Impact of finite frequency deviation on the performance ofdual-filter heterodyne FSK lightwave systems

A detailed theoretical analysis is given of the impact of finite frequency deviation on the sensitivity of dual-filter heterodyne frequency-shift-keying (FSK) lightwave systems. The analysis provides closed-form signal-to-noise ratio (SNR) results for estimating the bit-error-ratio (BER) performance of the system. These closed-form results provide an insight into the impact of finite frequency deviation 2Δf_d, laser linewidth Δν, bit rate R_b, and IF filter bandwidths on the system performance. Simulation results indicate that the accuracy of the approximate theory presented is within 1 dB for linewidths up to 22% when BER=10^-9. It is shown that there is a well-defined relationship between the choice of frequency deviation and the tolerable amount of laser phase noise. The sensitivity degradation can be very severe for a fixed linewidth as the frequency deviation gets smaller     

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.     

Impact of laser phase noise on the performance of a {3×3}phase and polarization diversity optical homodyne DPSK receiver

An analysis of the impact of laser phase noise on the performance of a {3×3} phase- and polarization-diversity differential phase-shift keying (DPSK) receiver is done for the phase and shot-noise limited case. The results show that, for zero laser linewidths, the maximal signal power penalty of the {3×3} phase- and polarization-diversity DPSK receiver with respect to the conventional heterodyne DPSK receiver is approximately 0.7 dB for P_e =10^-9. For nonzero laser linewidths, it appears that, depending on the laser linewidth, for large signal-to-noise ratios the performance of the analyzed {3×3} phase- and polarization-diversity DPSK receiver is close to that of the ideal conventional heterodyne DPSK receiver. For a rectangular intermediate-frequency filter, the maximum allowable normalized laser linewidth (Δυ×T) for the (3×3) phase and polarization diversity DPSK receiver is found to be approximately 0.46% for a power penalty of 1 dB     

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

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

Sensitivity penalty in multichannel coherent optical communications

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

Crosstalk penalty in a two-channel ASK heterodyne detection system with non-negligible laser line width

Crosstalk penalties as a function of channel spacing were measured in a two-channel ASK heterodyne system using 1·55?m DFB lasers. For an IF linewidth/bit rate ratio of 0.5, the channel spacing in the IF domain must be greater than 13 times the bit rate for negligible crosstalk penalty.     

Crosstalk and prefiltering in a two-channel ASK heterodynedetection system without the effect of laser phase noise

The authors present an experimental and theoretical study on the crosstalk in a two-channel amplitude-shift keying (ASK) heterodyne detection system in which the effect of laser phase noise is negligible. Three results are described: (1) the dependence of the crosstalk penalty on the ratio of channel separation to bit rate and on the optical power level of the image band (2) comparison of the measured crosstalk penalities with the ones obtained from a simple model, and (3) the effect of electrical prefiltering on the crosstalk penalty. It is concluded that the channel separation can be as low as four times the bit rate without incurring any crosstalk penalty as long as the optical power of the image band is comparable to the optical power of the desired channel. In addition, electrical prefiltering of the transmitted signals significantly reduces the crosstalk penalty in multichannel ASK heterodyne systems in which the effect of laser phase noise is negligible     

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.<>     

Impact of local oscillator intensity noise and the threshold levelon the performance of a {2×2} and {3×3} phase-diversity ASKreceiver

The impact of local oscillator intensity noise and the threshold level on the performance of the {2×2} and the {3×3} phase-diversity amplitude-shift keying (ASK) receiver has been investigated for the first time for non-Gaussian statistics. Exact equations are derived for the bit-error-rate (BER), taking into account the non-Gaussian statistics and the statistical dependency of the relative intensity noise (RIN) in the receiver branches. The results differ substantially from the case in which a priori Gaussian statistics were assumed. The sensitivity penalty of the receivers is calculated with respect to the performance of an ideal heterodyne ASK receiver for a BER of 10^-9. It is shown that for a minimum sensitivity penalty the threshold level should be chosen in relation to the local oscillator power and the intensity noise level     

Limiter-discriminator detection of a coherent optical heterodyneM-ary CPFSK receiver

The performance of a coherent optical M-ary continuous-phase frequency-shift-keying (CPFSK) receiver using limiter-discriminator (L-D) detection is investigated. It is shown that L-D detection of CPFSK optical signals offers the best performance for a large normalized IF beat spectral linewidth, ΔνT. When the modulation index is unity, the receiver is immune to laser phase noise and can produce (M/4) exp (-SNR) symbol error probability, which may be considered as the upper bound if the optimal modulation index is used (SNR is the signal-to-noise ratio per symbol). Optimum modulation indexes are 0.8 and 1 at ΔνT=1% and ΔνT=2%, respectively, for M=4, 8, and 16     

