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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

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Lecture 2 The Re- markable Properites

Lightwave Systems Modulation and Demodula- tion Codes and Coded Modula- tion Multiplexing Communication Channels

Lecture 2

Chapter 1 Continued

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Lecture 2 The Re- markable Properites

Lightwave Systems Modulation and Demodula- tion Codes and Coded Modula- tion Multiplexing Communication Channels

Some Numbers

A wavelength of 1500 nm corresponds to a frequency of f = c/λ = 2 × 1014 Hz. A photon at this wavelength has an energy of E = hf = 1.32 × 10−19 joules A one milliwatt (mW) lightwave source at this wavelength emits on average approximately P /hf = 7.5 × 1015 photons per second

means that we can often use continuous wave optics for analysis

One nanowatt lightwave at same wavelength emits on average approximately 7.5 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

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Lecture 2 The Re- markable Properites

Lightwave Systems Modulation and Demodula- tion Codes and Coded Modula- tion Multiplexing Communication Channels

More Numbers

A typical sheet of glass used for a window transmits approximately 90% of the incident lightwave power over a distance of a fraction of a centimeter A typical fiber used for a long-distance system transmits approximately 95% of the lightwave power over a distance of one kilometer

This means that one kilometer of fiber is more transparent than a typical window

Comparing the transmission loss for an optical fiber to the transmission loss for a typical electrical cable, the cable has a larger loss in one meter than the loss in

ne kilometer of a typical optical fiber

mean a guided lightwave signal can be transmitted approximately 1000× further than a guided electrical signal

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Lightwave Systems Modulation and Demodula- tion Codes and Coded Modula- tion Multiplexing Communication Channels

Still More Numbers

An ideal photon-optics receiver that can count photons is studied later With no other sources of noise, the reliable detection of a single pulse requires the detection of about ten signal photons For a one milliwatt lightwave signal this is an expected value of 7.5 × 1015 photons per second at the receiver If only ten detected photons are required to reliably determine whether a binary symbol is transmitted using that pulse, then this corresponds to an information rate of 7.5 × 1014 bits per second per milliwatt of received power At this data rate and a propagation speed of 2 × 108 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.

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Lecture 2 The Re- markable Properites

Lightwave Systems Modulation and Demodula- tion Codes and Coded Modula- tion Multiplexing Communication Channels

Radio Frequency Systems vs. Lightwave Systems

The energy of a single photon is not evident at any signal level at room temperature in the radio-frequency part of the electromagnetic spectrum because photon energy hf is much smaller than average thermal energy kT0 This means that continous signal models that ignore the discrete-energy nature

f a photon are appropriate for many lower-frequency systems

For lightwave signals, the choice between wave optics and photon optics depends

n the particular system

When the average energy is much larger than the energy of a single photon so 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.

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Lecture 2 The Re- markable Properites

Lightwave Systems Modulation and Demodula- tion Codes and Coded Modula- tion Multiplexing Communication Channels

Baseband Signals

Consider a baseband signal s(t). The instantaneous power in a baseband signal s(t) is P (t) = s2(t) The energy Eℓ in an interval of duration T starting at time ℓT is Eℓ =

(ℓ+1)T

ℓT

P (t)dt In many communication systems, the baseband signal s(t) modulates both the amplitude A(t) and the phase φ(t) of a deterministic carrier signal, or carrier, cos(2πfct), with a carrier frequency fc 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.

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Lightwave Systems Modulation and Demodula- tion Codes and Coded Modula- tion Multiplexing Communication Channels

Passband Signals

When a baseband signal s(t) is modulated onto the carrier, the resulting signal is called a passband signal, denoted as s(t) The modulated passband signal s(t) is often represented as the real part of a complex signal s(t) = A(t)ei(2πfct+φ(t)) with A(t)eiφ(t) called the complex-baseband signal The average power for a passband signal over a time interval that is long compared to the carrier period but short compared to the fastest time variation

f the baseband signal, which is approximately 1/B, is

Pave(t) = A2(t)cos2(2πfct + φ(t)) = A2(t) 1

2 + 1 2 cos(4πfct + 2φ(t))

≈

1 2 A2(t)

≈

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

f the complex-baseband signal representation s(t) of the passband signal

s(t).

