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Showing papers on "Frequency-division multiplexing published in 1991"


01 Jan 1991
TL;DR: In this paper, the influence of the nonlinear distortions introduced by the high power amplifier (HPA) of the transmitter is examined, and the degradation in power efficiency due to intermodulation effects and backoff operating, as well as spectral degradations are investigated.
Abstract: Orthogonal Frequency Division Multiplexing (OFDM) in conjunction with a 4-DPSK modulation format has been proposed for the future digital audio broadcasting system (DAB), that should provide compact disk sound quality in portable, vehicular and fixed receivers. With properly chosen parameters, this system should be appropriate for both terrestrial and satellite transmission. In this paper the influence of the nonlinear distortions introduced by the high power amplifier (HPA) of the transmitter is examined. In particular, the degradation in power efficiency due to intermodulation effects and backoff operating, as well as spectral degradations are investigated.It is shown for three different kinds of limiting amplifier models, that even with an output backoff (OBO) in the region of 5-6 dB, the degradation of, e.g., a 512-carrier 4-DPSK/OFDM system relative to the linear case is below 1.7 dB, while the regenerated sidelobes of the transmitted spectrum are kept below -20 dB.

712 citations


Journal ArticleDOI
TL;DR: In this paper, it was shown that solitons of different velocities are transparent to each other in a system using lumped amplifiers, as long as the length of the collision is long enough relative to the spacing between amplifiers or a possibly longer period of variation in some other parameter, such as the fiber's chromatic dispersion.
Abstract: One attractive feature of the all-optical approach to ultra long-distance transmission is that it greatly facilitates wavelength division multiplexing (WDM). It is known that solitons of different velocities are transparent to each other. It is shown, through numerical simulation, that such transparency is also maintained in a system using lumped amplifiers, as long as the length of the collision (the distance the solitons travel down the fiber while passing through each other), is long enough relative to the spacing between amplifiers, or to a possibly longer period of variation in some other parameter, such as the fiber's chromatic dispersion. This result implies the potential for at least several multigigabits-per-second WDM channels spanning just 1 or 2 nm, in a system of transoceanic length (7000-9000 km). >

262 citations


Journal ArticleDOI
M.G. Hluchyj1, Mark J. Karol1
TL;DR: A multihop wavelength-division multiplexing (WDM) approach, referred to as Shuffle Net, for achieving concurrency in distributed lightwave networks is proposed, avoiding both wavelength-agility and pretransmission-coordination problems.
Abstract: A multihop wavelength-division multiplexing (WDM) approach, referred to as Shuffle Net, for achieving concurrency in distributed lightwave networks is proposed. A Shuffle Net can be configua19 red with each user having as few as one fixed-wavelength transmitter and one fixed-wavelength receiver, avoiding both wavelength-agility and pretransmission-coordination problems. The network can achieve at least 40% of the maximum efficiency possible with wavelength-agile transmitters and receivers. To transmit a packet from one user to another may require routing the packet through intermediate users, each repeating the packet on a new wavelength until the packet is finally transmitted on a wavelength that the destination user receives. For such a multihop lightwave network, the transmit and receive wavelengths must be assigned to users to provide both a path between all users and the efficient utilization of all wavelength channels. >

242 citations


Journal ArticleDOI
TL;DR: In this paper, the effect of weak refractive-index nonlinearity of optical fibers on pulse shape was investigated using computer simulations of long-distance transmission and the analysis was confined to normal pulses and does not consider solitons.
Abstract: The effect of the weak refractive-index nonlinearity of optical fibers on pulse shape is investigated using computer simulations of long-distance transmission. Fiber losses are canceled by periodically spaced optical amplifiers whose spontaneous emission noise is, however, not included in the simulations. The analysis is confined to normal pulses and does not consider solitons. Several conclusions are drawn. (1) If wavelength division multiplexing (WDM) of two channels is used in a uniform fiber without dispersion fluctuations, catastrophic buildup of four-wave mixing occurs if one primary channel is located at the zero-dispersion wavelength. (2) If two pulses with different carrier frequencies collide in a uniform fiber with no gain or loss discontinuities, their four-wave mixing products reach a peak during complete pulse overlap, but this spurious power dies away as the pulses separate. (3) Two-channel WDM transmission of light modulated in amplitude-shift keying format appears feasible at 2.5 GB/s over distances of 7500 km. >

