# Modulation Formats.

## Presentation on theme: "Modulation Formats."— Presentation transcript:

Modulation Formats

Modulation Formats General
Optical communication systems are carrier systems. This implies that a wave of a frequency much higher than that of the information ( signal) is used to enable the information to be transported through the channel. The range of wavelength over which optical communications operate ranging from , say, 1 to 2 μm. This wavelength range corresponds to a frequency range 1.5x102 to 3x102 THertz. Remember, 1 THerz=1x1012 Hertz. The bandwidth of the information sources currently available to us is far away from this number. The carrier features should be suitable to propagate in the channel under consideration and the next question is how does a information carrying signal is “loaded” on a carrier to go through the channel? The process that achieves this objective is called “modulation” and has been a subject of intensive study since the inception of electronic communications back in the 1920s. Modulation is the process of conveying an information signal inside another signal (carrier) that can be physically transmitted. This is achieved by varying one or more of the properties of the signal that can be transmitted.

Modulation Formats General
There is two classes of modulation processes; analogue and digital. Analogue modulation; a signal is defined as analogue if it is continuous in both time and any other parameter that characterised it. Then, if that signal is applied continuously on the carrier the outcome is an analogue modulated signal. Mathematically, the concept is defined through the definition of the continuous function. A function f (x) is continuous at x = a if Digital modulation; a signal is defined as digital if its parameters are allowed to take values that belong to a discrete set of values. A typical digital signal is

Modulation Formats General
Then, if this signal is applied continuously on the carrier the outcome is a digital modulated signal. Mathematically, modulation can be seen as a mapping from one domain to another. The figure below illustrates the mapping and its inverse in recovering the information. Information domain Carrier Channel M1 M2 IM2 IM1 M1 x IM1 = 1 and M2 x IM2 = 1 The mappings in the figure above appear to be 1:1 but in a real communication system the noise and other impairments destroy the 1:1 mapping and give rise to detection errors. These concepts are illustrated in the next slide.

Modulation Formats General
“0” ● “1” ● Signal processing and channel Transmitter Receiver One → Many Input alphabet Receiver decision space The concept of one – to - many mapping in communications. Modulation is a vast subject and by virtue of necessity we limit ourselves to digital modulation as applied to optical communication systems.

Modulation Formats General
The electric field of a e - m wave is given by where E is the peak electric field amplitude, P is the polarisation matrix, k is the wave vector, r is the position vector, wc is the carrier angular frequency, t is the time, and θ is the phase. The average density of energy flow in the direction of z , intensity = I, of the wave is defined as the time average of the Poynting vector S = Sez. where n the refractive index of the medium, Z0 the impedance of free space (377 ohms), P the power and A the cross sectional area. The units of the intensity is (watts / unit area). In the communication field the optical device of choice is the semiconductor laser. Therefore, the modulation formats possible with the semiconductor laser are of singular importance

Modulation Formats General
The complete equation for an e – m wave can be substantially simplified if we limit ourselves to modulation formats for high capacity transmission. Then, where β the propagation constant. In optics the symbol k is used instead of β so one should be aware of the implications in terminology. The equation above indicates that there are three parameters that can be used to impart information on the optical carrier. [1] Amplitude, E0; the format that modulates the amplitude of the optical carrier is called “amplitude modulation”. If the information is digital then the format is known as “ amplitude shift keying” or ASK for short. The format is also known in optical communications as “on off keying”, (OOK). In terms of the baseband signal the format is known as “non return to zero”, (NRZ). All these terms are used in the literature without restrictions. The basics of the ASK format is shown in the next slide for a NRZ baseband format.

Modulation Formats General
time Amplitude Tb Baseband signal Carrier Envelope ASK signal 1 The ASK format with a binary NRZ baseband signal. [2] Frequency, ω; when the baseband signal modulates the frequency of the optical carrier the process is called “frequency nodulation”. For digital baseband signals it is called “ frequency shift keying”, (FSK). In the FSK format the frequency of the carrier changes between “1” and “0”. The difference between the two frequencies is not big but it is sufficient for the receiver to distinguish the two frequencies and make the correct decisions.

Modulation Formats General
A typical FSK modulated signal is shown in the diagram below. time Amplitude Tb Baseband signal Constant envelope FSK signal 1 f0 carrier f1 carrier The FSK format with a binary NRZ baseband signal with f0 < f1. Notice the contact envelope of the format in contrast to that of ASK where the short term power depends on the statistics of the baseband signal. This feature is helpful in designing the dynamic range of subsystems.

Modulation Formats General
[3] Phase, θ; the modulation of the phase of the optical carrier is known as “phase modulation”. For digital baseband signals is known as “phase shift keying”, (PSK). In this format the phase of the carrier between “1” and “0” shifts by, say, 180o. The actual details depend on the application. The PSK format for a binary baseband signal is illustrated below. Amplitude PSK signal time Tb Baseband signal 1 Constant envelope Phase 0 Phase π The PSK format with a binary NRZ baseband signal with the phase of “1” been 0 and the phase of “0” been shifted by π.

Modulation Formats General
The digital modulation formats were presented using a binary baseband signal. However, each format can support multilevel signalling is necessary. For example, A M-ary ASK signal has M -1 discrete “1” levels and the “0” level. Each pulse now corresponds to As a result the M-ary signalling has been reduced to With M = 2 the baud rate equals the bit rate, Bb.

Modulation Formats The constellation concept
Until now the symbols of “1” and “0” for binary transmission have been defined as level of, say, voltage or current. There is however an alternative representation that conveys the same amount of information. Consider again a binary signal of “1” and “0” and let us say that they correspond to voltages1 V and 0V that change with time. Then, the complete description is one that contains also the phase, that is, phasors are used for the complete description. The conventional representation is shown below on the left. On the right there is the description using the complex plane. Clearly, both representation contain the same about of information .The representation on the right is called for reason that will become apparent very soon, the “constellation” “1” (1, angle )V “0” (0, angle 0)V Real axis Imaginary axis Complex plane 1+ j 0 0+ j 0 (a) Conventional representation. (b) The “constellation” representation

Modulation Formats The constellation concept
Perhaps, this example does not demonstrate the power of the new representation. Consider now four voltages corresponding to four signal level represented by ; v1=1+j 0, v2= 0+ j1, v3= -1+ j 0 and v4= 0 – j. The constellation is as shown below and it should be clear now the advantages of the representation. In fact that constellation represents a four level phase shift keying, (PSK), format. Now, let us farther assume that the PSK four level format encodes bits according the following rule v1=00, v2=01,v3=10 and v4=11. Then, instead of depicting the voltages the symbols can be directly represented in the constellation diagram. Real Imaginary v1 v4 v3 v2 00 01 10 11 Voltage Symbol 1+ j 0 00 0 + j 01 -1+ j 0 10 0 - j 11

Modulation Formats The constellation concept
The constellation diagram in the previous slide showed very clearly the position of the symbols in the plane. In order to see the impact of transport consider the 4-symbol PSK again but now rotated by 45o and using the unit circle for reference . Notice, the defined amplitude and phase of each symbol. This is the transmitted constellation. 00 01 10 11 φ Amplitude Phase Amplitude – Random variable Phase – During transmission the constellation has been subjected to random amplitude and phase variations so the receiver has to estimate what was transmitted. See more on the use of signal constellation in assessing performance later.