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Baseband vs. Passband Signals

The term cos(2πfct + φ(t)) distinguishing a passband signal from a baseband signal yields an average power in the passband signal that is a factor of two smaller than a baseband signal with the same amplitude. This is also true for the passband signal energy. This factor of two is ubiquitous in the theory of communication systems that use both baseband and passband signals

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Lightwave Systems Modulation and Demodula- tion Codes and Coded Modula- tion Multiplexing Communication Channels

Phase-Synchronous and Phase-Asynchronous Modulation

The passband signal for phase-synchronous modulation is generated by multiplying, or mixing the baseband signal with the carrier signal cos(2πfct) This modulation process produces the amplitude-modulated passband signal s(t) centered at the carrier frequency fc When the bandwidth W of the baseband signal is much smaller than the carrier frequency fc, the passband signal is a narrowband signal

means the baseband signal s(t) is varying slowly as compared to the carrier frequency fc

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) = fc + (1/2π)dφ(t)/dt.

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Lightwave Systems Modulation and Demodula- tion Codes and Coded Modula- tion Multiplexing Communication Channels

Phase-Synchronous Demodulation-1

In phase-synchronous demodulation, the carrier phase may be unknown but is regarded as a constant The phase must be recovered by adjusting the phase of another sinusoidal signal, with frequency fLO which is generated at the receiver This signal is called the local oscillator and provides a phase reference that is used to estimate the unknown phase of the incident carrier The baseband signal is recovered by multiplying the passband signal s(t) by the local oscillator signal The local oscillator is at the same frequency as the carrier so that fLO = fc, and the demodulation process is called homodyne demodulation For heterodyne demodulation the frequency difference fc − fLO called the intermediate frequency fIF, and the passband signal at frequency fc translated to a passband signal at fIF.

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Lightwave Systems Modulation and Demodula- tion Codes and Coded Modula- tion Multiplexing Communication Channels

Phase-Synchronous Demodulation-2

The resulting signal after the multiplication process by LO is time-averaged (1) For homodyne demodulation of the passband waveform s(t) cos(2πfct) using a coherent carrier and a coherent local oscillator, fLO = fc and r(t) = s(t) cos(2πfct) × cos(2πfct) =

1 2 s(t),

(2) where s(t) is a real-baseband signal For heterodyne demodulation, fLO = fc − fIF, and r(t) = s(t) cos(2πfct) × cos 2π(fc − fIF)t =

1 2 s(t) cos(2πfIFt)

(3) Phase-synchronous demodulation relies on a stable phase difference ∆φ(t) = φc(t) − φLO(t) where φc(t) is the phase of the carrier and φLO(t) is the phase of the local oscillator The carrier is then called a coherent carrier

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Phase-Synchronous Demodulation-2

In practice, the carrier signal and the local oscillator signal are not pure sinusoids and have a nonzero spectral width A carrier is considered coherent if its spectral width is much less than the baseband bandwidth W When this is not true, carrier is noncoherent and there are significant additional amplitude and phase variations in the demodulated signal If the modulation is phase-asynchronous, then the corresponding phase-asynchronous demodulation process does not require knowledge of the carrier phase Demodulator can be implemented by adding a constant cosinusoidal signal with a frequency equal to the carrier frequency fc. For a real-baseband signal s(t), the form of the asynchronously modulated signal is

s(t) =

1 + s(t) cos 2πfct + φ(t) , (4) where the magnitude s(t) of the signal is constrained to be smaller than one, and φ(t) is the phase noise causing the carrier to be noncoherent. The term 1 + s(t) is the biased signal envelope

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Lightwave Systems Modulation and Demodula- tion Codes and Coded Modula- tion Multiplexing Communication Channels

Phase-Synchronous Demodulation Figure

Real Baseband signal Baseband signal plus bias Modulated signal Retified signal Lowpass signal Signal with bias removed

Modulation Demodulation (a) (b) (c) (d) (e) (f)

s(t) 1+s(t) 1+s(t) s(t)

Figure: Phase-asynchronous modulation and demodulation using a noncoherent carrier. The received signal is first rectified to remove the negative amplitude components and then lowpass-filtered to remove the carrier frequency.

This type of phase-asynchronous demodulation is referred to as envelope demodulation.

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Lightave Phase-Synchronous Demodulation

The transmitted signal for a phase-asynchronous lightwave communication system is generated by modulating the power, or intensity, of the lightwave carrier without regard to the phase At the receiver, direct photodetection implements a form of phase-asynchronous demodulation in which the received electrical signal is proportional to the lightwave signal power defined in (1) This type of phase-asynchronous system is called an intensity-modulated direct-photodetection system and is widely used in elementary lightwave communication systems because of its simplicity Intensity modulation is widely used, but is inefficient because the unmodulated signal that was added to ensure a nonnegative baseband signal contains at least half the total transmitted power but conveys no information These issues motivate the use of modulation formats that convey information using both the amplitude and the phase.

