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}).     

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.     

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.     

Multichannel coherent optical communications systems

Balanced coherent receivers perform substantially better than single-detector receivers in multichannel optical fiber FDM communications systems since the balanced approach eliminates the direct-detection and signal-cross-signal interference. The permissible channel spacingDdepends on the intermediate frequency fIF, on the bit rate Rb, and on the modulation/demodulation format. In particular,Dincreases by 2 Hz for every 1-Hz increase of the fIF. The signal-to-interference ratio SIR, as defined in the text, provides a simple measure of the amount of the interference generated by undesired channels. The criterion SIR = 30 dB is selected in this paper and leads to the following minimum channel spacings: for heterodyne systems,3.8R_{b}for FSK,9.5R_{b}for ASK, and12.4R_{b}for PSK; for homodyne systems,7.5R_{b}for ASK and10.5R_{b}for PSK. Simultaneous transmission of several channels generates an excess shot noise studied here for the first time. If the local oscillator power is 40 dB above the received signal power and 2000 channels are transmitted without optical prefiltering, the excess shot noise power penalty is less than 1 dB.     

Exact evaluation of laser linewidth requirements for optical PSKhomodyne communication systems with balanced PLL receivers

The power penalty induced by imperfect phase recovery in PSK homodyne communication systems with balanced phase-locked loop receivers are exactly evaluated. Optimum phase deviations between the mark-state and the space-state bits are used in this study. This study for the first time shows the imperfect-phase-recovery-induced power penalty as a function of laser linewidth with optimum phase deviations considered. It can be estimated from the theoretical result that an optimal balanced PLL receiver requires the laser linewidth as Δν⩽1.15×10^-6× (bit rate) in contrast to the previous reported one Δν⩽5.88×10^-6× (bit rate). We also point out here that the previously reported laser linewidth requirement was wrongly estimated     

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     

Optical homodyne receiver based on an improved balance phase-lockedloop with the date-to-phaselock crosstalk suppression

An improved balanced phase-locked loop (PLL) with postdetection processing is proposed to eliminate the data-to-phaselock crosstalk which potentially limits the usable ratio of laser linewidth to bit rate in pilot-carrier phase-shift keying (PSK) optical homodyne systems. The phase-lock current is first subtracted from the output signal of the data receiver before input to the loop filter. An attenuator is used to ensure the equilibrium of the feedback output signal and data-to-phaselock crosstalk. A shaping filter is introduced to simulate the distortion of data signals at the output of the preamplifier. The homodyne receivers based on this kind of PLL have the advantage of a large tolerance for the laser linewidth compared with the conventional balanced PLL receivers     

PSK optical homodyne detection using external cavity laser diodesin Costas loop

5-Gb/s optical PSK (phase-shift keying) homodyne detection experiments are discussed. In these experiments, the optical carrier is recovered by a Costas optical phase-locked loop using a multielectrode local oscillator (DFB) laser diode at 1.55 μm with a flat FM response. Although the beat linewidth of 80 kHz is broad compared to the loops in other phase-locked loop (PLL) experiments, phase locking with Costas loop is confirmed at 5 Gb/s by increasing the loop natural frequency. The receiver sensitivity is -42.2 dBm or 93 photon/bit for a 2⁷-1 pseudorandom bit sequence (PRBS) in front of a 90° hydride     

Receiver analysis for synchronous coherent optical fiber transmission systems

A receiver sensitivity expression applicable for both PSK homodyne and heterodyne optical fiber transmission systems is derived taking account of polarization misalignment, reduced modulation depth, preamplifier thermal noise, power coupling ratio of the fiber coupler, local oscillator excess intensity noise, and reference phase errors. From a comparison of recent studies on system performance degradation due to laser phase noise a generalized expression relating beat linewidth to phase error variance for pilot carrier and Costas phase-locked-loop receivers is defined.     

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     

1 Gbit/s PSK homodyne transmission system using phase-lockedsemiconductor lasers

Homodyne detection of 1 Gb/s pilot-carrier (BPSK) optical signals using phase-locked 1.5 μm external-cavity semiconductor lasers is discussed. After 209 km fiber transmission of a 2¹⁵-1 pseudorandom binary sequence (PRBS), the measured receiver sensitivity is 52.2 dBm or 46 photons/bit. Experimental evidence of the data-to-phase-lock crosstalk that potentially limits the usable ratio of linewidth to bit rate in pilot-carrier PSK homodyne systems is presented     

Carrier synchronization for homodyne and heterodyne detection ofoptical quadriphase-shift keying

