photodetector for the demodulation of the in-phase and quadrature Two Signal components based on a 90-degree hybrid coupler. Components Shot Noise for Direct Conversion 3 ECE243b Lightwave Communications - Spring 2019 Lecture 8
Linear Lightwave Demodulation - functional level Lecture 8 Demodulation Heterodyne Demodula- tion Output Sample s I ( t ) Baseband Shot Noise in Output Signal for the Sample I -component + Sample cos(2 πf c t ) s I ( t ) cos(2 πf c t ) Statistic s I ( t ) + i s Q ( t ) + Shot Noise − s Q ( t ) sin(2 πf c t ) − 90 o Limit Complex 2 - Baseband Baseband s Q ( t ) Homodyne Signal Signal for the Demodula- Q -component tion One Signal Component Shot Noise Figure: Functional block diagram of a phase-synchronous demodulator. Limit Two Signal Components Shot Noise for Direct Conversion 4 ECE243b Lightwave Communications - Spring 2019 Lecture 8
Heterodyne Demodulation Block Diagram Lecture 8 Demodulation Heterodyne Demodula- tion (a) Optical Electrical Output Sample s ( t ) + n o ( t ) Shot Noise Balanced Electrical in Output � r ( t ) r ( t ) = r I ( t ) + i r Q ( t ) Photodetector Demodulation Sample s LO ( t ) Sample Statistic Shot Noise � s ( t ) Limit B (b) Homodyne n ( t ) Demodula- tion − f c − f c f c f c − f IF f IF One Signal Lightwave signal before noise filtering Lightwave signal after noise filtering Electrical signal after Component heterodyne demodulation Shot Noise Limit Figure: Functional block diagram of phase-synchronous heterodyne demodulation of a lightwave Two Signal Components signal. (a) Block diagram of a lightwave passband demodulator. (b) Signal and noise spectra Shot Noise after each stage along with the passband signal bandwidth B . for Direct Conversion 5 ECE243b Lightwave Communications - Spring 2019 Lecture 8
Heterodyne Demodulation Block Diagram Lecture 8 Demodulation Using ( ?? ) with a = � s ( t ) + n o ( t ) � e i2 πf c t and b = A LO e i2 πf LO t with Heterodyne Demodula- f LO = f c − f IF , the passband electrical waveform � tion r ( t ) can be written as (cf. Output ( ?? )) Sample A LO Re �� h ( t ) ⊛ s in ( t ) + n o ( t ) � e i2 πf IF t � Shot Noise in Output � r ( t ) = (1) Sample A LO Re �� s ( t ) + n o ( t ) � e i2 πf IF t � Sample = (2) Statistic A LO s ( t ) cos � 2 πf IF t + φ s ( t ) � Shot Noise + A LO � Limit = n IF ( t ) , (3) Homodyne Demodula- where the passband noise process � n IF ( t ) = Re [ n o ( t ) e i2 πf IF t ] is centered at the tion One Signal intermediate frequency f IF = f c − f LO Component Shot Noise Limit Additional noise filtering, now in the electrical domain, may be used on this Two Signal passband electrical waveform Components Shot Noise for Direct Conversion Show in Chapter 9 that for additive white gaussian noise, the impulse response of the detection filter that maximizes the sample signal-to-noise ratio, called a matched filter is a time-reversed replica of the received pulse waveform 6 ECE243b Lightwave Communications - Spring 2019 Lecture 8
Output Pulse Energy used for Symbol Detection Lecture 8 The peak output of a matched filter to an input pulse is 2 E p / N 0 Demodulation E p in the electrical pulse energy (not bit energy yet.) Heterodyne N 0 is the power density spectrum of the white noise Demodula- tion The energy E p in the passband electrical pulse is (cf. Chapter 2) Output Sample � ∞ Shot Noise in Output � r 2 ( t ) d t E p = Sample Sample −∞ � ∞ Statistic 2 s 2 ( t ) cos 2 � 2 πf IF t + φ s ( t ) � Shot Noise 1 = 4 r LO d t Limit Homodyne −∞ Demodula- = 2 r LO W p (4) tion = One Signal 2 r LO e W p (5) Component Shot Noise Limit r LO = A 2 LO / 2 is the photodetected electrical signal generated from the lightwave Two Signal Components local oscillator signal, Shot Noise rapidly-varying cosine carrier averages to one half � ∞ for Direct W p = 1 −∞ s 2 ( t ) d t is the directly-photodetected photocharge in the received Conversion 2 lightwave pulse s ( t ) . W p = W p / e number of photoelectrons Express using photoelectrons to make including shot noise easier 7 ECE243b Lightwave Communications - Spring 2019 Lecture 8
