modulation and demodulation s-108.199 / 17.3 -...

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Modulation and demodulationS-108.199 / 17.3.2004

Ari Tervonen

Nokia Research Center

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Modulation

• Dominating modulation scheme in optical communication is on-off keying – amplitude modulation encoding 1 bit as light pulse and 0 bit byabsence of light pulse.

• Either direct modulation of light source (laser/LED) or using external modulator after the laser source.

Signal formats:• non-return-to-zero (NRZ)• return-to-zero (RZ)

NRZ

RZ

1 0 1 1 0 1

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Signal formats: line coding and scrambling

• Ensuring sufficient DC balance is important in NRZ and RZ formats, to maintain constant output power for setting decision threshold and for clock recovery (NRZ format) at receiver

• Two approaches: line coding or scrambling

• Binary block line coding encodes a block of k data bits into n (> k) bits for transmission in fiber, at the receiver these are mapped back into the original. Encoded sequences provide DC balance and sufficient transitions for clock recovery. An example is the (8, 10) code used in Fibre Channel and Gigabit Ethernet.

• Scrambling is a one-to-one mapping of data stream for transmission, doing EXOR operation with carefully chosen sequence of bits, at receiver signal is descrambled. Advantage is that no extra bandwidth is required, disadvantage is that DC balance is not quaranteed. SDH/SONET uses scrambling.

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Subcarrier modulation and multiplexing

• Subcarrier modulation: Unlike on-off keying, data is not directly modulated on optical carrier. Data first modulates a microwave carrier, this modulated microwave carrier then modulates the optical transmitter.

• Subcarrier multiplexing: multiple microwave carriers at different frequencies can simultaneously modulate the optical transmitter. At the receiver, the combined signal is detected, and demultiplexing of microwave frequencies and extraction of data is carried out at electrical level.

drive current

optical

powerlaserX

microwave oscillator

data

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Subcarrier modulation and multiplexing: clipping and intermodulation

• Subcarriers are modulated over mean DC current to maintain suitable average optical power level.

• Nonlinear response of laser power vs. input current generates intermodulation products at sum and difference microwave frequencies, thus relatively low modulation need to be used. Frequency values limited within one octave: second-order intermodulation products do not overlap signals, only weaker third-order intermodulation products are critical.

• Signal clipping occurs when multiplexed modulation decreases temporarily the current below the threshold for laser emission (when all subcarriers align in phase). SCM systems are designed to have sufficient low clipping propability.

• SCM is used by CATV operators for analog video transmission. In WDM systems, additional network control information can be added to optical signals at relatively low data rates and modulation indices (pilot tones).

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Spectral efficiency in WDM

• Available optical bandwidth in singlemode fiber is about 50 THz. With 0.4 bit/s/Hz, total WDM transmission capacity would be 20 Tbit/s. More than 10 Tbit/s has already been demonstrated in laboratory experiments.

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Optical duobinary modulation• Can increase spectral efficiency by a factor of about 1.5

• Fundamental idea is to add a data sequence to a one-bit delayed copy of itself, resulting in a ternary sequence to be transmitted

• Mathematically y(nT) = x(nT) + x(nT-T), where T is the bit period

• Recovery of the input sequence at the receiver: z(nT) = y(nT) - z(nT-T), with initialization z(0) = 0 this gives x(nT) = z(nT)

• Problem of error propagation: if there is an error in a single bit in the transmission, all subsequent bits will be in error, until there is another error!

0 1 0 1 1 0 0 1 0 x(nT)0 1 0 1 1 0 0 1 0 x(nT-T)

0 1 1 1 2 1 0 1 1 y(nT) = x(nT) + x(nT-T)

0 1 0 1 1 0 0 1 0 z(nT) = y(nT) - z(nT-T) modulo 2

0 1 0 1 1 0 0 1 0 x(nT)0 1 0 1 1 0 0 1 0 x(nT-T)

0 1 1 1 2 1 0 1 1 y(nT) = x(nT) + x(nT-T)

1 0 1 0 0 1 1 0 1 z(nT) = y(nT) - z(nT-T) modulo 2

error

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Optical duobinary modulation

• Solution to error propagation: actual data is not the x(nT), but d(nT), the sequence showing changes in x(nT)

• Recovery of the actual data at the receiver: D(nT) is formed as a sequence giving changes in z(nT)

error

1 1 1 0 1 0 1 1 0 d(nT) original data0 1 0 1 1 0 0 1 0 0 x(nT)

0 1 0 1 1 0 0 1 0 x(nT-T)0 1 1 1 2 1 0 1 1 y(nT) = x(nT) + x(nT-T)

0 1 0 1 1 0 0 1 0 0 z(nT) = y(nT) - z(nT-T) modulo 21 1 1 0 1 0 1 1 0 D(nT) recovered data


0 1 0 1 1 0 0 1 0 x(nT-T)0 1 1 1 2 1 0 1 1 y(nT) = x(nT) + x(nT-T)


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• In the preceding all sequences are binary except y(nT). If y(nT) would also be taken modulo 2, it would be the original d(nT), but this would not change the data recovery ! However, the bandwidth advantage in transmission would be lost !