Modulation Formats The spectral efficiency concept
Intuitively one expects that the available channel bandwidth is efficiently used to transport information. This is achieved by using an efficient modulation format subject to a number of constrains associated with system design. Some definitions [1] Bit rate; the bit rate defined the rate information is passed forward. [2] Baud (or signalling) rate; defines the number of symbols per second. Each symbol represents n bits, and has M signal states, where M = 2n. This is called M-ary signalling. When n = 1, that is, one symbol is used to represents the elements of the alphabet the signal has two states , M = 2. Consider a simple example. A link can transport bit/s from A to B. The bandwidth of the channel is 4000 Hertz. The spectral efficiency of the link, also known as modulation efficiency, is 12.5 bit/s / Hz. In spite of the similarity of definitions on spectral efficiency there are two variants that are used; spectral efficiency in bits/Hz and modulation efficiency bits/baud.

Modulation Formats The spectral efficiency concept
Consider a system operating at 10 Gbit/s with channel spacing of 50 GHz. The spectral efficiency is 10GBits / 50GHz = 0.2 bits/Hz. In this example the bits/baud is 10GBits/10Gbauds = 1 bit/baud. The effective baud rate (symbol rate) is 10Gbauds.

Modulation Formats The Hartley – Shannon Law
The objective of any communication system is to transfer the maximum amount of information with the minimum bandwidth. The famous Hartley – Shannon law establishes an upper limit for reliable information transmission over a band limited additive white Gaussian noise ,(AWGN), channel. The Hartley – Shannon law can be stated as where C the channel capacity in bit/s, B the one sided channel bandwidth in Hz, S/N the signal to noise ratio, (SNR), but not in dB. If the SNR is given in dB it must be converted using the expression The information rate, R, must satisfy the equation

Modulation Formats The Hartley – Shannon Law
One useful variant of the Hartley – Shannon law is in terms of the average energy/bit, Eb, (joules /bit) and the AWGN with two – sided noise spectral density N0/2. Then, the signal power is S=Eb R and the noise power N=N0B and Now, Eb/N0 represent the SNR at the receiver in normalise form. The ratio R/B represents the spectral efficiency whose upper limits is C/B. The graph in the next slide illustrates the Harley – Shannon law. The curve corresponding to R = C separates the regions; below the line the spectral efficiencies are potentially achievable but above the curve they are unachievable. Clearly the question now is how do we calculate the [Eb/N0] (dB) for a given system? AS a simple example consider a 10 Gbit/s with an “on-off” NRZ format whose receiver has a sensitivity of dBm for 10-9 BER with detector responsivity R = 1.

Modulation Formats The Hartley – Shannon Law
R > C - Out of bounds area R = C Spectral efficiency (bit/s/Hz) 10 GBit/s example: BER=10-9 R < C – Accessible area R < C – Accessible area Eb/N0 (dB) Graph of the maximum achievable spectral efficiency [Bit/s/Hz ]as function of Eb/N0 (dB).

Modulation Formats The Hartley – Shannon Law
Step 1 We convert the power (-20 dBm) into the average optical power; thus Step 2 Assuming that the optical power is maximum for “1”, zero for “0” and a 50% probability of ”1” and “0” the peak optical power and energy/bit is Step 3 The value of N0-rms will be found from the BER. For a BER of 10-9 the ratio of peak optical power to rms noise is defined by the Q which is 12 for 10-9 BER.

Modulation Formats The Hartley – Shannon Law
Step 4 The value of N0 will be found by diving the N0-rms by the receiver bandwidth which for the sake of simplicity is 10 GHz; thus Step 5 The value of Eb/N0 is now Step 6 The spectral efficiency of the system is found by dividing the capacity by the bandwidth occupied by the spectrum ;since it is a NRZ format the effective spectral width is 20 GHz. Step 7 In the Hartley - Shannon graph the point for this system is at [8.0,0.5]. This point is plotted in the graph. Be aware that the derived noise spectral density was based on the BER.

Modulation Formats The Hartley – Shannon Law
There are two key features of spectral efficiency: [1] Fundamental feature; higher signal-to-noise ratio is required for higher order modulation. [2] Practical feature; the implementation penalties are higher for higher constellations and symbol rates.

The diagram on the right shows the electronic and optical waveforms.
Modulation Formats Intensity modulation Historically, the first modulation format is intensity modulation. The reason for this is the simple fact that semiconductor lasers are electrically pumped and they have very short photon lifetimes. The circuit below is the basic circuit used for the intensity modulation of semiconductor lasers. P1 P0 Ibias Ithr Isignal Output pulses I Laser output Input pulses Laser Constant current source: Bias source: Modulator Modulating signal Ibias Imod The diagram on the right shows the electronic and optical waveforms.

Modulation Formats Intensity modulation
In addition to a simple transmitter an intensity modulated optical carrier offers the use of a very simple receiver for detection. All it requires is a p-i-n or apd detector followed by a low noise electronic amplifier. This combination of intensity modulated carrier and a p-i-n ( apd) receiver is referred to as “intensity modulated direct detection “,(IMDD), system. Optical communications are used in a large number of diverse applications and IMDD systems constitute the majority of systems used. The simplicity of the direct intensity modulation of semiconductor lasers made possible the introduction of optical fibre communications at an early date which required the minimum of technical development. Hoverer, this simplicity brought a number of issues such as; turn-on delay, relaxation oscillations, frequency response issues, frequency chirping and unwanted frequency modulation. But continuous progress in device design and material processing made possible to minimise these issues. Directly modulated lasers cannot perform satisfactory for bit rates above 2.4 Gbits because even with the up to date DFB lasers the impairments, especially dispersion, reduce the performance to such an extent that cost effective systems cannot be designed.

Modulation Formats Intensity modulation
Measured spectrum of a directly modulated laser under 622 MBit/s NRZ modulation with 0.7 mW between ‘1’ and ‘0’ level.

Modulation Formats Intensity modulation
Chirped spectrum; black. Theoretically expected spectrum; gray. Spectra calculated for the directly modulated laser under 622 MBit/s NRZ modulation.

Modulation Formats Intensity modulation
The key issue here is that any attempt to directly modulate the laser impairs its ability to function as a very high quality oscillator. The solution to this problem is the use of external modulators. These are devices modulate the optical radiation but they are external to the laser cavity and they do not affect to the first order at least the dynamics of the cavity. The use of an external modulator in addition to isolating the function of modulation from that of the generation of very high quality optical radiation makes also possible to use modulation schemes not supported by direct modulation.