202 citations


Journal ArticleDOI
J.P. Gordon1, L. F. Mollenauer1
TL;DR: In this paper, it was shown that it is possible to send error-free signals at a 2.5-Gb rate (or higher) over distances of at least 9000 km using an amplitude shift keying (ASK) soliton modulation system.
Abstract: It is shown that it should be possible to send error-free signals at a 2.5-Gb rate (or higher) over distances of at least 9000 km using an amplitude shift keying (ASK) soliton modulation system. To accomplish this, the amplifiers must be kept close enough that their power gain is less than 10 dB. (It is noted that timing jitter and other noise effects measured in recent soliton transmission experiments carried out at low D and with amplifier spacing of 25 km are in close accord with predictions of this work). Frequency division multiplexing of several channels over the same fiber should also be possible, as solitons of different frequencies interact very weakly, provided the distance over which they pass through one another is large compared to the amplifier spacing. >

156 citations


Journal ArticleDOI
TL;DR: The performance of OFDM/FM modulation for digital communication over Rayleigh-fading mobile radio channels is described and results obtained from the hardware measurements agree closely with the numerical results.
Abstract: The performance of OFDM/FM modulation for digital communication over Rayleigh-fading mobile radio channels is described. The use of orthogonal frequency division multiplexing (OFDM) over mobile radio channels was proposed by Cimini (1985). OFDM transmits blocks of bits in parallel and reduces the bit error rate (BER) by averaging the effects of fading over the bits in the block. OFDM/FM is a modulation technique in which the OFDM baseband signal is used to modulate an FM transmitter. OFDM/FM can be implemented simply and inexpensively by retrofitting existing FM communication systems. Expressions are derived for the BER and word error rate (WER) within a block when each subchannel is QAM-modulated. Several numerical methods are developed to evaluate the overall BER and WER. An experimental OFDM/FM system was implemented and tested using unmodified VHF FM radio equipment and a fading channel simulator. The BER and WER results obtained from the hardware measurements agree closely with the numerical results. >

144 citations


Patent
28 Jan 1991
TL;DR: In this article, a compact, flexible, communications cable capable of electrical and optical signal propagation simultaneously is provided, which is carried by coaxial inner and outer conductors of metal having suitable conductivity which surround and enclose a centrally disposed optical fiber conductor.
Abstract: A compact, flexible, communications cable capable of electrical and optical signal propagation simultaneously is provided. The electrical signal is carried by coaxial inner and outer conductors of metal having suitable conductivity which surround and enclose a centrally disposed optical fiber conductor. The cable allows electrical signal propagation over a bandwidth from about 60 cycle D.C. or A.C. as well as radio frequency and microwave signals up to about 100 gigahertz without appreciable signal loss.

108 citations


Proceedings ArticleDOI
07 Apr 1991
TL;DR: A wavelength division multiplexing transmissive star network is investigated, in which each node has one tunable transmitter with limited tuning capability and multiple fixed receivers and an efficient approximate analysis with drastically reduced computational complexity is presented.
Abstract: A wavelength division multiplexing (WDM) transmissive star network is investigated, in which each node has one tunable transmitter with limited tuning capability and multiple fixed receivers. Two synchronous channel access protocols requiring no pretransmission penalty are considered: random access and fixed transmission scheduling. An efficient approximate analysis with drastically reduced computational complexity is presented. In spite of the reduced complexity, the presented approach produces very accurate results and can serve in producing the most cost-effective system design for given performance requirements. >

90 citations


Proceedings ArticleDOI
02 Dec 1991
TL;DR: A static code design with unequal error protection (UEP) is presented that also takes auxiliary data services into account and emphasis is on the use of source-adapted channel coding with rate-compatible punctured convolutional (RCPC) codes.
Abstract: A system proposal for DAB is investigated. The kernel is orthogonal frequency division multiplexing (OFDM) with 4-DPSK (differential phase shift keying) modulation, rectangular pulse-shaping, and a guard interval to reject multipath distortions. Emphasis is on the use of source-adapted channel coding with rate-compatible punctured convolutional (RCPC) codes. Based on analytical and simulated BER (bit error rate) curves for several propagation conditions and on preliminary source significance information (SSI), a static code design with unequal error protection (UEP) is presented that also takes auxiliary data services into account. The gain due to UEP is on the order of 8dB in signal power or 25% in bandwidth. >

