Performance analysis and laser linewidth requirements for optical PSK heterodyne communications systems

An optical PSK heterodyne communications receiver is investigated. The receiver is based on the decision-directed phase-locked loop. The performance of the phase-locked loop subsystem is analyzed taking into account both shot noise and laser phase noise. It is shown that for reliable phase locking (rms phase error less than 10°), heterodyne second-order loops require at least 6771 electrons/s per volt every hertz of the laser linewidth. This number corresponds to the limit when the loop dumping factor η is infinitely large; ifeta = 0.7, then the loop needs 10 157 electrons/(s . Hz). If the detector has a unity quantum efficiency andlambda = 1.5 mum, the above quoted numberers give 0.9 pW/ kHz foreta rightarrow inftyand 1.35 pW/kHz fornu = 0.7. The loop bandwidth required is also evaluated and found to be155 Deltanu, whereDeltanuis the laser linewidth. Finally, the linewidth permitted for PSK heterodyne recievers is evaluated and found to be2.26 cdot 10^{-3} R_{b}where Rbis the system bit rate. ForR_{b}=100Mbit/s, this leads toDeltanu < 226kHz. Such and better linewidths have been demonstrated with laboratory external cavity lasers. For comparison, ASK and FSK heterodyne receivers are much more tolerant to phase noise,-they can tolerateDeltanuup to 0.09 Rb. At the same time, homodyne receivers impose much more stringent requirements on the laser linewidth (Deltanu < 3 cdot 10^{4} R_{b}).     

Balanced phase-locked loops for optical homodyne receivers: Performance analysis, design considerations, and laser linewidth requirements

Balanced phase-locked loops for optical homodyne receivers are investigated. When a balanced loop is employed in a communications system, a part of the transmitter power must be used for unmodulated residual carrier transmission. This leads to a power penalty. In addition, the performance of the balanced loops is affected by the laser phase noise, by the shot noise, and by the crosstalk between the data-detection- and phase-lock-branches of the receiver. The impact of these interferences is minimized if the loop bandwidthBis optimized. The value of Boptand the corresponding optimum loop performance are evaluated in this paper. Further, the maximum permissible laser linewidthdeltanuis evaluated and found to be5.9 times 10^{-6}times Rb, where Rb(bit/s) is the system bit rate. This number corresponds toBER = 10^{-10}and power penalty of 1 dB (0.5 dB due to residual carrier transmission, and 0.5 dB due to imperfect carrier phase recovery). For comparison, decision-driven phase-locked loops require onlydeltanu = 3.1 times 10^{-4}. R_{b}. Thus, balanced loops impose more stringent requirements on the laser linewidth than decision-driven loops, but have the advantage of simpler implementation. An important additional advantage of balanced loops is their capability to suppress the excess intensity noise of semiconductor lasers.     

Noise figure of UHF transistors as a function of frequency and bias conditions

It is shown that the observed values of the minimum noise figureF_{min}of UHF transistors in common base connection can be explained in terms of the device parameter(1-alpha_{dc}) r_{b'b}/R_{e0}and fαfor frequencies up to 1000 MHz. An interesting collector saturation effect is observed that gives a strong increase in UHF noise figure at high currents. Many features of the dependance ofF_{min}on operating conditions can be explained by this effect. The current dependence ofF_{min}for large values of |VCB| and high currents suggests a distribution in diffusion times through the base region. At intermediate frequencies, the noise figure increases with increasing collector bias |VCB| due to an increase inr_{b'b}, which in turn is caused by the dependence of the base width on |VCB|.     

On the weight distribution of binary linear codes (Corresp.)

LetVbe a binary linear(n,k)-code defined by a check matrixHwith columnsh_{1}, cdots ,h_{n}, and leth(x) = 1ifx in {h_{1}, cdots , h_{n}, andh(x) = 0ifx in neq {h_{1}, cdots ,h_{n}}. A combinatorial argument relates the Walsh transform ofh(x)with the weight distributionA(i)of the codeVfor smalli(i< 7). This leads to another proof of the Plessith power moment identities fori < 7. This relation also provides a simple method for computing the weight distributionA(i)for smalli. The implementation of this method requires at most(n-k+ 1)2^{n-k}additions and subtractions,5.2^{n-k}multiplications, and2^{n-k}memory cells. The method may be very effective if there is an analytic expression for the characteristic Boolean functionh(x). This situation will be illustrated by several examples.     