Modulation Formats Technology - Modulators
The discussion on modulation formats will be based on an external LiNbO3 modulator. There are two reasons for this choice; firstly the devices and technology are mature and deliver excellent performance and secondly it can deliver all the modulation formats to be discussed. The basic outline of a amplitude travelling wave modulator is shown below. The choice of a travelling wave modulator is dictated by bandwidth requirements. Waveguide Electrical Contacts Ein Eout Ein / 2 kEin / 2 v1(t) v2(t) The equation of the operation of an amplitude modulator also known as Mach-Zehnder (MZ) is given by,

Modulation Formats Technology - Modulators
With k = 1 the normalised output is written and with v1(t) = - v2(t) the phase term is removed and The details of the operation of a MZ amplitude modulator depend on the bias point of the device. In the next slide the power vs. input signal is shown. In the simplest application the device is biased at the point where the output power is half. This point is also known as the quadrature point. Then a drive peak-to-peak signal of Vπ is applied and the output swings between zero and full power. Different bias points enable the use of different modulation formats.

Modulation Formats Technology - Modulators
4Vπ 3Vπ 2Vπ π Drive voltage M - Z Modulator output Quadrature point Power Field The field and power output vs. drive voltage of a M - Z modulator. One word of caution regarding the biasing point. Because of the material the bias point drifts and careful design is necessary for ensuring the stability of the bias point. One of the key features of modulation schemes is the bandwidth after modulation.

Modulation Formats Technology - Modulators Left ; the basic modulator.
Right ; the modulator with driver, terminating load and monitoring photodiode. The architecture of a Mach – Zehnder modulator; from Photline

Modulation Formats Technology - Modulators
The architecture of an optical transmitter using an external modulator is, as expected, more complex than that of a direct modulated one. The block diagram of a frequency stabilised laser with a co-packaged external modulator is shown below. Frequency stabilised DFB laser Optical isolator External modulator Electronic amplifier Data High quality optical connector Device fibre tail Laser TE Controller Transmission fibre TE element Constant current bias source Laser package Temperature Power to TE Power monitor Bias current

The ASK format is a very popular formats because of its simplicity and flexibility. In some of the literature the term “on-off keying”, (OOK), is used instead. Starting with a binary baseband signal one distinguishes two classes of ASK signalling: [1] Non - return to zero format , (NRZ). [2] Return to zero format, (RZ). [1] Non – return to zero format; in this format the duration of the pulse (Tp) equals the signalling interval (Tb) which is the inverse of the bit rate, Bb. A unity amplitude NRZ pulse is shown below. A Tp -Tb/2 Tb/2 time Tb For a NRZ pulse the MZ is biased at quadrature and the input signal swings the modulator drive voltage between zero and Vπ.

4Vπ 3Vπ 2Vπ Drive voltage M -- Z power transmission Bias Vπ / 2 Signal drive Phase 0 Phase π The biasing and drive of a M-Z modulator for the NRZ format ASK format. Biasing the M-Z at the quadrature point and driving with a signal of Vπ amplitude the optical carrier swings between zero and the maximum value E0.

One of the most important features of a carrier system is the bandwidth after modulation. This feature is particular important in the context of WDM systems. For a random binary stream of data in the baseband with equal probability for “1” and “0” and with each pulse modelled as a rectangular pulse the baseband signal power spectral density, (PSD), is given by the two sided function, The one sided PSD of this function is shown in the next slide with A = Tb = 1. Notice that the impulse at f = 0 carries half the power on the baseband signal and this is one of detrimental features of NRZ format because the power Is not used for information transmission.

PSD f The PSD of the random unipolar signal for a NRZ rectangular pulse stream.

When the baseband signal modulates the carrier the combined signal can be represented as The two - sided PSD of the modulated carrier is now given by Since sinc2(f ± fc) = 0 the summation over k is zero. The one sided PSD of the ASK signal is shown in the next slide. The bandwidth after modulation is ≈ 2Bbase. This should not be a surprise because this a key feature of amplitude modulation in general.

fc f Bandwidth ≈ 2Bbase Scarrier(f) 90% of power 95% fc = optical carrier Deterministic signal Stochastic signal The PSD of a binary ASK signal in the optical domain.

The modulation spectrum of a Mach – Zehnder modulator at 2.5 Gbit/s.
Modulation Formats ASK signalling format The modulation spectrum of a Mach – Zehnder modulator at 2.5 Gbit/s.

It is very instructive to construct the state and constellation diagram for the binary ASK signalling format. Symbol “0” real Symbol “1” E0 imaginary threshold State “1” State “0” “0” “1” “1 to 0” “0 to 1” State diagram “0” “1” 0.5 Transition probabilities Constellation diagram for binary ASK signalling. State diagram and transition probabilities for binary ASK signalling.

DC impulse Spectral nulls. The PSD of a binary NRZ ASK signal for 10 Gbit/s data without filtering.

The spectral of NRZ modulation at 10 and 40 Gbit/s.
Modulation Formats ASK signalling format 10 Gbit/s. 40 Gbit/s. The spectral of NRZ modulation at 10 and 40 Gbit/s.

The key features of ASK signalling is that there is a DC term whose energy is not used and it is difficult to recover timing information with long strings of “1” and “0”. The fact that there will be long strings of “1” and “0” can be deduced from the state diagram of NRZ format. Additionally, NRZ pulses are sensitive to the fibre dispersion. [2] Return to zero format, (RZ); in this format the pulse width (Tp) is less than the signalling interval ( Tb). Three typical RZ formats are shown below. Tb Tp time A Tb Tp time A Tp= 67% Tb Tp time A Tb Tp= 50% Tb Tp= 33% Tb

The reasons for using RZ pulses are: [1] High timing content. [2] Reduced sensitivity to fibre dispersion. However, these advantages are not without a price. The bandwidth of RZ pulses is broader than that of NRZ and uses therefore more fibre bandwidth. This becomes an issue in dense WDM,(DWDM), systems. In order to generate RZ optical pulses the M - Z is biased at quadrature and the device is driven with a pulse of appropriate width. For 50% duty cycle the M - Z is biased as per NRZ format. However, as the pulse width is reduced it becomes progressively difficult to generates the narrow pulses required. An alternative approach has been developed using two M - Z in tandem and driven by different pulse streams. The concept is illustrated in the next slide. The duty cycle of the output format depends on the bias and driving voltage of the sinewave drive. Of course the transmitter is more complicated now but the generation of RZ pulses with arbitrary duty cycle is much easier.

CW light NRZ data NRZ Optical RZ format Data MZ Pulse carver MZ Clock or sinusoid The concept of pulse carver modulator. In order to generate RZ50 pulses ( RZ pulse of 50% duty cycle) the pulse carver is bias at quadrature and driven by a sinusoid of Vπ peak-to-peak voltage at the data rate. The output pulses have an approximate 50% duty cycle and no additional phase flipping. A RZ33 pulse is created by driving the pulse carver with a 2Vπ voltage (peak to peak) sinusoid at half the data rate, Bb/2, which is biased at the maximum of the transfer curve. Again, there is no phase flipping in the output.