69 citations


Journal ArticleDOI
Ian H. White1
TL;DR: In this paper, a novel form of wavelength selectable diode laser source is proposed for wavelength division multiplexing (WDM) applications, which can operate at specific wavelengths across the complete gain spectrum of the laser diode material, but does not require any moving parts.
Abstract: A novel form of wavelength selectable diode laser source is proposed for wavelength division multiplexing (WDM) applications. The source may be used to operate at specific wavelengths across the complete gain spectrum of the laser diode material, but does not require any moving parts. Theoretical simulations indicate that the device can be expected to operate in a single longitudinal mode for channel separations on the order of 1 nm. The potential of using the device to generate parallel streams of WDM data is considered. >

65 citations


Patent
27 Nov 1991
TL;DR: In this paper, a node composed of a selection unit for selecting signals having optical frequencies to be sent to the plurality of terminals, respectively, from signals transmitted through the second optical communication path in optical frequency division multiplexing, a conversion unit for converting the selected signals into signals having a single optical frequency and an output unit for producing the converted signals to the terminals through the first optical communication paths, respectively.
Abstract: An optical frequency division multiplexing network includes first optical communication paths connected to terminals, respectively, a second optical communication path connected to the outside and a node composed of a selection unit for selecting signals having optical frequencies to be sent to the plurality of terminals, respectively, from signals transmitted through the second optical communication path in optical frequency division multiplexing, a conversion unit for converting the selected signals into signals having a single optical frequency and an output unit for producing the converted signals to the terminals through the first optical communication paths, respectively.

Journal ArticleDOI
B. Glance1, U. Koren1, C.A. Burrus1, J.D. Evankow1
TL;DR: In this paper, a fast tunable laser for packet switching applications based on wavelength division multiplexing (WDM) is presented, which can be switched randomly in less than 5 ns among these frequencies.
Abstract: A fast tunable laser for packet switching applications based on wavelength-division multiplexing (WDM) is presented. The laser is tunable to 16 discrete frequencies regularly spaced by 43 GHz over a tuning range of 645 GHz centred around a wavelength of 1.53 mu m. It can be switched randomly in less than 5 ns among these frequencies. Importantly, the same comb of frequencies is obtained from different lasers fabricated by the same lithographic process. This greatly simplifies the implementation of optical WDM systems.

Proceedings ArticleDOI
02 Dec 1991
TL;DR: It is shown how to double the existing spectrum efficiency of the system with the association of trellis-coded modulation and an orthogonal frequency-division multiplexing technique with the aim of offering the transmission capacity in a TV channel necessary for a high-quality video signal.
Abstract: The combination of an orthogonal frequency division multiplexing (OFDM) technique and a coding scheme is seen as a promising broadcasting system to cope with the frequency-selective and time-variant channel. The first application of this technique using a convolutional coding scheme has been implemented within the framework of the Eureka DAB (digital audio broadcasting) project. It is shown how to double the existing spectrum efficiency of the system with the association of trellis-coded modulation and an orthogonal frequency-division multiplexing technique with the aim of offering the transmission capacity in a TV channel necessary for a high-quality video signal. >

Patent
10 Jul 1991
TL;DR: In this article, a frequency tracking circuit was used to adjust the tunable laser frequency and lock it to the present reference frequency in an optical frequency division multiplexing (OFDM) system.
Abstract: An Optical Frequency Division Multiplexing system achieves close channel spacings and thus high density of communications channels in a particular frequency band by providing a very precise carrier frequency stabilization technique. Each laser-generated local carrier signal is locked to a corresponding reference signal. All of the reference signals are generated by a common tunable laser circuit (2) that produces a sequence of bursts of successively higher frequencies determined by resonant points of single Fabry-Perot filter. Each transceiver of the Optical Frequency Division Multiplexing system includes a frequency tracking circuit (1) that converts received signals (P1 in (t)) from the optical domain to the electrical domain (P2) and utilizes an intermediate frequency filter circuit (10) and a servo control circuit (16) to adjust the tunable laser frequency and lock it to the present reference frequency.

