Pub Date : 1973-09-01DOI: 10.1002/J.1538-7305.1973.TB02016.X
A. Netravali
Concept of n-width and extremal subspaces, first introduced by Kolmogorov, plays an important part in mathematical problems of approximation of classes of functions and in engineering problems of signal representation and reconstruction. In this short paper, explicit expressions for n-width and extremal subspaces are obtained for a class which is of some engineering importance.
{"title":"A note on optimal approximating manifolds of a function class","authors":"A. Netravali","doi":"10.1002/J.1538-7305.1973.TB02016.X","DOIUrl":"https://doi.org/10.1002/J.1538-7305.1973.TB02016.X","url":null,"abstract":"Concept of n-width and extremal subspaces, first introduced by Kolmogorov, plays an important part in mathematical problems of approximation of classes of functions and in engineering problems of signal representation and reconstruction. In this short paper, explicit expressions for n-width and extremal subspaces are obtained for a class which is of some engineering importance.","PeriodicalId":55391,"journal":{"name":"Bell System Technical Journal","volume":"1 1","pages":"1237-1242"},"PeriodicalIF":0.0,"publicationDate":"1973-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79825162","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1973-09-01DOI: 10.1002/J.1538-7305.1973.TB02015.X
R. M. Derosier, J. Stone
Several methods are reported for making splices in optical fibers. The methods have application to both liquid-core and solid-core fibers and have been demonstrated for liquid-core fibers. The lowest-loss splice consists of an inserted glass pin and an outer sleeve. Best repeatable results are 0.4 dB loss in the splice. A splicing device has been constructed which provides automatic alignment of the components and automatic assembly for several fibers at once. The technique may be directly extended to multiple splicing as for fiber cables.
{"title":"Low-loss splices in optical fibers","authors":"R. M. Derosier, J. Stone","doi":"10.1002/J.1538-7305.1973.TB02015.X","DOIUrl":"https://doi.org/10.1002/J.1538-7305.1973.TB02015.X","url":null,"abstract":"Several methods are reported for making splices in optical fibers. The methods have application to both liquid-core and solid-core fibers and have been demonstrated for liquid-core fibers. The lowest-loss splice consists of an inserted glass pin and an outer sleeve. Best repeatable results are 0.4 dB loss in the splice. A splicing device has been constructed which provides automatic alignment of the components and automatic assembly for several fibers at once. The technique may be directly extended to multiple splicing as for fiber cables.","PeriodicalId":55391,"journal":{"name":"Bell System Technical Journal","volume":"119 1","pages":"1229-1235"},"PeriodicalIF":0.0,"publicationDate":"1973-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86113867","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1973-07-08DOI: 10.1002/J.1538-7305.1973.TB01998.X
S. Neal, A. Kuczura
A theory of traffic-measurement errors for loss systems with renewal input is developed. The results provide an accurate approximation for the variance of any differentiable function of one or more of the following basic traffic measurements taken during a given time interval: (i) The total number of attempts (peg count) (ii) The number of unsuccessful attempts (overflow count) (iii) The usage based on discrete samples (TUR measurement) or on continuous scan. The approximation is given in terms of the individual variances and covariance functions of the three measurements. Asymptotic approximations for these moments are obtained using the concept of a generalized renewal process, and are shown to be sufficiently accurate for telephone traffic-engineering purposes. As an application of the theory, we examine the variances of the standard estimates of the load and peakedness (variance-to-mean ratio) of an input traffic stream for a time interval of one hour. Other possible applications to Bell System trunking problems are discussed.
{"title":"A theory of traffic-measurement errors for loss systems with renewal input","authors":"S. Neal, A. Kuczura","doi":"10.1002/J.1538-7305.1973.TB01998.X","DOIUrl":"https://doi.org/10.1002/J.1538-7305.1973.TB01998.X","url":null,"abstract":"A theory of traffic-measurement errors for loss systems with renewal input is developed. The results provide an accurate approximation for the variance of any differentiable function of one or more of the following basic traffic measurements taken during a given time interval: (i) The total number of attempts (peg count) (ii) The number of unsuccessful attempts (overflow count) (iii) The usage based on discrete samples (TUR measurement) or on continuous scan. The approximation is given in terms of the individual variances and covariance functions of the three measurements. Asymptotic approximations for these moments are obtained using the concept of a generalized renewal process, and are shown to be sufficiently accurate for telephone traffic-engineering purposes. As an application of the theory, we examine the variances of the standard estimates of the load and peakedness (variance-to-mean ratio) of an input traffic stream for a time interval of one hour. Other possible applications to Bell System trunking problems are discussed.","PeriodicalId":55391,"journal":{"name":"Bell System Technical Journal","volume":"26 1","pages":"967-990"},"PeriodicalIF":0.0,"publicationDate":"1973-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76780379","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1973-07-08DOI: 10.1002/J.1538-7305.1973.TB01991.X
D. Gloge
Loss, coupling, and delay differences among the modes of multimode fibers influence their response to intensity-modulated optical signals. This “baseband” response is derived here from a time-dependent continuous description of the power flow in the fiber. Particular attention is given to the output as a function of angle and to the impulse response, its width and symmetry. We find that coupling narrows the impulse response but, at the same time, causes additional loss. Under practical conditions, this loss may limit the usefulness of coupling for the purpose of reducing the mode dispersion. We calculate a possible data rate of 12 Mb/s for a 10-km repeater spacing and an effective numerical aperture of 0.1, but we show that further improvements can be gained from an optimization of the coupling characteristic and of other parameters.