RZ67 is created by driving the pulse carver with a 2Vπ voltage (peak to peak) sinusoid at half the data rate, Br /2, which is biased at the null of the transfer curve. The key effect of this type of pulse carving is that adjacent pulses always have alternating zero and phase. In other words, the DC tone averages to zero since alternating bits have opposite phase. As a result, the carrier is suppressed on average and harmonic tones at +/- Br / 2 appear . The format is also known as Carrier Suppressed RZ. The state diagram and the constellation for RZ formats is shown below. Symbol “0” real Symbol “1” E0 imaginary State ”0” State ”1” ”0” “1” Tb / D RZ67 D = 1.5 RZ50 D = 2 RZ33 D = 3 The state diagram and the constellation for RZ formats.

Phase 0 Phase π M - Z voltage M - Z power output Vπ/2 2Vπ 3Vπ 4Vπ Bias RZ67 signal drive RZ50 signal drive RZ33 signal drive The bias and drive requirements for generation of RZ pulses using the carver concept.

The pulses of various RZ formats. The two sided PSD of RZ33 and RZ50 format is given by

Modulation Formats ASK signalling format For RZ67 the PSD is given by
The PSDs for RZ33, 50 and 67 from computer simulations are shown below. Modulation Formats Conversion for Future Optical Networks: Javier Cano Adalid MSc Thesis , TUD, 2009

In order to understand how the carrier is suppressed with RZ67 one has to consider the impact of phase. The optical pulses and their phase relationship is shown below. The sign of the carrier is changing at every bit transition and they are complete independent of the information carrying part of the signal. On average therefore The filed has a positive sign for half the ”1” bits and negative for the other half. This phase changes results in a zero mean optical field envelope. As a result the carrier at the optical centre frequency vanishes giving the format its name. Modulation Formats Conversion for Future Optical Networks: Javier Cano Adalid MSc Thesis , TUD, 2009

The concept of ASK can also be used for multilevel transmission. A typical 4-level NRZ ASK format is shown below where the original pulse width is Tb. 1 2 3 Amplitude levels time Tb A typical 4-level ASK format. With four levels of signalling the number of bits, n, transmitted by one symbol is A typical encoding scheme for a 4 - level ASK is Binary Symbol 00 10 2 01 1 11 3

B Z 1 2 3 Power combiner Stream A Stream B Z (a) Multilevel signal generation. (a) Multilevel signal decoding. The generation and decoding of multilevel signals.

and the different optimum sampling times change with distance .
Modulation Formats ASK signalling format Experimental eye diagrams for 4-ary ASK signalling; notice how the inner eye shapes and the different optimum sampling times change with distance .

Because the pulse width in the 4 – level ASK is twice that of the initial binary data the symbol rate has been halved to B r /2. Generalising this result to M – level waveforms in which blocks of n-bits are represented by one of the M – level waveform with Now, each pulse corresponds to and as a result the M – ary signalling rate has be reduced to On the face of it by reducing the signalling rate through M - ary transmission we have reduced the requirements on the system parameters..

The bandwidth reduction can be staggering at least theoretically. The table below summarises the reduction in bandwidth.. The B stands for the bandwidth of the original binary signal. The ± implies the bandwidth around an notional optical carrier. Levels of M-ary Bandwidth 2 ± B 4 ±B/2 8 ±B/3 16 ±B/4 32 ±B/5 64 ±B/6 All seem to be easy, but is it? In order to understand what we have done we have to go back to the binary transmission format and investigate its subtle features.

For a binary format the transmitted constellation and the constellation in the receiver before decision are shown below with the effect of noise exaggerated. . “0” “1” Noise processes Detection threshold Space of “0” Space of “1” “0” “1” Symbol dynamic range Transmitted constellation Constellation at the receiver decision point At the receiver decision point noise has been added to the transmitted constellation And in order to minimise the errors in detection the threshold should be set in the middle of the receiver dynamic range. The overlap between the two noise processes give rise to detection errors. Consider now the case of a 4-level ASK with the same power. The new transmitter and receiver constellations are shown in the next slide.

“00” “01” “10” Symbol dynamic range for 4-ary “11” Symbol dynamic range for binary “00” “01” “10” “11” Noise processes Detection thresholds Transmitted constellation Constellation at the receiver decision point In order to achieve the same detection errors with the reduced dynamic symbol range as in the binary case either the variance of the noise processes must be reduced, unlikely, or the power must increase. The latter usually happens and it is for this reason that M-ary ASK is not as wide spread as perhaps expected. In optical power required for a M - ary ASK format is For example with M=4 the optical power required is 3.3 dB more than that for M = 2 ( binary).

the phase of “0” been shifted by π.
Modulation Formats PSK signalling format The basic features of the “phase shift keying”, (PSK), format as shown below. Amplitude PSK signal time Tb Baseband signal 1 Constant envelope Phase 0 Phase π The PSK format with a binary NRZ baseband signal with the phase of “1” been 0 and the phase of “0” been shifted by π. Conceptually, an optical phase modulator is one of the simplest devices. The next slide illustrates the concept of an optical phase modulator.

Modulation Formats PSK signalling format
Basic concept; waveguide μm depth. A travelling wave phase modulator: from: Sumitomo Osaka Cement Co. Ltd. Actual device. Driving voltage V0; N peaks of wave. Driving voltage V1; N+1 peaks of wave.

The electrode configuration for phase modulator.
Modulation Formats PSK signalling format Electrical contacts x z y waveguide X - cut signal ground Z - cut The electrode configuration for phase modulator.

Modulation Formats PSK signalling format
The phase shift induced by the applied voltage is given by where L; the length of the device, ne; the extraordinary index, r33; the electro-optic coefficient , V; the applied voltage, g; the distance between the two electrodes and Γ; the overlap integral value. For LiNbO3 at 1550 nm ne = 2.15; r33=30.8 x m/V and Γ ~ 0.3 to 0.5. With symmetric drive V is replaced by V/2. Defining Vπ as the value for which the phase shift is π the phase shift can be written as For fibre communication modulators Vπ ~ V.

Modulation Formats PSK signalling format
The transmitter for “Binary PSK” (BPSK) with coherent detection is very simple. CW optical source Binary phase modulator Binary data Phase modulated light On the phase of it seems that nothing more is required for BPSK with coherent detection. However the issues will emerge if one looks at the details of the operation of the modulator. For this the relation between voltage and phase shift is required; . It is clear that to get a phase shift of π rads V=Vπ is required. But, if the voltage fluctuates around Vπ or if the phase of the carrier changes it will distort the constellation of BPSK. If unchecked the fluctuations will have a serious impact on detection.

