Coherent Lightwave Systems

CONTENTS Principles of coherent and non-coherent detection : heterodyne and homodyne detection; Modulation formats: ASK,PSK,FSK,PPM,DPSK;

CONTENTS Demodulation schemes : Bit error rate performance analysis; synchronous and asynchronous demodulation; Bit error rate performance analysis;

CONTENTS Performance degradation due to: laser phase noise, group velocity dispersion, self phase modulation, polarization mode dispersion, relative intensity noise, effect of timing jitter;

CONTENTS System design considerations: power budget, rise time budget, power penalty.

Modulation Modulation process: Switching or keying the amplitude, frequency, or phase of the carrier in accordance with the information binary bits. The modulation can be either: Direct modulation Light is directly modulated inside a light source External modulation Using external modulator

IM-DD system Optical detection Applied in the first generation (1970’s) intensity modulation direct detection is still the most used for optical communications Information is carried only by the intensity not frequency or phase Optical detection The received signal is applied directly to photodetector Photo-detection of light represents the key operation in the optical receiver. Converting the collected field onto a current or voltage.

Light is described as a stream of photons (quanta) The theory of quantum states that the energy of a photon is proportional to the frequency of light Where the Plank constant h = 6.6261  10-34 W s2

Let P the optical power of a light beam, then the number of photons per second is: For modulated optical signal with power P(t), the instantaneous photon intensity (photon flux) varies with time: photons/s

For a PIN-diode photodetector, the average number of electron-hole pairs generated in a time interval of T is given by Where  is the quantum efficiency of the device and E is the energy received in a time interval T.

The ideal receiver Consider an ideal OOK transmission system over an ideal channel The transmitter sends light for a one No light for a zero The receiver counts N, the number of photons it receives in a bit interval of T seconds, and zero otherwise

If a zero is transmitted, then there is a zero probability of receiving zero photons. If a one is transmitted, then the photons arrive according to a Poisson process with mean m For a ONE, the probability of receiving N photons in T seconds is given by by the Poisson distribution.

Quantum limit It is possible that no photons arrive when a ONE is transmitted. This leads to a probability of error or a Bit-error-ratio (BER), of This leads to an important lower bound on the BER called the quantum limit It indicates a minimum signal power required by an OOK receiver to achieve a given BER

Example: Letting BER= 10-9 gives m = 20.03. Hence, to achieve a BER of 10-9, the pulse must have an optical energy corresponding to an average of 20 photons. On average, half the signal intervals contain optical pulses, and the average number per transmitted bit is: This quantity of of 10 photons/bit is called the quantum limit for optical detection. It represents a lower limit on the received power necessary in a direct detection.

Practical receiver Receiver configuration IM-DD system can only be used for OOK modulation format

is a stationary random process with Poisson statistics Shot noise Shot noise (from O-E counting process in PIN): is the average photocurrent is a stationary random process with Poisson statistics is(t) can be approximated by the Gaussian statistics with its variance given by:

current fluctuation induced by thermal noise Including thermal noise (from carrier moving in any conductor): current fluctuation induced by thermal noise iT(t) can be modeled as a stationary Gaussian random process with its variance given by: Its spectral density (“white noise”) is given by:. Boltzmann constant, the absolute temperature, and the load resistor

Total receiver noise Considering the dark current from PIN and the enhancement to thermal noise from the components other than the load resistor in the linear channel, the total noise variance is: the PIN dark current and the amplifier noise figure

Receiver signal to noise ratio PIN receiver: APD receiver: Where the APD gain and the APD excess noise factor is the ionization-coefficient ratio.

PIN and APD Noise limitations

BER Analysis for IM/Direct Detection The bit error rate can be computed as: where Pr(0/1) is the probability that a "0" is received when a "1" is transmitted. Pr(1/0) is the probability that a "1" is received when a "0" is transmitted The values of Pr(0/1) and Pr(1/0) depends on the statistical nature of the output signal in the presence of noise.

For a binary symmetric channel, p(0)=p(1)=1/2 which indicates equal probability of occurrence for a "1" and a "0" bit. The output signal current is given by Where in is the noise current due to shot and thermal noise. The probability density function of in is given by where imean=0 is the mean value of in.

Bit Error Rate The bit error rate can be computed as:

Since in is Gaussian with zero mean and variance n2 , the probability density function (pdf) of the receiver output corresponding to bit "1" and bit "0" are also Gaussian with mean I1 and I0 respectively and given by where 12 and 02 are the noise variances corresponding to bit "1" and bit "0" respectively.

