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.     

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.     

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}).     

相干光纤通信系统对激光器线宽的要求

通过仿真相干光接收机载波相位估计性能,研究了采用不同调制格式时对所使用激光器线宽的要求,分析了16-QAM采用Star和Square两种不同星座图时线宽要求差异的原因.仿真结果表明:对于既定的比特速率,采用高阶调制格式的系统降低了线路符号速率,但要求激光器线宽更窄;同一调制格式对激光器线宽的要求与所采用的星座图有关.     

The effect of laser linewidth on coherent optical receivers with nonsynchronous demodulation

Recent theoretical analysis of the effect of using lasers with significant linewidths in coherent optical fiber transmission systems has shown how the design of the optical receiver, particularly the IF stage, affects the sensitivity. This paper reviews this theory for two classes of coherent systems-those making a differential phase measurement, and those not using phase information-where the requirements on laser linewidth are not stringent. We discuss the factors that affect the performance of systems with significant laser phase noise. Wherever possible, we compare the theoretical results with published system experiments. We show that our theory fits the experimental data well and indicates why experimental results have fallen short of the theoretical limits.     

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.     

Impact of laser linewidth on optical channel spacing requirements for multichannel FSK and ASK systems

The sensitivity penalty is evaluated for amplitude-shift-keyed and frequency-shift-keyed multichannel coherent systems that use lasers with linewidths which are a significant fraction of the bit rate. The study was conducted for both ASK and FSK systems using a single-filter receiver with nonsynchronous detection. For FSK systems, both NRZ (nonreturn-to-zero) and alternate mark inversion (AMI) signal formats were studied. The optical channel spacing is strongly determined by the laser linewidth. For example, with the FSK-NRZ data rate of 150 Mb/s, the optical channel spacing which gives 1-dB crosstalk penalty is 4 GHz when the intermediate frequency linewidth is 50 MHz (laser linewidth is 25 MHz), as opposed to 1.8 GHz when the linewidth is negligible.<>     

Effect of optical amplifier noise on laser linewidth requirementsin long haul optical fiber communication systems with Costas PLLreceivers

The impact of optical amplifier noise is analyzed in investigating the performance of optical long-haul PSK homodyne communication systems with Costas phase locked loop (PLL) receivers. The laser linewidth requirement for an optically amplified system becomes relaxed in comparison with the system with no optical amplifier, owing to the fact that the effect of incomplete phase tracking becomes less important as a larger signal power is demanded to maintain a fixed bit-error rate. Also, it is found that the power splitting ratio regarding the power distributions for the I-arm and the Q-arm of a Costas loop can vary in a wide range without having much influence on the performance of an optically amplified system. As a matter of fact, the power penalty induced by incomplete phase tracking for a system with a large number of cascaded optical amplifiers is mainly due to the finite phase error and not due to the power splitting ratio, and this may fail a previously-reported method for finding the required laser linewidth by assigning a certain amount of power penalty that is due to the power splitting ratio     

Damping factor influence on linewidth requirements for optical PSKcoherent detection systems

Spectral linewidth requirements for optical phase-shift-keying (PSK) coherent detection systems are found to depend on the phase-locked loop (PLL) parameters. Until now, the damping factor of the PLL has been assumed to be 1/√2 when deriving the required spectral linewidth of a light source, because it is at this value that an electrical PLL offers near optimum performance in many cases. By increasing the PLL damping factor above 1/√2, it is shown that there exists a maximum value of the required linewidth that achieves a received optical power penalty of 1 dB at a bit error rate of 10^-10. The required beat linewidths so obtained are 50% larger than previously reported results (which assume a damping factor of 1/√2). As for PLL frequency acquisition performance, it is shown that raising the camping factor above 1/√2 does not seriously affect the hold-in limit or the pull-in limit. It is also shown that the normalized loop gain that optimizes PLL performance is roughly one half the normalized loop gain at which the PLL oscillation commences     

Theoretical analysis of heterodyne optical receivers for transmission systems using (semiconductor) lasers with nonnegligible linewidth

We present a general theoretical model of receivers for coherent optical communication systems where transmitters and local oscillators having nonzero linewidth are used. Key issues in the model are the concept of single realization measurements of a stochastic intermediate frequency, and development of the probability density function for this stochastic process. Analytical results are derived for heterodyne ASK and dual filter FSK receivers and include the shot-noise limit, the asymptotic error-probability limits in ASK and FSK receivers, the influence of the IF on receiver noise, and the effective local oscillator strength. Detailed numerical results for typical p-i-n-FET wide-band receivers illustrate the influence on receiver sensitivity of IF filter bandwidth and relative threshold setting in ASK systems and of modulation index and IF filter bandwidth in FSK systems. A receiver sensitivity penalty for nonzero linewidth is found to be, for IF linewidths of 0.1 to 0.3 of the bit-rate, 3 to 9 dB in optimum ASK receivers, and 2 to 8 dB in optimum FSK receivers. Thus DFB lasers of linewidth 5 to 20 MHz could be used without external cavities in simple systems with near-ideal performance, which could find application wherever the great multiplexing advantage of coherent systems is a prime advantage. We present some guidelines for system design based on the results of this work.     

