Noncoherent detection of coherent lightwave signals corrupted byphase noise

Waves are treated that modulate by either on-off keying (OOK) or binary frequency-shift keying (FSK) and are further impaired by additive Gaussian noise. Heterodyne detection of such a waveform produces an electronic bandpass signal, which, to ease demodulation in the presence of phase noise, is noncoherently demodulated to extract the baseband pulse stream. The treatment goes beyond previous bit error rate (BER) analyses of optical heterodyne receivers for OOK and FSK. First, there is full adherence to the standard (Brownian motion) model of phase noise. Also, the receiver structure is formulated in such a way that the probability density function of the receiver output samples can be accurately determined. This permits calculations of the additive noise and phase noise tolerable when achieving bit error rates as small as 10 ^-9. Finally, the study is comprehensive regarding the range of parameters explored. Filtering at an intermediate frequency (IF) alone, as well as IF filtering plus postdetection low-pass filtering, is considered. When the receiver parameters decision threshold (for OOK) and IF filter bandwidth are optimized, large amounts of phase noise can be accommodated with only minor increases in required signal-to-noise ratio. This is especially important when the bit rate is moderate compared to the laser linewidth     

Theoretical analysis of phase diversity optical homodyne receiverwith FSK demodulation

A detailed analysis of optical coherent phase diversity single-filtered and dual-filtered frequency-shift keying (FSK) receivers corrupted by shot and phase noise is presented. With delay and cross-product detection, the effect of various parameters, including bandwidths of filters, delay time, frequency deviation and noises, are investigated. The tolerance of phase noise is quite large, when small time delay in the demodulator and appropriately large frequency deviation is selected. It is also shown that there exists an optimal bandwidth for the first filter in the dual-filtered FSK receiver. For a total linewidth equal to half of the bit rate, the power penalty incurred (at BER=10^-9) is 1.92 dB when the modulation index is 4, provided that an optimal filter bandwidth and a frequency deviation-delay product of 0.25 are used     

Theory for optical heterodyne narrow-deviation FSK receivers withdelay demodulation

A theoretical model is presented that includes the effects of laser phase noise, receiver noise, imperfect modulation, IF bandwidth, and postdetection filtering. Detailed numerical results for 140-Mb/s and 400-Mb/s systems are presented, showing excellent agreement with independent published experimental results and strongly supporting the theoretical analysis. It is found that an IF linewidth of less than 0.25% of bit rate is required to avoid degrading the receiver sensitivity by more than 1 dB in a system with a strong local oscillator and modulation index of 0.7. A larger modulation index allows a larger linewidth to be accommodated. If the demodulation is not optimal, a narrower linewidth is necessary     

Wide-linewidth phase diversity homodyne receivers

The use of phase diversity homodyne receivers, which have excellent performance even when the laser linewidth is of the same order of magnitude as the bit rate, to construct coherent systems with semiconductor lasers and moderate bandwidth receivers is considered. Theoretical, experimental, and computer simulation results of a study of a linewidth homodyne phase-diversity receiver is presented. A 150-Mb/s system with an IF linewidth of more than 50% of the bit rate is investigated in depth and is experimentally shown to operate within 1.8 dB from its theoretical limit     

Experiment in frequency-shift-keying adjacent-channel interference

The error performance of a frequency-shift-keying system is investigated experimentally in the presence of Gaussian noise and adjacent-channel interference. It has been found that, for a peak-to-peak frequency deviation of 0.7 times the bit rate and a receiver bandwidth of 1.0 times the bit rate, the frequency spacing between channels can be set to about 1.6 times the bit rate without causing an undue amount of performance degradation.     

Performance of coherent optical CPFSK-DD with intersymbolinterference, noise correlation, and laser phase noise

An exact probability of error expression is presented for a narrow-deviation binary CPFSK coherent optical receiver utilizing differential detection (CPFSK-DD). The result is given in terms of the Marcum Q-function and takes into account the non-Gaussian noise statistics at the decision moment, intersymbol interference, noise correlation, and laser phase noise. Numerical results indicate a local oscillator shot-noise-limited receiver sensitivity of 23.4 photons/b when using a modulation index of 0.67 in combination with an IF filter having a sixth-order Butterworth magnitude response and a normalized 3-dB bandwidth of 1.09. For a given IF filter and IF linewidth, it is found that the modulation index and the IF filter bandwidth should be jointly optimized in order to achieve the best overall receiver sensitivity. When the IF linewidth times the differential delay product is 0.34 %, modulation index and the optimum normalized 3-dB bandwidth are found to be 0.72 and 1.1, respectively. By using Monte Carlo simulation, it is demonstrated that adding laser phase noise at the demodulation stage of the analysis is a valid simplifying assumption for a wide range of practical design parameters     

M-ary FSK Performance for Coherent Optical Communication Systems Using Semiconductor Lasers