{"title":"Impulse response of clad optical multimode fibers","authors":"D. Gloge","doi":"10.1002/J.1538-7305.1973.TB01991.X","DOIUrl":"https://doi.org/10.1002/J.1538-7305.1973.TB01991.X","url":null,"abstract":"Loss, coupling, and delay differences among the modes of multimode fibers influence their response to intensity-modulated optical signals. This “baseband” response is derived here from a time-dependent continuous description of the power flow in the fiber. Particular attention is given to the output as a function of angle and to the impulse response, its width and symmetry. We find that coupling narrows the impulse response but, at the same time, causes additional loss. Under practical conditions, this loss may limit the usefulness of coupling for the purpose of reducing the mode dispersion. We calculate a possible data rate of 12 Mb/s for a 10-km repeater spacing and an effective numerical aperture of 0.1, but we show that further improvements can be gained from an optimization of the coupling characteristic and of other parameters.","PeriodicalId":55391,"journal":{"name":"Bell System Technical Journal","volume":"23 1","pages":"801-816"},"PeriodicalIF":0.0,"publicationDate":"1973-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72894438","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1973-07-08DOI: 10.1002/J.1538-7305.1973.TB01997.X
G. Foschini, R. Gitlin, S. Weinstein
A long-standing communications problem is the efficient coding of a block of binary data into a pair of in-phase and quadrature components. This modulation technique may be regarded as the placing of a discrete number of signal points in two dimensions. Quadrature amplitude modulation (QAM) and combined amplitude and phase modulation (AM-PM) are two familiar examples of this signaling format. Subject to a peak or average power constraint, the selection of the signal coordinates is done so as to minimize the probability of error. In the design of high-speed data communication systems this problem becomes one of great practical significance since the dense packing of signal points reduces the margin against Gaussian noise. Phase jitter, which tends to perturb the angular location of the transmitted signal point, further degrades the error rate. Previous investigations have considered the signal evaluation and design problem in the presence of Gaussian noise alone and within the framework of a particular structure, such as conventional amplitude and phase modulation. We present techniques to evaluate and optimize the choice of a signal constellation in the presence of both Gaussian noise and carrier phase jitter. The performance of a number of currently used or proposed signal constellations are compared. The evaluation and the optimization are based upon a perturbation analysis of the probability density of the received signal given the transmitted signal. Laplace's asymptotic formula is used for the evaluation. Discretizing the signal space reduces the optimal signal design problem under a peak power constraint to a tractable mathematical programming problem. Our results indicate that in Gaussian noise alone an improvement in signal-to-noise ratio of as much as 2 dB may be realized by using quadrature amplitude modulation instead of conventional amplitude and phase modulation. New modulation formats are proposed which perform very well in Gaussian noise and additionally are quite insensitive to moderate amounts of phase jitter.
{"title":"On the selection of a two-dimensional signal constellation in the presence of phase jitter and Gaussian noise","authors":"G. Foschini, R. Gitlin, S. Weinstein","doi":"10.1002/J.1538-7305.1973.TB01997.X","DOIUrl":"https://doi.org/10.1002/J.1538-7305.1973.TB01997.X","url":null,"abstract":"A long-standing communications problem is the efficient coding of a block of binary data into a pair of in-phase and quadrature components. This modulation technique may be regarded as the placing of a discrete number of signal points in two dimensions. Quadrature amplitude modulation (QAM) and combined amplitude and phase modulation (AM-PM) are two familiar examples of this signaling format. Subject to a peak or average power constraint, the selection of the signal coordinates is done so as to minimize the probability of error. In the design of high-speed data communication systems this problem becomes one of great practical significance since the dense packing of signal points reduces the margin against Gaussian noise. Phase jitter, which tends to perturb the angular location of the transmitted signal point, further degrades the error rate. Previous investigations have considered the signal evaluation and design problem in the presence of Gaussian noise alone and within the framework of a particular structure, such as conventional amplitude and phase modulation. We present techniques to evaluate and optimize the choice of a signal constellation in the presence of both Gaussian noise and carrier phase jitter. The performance of a number of currently used or proposed signal constellations are compared. The evaluation and the optimization are based upon a perturbation analysis of the probability density of the received signal given the transmitted signal. Laplace's asymptotic formula is used for the evaluation. Discretizing the signal space reduces the optimal signal design problem under a peak power constraint to a tractable mathematical programming problem. Our results indicate that in Gaussian noise alone an improvement in signal-to-noise ratio of as much as 2 dB may be realized by using quadrature amplitude modulation instead of conventional amplitude and phase modulation. New modulation formats are proposed which perform very well in Gaussian noise and additionally are quite insensitive to moderate amounts of phase jitter.","PeriodicalId":55391,"journal":{"name":"Bell System Technical Journal","volume":"20 1","pages":"927-965"},"PeriodicalIF":0.0,"publicationDate":"1973-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89069584","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1973-07-08DOI: 10.1002/J.1538-7305.1973.TB02000.X
W. H. Kent
This paper studies charge distribution in buried-channel charge-coupled devices. Detailed development of a one-dimensional electrostatic model is presented and a numerical solution of the resulting nonlinear potential equations is described. Graphical results show the charge-filling mechanism and the relationship between the oxide-semiconductor interface potential and total free positive charge.