Decision-driven phase-locked loop for optical homodyne receivers: Performance analysis and laser linewidth requirements

Optical homodyne receivers based on decision-driven phase-locked loops are investigated. The performance of these receivers is affected by two phase noises due to the laser transmitter and laser local oscillator, and by two shot noises due to the two detectors employed in the receiver. The impact of these noises is minimized if the loop bandwidthBis chosen optimally. The value of Boptand the corresponding optimum loop performance are evaluated in this paper. It is shown that second-order phase-locked loops require at least 0.8 pW of signal power per every kilohertz of laser linewidth (this number refers to the system with the detector responsivity 1 A/W, dumping factor 0.7, and rms phase error 10°). This signal power is used for phase locking, and is, therefore, lost from the data receiver. Further, the maximum permissible laser linewidthDeltanuis evaluated and for second order loops with the dumping factor 0.7 found to be3.1 times 10^{-4} cdot R_{b}, where Rb(bit/s) is the system bit rate. ForR_{b} = 100Mbit/s, this leads toDeltanu = 31kHz. For comparison, heterodyne receivers with noncoherent postdetection processing only requireDeltanu = 0.72-9MHz forR_{b} = 100Mbit/s. Thus, the homodyne systems impose much more stringent requirements on the laser linewidth than the heterodyne systems. However, homodyne systems have several important advantages over heterodyne systems, and the progress of laser technology may make homodyning increasingly attractive. Even today, homodyne reception is feasible with experimental external cavity lasers, which have been demonstrated to haveDeltanuas low as 10 kHz.     

Multiplierless Implementations of MF/DTMF Receivers

The ever-increasing use of VLSI in telecommunications systems is leavening the search of new algorithms for task realizations suited to VLSI implementations of systems. Toward this search, the paper presents implementations for MF/DTMF receivers, which are based on multiplierless basic filters or primitive VLSI cells such as(1 + z^{-n}),(1 - z^{-n}), and(1 pm z^{-n} + z^{-2n}). These implementations require parallel processing and are designed to meet the requirements of a switching system.     

Second-harmonic generation in KB5O8· 4H2O from 217.1 to 315.0 nm

Second-harmonic generation (SHG) has been observed in KB5O8ċ 4H2O (KB5) between 217.1 and 315.0 nm by angle tuning in a single crystal using a single cut. A conversion efficiency of 9.2 percent was observed for type I noncritical phase matching at 217.1 nm for a peak power of 15 kW at 434.2 nm. The nonlinear coefficients d31and d32are estimated to be approximately1.1 times 10^{-10}ESU (4.0 times 10^{-25}m/V) and0.08 times 10^{-10}ESU (0.29 times 10^{-25}m/V), respectively.     

Noise temperature in silicon in the hot electron region

The noise temperature as a function of the applied field has been measured on an epitaxial silicon layer at the frequencies 2 GHz and 4 GHz. It has been found that the experimental results are in good agreement with the theory given by Moll. It is shown that for noise calculations in silicon field-effect transistors with pronounced carrier velocity saturation the noise temperature Tnversus field E may be approximated byT_{n}/T_{0}= 1 + γ(E/E_{c})^{2}with T0= lattice temperature, Ec= saturation field, γ = const.     

Decision-driven phase-locked loop for optical homodyne receivers: Performance analysis and laser linewidth requirements

Optical homodyne receivers based on decision-driven phase-locked loops are investigated. The performance of these receivers is affected by two phase noises due to the laser transmitter and laser local oscillator, and by two shot noises due to the two detectors employed in the receiver. The impact of these noises is minimized if the loop bandwidthBis chosen optimally. The value of Boptand the corresponding optimum loop performance are evaluated in this paper. It is shown that second-order phase-locked loops require at least 0.8 pW of signal power per every kilohertz of laser linewidth (this number refers to the system with the detector responsivity 1 A/W, dumping factor 0.7, and rms phase error 10°). This signal power is used for phase locking, and is, therefore, lost from the data receiver. Further, the maximum permissible laser linewidthDelta vis evaluated and for second order loops with the dumping factor 0.7 found to be 3.1 × 10^-4. Rb, where Rb(bit/s) is the system bit rate. ForR_{b} = 100Mbit/s, this leads toDelta v = 31kHz. For comparison, heterodyne receivers with noncoherent postdetection processing only requireDelta v = 0.72-9MHz forR_{b} = 100Mbit/s. Thus, the homodyne systems impose much more stringent requirements on the laser linewidth than the heterodyne systems. However, homodyne systems have several important advantages over heterodyne systems, and the progress of laser technology may make homodyning increasingly attractive. Even today, homodyne reception is feasible with experimental external cavity lasers, which have been demonstrated to haveDelta vas low as 10 kHz.     