Modulation Formats PSK signalling format
Ideal constellation. Perturbed constellation. π φ1 φ2 φ3 threshold The impact of a fluctuating phase of an optical carrier. For the BPSK format the optical field is given by where only the phase φc(t) is modulated by the data where the random variable αn= 0 or 1 depending on the data sequence. For αn= 0

Modulation Formats PSK signalling format and for αn= 1
The state diagram of a BPSK format is shown below. Some key observations can now be made. 1 Phase Intensity Time

Modulation Formats PSK signalling format
For a genuine random source of information the number of consecutive “1” and “0” can be very large and consequently the phase of the source will fluctuate leading to detection problems. One other key feature of the BPSK with a phase modulator is that it is a continuous envelope format. Yes, the phase changes from “1” to “0” but the power, Popt, stays the same per bit and the energy per bit, Eb, is Also, from the information point of view BPSK is a symbol per bit format. It will be more productive to reassigned the set of the input bit set {1,0} to the symbol set (1,-1}, that is, phase for “1”= 0 and phase for “0” = π. Another key feature of using a phase modulator in the chirping introduced as the drive signal changes. This chirping forces the optical way to move along the unit circle rather than straight from 0 → π and π→ 0. It is customary to express the constellation in terms of the energy /bit; see next slide. The signalling for NRZ and RZ pulses is shown in the next slide.

Modulation Formats PSK signalling format
Phase Euclidean distance Time 1 d 1 The constellation in terms of energy per bit. The Euclidean distance is now twice that in ASK signalling leading to a better S/N ratio.

Modulation Formats PSK signalling format ≈
+1 -1 time 1 BPSK – NRZ format BPSK – RZ format e(t) The power spectral density of the BPSK - NRZ format is The important observation is that because the average phase is zero there is no DC term which means that all the power is available for signalling. When the baseband modulates the carrier again there is no power in the carrier. This form of signalling is known as “suppressed carrier signalling.”

The single sided PSD of a BPSK – NRZ format; bandwidth ~ 2Rb.
Modulation Formats PSK signalling format fc f Bandwidth ≈ 2Bbase Scarrier(f) 90% of power 95% fc = optical carrier Stochastic signal The single sided PSD of a BPSK – NRZ format; bandwidth ~ 2Rb. The PSD of a RZ-50% BPSK pulse is shown in the next slide together with the PSD of BPSK with NRZ format.

The spectra of BPSK with NRZ and RZ - 50% pulses.
Modulation Formats PSK signalling format Scarrier(f) BPSK - NRZ BPSK - RZ 50% fT The spectra of BPSK with NRZ and RZ - 50% pulses.

Modulation Formats PSK signalling format
The spectral densities for BPSK have been calculated for rectangular pulses, without filtering before modulating the carrier and modulators without frequency chirping. If these conditions apply then the electrical and optical spectral are the same. However, if this is not the case then the electrical and optical spectra differed to a degree that depends on the filtering and the chirping. The absence of the carrier in the BPSK format makes the carrier recovery in the receiver difficult. The BPSK format can be slightly modified by transmitting a residual carries element. This is achieved by not modulating the carrier by π- rads but at say 0.9 π rads. Then the constellation becomes; Suppressed carrier constellation Residual carrier constellation Φ=π Φ < π

Schematic of a RZ BPSK transmitter architecture.
Modulation Formats PSK signalling format The architecture of a RZ BPSK transmitter is similar to the one used in ASK. CW light NRZ data NRZ Optical RZ format Pulse carver MZ Clock Phase modulator Schematic of a RZ BPSK transmitter architecture. The key assumption underlining the development of the concept of BPSK is that the phase of the carrier evolves as a constant vs. time. This implies an optical oscillator of zero linewidth and a great stability. In general these conditions cannot be met in practice and a solution has emerged through signal processing.

Modulation Formats PSK signalling format
The study of PSK signalling will be concluded with the study of the differentially encoded PSK, (DPSK). With the PSK format the information is embedded in the phase of the carrier so in order to retrieve the information a detection system sensitive to the phase must be used. Such a system is refer to as “coherent” and the receiver is very complex compared to the ASK receiver. One way to recover information embedded in the phase of the carrier without a coherent receiver is to encode the information before modulation “differentially”. To understand the process consider a data stream that for PSK signalling the “1” are associated with 0 - phase and the “0” with π – phase. Then, Data 1 Transmitted phase π The key feature of this table is that the data set the phase.

Modulation Formats PSK signalling format
To demodulate a binary PSK signal the receiver has to have a local oscillator synchronous with the oscillator in the transmitter. However, the carrier phase can be recovered only with a synchronous receiver but also by using the phase of the transmitted carrier itself. This is the basic idea behind the differential PSK. The basic algorithm for DPSK is where xi the current bit (symbol) and yi-1 the last transited symbol (bit). Now all the x’s arriving to be transmitted are independent but the encoding process introduces a correlation between the y’s and x’s at the output of the transmitter. At the receiver the decoding is simply, Now, xi depends not one the absolute value of y’s but on their difference. That means that if the constellation is rotated for some reason in the channel the correct data can still be detected if the difference does not change. The circuit diagram of a differential encoder / decoder is shown overleaf.

Modulation Formats PSK signalling format Sometimes the expressions and
xi yi Delay Tb yi - 1 Differential encoder. Logic circuit for differential encoder. Delay Tb I1 I2 Out 1 Differential decoder. Modulo-2 addition - Exclusive OR Sometimes the expressions and are found in the literature.

Modulation Formats PSK signalling format
. Consider the following table as an example of differential encoding K -1 1 2 3 4 5 6 7 Xk Yk Decoding with correct channel polarity. where k-1 the reference digit, and the estimated yk and xk. If for some reason the channel inverts the polarity , that is, the y - sequence is the one’s complement then the original signal can still be recovered ( next slide).

Modulation Formats PSK signalling format
-1 1 2 3 4 5 6 7 Xk yk y*k x*k Sequence inverted Reference digit Decoding with inverted channel polarity. If the PSK format is used to transmit a binary sequence without differential encoding the format is known as “binary PSK” ( BPSK). When differential encoding is added then it becomes “differential binary PSK” ( DBPSK).

Modulation Formats PSK signalling format
It is now straightforward to translate this encoding scheme to PSK. The basic rule is that if the current input signal and the previous encoded signal are the same ( no change) the phase of the carrier does not change. If they are different the phase changes. The table below summarises the encoding and decoding process. k -1 1 2 3 4 5 6 7 xk yk Phase π Received signal Complement Decoded

Modulation Formats PSK signalling format
The architecture of a DBPSK transmitter is shown below. CW light Synchronisation NRZ Optical RZ format Pulse carver MZ DBPSK encoder Phase modulator Data Tb Clock or RF The constellation and state diagram is shown overleaf.

The constellation and state diagram of the DBPSK format.
Modulation Formats PSK signalling format 1 Phase Intensity Time The constellation and state diagram of the DBPSK format. The phase modulator is a simple device but its features do not lead to a simple transmitter because of the control circuits required. However, the MZ amplitude modulation can also be used for phase modulation.

Modulation Formats PSK signalling format
The additional processing in the transmitter required for the DBPSK format pays dividend at the receiver where the simplicity for a phase modulated format is staggering. Consider the following example. From: Iidefonso M. Polo 1 October 2009 SUNRISE TELECOM. com

Direct detection receiver for the DBPSK format.
Modulation Formats PSK signalling format 1/Tb A B DI transmission Optical frequency Tb Delay interferometer A B Direct detection receiver Direct detection receiver for the DBPSK format.

