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.     

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.     

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.     

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.     

The performance of optical phase-locked loops in the presence of nonnegligible loop propagation delay

The optical phase-locked loop is analyzed taking into account shot noise, phase noise, and loop propagation delay. The degradation of loop phase error due to propagation delay is evaluated in terms of the delay bandwidth productomega_{n} cdot tau_{D}. This product was found to have a maximum value of 0.736 for absolute loop stability. The resulting effect on a Costas loop system optimized for zero time delay is discussed. It is found that in order to maintain a 10^-9BER system performance withxi = 1/2^{0.5}, R = 0.85A/W,P_{DATA} = -59.2dBm, and a 1-MHz beat linewidth, the delay time must be kept below 1.8 ns. If the beat linewidth increases to 15 MHz this figure drops to 0.12 ns.     

Absorption in the near-ultraviolet wing of the Kr2F*(410 nm) band

An intracavity laser technique has been used to study the absorption of electron-beam pumped Ne/Kr/F2gas mixtures (196 and 300 K) in the "blue wing" of the Kr2F emission continuum. The experiments were conducted at 358 nm using theupsilon' = 0 rightarrow upsilon" = 1transition of the N2(C rightarrow B) laser. Comparing the results with the predictions of a computer model, the species primarily responsible for absorption have been identified as Ne+2, Kr+2, and Kr2F*. The photoabsorption cross sections for Ne+2and Kr2F (Kr+2F-) at 358 nm have been estimated to be8.1 cdot 10^{-19}and5.4 cdot 10^{-18}cm², respectively. The Kr2F* absorption cross section is roughly 20 percent of that reported for Kr+2at the same wavelength. The fluorescence efficiency of Kr2F* ine-beam excited 94.93 percent Ne/5 percent Kr/0.07 percent F2(P_{total} = 4000torr) gas mixtures has been found to be a factor of 2.8 higher than that of the N2(C rightarrow B) band in Ar/5 percent N2mixtures. Also, the rate constant for quenching of Kr2F* by F2was measured to be(4.1 pm 0.5) cdot 10^{-10}cm³. s^-1at 300 K and(3.0 pm 0.5) cdot 10^{-10}cm². s^-1at 196 K.     

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     

Some cross correlation properties for distorted signals

For a nondecreasing distortion characteristicphi(cdot)and a given signalx(cdot), the "cross correlation" function defined byR_{phi} (tau) triangleq int_{-infty}^{infty} phi[x(t)]x(t - tau) dtis shown to satisfy the inequalityR_{phi}(tau) leq R_{phi}(0), for alltau, generalizing an earlier result of Richardson that requiredphi(cdot)to be continuous and strictly increasing. The methods of the paper also show that, under weak conditions, begin{equation} R_{phi,psi}(tau) triangleq int_{-infty}^{infty} phi[x(t)]psi[x(t - tau)] dt leq R_{phi,psi}(0) end{equation} whenpsiis strictly increasing andphiis nondecreasing. In the case of hounded signals (e.g., periodic functions), the appropriate cross correlation function is begin{equation} mathcal{R}_{phi,psi}(tau} triangleq lim_{T rightarrow infty} (2T)^{-l} int_{-T}^T phi[x(t)]psi[x(t - tau)] dt. end{equation} For this case it is shown thatmathcal{R}_{phi,psi} (tau) leq mathcal{R}_{phi,psi}(0)for any nondecreasing (or nonincreasing) distortion functionsphiandpsi. The result is then applied to generalize an inequality on correlation functions for periodic signals due to Prosser. Noise signals are treated and inequalities of a similar nature are obtained for ensemble-average cross correlation functions under suitable hypotheses on the statistical properties of the noise. Inequalities of this type are the basis of a well-known method of estimating the unknown time delay of an observed signal. The extension to nondecreasing discontinuous distortion functions allows the use of hard limiting or quantization to facilitate the cross correlation calculation.     

