Lecture 2 The Re- markable Properites of Lightwave Systems Modulation and Lecture 2 Demodula- tion Chapter 1 Continued Codes and Coded Modula- tion Multiplexing Communication Channels 1 ECE243b Lightwave Communications - Spring 2019 Lecture 2
Some Numbers Lecture 2 The Re- markable Properites of Lightwave Systems A wavelength of 1500 nm corresponds to a frequency of f = c / λ = 2 × 10 14 Hz. Modulation and Demodula- A photon at this wavelength has an energy of E = hf = 1.32 × 10 − 19 joules tion Codes and Coded A one milliwatt (mW) lightwave source at this wavelength emits on average Modula- approximately P / hf = 7.5 × 10 15 photons per second tion means that we can often use continuous wave optics for analysis Multiplexing Communication One nanowatt lightwave at same wavelength emits on average approximately 7.5 Channels photons per nanosecond discrete-energy nature of a lightwave signal is evident use of a photon-optics signal model is needed to correctly analyze the system 2 ECE243b Lightwave Communications - Spring 2019 Lecture 2
More Numbers Lecture 2 The Re- markable Properites of Lightwave Systems A typical sheet of glass used for a window transmits approximately 90% of the Modulation and incident lightwave power over a distance of a fraction of a centimeter Demodula- tion A typical fiber used for a long-distance system transmits approximately 95% of Codes and the lightwave power over a distance of one kilometer Coded Modula- This means that one kilometer of fiber is more transparent than a typical window tion Multiplexing Comparing the transmission loss for an optical fiber to the transmission loss for a Communication typical electrical cable, the cable has a larger loss in one meter than the loss in Channels one kilometer of a typical optical fiber mean a guided lightwave signal can be transmitted approximately 1000 × further than a guided electrical signal 3 ECE243b Lightwave Communications - Spring 2019 Lecture 2
Still More Numbers Lecture 2 The Re- markable Properites An ideal photon-optics receiver that can count photons is studied later of Lightwave Systems With no other sources of noise, the reliable detection of a single pulse requires Modulation the detection of about ten signal photons and Demodula- tion For a one milliwatt lightwave signal this is an expected value of 7.5 × 10 15 Codes and photons per second at the receiver Coded Modula- tion If only ten detected photons are required to reliably determine whether a binary Multiplexing symbol is transmitted using that pulse, then this corresponds to an information rate of 7.5 × 10 14 bits per second per milliwatt of received power Communication Channels At this data rate and a propagation speed of 2 × 10 8 meters/second, the entire 35 million book collection of the Library of Congress could be transmitted, in principle, across a continent in a fraction of a second The combination of these unprecedented and remarkable properties has enabled the global information infrastructure. 4 ECE243b Lightwave Communications - Spring 2019 Lecture 2
Radio Frequency Systems vs. Lightwave Systems Lecture 2 The Re- markable Properites The energy of a single photon is not evident at any signal level at room of Lightwave temperature in the radio-frequency part of the electromagnetic spectrum because Systems photon energy hf is much smaller than average thermal energy kT 0 Modulation and Demodula- This means that continous signal models that ignore the discrete-energy nature tion of a photon are appropriate for many lower-frequency systems Codes and Coded Modula- For lightwave signals, the choice between wave optics and photon optics depends tion on the particular system Multiplexing Communication When the average energy is much larger than the energy of a single photon so Channels that many photons are to be observed, the wave-optics signal model is typically used When the average energy is on the order of tens of photons or less, the discrete-energy property of a lightwave signal incorporated into the photon-optics signal model must be considered. 5 ECE243b Lightwave Communications - Spring 2019 Lecture 2