On the capacity of permanent memory

Many forms of digital memory have been developed for the permanent storage of information. These include keypunch cards, paper tapes, PROMs, photographic film and, more recently, digital optical disks. All these "write-once" memories have the property that once a "one" is written in a particular cell, this cell becomes irreversibly set at one. Thus, the ability to rewrite information in the memory is hampered by the existence of previously written ones. The problem of storing temporary data in permanent memory is examined here. Consider storing a sequence oftmessagesW_{1}, W_{2}, cdots , W_{t}in such a device. Let each messageW_{i}consist ofk_{i}bits and let the memory contain n cells. We say that a ratet-tuple(R_{1} = k_{1} / n, R_{2} = k_{2} / n, cdots , R_{t} = k_{t} / n)is achievable if we can store a sequence of messages at these rates for somen. The capacityC_{t}^{ast} subset R_{+}^{t}is the closure of the set of achievable rates. The capacityC_{t}^{ast}for an optical disk-type memory is determined. This result is related to the work of Rivest and Shamir. A more general model for permanent memory is introduced. This model allows for the possibility of random disturbances (noise), larger input and output alphabets, more possible cell states, and a more flexible set of state transitions. An inner bound on the capacity regionC_{t}^{ast}for this model is presented. It is shown that this bound describesC_{t}^{ast}in several instances.     

On source coding with side information at the decoder

Let{(X_k, Y_k, V_k)}_{k=1}^{infty}be a sequence of independent copies of the triple(X,Y,V)of discrete random variables. We consider the following source coding problem with a side information network. This network has three encoders numbered 0, 1, and 2, the inputs of which are the sequences{ V_k}, {X_k}, and{Y_k}, respectively. The output of encoder i is a binary sequence of rateR_i, i = 0,1,2. There are two decoders, numbered 1 and 2, whose task is to deliver essentially perfect reproductions of the sequences{X_k}and{Y_k}, respectively, to two distinct destinations. Decoder 1 observes the output of encoders 0 and 1, and decoder 2 observes the output of encoders 0 and 2. The sequence{V_k}and its binary encoding (by encoder 0) play the role of side information, which is available to the decoders only. We study the characterization of the family of rate triples(R_0,R_1,R_2)for which this system can deliver essentially perfect reproductions (in the usual Shannon sense) of{X_k}and{Y_k}. The principal result is a characterization of this family via an information-theoretic minimization. Two special cases are of interest. In the first,V = (X, Y)so that the encoding of{V_k }contains common information. In the second,Y equiv 0so that our problem becomes a generalization of the source coding problem with side information studied by Slepian and Wo1f [3].     

Ellipse rotation studies in laser host materials

Using a TEM00qnear Gaussian mode ruby laser system we report the first experimental measurements of intensity induced changes of optical polarization (ellipse rotation) in a cubic crystalline medium, YAG, for which we obtain the nonlinear susceptibilitieschi_{3}^{1221} (- omega, omega, omega, -omega) = 6.34 times 10^{-15}ESU andfrac{1}{2} (chi_{3}^{1111} + chi_{3}^{1221} - 2chi_{3}^{1212}) = 7.18 times 10^{-15}ESU, accurate to better than ±7 percent relative tochi_{3}^{1221} (- omega,omega,omega, -omega)for liquid CS2. These values are compared with further results obtained for fused quartz and two laser glasses. Moreover, by time resolving the ellipse rotation data we demonstrate the capability to plot ellipse rotation versus input power on a single laser shot, thus increasing the practical feasibility of the technique and introducing the possibility of resolving transient contributions to the measurement.     

On combined symbol-and-bit error-control [4,2] codes over{0,1}^8to be used in the

The construction, properties, and decoding of four nonequivalent[4,2]codes over the alphabet{0,1}^{8}are described. These codes are able to correct the following error patterns:1)error patterns containing one nonzero byte,2)error patterns containing up to three nonzero bits, and3)error patterns containing one byte erasure and at most one nonzero bit. In addition, all error patterns containing one byte erasure and two nonzero bits can be detected. These codes can be used in the     

Electromigration and low-frequency resistance fluctuations in aluminum thin-film interconnections

Low-frequency noise spectra originating from resistance fluctuations in Al films during electromigration were measured in the absolute temperature and current density intervals327 leq T leq 396K and1.34 times 10^{6} leq j leq 2.22 times 10^{6}A/cm². The values of SR, the resistance power spectral density, at 20 × 10^-3Hz allowed the construction of an Arrhenius plot from which a grain-boundary activation energy value of about 0.6 eV was deduced. This value lies in the range of values found by other authors using different techniques. A first attempt to model the observed dependence of SRonjandTis also described.     

