Photodetector Shot Noise Research Articles

Impact of Pointing Error on the BER Performance of an OFDM Optical Wireless Communication Link over Turbulent Condition

Abstract An analytical approach is developed in this paper to evaluate the bit error rate (BER) performance of an optical wireless (OW) communication system with multiplexing of the RF orthogonal frequency division (OFDM) over turbulent condition taking into account the effect of pointing error. The received signal is detected through direct detection receiver followed by RF synchronous demodulation including the effect of OW channel and different form of noises such as receiver thermal noise, background channel noise and photo detector shot noise. Analysis is developed for an OFDM system over the OW channel, taking into account the effect of pointing error between the transmitter and the receiver in turbulent condition and the analysis reveals that the OFDM OW system is less affected by pointing error with deference to the major power penalty at BER performance. For instance, power penalty at BER 10−9 is found to be 3 dB for 256 OFDM subcarriers with 9 millidegree displacement angle at a data rate of 10 Gbps under turbulent condition. It is found that the system is more influenced by the atmospheric turbulence at a higher data rate.

Large-Scale Optical Neural Networks Based on Photoelectric Multiplication

Recent success in deep neural networks has generated strong interest in hardware accelerators to improve speed and energy consumption. This paper presents a new type of photonic accelerator based on coherent detection that is scalable to large ($N \gtrsim 10^6$) networks and can be operated at high (GHz) speeds and very low (sub-aJ) energies per multiply-and-accumulate (MAC), using the massive spatial multiplexing enabled by standard free-space optical components. In contrast to previous approaches, both weights and inputs are optically encoded so that the network can be reprogrammed and trained on the fly. Simulations of the network using models for digit- and image-classification reveal a "standard quantum limit" for optical neural networks, set by photodetector shot noise. This bound, which can be as low as 50 zJ/MAC, suggests performance below the thermodynamic (Landauer) limit for digital irreversible computation is theoretically possible in this device. The proposed accelerator can implement both fully-connected and convolutional networks. We also present a scheme for back-propagation and training that can be performed in the same hardware. This architecture will enable a new class of ultra-low-energy processors for deep learning.

Pull-in analysis of dither optical phase-lock loop

The pull-in behavior of dither optical phase-lock loop (OPLL) is analyzed, neglecting the shot noise and phase noise of the loop. Expressions are derived analytically for computing the pull-in voltage, pull-in limit and acquisition time for a second-order type-II dither OPLL that employs an active low pass loop filter. The influence of dither signal on the acquisition of the dither OPLL is studied in detail. It is found that dither signal allows pull-in from much larger frequency offset, decreases the acquisition time of the loop and also improves the acquisition characteristics of the OPLL in terms of the pull-in voltage. This paper also analyzes the effect of loop-delay on the pull-in behavior of the dither OPLL. The performance of the dither OPLL regarding the phase-error variance and noise bandwidth is investigated considering laser phase noise, photo-detector shot noise and dither noise. Analytical results are supported by simulations.

Influence of Time Delay on Pull-in Behaviour of Dither Optical Phase-Lock Loop

ABSTRACTThis paper analyses the impact of loop propagation delay on the pull-in behaviour of dither optical phase-lock loop (OPLL), neglecting the shot noise and phase noise of the loop. Analytical expressions of pull-in voltage, pull-in range, and acquisition time are presented in terms of all the parameters affecting the loop acquisition. Also, the influence of dither signal on the pull-in performance of dither OPLL is studied in the presence of loop propagation delay. It is found that the time delay associated with the filtering process within the loop gives rise to degradation in acquisition capability. In addition, dither signal allows pull-in from much larger frequency offset, decreases the acquisition time of the loop, and improves the acquisition characteristics of dither OPLL in terms of the pull-in voltage in the presence of loop delay. The tracking performance of dither OPLL regarding phase-error variance is investigated considering laser phase noise, photo-detector shot noise, and loop propagation delay. Simulation results are given in support of the analytical results.

Partial Gap Transduced MEMS Optoacoustic Oscillator Beyond Gigahertz

Electrostatically actuated microelectromechanical system (MEMS) oscillators are limited to few megahertz–gigahertz range on account of transduction inefficiency at higher frequencies. Piezoelectric transduction affords lower motional impedances at high frequencies, however mass-loading on account of metal electrodes imposes practical limits on the mechanical quality factor of piezoelectric resonators in the gigahertz frequency regime. In this paper, we present a silicon optoacoustic oscillator operating at 2.05 GHz with signal power 18 dBm and phase noise −80 dBc/Hz at 10-kHz offset from carrier. We employ displacement amplification and partial air gap capacitive transduction to enhance the transduction efficiency. An unconventional photolithography step is performed on a released MEMS structure, which greatly simplifies the fabrication process and allows electrical contact with the electrodes. Built-in nonlinear optomechanical modulation provides noiseless up-conversion of the oscillation signal all the way up to 16.4 GHz with −45-dBm signal power. We develop a phase noise model for the oscillator and identify the photodetector shot noise to be the dominant noise source. Using a high gain and low noise avalanche photodetector enables reduction of the far-from-carrier phase noise floor by 15dB. The phase noise model provides insights into understanding the influence of laser detuning on the oscillator noise performance, which has not been studied to date. [2013-0291]