This paper describes the design and performance of anMary frequency shift keyed (FSK) signaling and demodulation scheme for an optical communication system using semiconductor lasers and heterodyne detection. Frequency or phase noise in semiconductor lasers causes spectral spreading, producing a nonzero linewidth laser signal. This degrades communication performance when compared to a system using an ideal laser with zero linewidth. We present estimates of the bit error rate (BER) performance ofM-ary frequency shift keying (FSK) with noncoherent demodulation in the presence of white Gaussian frequency noise and additive channel noise. This is typical of an optical system using semiconductor lasers and heterodyne detection. Estimates use the union-Chernoff bound with a simplified channel model to predict the effects of frequency noise. Two effects of frequency noise are identified: signal attenuation or suppression, and crosstalk. These cause an offset in the BER curve from the BER in the absence of frequency noise, and an error rate floor, respectively. The error rate floor is lower than previously predicted. When performance is not crosstalk limited,M-ary FSK is found to perform better than binary FSK with the same system bandwidth constraints, as would be predicted if ideal lasers are used. Theoretical results are compared with Monte Carlo simulations of the system.     

Performance of Narrow-Band Manchester Coded FSK with Discriminator Detection

Due to the large discrepancies m the published results, the bit error rate (BER) performance of narrow-band Manchestercoded frequency-shift-keyed systems (MCFSK) with discriminator detection is reviewed and new results are presented which agree closely with measurements. It is found that a minimum BER is obtained for a peak-to-peak frequency deviation of about 1.35 times the bit rate and a receiver bandwidth of about 1.8 times the bit rate. The published results are shown to be rather optimistic. A coherent MCFSK demodulator is then shown to perform 3 dB better than discriminator detection. It is further shown that in the range of receiver bandwidths larger than the bit rate, it is sufficient to consider the intersymbol interference effects to have come only from the two bits adjacent to the bit being detected. Finally, if the phase noise components are assumed to be Gaussian distributed, the error probability formulas obtained do not predict the correct error performance.     

Error rates for biternary frequency modulation

The performance of a biternary f.m. system is investigated in the presence of additive Gaussian noise and receiver band limitation. The receiver bandpass-filter bandwidth is varied and, for each bandwidth, the frequency-deviation index that minimises the error probability is found. Comparisons with binary frequency modulation of the same data rate show that biternary frequency modulation can offer lower error rates only for receiver bandwidths less than 0.63 times the bit rate.     

Multichannel CPFSK coherent optical communications systems

A detailed theoretical analysis of multichannel coherent CPFSK communications systems is presented. The analysis accounts for the crosstalk between adjacent channels, the intersymbol interference and correlation between noise samples stemming from the limited IF bandwidth the non-Gaussian statistics of the noise at the decision gate, and the impact of the laser phase noise. It is found that the IF bandwidth needed to avoid intersymbol interference is 2.2 bit rates for a modulation index m=1; it is larger for other modulation index values. For m=1, receiver sensitivity is within 1 dB of the shot noise limit, and the electrical domain channel spacing can be as small as 2.05 bit rates with 1-dB sensitivity penalty. The foregoing conclusions are valid for a negligibly narrow linewidth; the degradation due to phase noise is shown to be modest as long as the linewidth does not exceed 1% of the bit rate if m=1. Larger linewidth can be tolerated if the modulation index is larger than unity     

Impact of laser intensity noise on ASK two-port optical homodyne receivers

The letter describes initial experimental results obtained with a multiport optical homodyne receiver employing a DFB laser. The receiver performance is found to be limited by the intensity noise of the local oscillator rather than by the phase noise, even when the product of the IF linewidth and the bit duration is as large as 0.56. A relative intensity noise level of at least ? 140dB/Hz will be required for a satisfactory receiver performance with ? 15dBm local oscillator power.     

Performance analysis of polarization-insensitive phase diversityoptical FSK receivers

A polarization-insensitive phase-diversity optical frequency-shift-keying (FSK) receiver is proposed, and its performance is evaluated. The basic model and signal processing formulation are developed to describe the functions and features of this receiver. Two different approaches (one of which is an upper bound) are used to treat the mixed noise terms, and Gaussian approximation is employed to estimate the receiver performance in terms of the laser linewidth, the modulation index, and the filter bandwidth. The virtually polarization-insensitive property is also verified. As an example, numerical results are presented for a 150-Mb/s receiver, which show that the difference between the upper bound and the other approximation is about 2 to 3 dB. It is also shown that the receiver with small modulation index is less tolerant of the linewidth so that an error floor may appear. When the modulation index is large, the receiver can tolerate linewidths comparable with the bit rate     

Modulation performance of a semiconductor laser coupled to anexternal high-Q resonator

The dynamic response of a semiconductor laser coupled to an external resonator is studied using the single-mode rate equations modified to account for the dispersive feedback. Both the frequency and the damping rate of relaxation oscillations are affected by the feedback. The frequency chirp that invariably accompanies amplitude modulation is significantly reduced. The feedback also reduces the phase noise and the linewidth. To investigate the usefulness of external-resonator lasers in high-speed optical communication systems, the rate equation have been solved numerically to obtain the emitted chirped pulse; the pulse is propagated through the fiber, detected, and filtered at the receiver. The simulated-eye diagrams show that such lasers can be operated at high bit rates with negligible dispersion penalty owing to their reduced frequency chip     

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}).     