Journal ArticleDOI
TL;DR: In this paper, an upgrade method is described for a two-way broadband service transmission of a previously proposed passive optical subscriber network (PASS-NET) using OFDM/TDM techniques for downstream transmission and time division multiple access (TDMA) for upstream.
Abstract: An upgrade method is described for a two-way broadband service transmission of a previously proposed passive optical subscriber network (PASS-NET) PASS-NET uses optical frequency division multiplex/time-division multiplex (OFDM/TDM) techniques for downstream transmission and time division multiple access (TDMA) for upstream. Fundamental experiments for downstream transmission to two subscribers are executed to demonstrate the possibility of the upgrade method. Two wavelengths emitted by a distributed Bragg reflector-laser diode (DBR-LD) tunable laser with a 5-GHz (0.04-nm) space between them are directly intensity modulated at 32 Mb/s. Each wave transmits narrowband service to each subscriber. The third wavelength emitted by another DBR-LD tunable laser with an 11-nm separation from the two wavelengths is directly intensity modulated at 100 Mb/s and overlaid. >

Journal ArticleDOI
TL;DR: In this article, a polarization independent narrow channel (PINC) wavelength division multiplexing (WDM) coupler for operation at 1.55 mu m has been designed based on the birefringent properties of fused single-mode couplers.
Abstract: A polarization-independent narrow-channel (PINC) wavelength division multiplexing (WDM) coupler for operation at 1.55 mu m has been designed based on the birefringent properties of fused single-mode couplers. These couplers are made from both conventional single-mode fiber (SMF) and dispersion shifted fiber (DSF). The couplers are designed so that the coupling-coefficient-length products for the two orthogonal polarizations are pi out of phase. As a result of the long coupling lengths required, these couplers have very small cross-sectional dimensions, typically on the order of 10 mu m. >

Journal ArticleDOI
TL;DR: In this article, an electronically integrated, four-channel optical receiver is demonstrated which is designed for electronic channel selection of different wavelength channels in a wavelength-division-multiplexing-based optical network.
Abstract: A novel, electronically integrated, four-channel optical receiver is demonstrated which is designed for electronic channel selection of different wavelength channels in a wavelength-division-multiplexing-based optical network. The receiver consists of four InAlAs-InGaAs metal-semiconductor-metal (MSM) photodetectors that can be independently switched on or off electronically by a digital signal. An optical extinction ratio of 20 dB for the MSM detector was observed. The sensitivity of this optoelectronic integrated circuit receiver is -25.2 dBm at 1.2 Gb/s data rate. >

Patent
19 Apr 1991
TL;DR: In this paper, a planar optical waveguide is used as a shared medium for a plurality of subsystems in an information processing system, where each subsystem is provided with a light emitting diode to broadcast information pulses into the shared medium and a photodetector for receiving the information pulses broadcast by the light emitting diodes.
Abstract: An information processing system uses a planar optical waveguide as a shared medium for a plurality of its subsystems. To this end, each subsystem is provided with a light emitting diode to broadcast information pulses into the shared medium and a photodetector for receiving the information pulses broadcast by the light emitting diodes. This thereby reduces the need for conductive interconnections between subsystems. Additionally, a number of planar optical waveguides can be stacked on a support and different compositions of subsystems communicate with one another by using different waveguides of the stack. The system can be adapted for time-division, space-division and frequency division multiplexing.

Journal ArticleDOI
TL;DR: In this paper, the design and performance of an optical frequency-division-multiplexing (FDM) system that uses a frequency-shift-keying (FSK) direct detection scheme are described.
Abstract: The authors describe the design and performance of an optical frequency-division-multiplexing (FDM) system that uses a frequency-shift-keying (FSK) direct detection scheme. This system utilizes a Mach-Zehnder type periodic filter as a channel selective filter and optical frequency discriminator. Requirement conditions for laser diode linewidth, frequency deviation, channel frequency spacing, detuning of optical filters, and signal power variance are discussed. These characteristics are experimentally confirmed using planar waveguide type filters. >

Journal ArticleDOI
G.R. Walker1, N.G. Walker1, R.C. Steele1, M.J. Creaner1, M.C. Brain1 
TL;DR: In this article, the requirements and practicalities of amplifier cascades for multichannel coherent transmission are discussed, and a four-amplifier cascade which maintains an overall noise figure of less than 13 dB across a 20-nm optical bandwidth for total input powers up to -10 dBm is described.
Abstract: The requirements and practicalities of amplifier cascades for multichannel coherent transmission are discussed. A four-amplifier cascade which maintains an overall noise figure of less than 13 dB across a 20-nm optical bandwidth for total input powers up to -10 dBm is described. A potential capacity of 100 wavelength division multiplexing channels is demonstrated in a 300-km 622-Mb/s DPSK (differential phase shift keying) coherent transmission experiment. >