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Coded Modulation

A major component of the physical layer consists of coding and coded modulation Coding can be divided into source coding and channel coding Channel coding maps datawords, which usually consist of source-coded data, into codewords that are designed to control errors Coded modulation refers to the integration of channel coding and modulation into a single entity In modern practice, a modem not only includes the modulator and the demodulator, but also includes the coding and decoding, detection, and timing recovery The system performance is measured by the bit error-rate, the codeword error-rate, or the message error-rate This aspect of communication system design has seen huge growth due to the explosive increase in available processing power.

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Lightwave Systems Modulation and Demodula- tion Codes and Coded Modula- tion Multiplexing Communication Channels

Multiplexing

Multiplexing is the process of combining multiple, independent datastreams or subchannels in the same physical medium A multi-input multi-output channel transmits and receives separate datastreams using the same physical channel A system that uses spatially distinct guiding structures is called a space-multiplexed system

Space multiplexing may use separate optical fibers or spatially-separated cores within a single optical fiber

A system that uses separate modes within the same single core is called a mode-multiplexed system

different than space-multiplexed systems that use multiple cores

System that uses two polarization modes per spatial mode is called a polarization-multiplexed system

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Wavelength and Time Multiplexing

A further distinction is based on whether the datastreams are multiplexed in time

r in frequency (wavelength)

In frequency-division multiplexing, channel bandwidth is divided into subchannels

each subchannel assigned a distinct subcarrier frequency and a baseband bandwidth around this subcarrier requires accurate control of the channel-to-channel wavelength spacing

Frequency-division multiplexing is typically called wavelength-division multiplexing (WDM) Many lightwave systems use a combination of time-division multiplexing and wavelength-division multiplexing.

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Multiplexing

Time Division Multiplexing

TDM N channels at R bit/s/channel M channels at R N bits/s/wavelength WDM

Wavelength Division Multiplexing

MRN bit/s/fiber

λ1 λ2 λ3 λ1 λ2 λ3 Figure: Most long-distance lightwave communication systems use a combination of time-division multiplexing and wavelength-division multiplexing.

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Communication Channels

The discrete logical symbols that represent the information undergo several transformations that will be described at several nested levels Each of these levels describes a communication channel Communication channels described by the propagation characteristics of a lightwave signal or an electrical signal are physical channels

modeled using either wave optics or photon optics.

The channel described by the input and output probability distributions that represent information is called an information channel

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Lightwave Systems Modulation and Demodula- tion Codes and Coded Modula- tion Multiplexing Communication Channels

Communication Channel Figure

Baseband Signal Frequency Translation Photodetection/ Demodulation s(t)

s(t)
r(t)

Codeword Sensed Codeword Modulated Lightwave Signal

Transmitter

Fiber Channel Received Lightwave Signal Electrical Signal Filtering/ Symbol Detection Codeword Detection

Channel Receiver Information Channel

(discrete or continuous) Baseband Modulation

Lightwave Channel

(waveform)

Electrical Channel

(waveform or discrete-time) Transmitted Dataword Encoding Detected Codeword Decoding Decoded Dataword s

r(t) r

d

Figure: Communication channels with the lightwave channel and the electrical channel modeled using wave optics.

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Lightwave Systems Modulation and Demodula- tion Codes and Coded Modula- tion Multiplexing Communication Channels

Types of Communication Channels

The lightwave channel is a physical channel whose input is the modulated lightwave signal coupled into the fiber The output is the lightwave signal at the output face of the fiber The electrical channel is a different level of physical channel that surrounds the lightwave channel. The input to this channel is the baseband electrical signal before modulation. The output from this channel is the baseband electrical signal after demodulation. While a lightwave channel is typically analyzed using continuous-time signals, electrical channels may be analyzed using a discrete-time electrical channel based on the sampling theorem. The information channel surrounds the electrical channel. The input to this channel is a stream of encoded symbols after the encoding process at the

transmitter. The output from this channel is a stream of detected symbols before

the decoding operation at the receiver.

Because the information channel surrounds the electrical channel, it is affected by all of the characteristics that define the electrical channel and the lightwave channel.