Minimum bit rate of DPSK transmission for semiconductor laser with a long external cavity and strong linewidth reduction

A numerical model for a laser diode, weakly coupled to an external cavity, is presented. Using this model, the actual frequency noise spectrum is considered rather than a white frequency noise for estimating the minimum bit rate in a differential-phase-shift-keying (DPSK)-system. Despite possible linewidth reductions by up to 200 with long external cavities, the minimum bit rate (BER = 10^-9) remains nearly unchanged. However, a longer laser cavity (approx600 mum) connected to an external cavity of moderate length ( ≈10 cm) yields a significant reduction of the minimum bit rate (BER = 10^-9) for DPSK-systems at low feedback levels. If more stringent criteria are applied (e.g., receiver penalty < 1 dB) the minimum bit rate remains high also for longer laser cavities.     

噪声对相干光通信锁相环性能影响的量化分析

以PSK(相移键控)外差光通信系统作为研究对象,对相位噪声和散弹噪声对锁相环的性能影响进行了深入的量化分析,得出了锁相环的最优带宽与激光器线宽的关系以及误码率和比特率对激光器线宽的要求,可以作为光锁相环设计的理论指导。     

An optical FSK heterodyne dual filter detection system for takingadvantage of DFB LD applications

An optimum system configuration for an optical frequency-shift keying (FSK) heterodyne dual-filter detection system with distributed feedback laser diodes (DFB LDs) is investigated, taking into consideration LD phase noise influence. Experimental and theoretical examination show that an IF filter bandwidth greater than 10 times the beat spectral linewidth is necessary to avoid LD phase noise influence. A 301-km long-span transmission experiment has been successfully carried out with an optimum configuration for 34 Mb/s. High receiver sensitivity, -61.8 dBm with more than 10 dB improvement over the direct detection system, has also been achieved. Experimental results at higher bit rates of 140, 200, and 280 Mb/s indicate that a modulation index greater than two is desirable to avoid cross talk between mark and space signals. With sufficient frequency deviations, high receiver sensitivities of -54.7 dBm (140 Mb/s) and -52.5 dBm (200 Mb/s) have been achieved. These represent 9.6- and 9-dB sensitivity improvement, respectively, over direct detection systems. A guide for FSK dual-filter detection system design is derived from the experimental and theoretical results. Potential application regions for a dual-filter detection system with DFB LDs are determined     

Adjacent-channel interference in f.s.k. transmission

The performance of a frequency-shift-keying system is investigated as a function of the amount of adjacent-channel interference. New quantitative results are presented which show that, for a peak-to-peak frequency deviation of 0.7 times the bit rate and a receiver bandwidth of one times the bit rate, the frequency separation between channels can be reduced to about 1.6 times the bit rate without causing an undue amount of performance degradation.     

正交多载波降噪差分混沌键控通信系统

为解决多载波差分混沌移位键控(MC-DCSK)系统传输速率低和误码性能差的缺点,该文提出一种正交多载波降噪差分混沌移位键控(QMC-NR-DCSK)系统.在发送端,预定义载波用于发送参考信号,剩余M-1个不同中心频率的载波及其经正交调制技术后得到的频率相同但相位正交的载波都用于传输信息信号,此外,通过进一步引入Hilb...     

Phase diversity techniques for coherent optical receivers

In the present state of the art, coherent optical receivers most often operate in the heterodyne mode. Here a photodiode-amplifier combination having bandwidth greater than twice the bit rate (B) is needed: indeed bandwidths considerably greater than2Bare preferably employed to ease design of the bandpass filter needed for noise limitation, and to avoid demodulator penalties in some modulation schemes. For the high bit rate systems now coming into service (560 Mbit/s-2.4 Gbit/s), the optical receiver design requirements become more stringent for coherent heterodyne operation. The various modes of "zero IF" operation, however, require only baseband receiver module bandwidth. The options available are either homodyne (phase locked) operation, or phase diversity (multiport) techniques. In this paper, we compare these options, and show that phase diversity techniques are capable of good performance for high bit rate coherent receivers. In phase diversity operation, not only is phase locking avoided, but also the necessary frequency locking does not have high stability requirements. Furthermore, there are advantages in operating with a small frequency offset from zero (of the order of 1 percent of the bit rate). An experimental receiver has been operated at 320 and 680 Mbit/s, demodulating both amplitude shift keying (ASK) and differential phase shift keying (DPSK). Operation with FSK is also possible. Sensitivities so far achieved of -47.5 dBm (320-Mbit/s ASK) and -42 dBm (680- Mbit/s ASK) with limited local oscillator power are capable of substantial improvement when higher power local oscillators and lower noise receive modules become available. Demodulation of DPSK at 320 Mbit/s has also been achieved and shows a measured receiver sensitivity improvement of over 4 dB over ASK at the same bit rate and local oscillator power. These practical results show clearly that phase diversity is a very realistic option for high bit rate systems.