Theory of direct-detection lightwave receivers using opticalamplifiers

A simple theory is presented for analyzing the sensitivity and bit-error rate (BER) performance of direct-detection lightwave receivers using optical amplifiers. The analysis provides closed-form expressions for the BER and receiver sensitivity, and includes the impact of phase noise. Furthermore, the proposed theory predicts the optimum filter bandwidth values required for linewidths of practical interest (up to 100% of the bit rate). For the special case of zero linewidth, the average signal energy predicted by this work is 42.3 photons/b at BER=10 ^-9. This result is within 0.47 dB of the sensitivity predicted by more accurate techniques     

ASK multiport optical homodyne receivers

Several types of ASK multiport homodyne receivers are investigated, and the impact of the phase noise and of the shot noise on these receivers is analyzed. The simplest structure is the conventional multiport receiver with a matched filter in each branch. This structure can tolerateDeltavT[deltavis the laser finewidth andTis the bit duration) of several percent with a small power penalty (3.6 percent for 1-dB penalty and 5.2 percent for 2-dB penalty). Optimization of branch filters of conventional multiport receivers does not help when the linewidth (and the penalty) is small but does improve the receiver performance for larger linewidths. The most important point of the paper is the novel wide-band filter-rectifier-narrow-band filter (WIRNA) structure, proposed and investigated here for the first time for optical communication systems. It is shown that the optimized WIRNA homodyne receivers are extremely robust with respect to the phase noise: the WIRNA tolerable value ofDeltavTis 3.6 percent for 1-dB penalty and more than 50 percent for 2-dB penalty. Thus, the WIRNA structure opens, for the first time, the possibility of constructing homodyne receivers operating at several hundred megabits per second with conventional DFB lasers without complicated external cavities. Under no-phase-noise conditions, all the multiport receivers investigated here have the same performance, which is identical to that of heterodyne ASK receivers. In addition, the optimized WIRNA receivers can tolerate tapproximately) the same laser linewidth as the heterodyne ASK receivers. Thus, the main difference between the WIRNA multiport homodyne and heterodyne receivers is that the former shifts the processing to a lower frequency range, in return for a more complicated implementation. This difference makes the WIRNA multiport homodyne receivers particularly attractive at high (say, several gigabit per second) bit rates.     

The effect of spurious intensity modulation in semiconductor diode lasers on the performance of optical heterodyne frequency shift-keyed communications systems

Analytical expressions are derived for the bit-error rate (BER) of anM-ary frequency shift-keyed (FSK), heterodyne, optical communication system with noncoherent demodulation in the presence of spurious intensity modulation (SIM) and frequency noise. The SIM degradation of an FSK system, implemented with semiconductor diode lasers, is estimated for lasers with zero and nonzero linewidths and will be discussed for a distributed feedback laser operating at 1.5μm and a channeled substrate planer laser operating at 0.83 μm. The SIM power penalty is typically less than 1 dB, but can exceed 1 dB for 2-, 4-, and 8-ary FSK at data rates above 1 Gbit/s.     

Signal processing in an optical polarization diversity receiver for560-Mbit/s ASK heterodyne detection

Polarization diversity is an alternative technique for coherent receivers to prevent loss to signal due to variations in the states of polarization (SOP) of the received signal field. It is shown experimentally and theoretically that there is no significant power penalty difference between a receiver with optimally adjusted gains and receivers with linear envelope detection and square-law detection. Experimentally, two amplitude-shift keying (ASK) heterodyne polarization diversity receivers with envelope detectors were demonstrated at 560 Mb/s, one using linear rectifiers, the other using square-law rectifiers. In both cases, the receiver sensitivity of -35 dBm at BER=10 ^-9 was degraded by less than 1 dB as the received signal SOP was varied, in agreement with theory     

Penalty free biphase linecoding for pattern independent FSKcoherent transmission systems

Biphase coding is used to eliminate the unwanted influence of nonuniform laser characteristics in frequency-shift-keying (FSK) transmission systems. Compared to other (ternary) linecoding schemes, biphase has the advantage that it does not give a 3-dB sensitivity penalty when properly decoded in the receiver. This has been demonstrated in a 140-Mb/s 280-Mbaud transmission experiment. The receiver features a new type of reliable unambiguous clock extraction. Due to the compact IF spectrum, as compared with ternary linecoding schemes, biphase equipped FSK systems are especially suited for efficiently spaced coherent multichannel (CMC) systems. FSK heterodyne transmission experiments show a sensitivity ηP of -56.7 dBm for 2¹⁰-1 pseudorandom patterns, only 4.8 dB from the shot-noise limit     

BER evaluation for phase and polarization diversity opticalhomodyne receivers using noncoherent ASK and DPSK demodulation