{"title":"Charge distribution in buried-channel charge-coupled devices","authors":"W. H. Kent","doi":"10.1002/J.1538-7305.1973.TB02000.X","DOIUrl":"https://doi.org/10.1002/J.1538-7305.1973.TB02000.X","url":null,"abstract":"This paper studies charge distribution in buried-channel charge-coupled devices. Detailed development of a one-dimensional electrostatic model is presented and a numerical solution of the resulting nonlinear potential equations is described. Graphical results show the charge-filling mechanism and the relationship between the oxide-semiconductor interface potential and total free positive charge.","PeriodicalId":55391,"journal":{"name":"Bell System Technical Journal","volume":"35 1","pages":"1009-1024"},"PeriodicalIF":0.0,"publicationDate":"1973-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80826480","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1973-07-08DOI: 10.1002/J.1538-7305.1973.TB01996.X
W. Aung
The trend in electronic circuit design is toward increasing power dissipation density. The performance and reliability of increasing number of electronic systems are now seriously threatened by thermal effects, so that it is necessary to reappraise the relevant thermal design procedures. This paper examines natural convection cooling and concerns the prediction of maximum temperatures of electronic cabinets containing arrays of vertically oriented circuit cards with unequal power dissipation levels. By means of a vertical channel model, the effects of channel spacing, channel height, and power dissipation level are assessed with emphasis on asymmetric powering of the channel walls. Methods are indicated for rapid evaluation of maximum temperatures and optimum channel spacing with asymmetric heating. The present results show that asymmetry reduces the thermal performance of the channel. Consequently, the power dissipation on the channel walls should be made nearly equal.
{"title":"Heat transfer in electronic systems with emphasis on asymmetric heating","authors":"W. Aung","doi":"10.1002/J.1538-7305.1973.TB01996.X","DOIUrl":"https://doi.org/10.1002/J.1538-7305.1973.TB01996.X","url":null,"abstract":"The trend in electronic circuit design is toward increasing power dissipation density. The performance and reliability of increasing number of electronic systems are now seriously threatened by thermal effects, so that it is necessary to reappraise the relevant thermal design procedures. This paper examines natural convection cooling and concerns the prediction of maximum temperatures of electronic cabinets containing arrays of vertically oriented circuit cards with unequal power dissipation levels. By means of a vertical channel model, the effects of channel spacing, channel height, and power dissipation level are assessed with emphasis on asymmetric powering of the channel walls. Methods are indicated for rapid evaluation of maximum temperatures and optimum channel spacing with asymmetric heating. The present results show that asymmetry reduces the thermal performance of the channel. Consequently, the power dissipation on the channel walls should be made nearly equal.","PeriodicalId":55391,"journal":{"name":"Bell System Technical Journal","volume":"27 1","pages":"907-925"},"PeriodicalIF":0.0,"publicationDate":"1973-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90838937","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1973-07-08DOI: 10.1002/J.1538-7305.1973.TB01993.X
S. Personick
This paper is concerned with a systematic approach to the design of the “linear channel” of a repeater for a digital fiber optic communication system. In particular, it is concerned with how one properly chooses the front-end preamplifier and biasing circuitry for the photodetector; and how the required power to achieve a desired error rate varies with the bit rate, the received optical pulse shape, and the desired baseband-equalized output pulse shape. It is shown that a proper front-end design incorporates a high-impedance preamplifier which tends to integrate the detector output. This must be followed by proper equalization in the later stages of the linear channel. The baseband signal-to-noise ratio is calculated as a function of the preamplifier parameters. Such a design provides significant reduction in the required optical power and/or required avalanche gain when compared to a design which does not integrate initially. It is shown that, when the received optical pulses overlap and when the optical channel is behaving linearly in power,1 baseband equalization can be used to separate the pulses with a practical but significant increase in required optical power. This required power penalty is calculated as a function of the input and equalized pulse shapes.