Sensitivity penalty in multichannel coherent optical communications

The error rates and sensitivity penalties for multichannel coherent optical communications systems are evaluated for amplitude-shift keying (ASK), phase-shift keying (PSK), and frequency-shift keying (FSK) modulation, taking into account adjacent channel interference. Both time-domain and frequency-domain analysis are used, the latter being based on a Gaussian approximation. Both techniques yield similar results for sensitivity penalties below 1 dB. For FSK systems, larger values of the modulation index Δ do not necessarily lead to larger channel spacings. ASK and PSK systems both require larger channel spacings than FSK systems with Δ=1. The study was conducted for sources with linewidths narrow enough so that phase noise does not degrade the performance of receivers with matched filter demodulators     

Broadcast channels with confidential messages

Given two discrete memoryless channels (DMC's) with a common input, it is desired to transmit private messages to receiver1rateR_{1}and common messages to both receivers at rateR_{o}, while keeping receiver2as ignorant of the private messages as possible. Measuring ignorance by equivocation, a single-letter characterization is given of the achievable triples(R_{1},R_{e},R_{o})whereR_{e}is the equivocation rate. Based on this channel coding result, the related source-channel matching problem is also settled. These results generalize those of Wyner on the wiretap channel and of Körner-Marton on the broadcast Channel.     

The STARNET coherent WDM computer communication network:experimental transceiver employing a novel modulation format

We have designed, constructed, and investigated an experimental transceiver employing a novel combined PSK and ASK modulation format for the STARNET coherent WDM computer communication network. Using this experimental transceiver, we show that it is possible to transmit and receive 2.488 Gb/s PSK circuit-switched data and 125 Mb/s ASK packet-switched data on the same lightwave. The experimental transceiver employs a custom integrated-optic LiNbO₃ modulator with both phase and amplitude sections, a 2.488 Gb/s tunable PSK heterodyne receiver, and a 125 Mb/s ASK heterodyne receiver. Both receivers function properly with error rates less than 10^-9 and a sensitivity of -32.1 dBm; the corresponding optimum ASK modulation depth is 0.57. The resulting network power budget is 26.6 dB     

Hypothesis testing with multiterminal data compression

The multiterminal hypothesis testingH: XYagainstH̄: X̄Ȳis considered whereX^{n} (X̄^{n})andY^{n} (Ȳ^{n})are separately encoded at ratesR_{1}andR_{2}, respectively. The problem is to determine the minimumbeta_{n}of the second kind of error probability, under the condition that the first kind of error probabilityalpha_{n} leq epsilonfor a prescribed0 < epsilon < 1. A good lower boundtheta_{L}(R_{1}, R_{2})on the power exponenttheta (R_{1}, R_{2},epsilon)= lim inf_{n rightarrow infty}(-1/n log beta_{n})is given and several interesting properties are revealed. The lower bound is tighter than that of Ahlswede and Csiszár. Furthermore, in the special case of testing against independence, this bound turns out to coincide with that given by them. The main arguments are devoted to the special case withR_{2} = inftycorresponding to full side information forY^{n}(Ȳ^{n}). In particular, the compact solution is established to the complete data compression cases, which are useful in statistics from the practical point of view.     

Receiver performance evaluation of various digital optical modulation-demodulation systems in the 0.5-10 µm wavelength region

Error rate characteristics of various digital optical modulation-demodulation schemes are studied. The main concern is whether we can improve receiving power levels to achieve a prescribed error rate by employing a coherent optical transmission system in place of the presently available amplitude-shift-keyed (ASK) baseband direct detection system. The receiving power level reduction in various modulation-demodulation schemes is calculated by taking into account the optical carrier wavelength, data rate, photodetector performance, local oscillator power level, and number of levels in multilevel codes. The phase-shift-keyed (PSK) homodyne detection system requires the least receiving power. The improvement in the receiving power level compared to the conventional ASK baseband direct detection system is expected to be 16-22 dB at the carrier wavelength oflambda_{c} = 0.5-3 mum, 31-36 dB atlambda_{c} = 3-5 mum, and 35-40 dB atlambda_{c} = 5-10 mum.     

The Performance of Digital Matched Filters for Multilevel Signals

The analysis and optimization of digital matched filters (DMF's) with multilevel quantizers, which are matched to multilevel amplitude and phase modulated (AM/phi M) signals, are considered here. Quite general expressions for the DMF's output signal-to-noise ratio (SNR0) have been obtained for the case in which the interference has a symmetric, differentiable probability density distribution. For such interference, SNR0has been shown to be separable into two factors, which respectively represent the effects of the quantization and correlation operations of the DMF. The two factors can be optimized independently of each other. In particular, the optimal quantizer strategy for Gaussian interference is proven to be (within the limits of practical approximation and also asymptotically) one with equal spacings of the quantizer levels and thresholds. All the SNR0calculations have been carried out for a complex outputXrather than the commonly used real-valued, physical outputZ. The validity of the relationshipSNR_{0}X = 2 SNR_{0}Zhas been proven for all types of interference considered in this work. Finally, the optimalSNR_{0}Xfor Gaussian interference has been proven to be bounded from above bySNR_{0}Xfor the analog matched filter and from below by that of DMF with hard limiter as a quantizer.