• This shows that at the receiver, differentiation between levels 0 and 2 is not necessary !


0 1 0 1 1 0 0 1 0 x(nT-T)0 1 1 1 2 1 0 1 1 y(nT) = x(nT) + x(nT-T)



0 1 0 1 1 0 0 1 0 x(nT-T)0 1 1 1 0 1 0 1 1 y(nT) = x(nT) + x(nT-T) modulo 2


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• A ternary signaling alternative to using three optical power levels is to use a combination of amplitude modulation and phase-shift keying

• AM-PSK optical outputs are –a cos(ωt) = a cos(ωt+π), 0 and a cos(ωt), corresponding to logical 0, 1 and 2, respectively (here ω is optical carrier frequency, so 0 and 2 are simply optical pulses having opposite phases modulated on them)

• Direct detection is not sensitive to optical phase, so that ordinary receiver simply identifies 2 with 0, and can be used in duobinary AM-PSK

• An external Mach-Zehnder modulator can accomplish this AM-PSK scheme, with improved spectral efficiency compared with on-off keying

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Optical single sideband modulation

• Data modulation ωd of the order of 10 GHz is modulated on the optical carrier ωo of the order of 200 THz

• Direct modulation produces two sidebands on frequencies ωo - ωd and ωo+ ωd

• Digital signal has two sidebands, one on either side of carrier, both containing the modulated information – one of these can be eliminated to improve the spectral efficiency by a factor of 2

• The difficulty in implementing single sideband modulation is in obtaining filters with sufficient sharpness.

• Also, if implemented on the transmitter side, optical nonlinearities present in fiber optical transmission would recover the eliminated sideband.

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Vestigial sideband modulation

• One sideband is not filtered fully, but partial filtering in transmission can lead to improved spectral efficiency using a special alternative optical frequency spacing in WDM transmission

50GHz 75 GHz

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Multilevel modulation and fiber capacity limits

• Main technique to achieve spectral efficiencies in excess of 1 bit/s/Hz is multilevel modulation.

• An additional advantage is that as the pulses would be longer for a given bit rate, effects of dispersion and nonlinearities would be less.

• Main difficulty is in detecting multilevel signals at high bit rates.

• Shannon’s theorem gives the upper limit for spectral efficiency as log2(1+SNR), with SNR the signal-to-noise ratio.

• With SNR of about 100, 7 bit/s/Hz could be achieved.

• In practice, long-haul systems need to operate at high optical power levels to overcome fiber attenuation and noise from optical amplifiers. Then, optical nonlinearities become an additional limitation.

• Analysis has indicated that optical nonlinearities would limit spectral efficiency to 3 – 5 bit/s/Hz.

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Demodulation

• The receiver needs recover the data transmitted over fiber at anacceptable bit error rate (BER), typically 10-9 to 10-12 in high-speed optical transmission.

• Discussion here will focus on demodulation of OOK signals.

PhotodetectorFront-end

amplifierReceive filter Sampler Decision circuit

Clock/timing

recovery

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Eye diagram

• Eye diagram overlaps filtered pulse shapes in successive bit periods

• Represents signal available for sampling

• Vertical eye opening indicates the margin for bit errors due to noise

• Horizontal eye opening indicatesthe margin for timing errors due to imperfect clock

10 Gbit/s NRZ eye diagram

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An Ideal Receiver

• An ideal receiver simply looks for presence of photons in the given interval. No photons means 0 bit, detected photons means 1 bit.

• Optical pulse consists of discrete photons with Poissonian statistics, arriving at average rate P/hf, with optical power P and photon energy hf.

• At bit rate B, the propability of receiving no photons in bit interval 1/B is e-(P/hfB)

• Assuming equally likely 0 and 1 bits, BER = 1/2 e-(P/hfB)

• As P/hfB is the average number of photons per 1 bit, the quantum limit for BER = 10-12 can be calculated as 27 photons per 1 bit

• This is the quantum limited sensitivity for an ideal receiver. Receiver sensitivity in general gives the required signal power to achieve a given BER.