Modulation Formats PSK signalling format
The transfer function of the MZM is given by With v1(t) = - v2(t) the phase modulation is removed and For phase modulation the MZ is biased for zero output without signal and then driven by 2Vπ. The phase modulation is induced as the drive moves the modulator right and left of the bias. However, as the modulator moves from 0 to π phase a dip in the intensity occurs as it crosses the 0 - power line. The operation is similar to that of a MZ driven by a duobinary signal. The next view graph summarises the operation of the MZ as a phase modulator. It must be born in mind that the operation described is the theoretical one and the performance could deteriorate with real drive signal. However, because of the nonlinear transmission function of the MZ ameliorates the impact of overshoots and undershoots in sharp contrast to a phase modulator here all the imperfections pass on straight on the phase of the carrier.

Modulation Formats PSK signalling format
4Vπ 3Vπ 2Vπ π time Output power Drive voltage Difference v1(t) - v2(t) Intensity dips Optical power Optical field v1(t) - v1(t) CW light Phase modulated light Vπ for zero transmission The operation of the MZ modulator as phase modulator.

Modulation Formats PSK signalling format
The use of DBPSK offers the possibility of simple good performance systems but it also offers further possibilities if combined with advances in technology. Consider the MZ configuration shown below. VPM =-Vπ/2 vQ(t) - vI(t) Phase modulator CW light modulator I modulator Q DQPSK modulator vI(t) - vQ(t)

Modulation Formats PSK signalling format
Each individual MZ modulator ( I & Q) operates as a phase modulator. The phase modulator after the Q-modulator introduces a rotation of π/2 rads that give rise to the term “channel in quadrature”, (Q – channel ), the other channel is known as “ channel in phase”, ( I - channel). This form of signalling is known as “Differential Quadrature PSK”, (DQPSK). To see how the modulator works assume that the transfer function of each MZ is given by and expanding

tan -1 (cos(π vQ (t)/Vπ)/ cos (π vI(t)/Vπ)
Modulation Formats PSK signalling format Now, if VI and VQ take one of the values {0,π} then the phase shift induced on the input signal ein takes one of the four values as shown in the table below. vI(t) vQ(t) cos (πvI(t) /Vπ) j cos (πvQ(t) /Vπ) tan -1 (cos(π vQ (t)/Vπ)/ cos (π vI(t)/Vπ) 1 π/4 -1 -π/4 3π/4 5π/4 Q - axis (I,Q) = (1,0) (I,Q) = (0,0) The constellation diagram corresponding to this format is shown on the right:“0”→ voltage level 0 and “1” → voltage level Vπ. 3π/4 π/4 5π/4 I - axis -π/4 (I,Q) = (1,1) (I,Q) = (0,1)

Modulation Formats PSK signalling format
It should be clear now that QPSK can be combined with differential encoding for DQPSK. The figure below summarises a measured constellation for 40 Gbit/s DQPSK without dispersion. The constellation diagram for a 40 Gbit/s DQPSK format without dispersion. Comparison of spectrum of NRZ and DQPSK at 10 Gbit/s data rate.

Modulation Formats PSK signalling format
The DQPSK format operates at 20 Gbauds but single each channel operates as half the bit rate the impact of chromatic dispersion and polarisation mode dispersion Is limited compared to the full bit rate systems. This can be extended by using dual polarisation QPDK. The modulator for such a format is shown below. The approach appears to be wasteful in terms of hardware but in transmitting at the data rate of 40 Gbit/s but at the symbol rate of 10 Gsymbols the effects of dispersion are suppressed.

Modulation Formats FSK signalling format
Frequency shift keying ( FSK) has been used extensively in radio communications but its use in fibre communications has been limited to research only. The reason for that is simple; there is no optical source that can be frequency modulated in excess of 10 Gbit/s and maintain capabilities for long haul transmission. The obvious candidate is the semiconductor laser and a lot of effort was directed towards frequency modulated lasers but the rapid increase in speed helped to consolidate the LiNbO3 technology as the key technology for high speed long haul systems. So, all the recent effort has been directed towards that technology. In FSK the information is embedded in the carrier by shifting the carrier frequency, ω0 itself; For a binary digital signal ω0 takes the values [ω0 – Δω] or [ω0 + Δω] depending on a “0” or “1” bit been transmitted. The frequency 2Δf separates in the frequency space the symbols “0” and “1”. The total bandwidth of the modulated carrier is given approximately by

Modulation Formats FSK signalling format
where B the bandwidth of the information. Two classes of FSK are distinguished: [1] Wideband FSK; Δf >>B and the bandwidth approaches Δf ; [2] Narrowband FSK; Δf << B and the bandwidth approaches 2B. One of the difficulties in directly modulating the leasers, say DFBs, is the impact of FSK modulation on the amplitude modulation imparted on the field. In a relatively recent , 2004, Alcatel Lucent experiment the penalty due to the intensity modulation was set at 1 dB. That constrain limited the drive to 600 mV at 50 ohms leading to a peak-to-peak current of 12 mA. With an FM efficiency of 400 MHz/mA the peak-to- peak frequency swing is 4.8GHz and this is approximately 50% of the bit rate that was 10Gbit/s. The eye pattern below shows the intensity fluctuations at the output of the laser. The eye at the output of the laser- amplitude modulation. The eye at the output of the FSK-AM detector; a MZ interferometer with 11GHz FSR.

Modulation Formats FSK signalling format
Tuneable lasers can offer an alternative approach to FSK modulation. Consider the state of the art sampled grating Bragg grating laser (SGDBR) illustrated below. The section of the laser that controls the phase can be modulated by a binary sequence giving rise to FSK modulation. However, since lasers of that class were designed for wide tuneability their performance does not addresses the requirements for data FSK transmission. The FSK capabilities of one such laser were assessed and some results are quoted in the next slide.

Modulation Formats FSK signalling format -5 GHz +5 GHz 12 GHz / ma
f0 = 92.2 THz Output frequency vs. phase section current at THz. Time averaged spectrum of FSK modulation at THz ; Δf= + /- 5GHz.

The spectral of NRZ ASK modulation
Modulation Formats Single Sideband signalling format Up to now all the modulation formats studied generate a double sides spectrum. For example consider the ASK format for 40 Gbit/s. The residual carrier is a waste and other signalling formats suppress it. Then, there is the upper and low sidebands but only one sideband existed in the original baseband signal with a bandwidth of 40 GHz.( see figure on the left). The question now arises; is the lower sideband necessary? Mathematics; for any real value signal function f(t) there is ”conjugate symmetry” in the Fourier transform, that is, Residual carrier Upper sideband Original baseband signal Lower sideband and all the information embedded in f(t) is contained in either the positive or the negative frequency components. The conjugate symmetry exists because the The spectral of NRZ ASK modulation at 40 Gbit/s.