Baseband Signals Lecture 2 The Re- markable Properites Consider a baseband signal s ( t ) . The instantaneous power in a baseband signal of s ( t ) is Lightwave Systems P ( t ) = s 2 ( t ) Modulation and The energy E ℓ in an interval of duration T starting at time ℓT is Demodula- tion � ( ℓ + 1 ) T Codes and Coded E ℓ = P ( t ) d t Modula- tion ℓT Multiplexing In many communication systems, the baseband signal s ( t ) modulates both the Communication Channels amplitude A ( t ) and the phase φ ( t ) of a deterministic carrier signal , or carrier , cos ( 2 πf c t ) , with a carrier frequency f c The carrier frequency is always larger—and usually much larger—than the baseband bandwidth W measure of the spectral width of the baseband signal - defined several ways. The properties of the lightwave source determine whether the carrier is coherent or noncoherent . 6 ECE243b Lightwave Communications - Spring 2019 Lecture 2
Passband Signals Lecture 2 When a baseband signal s ( t ) is modulated onto the carrier, the resulting signal is The Re- markable called a passband signal , denoted as � s ( t ) Properites of Lightwave The modulated passband signal � s ( t ) is often represented as the real part of a Systems complex signal s ( t ) = A ( t ) e i ( 2 πf c t + φ ( t )) with A ( t ) e i φ ( t ) called the Modulation and complex-baseband signal Demodula- tion The average power for a passband signal over a time interval that is long Codes and Coded compared to the carrier period but short compared to the fastest time variation Modula- of the baseband signal, which is approximately 1 / B , is tion Multiplexing A 2 ( t ) cos 2 ( 2 πf c t + φ ( t )) P ave ( t ) = Communication A 2 ( t ) � 1 2 cos ( 4 πf c t + 2 φ ( t )) � Channels 2 + 1 = 2 A 2 ( t ) 1 ≈ 1 2 | s ( t ) | 2 , ≈ (1) where the overbar indicates a time average The term | s ( t ) | = A ( t ) is the passband signal envelope , which is the magnitude of the complex-baseband signal representation s ( t ) of the passband signal � s ( t ) . 7 ECE243b Lightwave Communications - Spring 2019 Lecture 2
Baseband vs. Passband Signals Lecture 2 The Re- markable Properites of Lightwave Systems Modulation and The term cos ( 2 πf c t + φ ( t )) distinguishing a passband signal from a baseband Demodula- tion signal yields an average power in the passband signal that is a factor of two Codes and smaller than a baseband signal with the same amplitude. Coded Modula- tion This is also true for the passband signal energy. Multiplexing Communication This factor of two is ubiquitous in the theory of communication systems that use Channels both baseband and passband signals 8 ECE243b Lightwave Communications - Spring 2019 Lecture 2
Phase-Synchronous and Phase-Asynchronous Modulation Lecture 2 The Re- markable Properites of The passband signal for phase-synchronous modulation is generated by Lightwave Systems multiplying, or mixing the baseband signal with the carrier signal cos ( 2 πf c t ) Modulation and This modulation process produces the amplitude-modulated passband signal � s ( t ) Demodula- tion centered at the carrier frequency f c Codes and Coded When the bandwidth W of the baseband signal is much smaller than the carrier Modula- frequency f c , the passband signal is a narrowband signal tion means the baseband signal s ( t ) is varying slowly as compared to the carrier frequency Multiplexing f c Communication Channels When a random time-varying phase φ ( t ) is imposed on the carrier either through the process of generating the carrier or by a random modulating waveform the resulting waveform is phase-asynchronous waveform The carrier frequency is noncoherent with f ( t ) = f c + ( 1 / 2 π ) d φ ( t ) / d t . 9 ECE243b Lightwave Communications - Spring 2019 Lecture 2
Phase-Synchronous Demodulation-1 Lecture 2 The Re- markable Properites In phase-synchronous demodulation , the carrier phase may be unknown but is of regarded as a constant Lightwave Systems Modulation The phase must be recovered by adjusting the phase of another sinusoidal signal, and with frequency f LO which is generated at the receiver Demodula- tion Codes and This signal is called the local oscillator and provides a phase reference that is Coded used to estimate the unknown phase of the incident carrier Modula- tion Multiplexing The baseband signal is recovered by multiplying the passband signal � s ( t ) by the Communication local oscillator signal Channels The local oscillator is at the same frequency as the carrier so that f LO = f c , and the demodulation process is called homodyne demodulation For heterodyne demodulation the frequency difference f c − f LO called the intermediate frequency f IF , and the passband signal at frequency f c translated to a passband signal at f IF . 10 ECE243b Lightwave Communications - Spring 2019 Lecture 2
Recommend
More recommend