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A Practical Direct Detection Receiver

• The optical signal at the receiver is first converted into an electrical current. In addition to the photocurrent due to signal there are noise currents.

• Thermal noise is due to random thermal motion of charge carriers.• Shot noise is due to random distribution of electrons generated by the

photodetection process.• Noise components may be described as Gaussian random processes.• Thermal noise is white, and noise current in bandwidth Be has the

variance (with temperature T and resistance R)

• The shot noise is also white, and noise current in bandwidth Be has the variance (with elementary charge e and signal photocurrent I)

• The two noise components are independent, so the total variance of noise current is obtained by adding together the two variances.

ethermal BRkT )/4(2 =σ

eshot eIB22 =σ

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Direct detection receivers: additional noise

• Front-end amplifier noise• Components within the front-end amplifier contribute additional

thermal noise. This is usually described by the noise figure, which is the ratio of the input SNR to output SNR, thermal noise is enhanced by this factor. Typical noise figure values are 3 to 5 dB.

• APD noise• The avalanche gain process in APDs increases the noise current at

output. This is modeled as an increase in the shot noise component. With responsivity ρ and avalanche gain G, the average photocurrent is I = GRP, and the shot noise current is

• Here APD excess noise factor is given by • Ionization coefficient ratio ka is 0.7 for typical APD materials.• ρ = ηe/hf, with η the quantum efficiency of photodetector.

eashot RPBGFeG )(2 22 =σ)/12)(1()( GkGkGF aaa −−+=

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Optical preamplifiers

• Optical preamplifier provides additional gain to optical signal before the photodetector, but also the amplified spontaneous emission (ASE) adds noise at the optical level, with optical noise power

PASE = 2nsphf(G - 1)Bo

• The factor of 2 is due to two fiber polarization modes, nsp is the spontaneous emission factor (nsp = 1 for complete inversion, in most cases higher), G optical gain, the Bo optical bandwidth.

• The photodetector generates current in proportion to optical power. At optical level, the electric fields of signal and noise are added and optical power is proportional to square of total field. Thus there is optical interference and beating between optical wave components of signal and ASE. At the photocurrent level, this adds noise components referred to as signal-spontaneous (signal beating with ASE) and spontaneous-spontaneous (uncorrelated ASE photons at different frequencies beating with each other)

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Optical preamplifier noise

• The signal-spontaneous beat noise current has the variance

• The spontaneous-spontaneous beat noise current has the variance

• Note that responsivity ρ converts optical power to photocurrent

• Typically optical amplifier gain is large (> 10 dB), so the shot noise and thermal noise are negligible in comparison to the components above.

• By decreasing optical bandwidth Bo, the signal-spontaneous beat noise can be made dominant.

• Optical amplifier noise properties can be described in terms of noise figure.

espspontsig BGhfPnG )1(4 22 −=− ρσ

eeospspontspont BBBGhfn )2()]1([2 222 −−=− ρσ

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Optical preamplifier noise figure• The noise figure is ratio of the input SNR to the output SNR• At the input side, assuming only signal shot noise is present, the SNR is

• Note that this is referred to electrical level, where power is proportional to square of photocurrent and optical power (square-law receiver)

• At the output side signal-spontaneous beat noise dominates

• The noise figure of the optical amplifier is then

Fn = SNRi / SNRo ≈ 2nsp

• The minimum noise figure is thus 3 dB, typical values are in 4 to 7 dB range.

ei ePB

PSNRρρ

2)( 2

=

espo hfBnGPG

GPSNR)1(4

)(2

2

−=

ρρ

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Bit Error Rates

• Calculating BERs for practical direct detection receivers takes into account the various noise components.

• The receiver makes decision for each bit period whether sampled bit corresponds to level 0 or 1. Noise can result in a wrong decision.

• For Gaussian noise components, both bits 0 and 1 have average levels I0 and I1and variances σ0 and σ1 for photocurrent. Photocurrent variances are obtained by adding together variances from various noise photocurrent components.

• This gives Gaussian probability density functions for photocurrents detected at the two bit values. From this, estimates can be evaluated for photocurrent to be on the wrong side of decision threshold.

• BER is the average of this probability for 0 and 1 bits.

Probability density

function for bit 0

Probability density

function for bit 1

I0 Ith I1

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Bit Error Rates

• As 1 and 0 bits are equally present, the optimum threshold current value is approximately Ith = (σ0 I1 + σ1 I0 ) / (σ0 + σ1 ).