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%     

Hypothesis testing with multiterminal data compression

The multiterminal hypothesis testingH: XYagainstH̄: X̄Ȳis considered whereX^{n} (X̄^{n})andY^{n} (Ȳ^{n})are separately encoded at ratesR_{1}andR_{2}, respectively. The problem is to determine the minimumbeta_{n}of the second kind of error probability, under the condition that the first kind of error probabilityalpha_{n} leq epsilonfor a prescribed0 < epsilon < 1. A good lower boundtheta_{L}(R_{1}, R_{2})on the power exponenttheta (R_{1}, R_{2},epsilon)= lim inf_{n rightarrow infty}(-1/n log beta_{n})is given and several interesting properties are revealed. The lower bound is tighter than that of Ahlswede and Csiszár. Furthermore, in the special case of testing against independence, this bound turns out to coincide with that given by them. The main arguments are devoted to the special case withR_{2} = inftycorresponding to full side information forY^{n}(Ȳ^{n}). In particular, the compact solution is established to the complete data compression cases, which are useful in statistics from the practical point of view.     

Algorithms for the generation of full-length shift- register sequences

Two algorithms are presented for the generation of full-length shift-register cycles, also referred to as de Bruijn sequences. The first algorithm generates2^{k cdot g(n,k)full cycles of length2^{n}, using3n + k cdot g(n, k)bits of storage, wherekis a free parameter in the range1 leq k leq 2^{((n-4)/2)}, andg(n, k)is of the order ofn - 2 log k. The second algorithm generates about2^{n^{2}/4}full cycles of length2^{n}, using aboutn^{2}/2bits of storage. In both algorithms, the time required to produce the next bit from the lastnbits is close ton. A possible application to the construction of stream ciphers is indicated.     

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     

Tunable Fiber Laser With Ultra-Narrow Linewidth Using A Tunable Phase-Shifted Chirped Fiber Grating

We experimentally demonstrate a tunable $C$ -band erbium-doped fiber ring laser with ultra-narrow linewidth using a tunable phase-shifted linearly chirped fiber Bragg grating (PS-LCFBG) as an intracavity ultra-narrowband filter. The center wavelength of the PS-LCFBG with an ultra-narrow bandwidth of ${≪}$10 pm is thermally tuned by scanning a current-controlled resistance wire along its length. The laser has an ultra-narrow linewidth of ${≪}$1.52 kHz, a tuning range of ${sim}$ 15.5 nm, a good sidemode suppression ratio of ${>}$30 dB, an output power of ${sim}$10 dBm, a small power variation of ${≪}$ 0.2 dB, and a small wavelength variation of ${≪}$0.01 nm. The laser structure is simple and cost-effective.      

A 5-GHz CMOS Type-II PLL With Low $K_{rm VCO}$ and Extended Fine-Tuning Range

A 5-GHz dual-path integer-$N$ Type-II phase-locked loop (PLL) uses an LC voltage-controlled oscillator and softly switched varactors in an overlapped digitally controlled integral path to allow a large fine-tuning range of approximately 160 MHz while realizing a low susceptibility to noise and spurs by using a low $K_{rm VCO}$ of 3.2 MHz/V. The reference spur level is less than $-$70 dBc with a 1-MHz reference frequency and a total loop-filter capacitance of 26 pF. The measured phase noise is $-$75 and $-$115 dBc/Hz at 10-kHz and 1-MHz offsets, respectively, using a loop bandwidth of approximately 30 kHz. This 0.25-${hbox{mm}}^{2}$ PLL is fabricated in a 90-nm digital CMOS process and consumes 11 mW from a 1.2-V supply.      

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     

Line competition in the neutral argon laser

Uncertainties in transition assignments for the neutral argon laser lines at 1.792 and 2.208 μm have been resolved by operation of a CW neutral argon laser with several simultaneous output wavelengths. The observed competition effects have established the correct transition for the 1.792-μm line to be3d(1/2)_{1}deg -4p(3/2)_{2}and for the 2.208-μm line to be3d(1/2)_{1}deg -4p'(3/2)_{2}.     