Hence

Minimum BER occurs when Pr(0/1)=Pr(1/0) which corresponds to an optimum value of the threshold current ith and can be determined as The optimum threshold is then given by Under the assumption that the noise current is same for bit "0" and bit "1", 1=0, then the optimum threshold is given by The above optimum threshold is applicable in absence of laser phase noise. In the presence of laser phase noise, the optimum threshold is to be determined numerically because 1 does not equal 0.

The value of the parameter Q at the receiver output under optimum threshold condition is expressed as and the corresponding BER for optimum threshold is given by

Where we assumed that I0=0 and 0= 0 which is valid when the The output SNR (= signal power to noise power ratio) for a PIN-receiver is given by where Be=Br/2. In terms of number of photons per bit N, the BER can be expressed as where Where we assumed that I0=0 and 0= 0 which is valid when the receiver is dominated by shot noise.

hence and

Principle of Coherent Detection

Coherent Detection Coherent detection receiver adds light to the received signal as part of the detection process Local Optical Oscillator Photo- Detector Electronic Circuits Optical Signal Input Electrical Signal Output Beam Combiner Coherent receiver model

Detection Schemes Homodyne detection The optical signal is demodulated directly to the baseband. It requires a local oscillator whose frequency match the carrier signal and whose phase is locked to the incoming signal ( c= LO). Information can be transmitted through amplitude, phase, or frequency modulation Heterodyne detection Neither optical phase locking nor frequency matching is of the local oscillator is required ( c  LO).

Demodulation schemes in coherent detection There are two basic types of demodulation in coherent detection of optical signals : (a) Synchronous demodulation (is essential for homodyne detection) (b) Asynchronous demodulation

ASK, PSK, DPSK, and FSK modulation Formats

Optical Detection Modulated signal: Local oscillator signal: The output power of the photodetector where

Homodyne Detection Heterodyne Detection The detector current: Heterodyne Detection The detector current:

Heterodyne Synchronous Coherent Receiver Optical Signal Input Baseband Signal Output Local Optical Oscillator Photo- Detector BPF Beam Combiner Delay Carrier Recovery LPF In which the IF modulated signal is mixed with an IF carrier recovered from the IF signal. At the output of the mixer the baseband signal is received which is filtered by a low pass filter and fed to the decision circuit.

Heterodyne detection needs neither frequency matching nor phase locking. The detected electrical signal is carried by the intermediate frequency and must be demodulated again to the baseband. This demodulation scheme can be used for ASK, FSK or PSK modulation formats.

Heterodyne Synchronous ASK The detector current: its mean square is : The thermal noise and shot noise variances : where

IF- Signal to noise ratio (IF-SNR) : Or

If the bit rate is Br=1/T, then average signal power Let Be=Br/2, then SNR can be expressed The corresponding BER for heterodyne ASK receiver is

Receiver sensitivity Receiver sensitivity can be defined as the minimum required received optical power to attain a BER of 10-9 which corresponds to Q=6 or when SNR=144 or 21.6 dB. Average received power Pr can be obtained as For an ideal photodetector =1 and the number of photons per bit required for BER=10-9 is 72 for ASK heterodyne.

Heterodyne Synchronous ASK in the presence of noise The current after photo-detection (the output of the photodiode is passed through a BPF centered at the IF frequency and the filter out put can be written as:) The noise at the output of the filter can be expressed in terms of its in-phase and quadrature components as : where (Gaussian random variables with zero mean) The variance are given by:

With noise included after BPF: After synchronous (coherent) demodulation and LPF It shows that only the in-phase noise component affects the performance of synchronous heterodyne receivers.

The analysis is analogous to that for direct detection receiver where The analysis is analogous to that for direct detection receiver and the BER is given by where Where we assumed that I0=0 and 0= 1 which is valid when the receiver is dominated by shot noise at higher values of PLO.

Using the relation SNR=2Np we get

Homodyne Synchronous ASK The detector current: its mean square is : The thermal noise and shot noise variances : where

IF- Signal to noise ratio (IF-SNR) : Or where R=e/h

If the bit rate is Br=1/T, then average signal power Let Be=Br/2, then SNR can be expressed The corresponding BER for homodyne ASK receiver is For an ideal photodetector =1 and the number of photons per bit required for BER=10-9 is 36 for Homodyne Syn. ASK.