Reconstructed signal F(ω)
. Modulation Formats Single Sideband signalling format ω ωm - ωm ωc - ωc F(ω) Upper sideband Lower sideband Double sideband SC Upper sideband only Lower sideband only Reconstructed signal F(ω) Fourier transform of a real function is Hermitian. Only a single sideband needs to be transmitted. To illustrate this concept consider the details of the diagram on the right. Let assume that the modulation signal is a real time function given by x(t) and let us define the analytic signal ( see appendix B) The Fourier transform of the analytic signal is When xa(t) modulates the carrier exp(j2πf0t) the frequency components are shifted by +f0 and there are no negative frequencies.

Modulation Formats Single Sideband signalling format
Carrier Lower sideband rb=10Gbits The output spectrum of a lower sideband transmitter; P.M. Watts et al., ECOC 2005, Paper TU 4.2.4 The Hilbert transformer was implemented using a four tap FIR digital filer; where x(n) is the input data sampled at twice the bit rate.

Modulation Formats Single Sideband signalling format Advantages:
ω0 ω Filter Residual carrier Interference from the lower band SSB Advantages: [1] The filter is realisable. [2] The residual carrier makes possible the detection without a coherent receiver. [3] The interference from the lower sideband is manageable. [4] It is possible to use electronic dispersion compensation at the receiver because the phase information is preserved. This approach is also called vestigial sideband and used extensively in radio communications. A number of successive experiments has taken place where a fibre Bragg filter is used as the optical filter because of its excellent performance.

Modulation Formats The detection of modulated optical carriers
In order to detect the information embedded on the optical carrier the receiver must be suitable equipped. In this part of the module the architectures of suitable receivers will be discussed. Before we embark on the stude of receiver architectures it is important to introduce the classes of detection and their ramifications. Since optical communications are carrier communications with the carrier frequency vastly larger than the information bandwidth the receivers cannot directly detect the optical frequencies as it is common in radio and microwaves. The detailed study of optical detection, that is the interaction between radiation and matter, belongs to quantum mechanics. However, in field optical communications the essentials of the interaction can be derived without recourse to quantum mechanics. This is achieved by assuming that the electric filed incident on the detector is classically described but the response of physically realisable detectors is modelled using the same statistics that a quantum mechanical model would have provided. This “quantum mechanically correct” detector response is then mused as the fundamental observable quantity on which the decisions are based. These receivers are called “semi classical” and have the advantage of using well known detection techniques.

Modulation Formats The detection of modulated optical carriers
Under the constraints imposed by the semi-classical approach the photocurrent of an optical detector is given by where e; the electronic change, nq the ability of the device to concert photons into electrons known as the quantum efficiency and nq <1, Popt(t); the envelope of the optical radiation, h the Planck constant and f the frequency of the radiation. Since hf Is the energy of one photon the ratio (Popt / hf) is the number of photons in Popt. The simplest possible receiver is based on this equation and the detection class is known as “direct detection” and the receiver as “direct detection receiver”. Optical envelope detector Low noise amplifier Electronic signal time The basic architecture of a direct detection receiver.

Modulation Formats The detection of modulated optical carriers
The direct detection is based on the assumption that information is embedded in the amplitude of the optical carrier, that is, ASK modulation. If the information is embedded in the phase of frequent of the carrier direct detection will not detect it and instead it will follow the envelope of the radiation. In general to detect information embedded in the phase or frequency a new class of detection must be used known as “ coherent detection”. Coherence is a property of waves that measures the ability of the waves to interfere with each other. [1] Two waves that are coherent can be combined to produce an unmoving distribution of constructive and destructive interference (a visible interference pattern) depending on the relative phase of the waves at their meeting point. [2] Waves that are incoherent, when combined, produce rapidly moving areas of constructive and destructive interference and therefore do not produce a visible interference pattern. These features are illustrated in the next slide.

Modulation Formats The detection of modulated optical carriers
Coherent waves (monochromatic). Incoherent waves of the same frequency (monochromatic). Incoherent waves with different frequencies (not monochromatic). A wave can also be coherent with itself, a property known as temporal coherence. If a wave is combined with a delayed copy of itself (as in an interferometer), the duration of the delay over which it produces visible interference is known as the coherence time of the wave, Δtc. From this, a corresponding coherence length can be defined;

Modulation Formats The detection of modulated optical carriers
The temporal coherence of a wave is related to the spectral bandwidth of the source. A truly monochromatic (single frequency) wave would have an infinite coherence time and length. In practice, no wave is truly monochromatic (since this requires a wave train of infinite duration), but in general, the coherence time of the source is inversely proportional to its bandwidth. The general description of, say, the electric component of an optical wave is where the instantaneous frequency is defined as The source bandwidth depends on the term ∂θ(t) /∂t.

Modulation Formats The detection of modulated optical carriers
The basic architecture of a coherent receiver is shown below. Optical carrier with information Local oscillator wave without information Beam combiner Optical detector The basic architecture of coherent detection. The essential features of coherent detection can be easily understood by making by making two assumptions; [1] the polarisation of the incoming signal and that of the local oscillator are the same; [2] the fields of the signal and local oscillator are of constant amplitude over the surface of the detector.

Modulation Formats The detection of modulated optical carriers
Under these two assumptions the derivation of the photocurrent proceeds as follows. The optical detectors used in optical communications are linear in terms of optical power but quadratic in the field. Then, assuming that The photocurrent is derived as follows; The terms containing the frequencies 2ωS, 2ωLO and ωS+ωLO are too high to be to detected so the expression of photocurrent is simplified to

Modulation Formats The detection of modulated optical carriers
Since the optical power contained in a signal is proportional to the square of the field the last equation can be written as where Ps and PLO the signal and local oscillator power respectively. The third term involves the expression that indicates that the signal filed is multiplied by the local oscillator field and it is also known as the coherent gain. It is this cross product that accounts for the superior performance in receiver sensitivity in coherent detection. The last equation makes possible two options for detection; Option I – ωS ≠ ωLO; heterodyne detection. Defining |ωS – ωLO|= ωIF where IF stands for intermediate frequency. Then, .

The key features of heterodyne detection are:
Modulation Formats The detection of modulated optical carriers The key features of heterodyne detection are: [1] The receiver sensitivity is shot-noise limited; increase in unrepeated transmission distance. [2] The phase information embedded in the carrier can be restored; improved receiver sensitivity and use of multi-level modulation format [3] The heterodyne receiver can achieve linear detection; electronic post – processing in the receiver. [4] The receiver bandwidth exceeds substantially the information bandwidth. Option II - ωS = ωLO; homodyne detection. Then, Simplifying the two equations the signal photocurrent is given by

Modulation Formats The detection of modulated optical carriers
The key features of heterodyne detection are: [1] The receiver sensitivity is shot-noise limited; Increase in unrepeated transmission distance. [2] The phase information embedded in the carrier can be restored; improved receiver sensitivity and use of multi-level modulation format. [3] The heterodyne receiver can achieve linear detection; electronic post – processing in the receiver. [4] The homodyne receiver is a baseband receiver; relative ease in increasing the bit rate. The architecture of the heterodyne and homodyne receiver are shown in the next slides. The function of the digital controller entails more that is shown in the diagrams. Especial important is the concept of channel acquisition which is initiated and controlled by the receiver controller. The details depend on the application. The last equation makes possible the comparison of the mean signal power for homodyne, heterodyne and direct detection. That is,

Modulation Formats The detection of modulated optical carriers Optical detector IF Amplifier Demodulator Baseband filter Decision Automatic frequency control Local oscillator Directional coupler Temperature control Data Signal optical carrier Power control Receiver digital controller Heterodyne coherent optical receiver.