Noise in Output Sample Lecture 8 Demodulation Heterodyne Demodula- tion Output The noise term N 0 includes: Sample Shot Noise additive lightwave noise, in Output shot noise, Sample additive electrical noise Sample Statistic When the bandwidth of the noise filter is large, statistical properties of � Shot Noise n IF ( t ) are Limit the same as the incident spontaneous emission noise before optical noise-limiting Homodyne filter Demodula- tion true when the local oscillator is deterministic One Signal Component Consequently, the electrical-noise power density spectrum N 0 caused by Shot Noise Limit spontaneous emission is proportional to the lightwave-noise power density Two Signal spectrum N sp after the noise filter Components Shot Noise for Direct Conversion 8 ECE243b Lightwave Communications - Spring 2019 Lecture 8
Noise Term - cont. Lecture 8 Demodulation Heterodyne Demodula- tion Output Sample Shot Noise For a photodetector with a responsivity R , the electrical-noise power density in Output Sample spectrum N 0 can be written in several equivalent forms Sample Statistic 2 R 2 P LO N sp = N 0 Shot Noise Limit = 2 er LO W n , (6) Homodyne Demodula- where R N sp = ( ηe / hf ) N sp = ηe N sp = e W n , and W n = η N sp tion One Signal Component N sp is the expected number of noise photons, and W n is the expected number of Shot Noise Limit noise photoelectrons generated during photodetection Two Signal Components Shot Noise for Direct Conversion 9 ECE243b Lightwave Communications - Spring 2019 Lecture 8
Shot Noise in Sample Lecture 8 Demodulation Heterodyne Demodula- tion The amount of shot noise depends on the total incident lightwave power, and on Output Sample the local oscillator power Shot Noise in Output Sample When the LO power ≫ signal power or ≫ additive spontaneous emission power: Sample shot noise can be modeled is stationary, independent of the incident lightwave signal, Statistic accurately modeled as an additive white gaussian noise process with an electrical power Shot Noise density spectrum (Chapter 6) Limit Homodyne = (7) N shot 2 er LO . Demodula- tion One Signal The total noise power density spectrum N 0 when both spontaneous emission Component noise and shot noise are present is Shot Noise Limit Two Signal N 0 = N shot + N sp e Components Shot Noise = 2 er LO ( 1 + W n ) . (8) for Direct Conversion 10 ECE243b Lightwave Communications - Spring 2019 Lecture 8
Spontaneous Emission Noise in the Sample Lecture 8 Demodulation Heterodyne Demodula- tion Output Sample The power density spectrum from the spontaneous emission defined in (6) is Shot Noise in Output written as Sample . = 2 er LO W n N sp e Sample Statistic where W n is the expected number of directly-detected photoelectrons generated Shot Noise Limit by spontaneous emission Homodyne Demodula- If N shot = 0 , then (8) reduces to (6) and N sp e = N 0 tion One Signal Component Additional thermal noise added after photodetection is typically small compared Shot Noise Limit to the noise due to spontaneous emission Two Signal Components Shot Noise for Direct Conversion 11 ECE243b Lightwave Communications - Spring 2019 Lecture 8
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