Comment on “Observation of anticorrelation in incoherent thermal light fields”

Recently, Chen et al. [Phys. Rev. A 84, 033835 (2011)] reported observation of anticorrelated photon coincidences in a Mach-Zehnder interferometer whose input light came from a mode-locked Ti:sapphire laser that had been rendered spatially incoherent by passage through a rotating ground-glass diffuser. They provided a quantum-mechanical explanation of their results, which ascribes the anticorrelation to two-photon interference. They also developed a classical-light treatment of the experiment and showed that it was incapable of explaining the anticorrelation behavior. Here we show that semiclassical photodetection theory, i.e., classical electromagnetic fields plus photodetector shot noise, does indeed explain the anticorrelation found by Chen et al. The key to our analysis is properly accounting for the disparate time scales associated with the laser's pulse duration, the speckle-correlation time, the interferometer's differential delay, and the duration of the photon-coincidence gate. Our result is consistent with the long-accepted dictum that laser light which has undergone linear-optical transformations is classical-state light, so that the quantum and semiclassical theories of photodetection yield quantitatively identical results for its measurement statistics. The interpretation provided by Chen et al. for their observations implicitly contradicts that dictum.

Performance Characterization of Ultrahigh SpeedOptically Amplified Spectral-Phase EncodedOCDMA Systems with Second-Harmonic-Generation Effect in Thin and Thick Crystal Receiver Structures

In this paper we study and evaluate the performance of a spectral-phase encoded optical CDMA (SPE-OCDMA) system using advanced receiver structures based on second harmonic generation (SHG) effect imposed in a Thick or Thin crystal. This receiver structure is employed as the nonlinear pre-processor prior to the conventional low-speed photodetector. In our performance evaluation amplified spontaneous emission (ASE) of the optical amplifiers, receiver front end thermal noise and photodetector shot noise which are effective in low power conditions, and multiple access interference (MAI) noise which is the dominant source of noise in high power conditions in any coherent OCDMA communications system have been considered. We begin by studying the statistical behavior of Thick crystals in an optically amplified digital lightwave communication system in the context of a SPE-OCDMA communication system. The error probability for Thick crystal receiver structure is evaluated using Saddle-Point approximation. Furthermore, we obtain a closed form approximation for the probability density function (pdf) of the decision variable in SPE-OCDMA systems with Thin crystal SHG receiver. In this analysis, to obtain approximate probability density function, we employ Gram-Charlier expansion based on the corresponding first order moments of the decision variable. The first three moments are obtained in a closed form approximation and consequently a closed form expression for the error probability is obtained by integrating the approximated pdf of the decision variables for transmitting bit "1" and "0" in Thin crystal receiver structure. The precision of the approximation is verified by the Monte-Carlo simulation. Finally the performance of SPE-OCDMA network for both Thin and Thick SHG crystals are analytically evaluated and discussed for different number of interfering users and different code-lengths and different speed of the conventional photodetectors. We deduce that the performance of Thin SHG crystal receiver is more sensitive to the transmitted power level especially in low power conditions. It is concluded that in low power conditions where ASE, thermal and shot noises are the dominant noise sources, Thick SHG crystal receiver outperforms the Thin crystal receiver. However, in high power conditions where MAI noise is the most effective noise term, Thin SHG crystal receiver structure outperforms the Thick crystal receiver.

Performance analysis and improvement of spectrally amplitude encoded/decoded OCDMA system

In this paper we have studied and analyzed the spectrally encoding/ decoding OCDMA system for different lengths of fiber in terms of quality factor (Q) and bit error rate (BER) performance. The performance characteristics like bit error rate, eye diagrams and eye closure penalty at the output are studied by simulating for different lengths of fiber. An upper bound on the bit error probability for phase encoded OCDMA system is maintained under the above considerations. The effect of both dark current and thermal noises is neglected. The advantages of this system over the conventional time-encoded system include the availability of larger number of low cross correlation sequences and the implementation of efficient decoders for low error probability detection. It has been observed that there are two major problems giving rise to performance degradation of the system in terms of no of users and type of code. In optical CDMA, multiple access interference (MAI) is dominant factor compared to photo detector shot noise, dark current and thermal noise that limits number of user as well as data rate of the system.

Simulation-based comparison of noise effects in wavelength modulation spectroscopy and direct absorption TDLAS

A simulative investigation of noise effects in wavelength modulation spectroscopy (WMS) and direct absorption diode laser absorption spectroscopy is presented. Special attention is paid to the impact of quantization noise of the analog-to-digital conversion (ADC) of the photodetector signal in the two detection schemes with the goal of estimating the necessary ADC resolution for each technique. With laser relative intensity noise (RIN), photodetector shot noise and thermal amplifier noise included, the strategies used for noise reduction in direct and wavelength modulation spectroscopy are compared by simulating two respective systems. Results show that because of the combined effects of dithering by RIN and signal averaging, the resolutions required for the direct absorption setup are only slightly higher than for the WMS setup. Only for small contributions of RIN an increase in resolution will significantly improve signal quality in the direct scheme.