An analysis of the performance of phase diversity receivers using amplitude-shift keying (ASK) and differential phase-shift keying (DPSK) is presented. Both {2×2} and {3×3} multiport receivers are investigated. Asymptotic methods are used to estimate the bit error rate (BER) and signal-to-noise power ratio (SNR) dependence for each type of the receiver. The analysis favors the squarers as the demodulators for ASK whose performance approaches that of the ideal heterodyne detector in the limit of large SNR. A modification of the ASK ({3×3}) receiver which cancels the local oscillator intensity noise is proposed. Receivers which comprise polarization and phase diversity techniques are also investigated for both ASK and DPSK. Their performance is independent of the polarization state of the received signal, and the value of SNR required to obtain the BER of 10^-9 is only a few tenths of a decibel greater than that needed by the phase diversity receivers     

Experimental study of stimulated Brillouin scattering by broad-bandpumping

A XeCl laser system has been used to investigate stimulated Brillouin scattering (SBS) cyclohexane and methanol with laser radiation of spectral width Δν_p much larger than the bandwidth of the excited acoustic wave Δν_a. The reflectivity and the phase conjugation (PC) fidelity of the SBS reflector versus pump intensity and bandwidth have been measured. It is shown experimentally that the PC fidelity and the reflectivity are strongly dependent on the pump spectral width and intensity. However, the experimental results show that the use of a liquid SBS reflector is still effective for correcting the spatial aberrations of laser radiation with Δν _p≃30 Δν_a in a double-pass amplifier     

A generalized suboptimum unequally spaced channel allocationtechnique. I. In IM/DD WDM systems

Four-wave mixing (FWM) is the most serious fiber nonlinearity associated with low-input optical power levels in long-haul multichannel optical systems employing dispersion-shifted fiber. To reduce the crosstalk due to FWM, a generalized suboptimum unequally spaced channel allocation (S-USCA) technique is proposed and investigated. Even though the developed technique is useful in combating FWM crosstalk in wavelength division multiplexing (WDM) lightwave systems with up to 12 channels, its main virtue is in designing multichannel WDM lightwave systems with more than 12 channels. Comparisons of power penalty due to FWM between equal channel spacing (ECS) systems and the S-USCA systems are presented. It is shown that for an intensity modulation/direct detection (IM/DD) transmission system operating in an optical bandwidth of 16 nm with 0 dBm (1 mW) peak optical input power per channel, while a conventional ECS WDM system with 0.84-nm channel spacing cannot even achieve a bit-error rate (BER)=10^-9, the suboptimum technique developed in this paper, for the same minimum channel spacing, can achieve a BER=10^-9 with an FWM crosstalk power of less than 1 dB at the worst channel in a 20-channel WDM system     

560 Mb/s optical PSK synchronous heterodyne experiment

A phase-locked optical heterodyne receiver constructed using a 1320-nm diode-pumped miniature Nd:YAG ring laser is discussed. Using this receiver and a transmitter based on another Nd:YAG laser, a 560-Mb/s phase-shift keying (PSK) synchronous heterodyne transmission was demonstrated over 78 km of single-mode fiber. With an optical phase-locked loop (PLL) natural frequency of 32 kHz and a damping factor of 1.46, the receiver sensitivity, measured at the output of the transmission link, was -48.7 dBm, or 159 photons/b. The corresponding detected sensitivity, measured on the surface of the p-i-n diode, was -51.8 dBm or 78 photons/b. This result suggests that the receiver sensitivity would have been about 82 photons/b if a balanced receiver with 0.2-dB excess coupler loss had been used. The impact of the finite intermediate frequency (IF) on heterodyne system performance was investigated; it was found that an IF of at least twice the bit rate is needed for a negligibly small penalty     

Relationship between ADC performance and requirements of digital-IF receiver for WCDMA base-station

The recent rapid development of digital wireless systems has led to the need for multistandard, multichannel radiofrequency (RF) transceivers. The paper presents the relationship between the performance of a bandpass-sampling analog-to-digital converter (ADC) and the requirements of a digital intermediate-frequency receiver for a wideband code-division multiple-access (WCDMA) base-station. As such, the ADC signal-to-noise ratio (SNR), the derivation of the receiver sensitivity using the SNR/spurious free dynamic range (SFDR) of the ADC, the effect of the ADC clock jitter and receiver linearity, plus the relationship between the receiver IF and the ADC sampling frequency are all analyzed. As a result, when a WCDMA base-station receiver has a data rate of 12.2 kbps, bit error rate (BER) of 0.001, and channel index, k, of 5 (sampling frequency of 122.88 MHz and IF of 92.16 MHz), the performance of a bandpass-sampling ADC was analytically determined to require a resolution of 14 bits or more, SNR of 66.6 dB or more, SFDR of 86.5 dBc or more, and total jitter of 0.2 ps or less, including internal ADC jitters and clock jitters.