Experiments on a semiconductor laser pumped rubidium atomic clock

Experiments were carried out to evaluate the performances of a semiconductor laser pumped rubidium (⁸⁷Rb) atomic clock. Two kinds of Rb gas cells were used and their performances were compared [gas cell A (natural rubidium (⁸⁷Rb/⁸⁵Rb =frac{3}{7}) and buffer gases) and gas cell B (⁸⁷Rb and buffer gases)]. The highest microwave frequency stabilities were estimated as3.4 times 10^{-12} tau^{-1/2}and2.7 times 10^{-12} tau^{-1/2}at the optimal gas cell temperatures of 60°C and 48°C for the gas cellsAandB, respectively (τ: integration time). The light shift, i.e., microwave frequency shift induced by laser light, was measured as -0.50 Hz/MHz and -0.11 Hz/MHz for the gas cellsAandBat their optimal operating conditions given above. As an improved experiment by utilizing high temporal coherence of the laser, a novel double resonance spectral line shape with a drastically narrower linewidth was demonstrated. A technique, similar to FM laser spectroscopy, was employed for this purpose by utilizing laser FM sidebands which are induced by microwave frequency modulation and nonlinear susceptibility of three-level⁸⁷Rb atoms. The minimum linewidth obtained was 20 Hz, which can be used as a sensitive frequency discriminator for an improved⁸⁷Rb atomic clock.     

A BiCMOS Dual-Band Millimeter-Wave Frequency Synthesizer for Automotive Radars

Design and implementation of a millimeter-wave dual-band frequency synthesizer, operating in the 24 GHz and 77 GHz bands, are presented. All circuits except the voltage controlled oscillators are shared between the two bands. A multi-functional injection-locked circuit is used after the oscillators to simplify the reconfiguration of the division ratio inside the phase-locked loop. The 1 mm $, times , $0.8 mm synthesizer chip is fabricated in a 0.18 $mu{hbox{m}}$ silicon-germanium BiCMOS technology, featuring 0.15 $mu{hbox{m}}$ emitter-width heterojunction bipolar transistors. Measurements of the prototype demonstrate a locking range of 23.8–26.95 GHz/75.67–78.5 GHz in the 24/77 GHz modes, with a low power consumption of 50/75 mW from a 2.5 V supply. The closed-loop phase noise at 1 MHz offset from the carrier is less than ${- }$ 100$~$dBc/Hz in both bands. The frequency synthesizer is suitable for integration in direct-conversion transceivers for K/W-band automotive radars and heterodyne receivers for 94$~$GHz imaging applications.      

Broadcast channels with confidential messages

Given two discrete memoryless channels (DMC's) with a common input, it is desired to transmit private messages to receiver1rateR_{1}and common messages to both receivers at rateR_{o}, while keeping receiver2as ignorant of the private messages as possible. Measuring ignorance by equivocation, a single-letter characterization is given of the achievable triples(R_{1},R_{e},R_{o})whereR_{e}is the equivocation rate. Based on this channel coding result, the related source-channel matching problem is also settled. These results generalize those of Wyner on the wiretap channel and of Körner-Marton on the broadcast Channel.     

A $Delta{-}Sigma$ PLL-Based Spread-Spectrum Clock Generator With a Ditherless Fractional Topology

A triangular-modulated spread-spectrum clock generator using a$Delta{-}Sigma$-modulated fractional-$N$ phase-locked loop (PLL) is presented. The PLL employs a multiphase divider to implement the modulated fractional counter with increased $Delta{-}Sigma$ operation speed. In addition, the phase mismatching error in the phase-interpolated PLL with multiphase clocks can be randomized, and finer frequency resolution is achievable. With a frequency modulation of 33 kHz, the measured peak power reduction is more than 11.4 dB under a deviation of $pm$0.37%. Without spread-spectrum clocking, the PLL generates 2.4-GHz output with 18.82-ps peak-to-peak jitter. After spread-spectrum operation, the measured up-spread and down-spread jitter can achieve 52.59 and 56.79 ps, respectively. The chip occupies $950times850 {rm mu}{rm m}^{2}$ in 0.18-${rm mu}{rm m}$ CMOS process and consumes 36 mW.