Journal ArticleDOI
TL;DR: It is shown that the network, in addition to providing an independent and asynchronous access to the optical fiber channel for the network subscribers, effectively utilizes the available bandwidth when the optical channel is sparsely utilized.
Abstract: A network architecture is presented for a fiber optic frequency hopping multiple access (FO-FHMA) communication system. It is shown that the network, in addition to providing an independent (from other users) and asynchronous access to the optical fiber channel for the network subscribers, effectively utilizes the available bandwidth when the optical channel is sparsely utilized. In this arrangement the network users employ pseudorandom codes to frequency modulate the optical signal on the fiber bus using an optical pulse modulator. A balanced optical phase discriminator followed by a standard frequency dehopping receiver are used to decode the user provided information at a desired point on the fiber bus. It is demonstrated that the system may easily be implemented with the aid of a number of available optical components and standard frequency hopping transmitter and receive. >

Proceedings ArticleDOI
C.M. Miller1
11 May 1991
TL;DR: The unique characteristics (stable optical performance, inherently pigtailed, insertion loss 100) of tunable, fiber Fabry-Perot (FFP) filters allow diverse optical signal processing necessary for third-generation WDM systems and wavelength division multiple access (WDMA) networks as mentioned in this paper.
Abstract: The unique characteristics (stable optical performance, inherently pigtailed, insertion loss 100) of tunable, fiber Fabry-Perot (FFP) filters allow diverse optical signal processing necessary for third-generation wavelength division multiplex (WDM) systems and wavelength division multiple access (WDMA) networks. After describing the FFP characteristics, the author discusses the WDM long-haul field experiment and the prototype IBM Rainbow WDMA network. Other applications for this filter technology are EDFA noise filters, channel switches, and signal processors for extremely broadband ISDN (integrated services digital network) and digital high-definition TV distribution systems. >

Journal ArticleDOI
TL;DR: In this article, a modulation scheme combining microwave phase-shift-keyed (PSK) and optical frequency modulation (FM) techniques is used in a two-channel optical frequency-division-multiplexed (FDM) system.
Abstract: A modulation scheme combining microwave phase-shift-keyed (PSK) and optical frequency modulation (FM) techniques is used in a two-channel optical frequency-division-multiplexed (FDM) system. Optical filtering and FM demodulation are carried out by a tunable fiber Fabry-Perot etalon. A transmission rate of 2 Gb/s and a channel spacing of less than 30 GHz are achieved with a crosstalk level of about -25 dB. This work shows that the modulation technique of combining optical FM/FDM and RF/microwave subcarrier multiplexing is transparent to either digital or analog signals. The modulation technique not only avoids the low-frequency nonuniform FM response problem, but also facilitates close optical channel spacing. >

Patent
29 Jan 1991
TL;DR: A modulation signal carrying a composite video signal representing a screen image composed of reduced frames corresponding to a plurality of channels and a modulation signal (13) carrying a digital graphics signal are subjected to frequency multiplexing as discussed by the authors.
Abstract: A modulation signal carrying a composite video signal (4) representing a screen image composed of reduced frames corresponding to a plurality of channels and a modulation signal (13) carrying a digital graphics signal are subjected to frequency multiplexing (5), and the multiplex signal is recorded to a single record medium (14) utilizing its capacity effectively. During reproduction, one reduced frame and a frame of the graphics are displayed simultaneously.