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Information Channel

The information channel depends on:

the coded-modulation process, which maps a sequence of encoded user data values into a physical quantity used for modulation the propagation characteristics of the physical channel the type of detection process, which maps a received physical quantity into a sequence

f detected symbols

This means that for the same physical channel, different detection techniques define different information channels As an example, a system that uses a hard-decision detection process to produce a discrete value for each detected letter leads to a different information channel than a system that uses a soft-decision detection process The goal of this class to understand how the physical characteristics of lightwave channels and electrical channels affect the form of the discrete information channel that conveys information.

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Example

Let’s compare two types of lightwave communication systems to a common phase-synchronous radio-frequency communication system shown in Figure 4a.

(a) (b)

Received RF signal

ne(t)

+ +

ne(t) | · |2 cos(2πfct)

Demodulation and filtering Added Noise Added Noise Square-law photodetection Received noisy lightwave signal Antenna (linear conversion) Demodulated noisy signal Demodulated noisy signal

s(t) cos(2πfct)

s(t) + no(t)
cos(2πfct)

r(t) = 1

2s(t) + ne(t)

r(t) = R

2 |s(t) + no(t)|2 + ne(t)

Figure: (a) A typical wireless communication channel modeled using continuous

electromagnetics. (b) A typical noncoherent intensity-modulated direct-photodetection

lightwave channel modeled using wave optics.

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Example of Different Channel Models - RF Channel

The passband radio-frequency signal is converted into an electrical signal by an antenna This linear conversion process preserves in the received passband electrical signal both the amplitude and the phase of the incident electromagnetic wave This means that the electrical channel after reception can be described as a scaled form of the physical channel with the noisy demodulated electrical signal r(t) given by r(t) = r(t) + ne(t), (5) where the underscore distinguishes the noisy waveform from the noiseless waveform r(t) = 1

2 s(t), and ne(t) is an additive gaussian noise source

Because this channel is linear, the sources of noise added at various stages of the system can be treated as a single equivalent noise source by proper scaling and summing This type of channel model is an additive-noise channel model with the noise being independent of the signal.

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Electrical Channel for Phase Synchronous Lightwave Com

The electrical channel for a phase-synchronous lightwave communication system is similar to the electrical channel for the phase-synchronous radio-frequency system shown in Figure 4a The linear conversion of the lightwave signal amplitude into an electrical signal amplitude, called balanced photodetection is achieved by adding a local

scillator signal to the received lightwave signal before photodetection

The nonlinear square-law characteristic of the photodetector provides the mixing

peration that translates the lightwave carrier frequency to a lower carrier

frequency converting the lightwave signal to an electrical signal preserving both the amplitude and phase of the lightwave signal Functionally, the distinction between the electrical channel and the lightwave channel is simply a scaling constant associated with the optical/electrical conversion process.

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Electrical Channel for Phase Asynchronous Lightwave Com

Phase-asynchronous lightwave communication system is based on intensity modulation and direct photodetection as shown in Figure 4b

ptical noise source no(t) is included before direct photodetection to model the

effect of optical amplification The use of direct photodetection produces an electrical channel that is not simply a scaled version of the lightwave channel The noisy electrical signal r(t) generated by direct photodetection is proportional to the squared-magnitude |sout(t) + no(t)|2 of received noisy lightwave signal (cf. (1)) so that r(t) =

R 2 |s(t) + no(t)|2 + ne(t),

where an electrical noise ne(t) is included after photodetection, and the scaling constant is the responsivity R (cf. Lecture 1) For this direct-photodetection demodulator, the square-law characteristic of the photodetector mixes sout(t) with no(t), producing signal-dependent noise This channel model is a signal-dependent-noise channel model.

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Electrical Channel for w/o Lightwave Noise

A different electrical channel is modeled if there is no additive lightwave noise. In this case, no(t) = 0. The equation then becomes r(t) = RP (t) + ne(t). where P (t) = |s(t)|2/2 When the transmitted lightwave signal power is proportional to the modulating electrical signal, then the electrical channel itself is linear for noncoherent intensity modulation The channels are based on a continuous-energy wave-optics signal model for both the signal and the noise sources If instead, a discrete-energy, photon-optics signal model is used and the lightwave signal is converted into an electrical signal by counting the number of received photons, then the electrical channel is modeled differently because the received signal and noise are modeled differently This difference also affects the form of the discrete information channel generated after the detection process.

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