Through analysis and simulation, the authors investigated the performance of four carrier-synchronization techniques suitable for both homodyne and heterodyne detection of optical quadriphase-shift keying: the discrete-time decision-directed loop, the analog decision-directed loop, the Costas quadriphase loop, and the fourth-power phase-locked loop. Accounting for shot noise, laser phase noise, and feedback delay, they optimize the loop natural frequency and specify laser-linewidth requirements. The performance discrepancy between the best and worst of these loops is found to be small; accounting for inherent loop delays only, the linewidth requirements range from ΔvT<2.5×10^-5 to ΔvT<5.2×10^-5, where Δv is the beat laser linewidth and T is the baud interval. Hence other considerations, such as ease of implementation, will govern the design choice for most practical systems. For the case when propagation delays in the feedback loop are significant, a simple and accurate method for estimating the laser-linewidth requirement and corresponding optimal natural frequency is presented     

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     

Optical phase-locked PSK heterodyne experiment at 4 Gb/s

A 4 Gb/s phase-locked optical PSK (phase shift keying) heterodyne communication system is demonstrated. The receiver was implemented with a single 100-Ω loaded p-i-n photodiode and a 1320-nm diode-pumped miniature Nd:YAG laser as a local oscillator. For a 2⁷-1 PRBS (pseudorandom bit sequence), the receiver sensitivity was -34.2 dBm or 631 photons/bit. The corresponding power on the surface of the detector was -37.3 dBm or 309 photons/bit. With a 2¹⁵-1 PRBS, a 2.6 dB additional sensitivity degradation was observed due to the nonideal frequency response of the phase modulator and the receiver amplifiers     

Phase-locked-loop analysis for pilot carrier coherent optical receivers

The optimum phase-locked-loop bandwidth which exists when shot and phase noise sources are present at the receiver is derived. This is then used to show beat linewidth to bitrate ratios smaller than 0.05% are needed for PSK homodyne/heterodyne systems.     

Performance analysis and experiment of a homodyne receiverinsensitive to both polarization and phase fluctuations

A detailed bit-error-rate analysis of a differential phase-shift keying (DPSK) homodyne receiver which comprises polarization and phase diversities is presented. It is shown that both the requirement for the laser linewidth and the receiver sensitivity are approximately equal to those of a conventional DPSK heterodyne receiver. The insensitivity of the receiver to the polarization state of the incoming signal is also investigated both theoretically and experimentally     

Homodyne optical phase locking of resonant cavity coupledsemiconductor lasers

Two confocal Fabry-Perot cavity coupled semiconductor laser diodes (CFP-LDs) have been constructed for optical phase-locking experiments. Their FM noise suppression characteristics were calculated and compared with measurements of FM noise using an optical resonator as the optical frequency discriminator (FM noise suppression ratio 39 dB). Spectral linewidth was measured and evaluated, and frequency drift of the heterodyne signal in the time domain (20 kHz/s), was also measured. A simple linearized model of the optical feedback system was used for the calculations. Using two CFP-LDs, homodyne optical phase-locking experiments were performed. The performance of the optical phase-locked loop (OPLL) was evaluated by measuring and calculating the phase error variance. The calculation took into account the actual power spectral density of FM noise of the lasers employed in the OPLL. The phase error variance, considering infinite bandwidth, is 2.26×10^-2 rad². Total phase-locked power concentration ratio of the slave laser in the OPLL was 97.7%     

Optimum optical power splitting ratio of decision drivenphase-locked loop in BPSK optical homodyne receiver

In a BPSK optical homodyne receiver that utilizes a decision-driven phase-locked loop, the splitting ratio of the received power and that of the local oscillator power are very important parameters in achieving high receiver sensitivity. This paper determines the optimum setting of these parameters considering the influence of the relative intensity noise of the local oscillator and the thermal noise of the preamplifier. The optimum splitting ratio of the local oscillator power to the Q-arm is found to be 0.5. The splitting ratio of the received power to Q-arm is obtained as a function of laser linewidth. The optimum setting of the received power and the local oscillator power Is independent of the relative intensity noise of the local oscillator, the thermal noise of the preamplifier and the bit rate, At the optimum splitting ratios, required beat linewidth is obtained as 1.3×10 ^-3/T_b(τ/T_b≪1) and 2.99×10 ^-3/τ(τ/T_b≫1), where T_b is the bit duration and τ is the loop propagation delay time. We show that the total power penalty of 0.8 dB from the shot noise limit can be realized with the relative intensity noise of -170 dB/Hz and equivalent input noise current of 10 pA/√(Hz), even if an imperfect balanced receiver is utilized; quantum efficiency ratio of the twin-photodetector is 0.96, propagation time difference T/T_b is 0.01. To confirm the theoretical model, a BPSK homodyne detection experiment is performed and good agreement is found between theoretical and experimental results     

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.