Modulation Formats The detection of modulated optical carriers Optical detector Baseband filter Decision Automatic phase control Local oscillator Directional coupler Temperature control Data Signal optical carrier Power control Receiver digital controller Homodyne coherent optical receiver.

Modulation Formats The detection of modulated optical carriers
In the diagrams of heterodyne and homodyne receivers a 3 - dB coupler was used to combine the signal and local oscillator fields. Because only one output was used from the coupler half of the power of the signal and half of the power of the local oscillator are wasted. This loss can be in principle eradiated if a balanced optical receiver is used. The operation relies on a fundamental properly of the coupler; the signal at one output fibre suffers a π/2 phase shift with relation to the throughput fibre. The diagram below shows the details of the configuration. Local oscillator Directional coupler Signal optical carrier Detector A Detector B + - vA vB The input to the optical detectors are ;

Modulation Formats The detection of modulated optical carriers
At the detector outputs the current will be Subtracting, This last equation shows that twice the we current of four time the power is obtained in comparison with the single optical detector or 6 dB improvement. Since the two components of the photocurrent are subtracted the large dc term generated by the local oscillator is cancelled and also any excess noise generated by the local oscillator. However, close matching of the two detectors is required if good excess noise cancellation is to be obtained.

Modulation Formats The detection of modulated optical carriers
The basic three modulation formats for coherent detection (ASK, FSK and PSK) can be detected with a heterodyne receiver. The homodyne receiver can operate only with ASK and PSK. We will now discuss some of the details for both receiver classes. [1] Homodyne Detection. In this case the photocurrent directly delivers the information baseband. In order to detect ASK or PSK signals the local oscillator (laser) must somehow be synchronised with the transmitter oscillator (laser). The signal photocurrent output for ASK homodyne detection is Since the transmitter and receiver are independent there will be a phase difference between the two waves therefore the angle θ is in reality θ – φ where φ is the arbitrary transmitter wave angle. In order to recover the symbol “1” the angle difference should be zero.

The impact of phase tracking error for ASK format.
Modulation Formats The detection of modulated optical carriers The impact of phase error in ASK is illustrated in the constellation diagram below. Ideal position of the symbol “1” (θ - φ) = 0. Position of the symbol “1” (θ - φ) ≠ 0. Penalty due to phase tracking error The impact of phase tracking error for ASK format. There are three possible approaches to carrier tracking for ASK; injection locking, selective amplification and optical phase locked loop. Injection locking requires high power level at the input exceeding substantial the receiver sensitivity of most homodyne systems. The selective amplification of the carrier without amplification of the signal sidebands is possible before the photodetector and the amplified carrier then acts as the local oscillator.

Modulation Formats The detection of modulated optical carriers
The last is the optical phase locked loop, (OPLL). Various variants of the OPPL theme have been Investigated and the most important are: [1] The balanced loop. [2] The decision driven loop. [3] The Costas loop. As expected all three variants are strongly sensitive to the phase noise as to require a narrow linewidth laser in order to operate at the quantum limit of sensitivity. From the viewpoint of phase noise the best performance is obtained by the decision driven phase locked loop.

Modulation Formats The detection of modulated optical carriers x
Clock recovery x Local oscillator tunable laser Polarisation controller Optical carrier signal 90o optical hybrid Local oscillator Lowpass filter Loop filter I - arm Q - arm Data Decision Driven Optical Phase Locked Loop.

Modulation Formats The detection of modulated optical carriers
With PSK signalling the signal photocurrent output is where cos θ represent the phase error in tracking. The techniques suitable for ASK homodyne are also suitably for PSK homodyne and again the phase error is translated into performance penalty in the same way as for ASK. It is not always necessary use a complete coherent receiver for the demodulation of PSK signals. If the transmitted PSK signal uses the DPSK format the detection can be very simple. Since the phase off the current DPSK pulse depends on the previous phase the signal has an in-built reference that can be for synchronous detection. The basic principle is shown in the next slide.

Modulation Formats The detection of modulated optical carriers
Tb Delay interferometer A B Direct detection receiver DPSK formatted signal Data A key feature of this approach is that a direct detection receiver can be used but the transmission advantages of the format are used in the design of the transmission system. Since PSK is a suppressed carrier format another option is to transmit a residual carrier by using incomplete phase modulation. The pilot carrier together with the signal are combined in a 3 dB directional coupler and detected by a balanced receiver. The output signal from the difference amplifier is a function of the phase error which can be used to drive the PLL. This approach is also known as balanced OPLL.

Modulation Formats The detection of modulated optical carriers
It should be understood that this approach will lead to a performance penalty at the receiver. A block diagram of the residual carrier approach is shown below. Baseband filter OPPL Loop filter Directional coupler Optical detector Local oscillator Optical PSK signal with residual carrier Optical phase locked loop Data Homodyne coherent optical receiver with optical phased lock loop using the residual carrier approach.

Modulation Formats The detection of modulated optical carriers
[2] Heterodyne detection: When heterodyne detection is used there is a bewildering range of options with respect o the second electronic detection. This is because all the techniques developed for radio communications can now be used in optical communications. Starting with PSK it is important to notice that the PSK spectrum contains no energy at the carrier frequency. It is therefore necessary to introduce a nonlinear element within the phase recovery subsystem to ensure carrier recovery. First, by squaring the PSK signal a signal at twice the original frequency is produced that can be filtered and used for phase estimation. The figure below illustrates the squaring loop technique.

Modulation Formats The detection of modulated optical carriers
The squaring loop technique for carrier recovery. Another approach to the recovery of the carrier is to reduce the depth of modulation so that a small competent of the carrier is transmitted. However, to detect the residual carrier satisfactory a substantial amount of signal power may be sacrificed leading to performance penalties. A variation on the residual carrier technique is to recover the carrier at the IF stage, see below.

Modulation Formats The detection of modulated optical carriers
IF signal Frequency doubler Bandpass filter divider Data Carrier recovery arm Data detection arm Carrier recovery synchronous demodulator. The DPSK can be detected without a synchronous receiver following the DPSK signal with an optical interferometer but now the interferometer is placed in the lf section of the receiver, see below. Lowpass filter Delay T Heterodyne DPSK signal Data Double balanced mixer Phase detector Demodulation of DPSK signal with an electrical interferometer.