Heterodyne Detection versus IM/DD Homodyne Syn. ASK Versus Heterodyne Syn. ASK ASK homodyne receiver requires 3 dB less power and is therefore 3-dB more sensitive than ASK heterodyne receiver. Heterodyne Detection versus IM/DD Sensitivity Improvement of 10 dB to 20 dB Frequency selectivity IF domain signal processing provides better performance Heterodyne Detection Receiver is more sensitive to the phase noise of lasers Additional signal power is required for the same reliability of operation which is called power penalty

Synchronous PSK Detection in the presence of noise The detector current at the receiver output is given by where so that the output current is positive or negative depending on the bit transmitted as: and

Using SNR=2N for heterodyne case And using SNR=4N for homodyne case

Heterodyne Synchronous Dual-Filter FSK Receiver FSK synchronous receiver is equivalent to two ASK asynchronous heterodyne receivers operating in parallel. The signal is received during both binary bits, the SNR is 3-dB higher than that for ASK heterodyne receiver. In dual filter FSK receiver, two band-pass filters are used to pass the mark and space frequencies separately. The BPF are centered at (IF+) and (IF-) corresponding to "mark" and "space" frequencies. The output of the BPF are passed through envelope detectors and low-pass filters. The differential signal at the output of the low-pass filter is then obtained by subtracting the one from the other. The data decision is then made by comparing the output samples with a threshold of zero value.

The BER is then given by

Heterodyne Asynchronous receiver Optical Signal Input Baseband Signal Output Local Optical Oscillator Photo- Detector BPF Beam Combiner Envelop Detector LPF Asynchronous demodulation does not require recovery of the microwave carrier at the intermediate frequency The output of the IF filter is passed through an envelope detector and is low-pass filtered. The output of the LPF is sampled and compared with a threshold of optimum value to make bit decisions. This demodulation scheme can be used for ASK and FSK.

Heterodyne Asynchronous Detection in the presence of noise The current after heterodyne photo-detection The noise at the output of the filter can be expressed in terms of its in-phase and quadrature components as : where (Gaussian random variables with zero mean) The variance are given by:

With noise included after BPF, envelope detector and LPF: It shows that both the in-phase and out-of-phase noise components affects the performance of asynchronous (incoherent) heterodyne receivers. The SNR is thus degraded comparing with that of synchronous (coherent) heterodyne receivers.

because the output of an envelop detector is square of its input. In case of asynchronous demodulation, the noise at the output of the envelop detector is no longer Gaussian because the output of an envelop detector is square of its input. So, the noise statistics are changed due to envelope detection and hence the BER calculation becomes complicated. The current at the output of the envelop detector when a signal pulse is present corresponding to bit "1" is given by

The probability density function (pdf) of the output current I is given by a Rice distribution as where I0 is the Bessel function of the first kind and 2 is the noise variance . The output of the envelop detector corresponding to a bit "0" is and the pdf of the output is given by a Raleigh distribution which can be obtained by putting Ip=0 in the expression for p(I,Ip).

The bit error rate (BER) is then obtained as and The final form of the BER is given by The minimum BER corresponding to optimum threshold can be obtained numerically. If I0=0 and I1>>, ith=I1/2. Under such conditions, BER is given by Using SNR=2N for heterodyne detection, BER can be expressed as

Heterodyne Asynchronous FSK- Single filter Receiver Optical Signal Input Baseband Signal Output Local Optical Oscillator Photo- Detector BPF Beam Combiner Frequency discriminator ------- Envelop Detector LPF The output of the IF filter is passed through a frequency discriminator followed by an envelope detector and is low-pass filtered. The output of the LPF is sampled and compared with a threshold of optimum value to make bit decisions. The single filter FSK receiver is suitable for narrow deviation FSK (for modulation index, <1)

Heterodyne Asynchronous Dual-Filter FSK Receiver Two band-pass filters are used to pass the mark and space frequencies separately. The BPF are centered at (IF+) and (IF-) corresponding to "mark" and "space" frequencies. The data decision is then made by comparing the output samples with a threshold of zero value.

Heterodyne Asynchronous DPSK Delay-Demodulation Receiver In this demodulation scheme, a replica of the IF signal is delayed by a fraction of a bit and then multiplied with the original signal. The resulting signal is a phase modulated signal of differential phase, =(t)-(t-) where  is delay time. The optimum value of  is T/2.

Bit-error rate curves for various modulation formats Synchronous Asynchronous

Tutorial Consider a 1.55- μm heterodyne receiver with a p–i–n photodiode of 90% quantum efficiency connected to a 50-Ω load resistance. How much local-oscillator power is needed to operate in the shot-noise limit? Assume that shot-noise limit is achieved when the thermal-noise contribution at room temperature to the noise power is below 1%.

Tutorial Calculate the sensitivity (in dBm units) of a homodyne ASK receiver operating at 1.55 μm in the shot-noise limit. Assume that η= 0.8 and ∆f = 1 GHz. What is the receiver sensitivity when the PSK format is used in place of ASK?