Coding to relax laser linewidth requirements and improve receiversensitivity for coherent optical BPSK communications

BPSK (binary phase-shift keying) modulation with heterodyne demodulation is used in conjunction with convolutional codes to illustrate the feasibility of using coding to relax the laser linewidth requirements and improve the receiver sensitivity. The Viterbi algorithm is used, and the performance of the phase-locked loop in the carrier recovery circuit is studied. The results show that the relaxing factor of the laser linewidth can be larger than 12 at 10^-9 bit error rate when a (2, 1) convolutional code with constraint length 11 is used. When the linewidth is fixed, this code can improve the receiver sensitivity by more than 9 dB     

Optical receivers for lightwave communication systems

As long-wavelength optical telecommunications systems are now being installed in countries throughout the world, this is an opportune time to review the successful developments in detectors and receivers for this application. We given prominence to receivers using p-i-n and avalanche photodiodes, describing in some detail the principles of their operation as well as the details of their development. However, we also consider bipolar phototransistors, photoconductive detectors, and the receiver requirements for coherent optical systems, concluding with a broad comparison of the various receiver designs.     

Optical receivers for lightwave communication systems

As long-wavelength optical telecommunications systems are now being installed in countries throughout the world, this is an opportune time to review the successful developments in detectors and receivers for this application. We given prominence to receivers using p-i-n and avalanche photodiodes, describing in some detail the principles of their operation as well as the details of their development. However, we also consider bipolar phototransistors, photoconductive detectors, and the receiver requirements for coherent optical systems, concluding with a broad comparison of the Various receiver designs.     

Design of wide-band optical heterodyne balanced mixer receivers

The optical heterodyne balanced mixer, or dual-detector receiver, offers significant advantages over a single detector receiver. Balanced mixer receivers are particularly attractive for use in optical heterodyne communication systems because they conserve local oscillator power and cancel excess intensity noise present in the local oscillator. Simple circuit models that illustrate the noise performance, small signal gain, and bandwidth of a balanced mixer receiver are developed. A figure-of-merit for receiver noise performance is also derived. An example design of a gigahertz bandwidth optical heterodyne balanced mixer receiver and the techniques used to characterize near-quantum-limited receiver performance are discussed.     

Influence of (semiconductor) laser linewidth on the error-rate floor in dual-filter optical FSK receivers

We discuss an error-rate floor in dual-filter optical FSK receivers in terms of the IF linewidth and the frequency shift between 0s and 1s, using a comprehensive model for the receiver which takes into account nonzero laser linewidth, noise correlation and signal overlap between the filters. We present calculated results for total error probability in terms of signal power, IF linewidth and frequency shift, illustrating the effect of the floor on receiver sensitivity, and we contrast it with a related effect in heterodyne ASK systems.     

扬氏光纤干涉仪测量激光谱线线宽

本文介绍了一个用二根单模光纤组成的扬氏干涉仪来测量连续或脉冲激光谱线宽度的方法,实测了几种激光的线宽及铜蒸气激光在一个脉冲时间内光谱线宽的时间过程。     

The transversely adjusted gap laser for optical communication systems

If a laser's energy gap is adjusted spatially so that it varies with position in a plane transverse to the direction of light propagation then each position in the transverse plane will amplify a different part of the spectrum. A simple optical technique is shown for dispersing an optical beam so that each frequency component passes through the appropriate part of a transversely adjusted gap (TAG) laser. A TAG laser can be constructed by subjecting a GaAs injection laser to a transverse thermal gradient. Calculations indicate that such a device would have a bandwidth of20 times 10^{12}Hz for a 25-fold increase compared to a conventional GaAs injection laser. An analysis of optical ray angle and spatial-dispersion alignment tolerances is presented. Two TAG-laser subsystems-a multiplex modulator and an amplifier-are proposed and discussed to indicate how the TAG laser's larger bandwidth and spatial dispersion may simplify optical communication systems. A preliminary-test TAG-laser oscillator has been constructed and tested. It verified the basic concept and exhibited a bandwidth of2.45 times 10^{12}Hz as predicted by the model.     

Tuned optical receivers for microwave subcarrier multiplexedlightwave systems

An analysis of tuned optical-receiver noise performance for microwave subcarrier multiplexed lightwave systems is presented. The effect of correlation between the gate and the drain HEMT noise sources and the design of tuning networks to obtain partial noise cancellation were investigated. Anoptimization algorithm is used to determine the tuning elements values for minimizing noise of 16 dB for a 60-video-channel subcarrier multiplexing (SCM) system, and 12 dB for a 120-channel system, which allows a significant increase in passive optical network distribution capacity. Design results for tuned front-end receivers encompassing the effects of p-i-n, HEMT, and SCM band parameters are presented     

Signal linewidth broadening due to fibre nonlinearities in long-haul coherent optical fibre communication systems

Signal spectral linewidth broadening due to the Kerr effect in long-haul coherent optical fibre communication systems is examined theoretically and experimentally. By recirculating loop experiments, it is shown that linewidth broadening becomes serious in a system of more than a few thousand kilometres.<>     

Long-haul high-speed optical communication systems using asemiconductor laser amplifier

High-speed long-haul systems using semiconductor laser amplifiers, which eliminate the need for high-speed electronics in repeaters and are transparent to the transmission speed are considered for application in undersea high-speed transmission systems. The potential of laser-amplifier-repeated transmission systems has been explored by transmission experiments, showing that a high-speed system above 2 Gb is possible by filtering out the spontaneous emission power of the laser amplifier. A theoretical estimation of SNR degradation due to noise accumulation of chained laser amplifiers shows that systems are possible, using 30 to 40 laser amplifier repeaters, if narrow-bandwidth optical filters are used