• Using value Q = (I1 - I0 ) / (σ0 + σ1 ), requirement for BER of 10-9 is Q ≈ 6 and for BER of 10-12 is Q ≈ 7.

• Variable threshold setting is important with signal-dependent noise. With similar noise for both 0 and 1 bits, simply setting (I1 + I0 ) / 2 is sufficient.

Probability density

function for bit 0

Probability density

function for bit 1

I0 Ith I1

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Receiver sensitivities

• Typical achievable sensitivities at 10 Gbit/s

• PIN photodiode receiver –18 to –21 dBm

• APD receiver –24 to –30 dBm

• Optical preamplifier down to –36 dBm

(about 100 photons per bit)

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Coherent Detection• Direct detection receivers are limited by thermal noise, and do not achieve the

shot noise limited sensitivity. Optical preamplifiers can improve significantly from this.

• Coherent detection provides signal gain by mixing it with light from local oscillator laser source. The dominant noise will then be the shot noise of local oscillator.

• In the case of a homodyne receiver, signal and local oscillator have the same frequency. Then these are mixed, photocurrents are

for a 1 bit

for a 0 bit

• Usually PLO ≈ 0 dBm and P < –20 dBm, thus P is negligible in comparison with PLOin signal power and both P and terms can be neglected in calculating the shot noise variance. This gives factor Q for BER

• This is roughly the square root for the number of photons per bit, thus for BER of 10-12 requirement is Q ≈ 7, corresponding to about 49 photons per bit.

)(1 LOLO PPPPI ++= ρLOPI ρ=0

LOPP

eeBPQ

2ρ=

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Timing recovery

• The process of recovering the bit boundaries is called the clock recovery. Clock frequency is extracted from the received signal. Also clock phase needs to be recovered.

• A nonlinear circuit gives the result containing spectral component at 1/T, where T is the bit period.

• Bandpass filter produces from this periodic timing signal.

• Phase locked loop cleans the timing signal from jitter.

Nonlinearity

(squarer)Bandpass filter Phase detector Loop filter

Voltage-controlled oscillator

Phase lock loop

Extracted clock

Received signal

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Error Detection and Correction

• An error-correcting code is a technique for reducing the BER. It involves transmitting additional bits, called redundancy, together with the data bits. Redundancy is used at the receiver to correct errors in transmission. This method is called forward error correction (FEC).

• An alternative is to use smaller redundancy, based on which receiver can detect the presence of errors, but not identify and correct these. This technique for error monitoring is used in for example in SDH/SONET.

• A simple example of error-detecting code is the bit interleaved paritycode. For example, the first bit of redundancy code provides even parity over the first bit of all N-bit sequences of the covered portion of signal, the second bit over the second bit of all sequences, etc.

• Extending optical links to higher capacity has made FEC a competitive solution for achieving sufficient BER level.

• Particularly systems may have BER floor problems, where BER si not limited by noise, but by for example crosstalk – increasing power or receiver sensitivity will not improve BER level. FEC will do it.

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Forward Error Correction

• The coding gain of an FEC code is the decrease in receiver sensitivity that it provides for given BER level compared to system without FEC. Note that FEC can lead to increase of BER before correction, as bit rate has to be increased in proportion with the redundancy used.

• Figure shows a different view on coding gain, the capacity increase enabled by FEC.

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Forward Error Correction:Reed-Solomon code

• Reed-Solomon code operates on symbols, each consists for example of 8 bits. It takes blocks of k data symbols and calculates for each r additional redundant symbols, so that n = k + r symbols are transmitted. Correction can be made with up to r/2 symbols in error in the block.

• The length of the code for m-bit symbols is n = 2m-1. For 8-bit bytes as symbols, n = 255. A widely used (255, 239) Reed-Solomon code has parameters n = 255, r = 16, k = 239 (< 7% redundancy), providing about 6 dB coding gain.

• Another code standardized by ITU-T is (255, 223). For both, chipsets are available and they are in use in high-performance optical systems.

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Interleaving

• Errors can often be correlated, occur in bursts, so that a large number of successive or close-by bits are in error. For example Reed-Solomon (255,239) can correct up to 8 x 8 = 64 successive bits in error.

• Interleaving can handle much larger bursts of error without increasing the redundancy.

• The simple principle is to take number d of successive codes of length n, transmit first d first symbols from each of these, after that d second symbols etc. The parameter d is interleaving depth.

• In a burst of b errors, only number b/d will occur in the same code. Thus length of bursts consecutive errors that can be corrected is increased by a factor of d.

modulation and demodulation s-108.199 / 17.3 -...

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