{"title":"Receiver design for digital fiber optic communication systems, II","authors":"S. Personick","doi":"10.1002/J.1538-7305.1973.TB01993.X","DOIUrl":"https://doi.org/10.1002/J.1538-7305.1973.TB01993.X","url":null,"abstract":"This paper is concerned with a systematic approach to the design of the “linear channel” of a repeater for a digital fiber optic communication system. In particular, it is concerned with how one properly chooses the front-end preamplifier and biasing circuitry for the photodetector; and how the required power to achieve a desired error rate varies with the bit rate, the received optical pulse shape, and the desired baseband-equalized output pulse shape. It is shown that a proper front-end design incorporates a high-impedance preamplifier which tends to integrate the detector output. This must be followed by proper equalization in the later stages of the linear channel. The baseband signal-to-noise ratio is calculated as a function of the preamplifier parameters. Such a design provides significant reduction in the required optical power and/or required avalanche gain when compared to a design which does not integrate initially. It is shown that, when the received optical pulses overlap and when the optical channel is behaving linearly in power,1 baseband equalization can be used to separate the pulses with a practical but significant increase in required optical power. This required power penalty is calculated as a function of the input and equalized pulse shapes.","PeriodicalId":55391,"journal":{"name":"Bell System Technical Journal","volume":"18 1","pages":"843-874"},"PeriodicalIF":0.0,"publicationDate":"1973-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74264914","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1973-07-08DOI: 10.1002/J.1538-7305.1973.TB01992.X
D. Marcuse
This paper presents a comprehensive theory of mode coupling in optical fibers with imperfections. The paper begins with the derivation of a general coupled wave theory based on the modes of the ideal fiber. The general theory is applied to a simplified description of guided and radiation modes of the fiber that is valid for small core-cladding index differences. The simplified theory results in expressions for the coupling coefficients that are nearly as simple as those of the slab waveguide. As an example, the theory is applied to the calculation of radiation losses caused by pure core diameter changes and by elliptical deformations of the fiber core.
{"title":"Coupled mode theory of round optical fibers","authors":"D. Marcuse","doi":"10.1002/J.1538-7305.1973.TB01992.X","DOIUrl":"https://doi.org/10.1002/J.1538-7305.1973.TB01992.X","url":null,"abstract":"This paper presents a comprehensive theory of mode coupling in optical fibers with imperfections. The paper begins with the derivation of a general coupled wave theory based on the modes of the ideal fiber. The general theory is applied to a simplified description of guided and radiation modes of the fiber that is valid for small core-cladding index differences. The simplified theory results in expressions for the coupling coefficients that are nearly as simple as those of the slab waveguide. As an example, the theory is applied to the calculation of radiation losses caused by pure core diameter changes and by elliptical deformations of the fiber core.","PeriodicalId":55391,"journal":{"name":"Bell System Technical Journal","volume":"451 1","pages":"817-842"},"PeriodicalIF":0.0,"publicationDate":"1973-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77043981","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1973-07-08DOI: 10.1002/J.1538-7305.1973.TB01995.X
W. Schlosser
The properties of modes in a slab structure with gain in the center region and loss in the surrounding medium are investigated. The propagation constant and field distribution of the lowest-order modes are determined. The cutoff frequencies and propagation constants of the next-higher mode are given. Furthermore, the effect of a refractive index depression or increase in the center region is determined. The depression does not destroy the mode, as may be expected, but causes it to have a cutoff frequency. Comparison of these results to the experimental data shows that gain-induced modes play an important part in the lateral confinement in stripe-geometry GaAs lasers.
{"title":"Gain-induced modes in planar structures","authors":"W. Schlosser","doi":"10.1002/J.1538-7305.1973.TB01995.X","DOIUrl":"https://doi.org/10.1002/J.1538-7305.1973.TB01995.X","url":null,"abstract":"The properties of modes in a slab structure with gain in the center region and loss in the surrounding medium are investigated. The propagation constant and field distribution of the lowest-order modes are determined. The cutoff frequencies and propagation constants of the next-higher mode are given. Furthermore, the effect of a refractive index depression or increase in the center region is determined. The depression does not destroy the mode, as may be expected, but causes it to have a cutoff frequency. Comparison of these results to the experimental data shows that gain-induced modes play an important part in the lateral confinement in stripe-geometry GaAs lasers.","PeriodicalId":55391,"journal":{"name":"Bell System Technical Journal","volume":"1 1","pages":"887-905"},"PeriodicalIF":0.0,"publicationDate":"1973-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90562225","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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