Journal ArticleDOI
TL;DR: In this paper, the authors investigate the behavior of multichannel signals in a high-density wavelength division multiplexing (WDM) system with the consideration of stimulated Raman scattering.
Abstract: The authors investigate the behavior of multichannel signals in a high-density wavelength division multiplexing (WDM) system with the consideration of stimulated Raman scattering. A parameter to evaluate the depth of Raman crosstalk is provided, and the transmission distance limitation imposed by Raman crosstalk is analyzed. To extend the system transmission distance, a post-transmitter fiber Raman amplifier is used. The allocation of signal channels on the pump gain profile is discussed. It is found that there exists an optimum pump power which results in a maximum amplifier gain. The example shows that the transmission distance limitation imposed by Raman crosstalk can be extended by 20 km for a 30-channel system with 0.25-dB/km fiber loss. >

Patent
05 Jun 1991
TL;DR: In this article, the phase of the data bit timing is maintained between transmitters and in the response from the meters to produce an appropriate signal level for coupling signals between a network of low but unknown impedance and a transceiver.
Abstract: Apparatus for coupling signals between a network of low but unknown impedance and a transceiver comprises a series resonant circuit (31, 32) terminated with a high impedance and a parallel resonant circuit (36, 37) terminated with a low value resistor (38). A power amplifier (39) is provided for transmitting and switching means (34) to switch between the two circuits. The signal is monitored to produce an appropriate signal level for coupling to the network. A particular use of this apparatus is in electricity supply to read meters. Polling messages are transmitted from a substation to a plurality of meters with the phase of the data bit timing maintained between transmitters and in the response from the meters. Transmission of the signals with high immunity to noise and narrow bandwidth is achieved by complex phase modulation of the carrier. A binary phase shift keyed signal produces signals with a bandwidth less than the frequencies allocated to metering applications and interference between signals can be avoided by frequency division multiplexing.

Patent
30 Jul 1991
TL;DR: In this paper, a page party system was proposed for industrial environments, having a plurality of stations joined by a page line and by a single party line for providing multiple full-duplex conference calls over the single-party line.
Abstract: A page party system for use in industrial environments, having a plurality of stations joined by a page line and by a single party line for providing multiple full-duplex conference calls over the single party line. Multiple full-duplex conferencing is achieved by combining single sideband suppressed carrier amplitude modulation and frequency division multiplexing.

Proceedings ArticleDOI
02 Dec 1991
TL;DR: A photonic access network architecture is proposed that can create the large capacity and extremely flexible network needed to offer B-ISDN services economically and uses WDM, FDM, and optical switching techniques to keep pace with service and demand growth.
Abstract: A photonic access network architecture is proposed that can create the large capacity and extremely flexible network needed to offer B-ISDN (broadband integrated services digital network) services economically. The networks are characterized by increased management flexibility and line capacity. Line capacity of over 100 Gb/s is possible with a single-mode fiber. This architecture uses WDM (wavelength division multiplexing), FDM (frequency division multiplexing), and optical switching techniques to keep pace with service and demand growth. A wavelength division optical switch is proposed that permits the establishment of this architecture. The switch is composed of Mach-Zehnder interferometers with a thermooptic phase shifter. By using LSI microfabrication technology, a switch that supports eight wavelength signals can be constructed on one silicon wafer. >

Journal ArticleDOI
TL;DR: In this paper, a frequency planning method based on regular lattices derived from factorial rhombic numbers was proposed to improve the spectrum efficiency of the DAB networks. But the authors only considered the VHF spectrum.
Abstract: A frequency planning method is proposed that is based on regular lattices derived from factorial rhombic numbers. It is shown theoretically that the spectrum efficiency can be improved by about 30% in comparison to existing broadcast networks. This implies less stringent constraints for frequency multiplexing at the transmitter sites. A frequency plan and model calculations of the network coverage are given for a test area. It is shown that the capacity of the VHF spectrum is sufficient to introduce DAB yet still broadcast the same amount of existing FM programs. >

Journal ArticleDOI
TL;DR: In this article, a modification of the offset frequency master-slave principle was proposed to improve the frequency stability of the laser frequency control system by allowing the frequency spacing between optical channels to be chosen independently, with an accuracy determined by the selectivity of the electronics.
Abstract: A novel method for locking the frequency spacing between semiconductor lasers electrically is presented. The method is a modification of the offset frequency master-slave principle. The method allows the frequency spacing between optical channels to be chosen independently, with an accuracy determined by the selectivity of the electronics, and it improves the frequency stability of the locked lasers. A rigorous analytical model of the locking configuration is presented. This model is used to investigate how laser frequency noise and electrical noise from the locking circuit affect the frequency stability of the locked lasers. It is found that the improvements in frequency stability can be achieved for up to 350 lasers, each having a linewidth of 1 MHz. Consequently, the method is suited to lock the transmitters in a coherent optical FDM system. >