Performance analysis of an optical CDMA MAC protocol with variable-size sliding window

A media access control protocol for optical code-division multiple-access packet networks with variable length data traffic is proposed. This protocol exhibits a sliding window with variable size. A model for interference-level fluctuation and an accurate analysis for channel usage are presented. Both multiple-access interference (MAI) and photodetector's shot noise are considered. Both chip-level and correlation receivers are adopted. The system performance is evaluated using a traditional average system throughput and average delay. Finally, in order to enhance the overall performance, error control codes (ECCs) are applied. The results indicate that the performance can be enhanced to reach its peak using the ECC with an optimum number of correctable errors. Furthermore, chip-level receivers are shown to give much higher performance than that of correlation receivers. Also, it has been shown that MAI is the main source of signal degradation

Performance analysis of a symbol slicing majority vote combining receiver for binary optical heterodyne ASK with phase-noise-optimised decision thresholds

The performance of a binary optical heterodyne ASK receiver in the presence of photodetector shot noise and laser phase noise has been investigated. To reduce the effects of phase noise on the receiver error rate, the maximum likelihood approach is used to optimise the decision threshold on the basis of the severity of phase noise indicated by the laser linewidth. It is assumed that the receiver uses symbol slicing and majority vote decision combining. Threshold optimisation is applied to each slice (chip) of the received bit duration. It is found that the receiver performance can be significantly improved by threshold optimisation. Majority voting is also found to improve the receiver performance for a wide range of signal-to-noise ratio values.

2-D optical CDMA networks using MWPM, double hard limiters and modified carrier-hopping prime sequences

This paper presents a two-dimensional optical code division multiple access (2-D-OCDMA) scheme using multiwavelength pulse modulation (MWPM), double optical hard limiters (DHL), and modified carrier-hopping prime sequences (MCHP) to increase the achievable system capacity. Design criteria to reduce multiaccess interference (MAI) are established and indicate that suitable signature sequences for 2-D-OCDMA/MWPM must have good cross-correlation property in terms of both time shift and wavelength shift. Performance analysis of 2-D-OCDMA/MWPM/DHL systems in the presence of MAI and photo detector shot noise is developed. Simulation and analytical results are in very good agreement and indicate that the proposed 2-D-OCDMA/MWPM/DHL systems using MCHP sequences can offer a much larger capacity than others, suitable for applications in broadband fiber-optic access networks.

Frame Time-Hopping Patterns in Multirate Optical CDMA Networks Using Conventional and Multicode Schemes

A class of generalized optical orthogonal codes (OOCs), namely, frame time-hopping (FTH) patterns with an extremely large cardinality, are studied for implementing multirate and multiservice (MR/MS) optical CDMA (OCDMA) networks. Conventional MR/MS methods, namely variable spreading rate and parallel mapping, are considered. Using FTH patterns, the problem of low OOC code cardinality in conventional MR/MS schemes is removed. Moreover, several new multicode methods, using subcode concatenation scheme, are proposed for MR/MS OCDMA. The proposed multicode schemes present flexibility for supporting MR/MS applications such as lower implementation complexity and cost, less need for service synchronization, and finally lower link power budget. Multiple-access performances of the systems are evaluated using saddle-point approximation methods considering photodetector shot-noise, dark current, and circuit thermal noise. The results show that the conventional parallel mapping outperforms the other schemes in high received powers, and the proposed multicode method, using Walsh subcode along with difference modulation, presents the best performance in low received powers for the cases considered.

Optical CDMA random access protocols with and without pretransmission coordination

The link layer of an optical direct-detection code-division multiple-access (CDMA) packet network is considered. Two different protocols that need pretransmission coordination are proposed. A variation of the second protocol that does not need pretransmission coordination is discussed. Both system throughput and average packet delay are derived and investigated for two different receiver models: the correlation and chip-level receivers. Both multiple-access interference and the photodetector's shot noise are taken into account in the analysis. The case where the number of users exceeds the available number of CDMA codes is numerically investigated. Our results reveal that the proposed protocols yield competitive system throughputs when used with the correlation receivers. Further, significant improvement in the throughput is achieved when using chip-level receivers along with the second protocol.

Analysis of temporal noise in CMOS photodiode active pixel sensor

Temporal noise sets the fundamental limit on image sensor performance, especially under low illumination and in video applications. In a CCD image sensor, temporal noise is primarily due to the photodetector shot noise and the output amplifier thermal and 1/f noise. CMOS image sensors suffer from higher noise than CCDs due to the additional pixel and column amplifier transistor thermal and 1/f noise. Noise analysis is further complicated by the time-varying circuit models, the fact that the reset transistor operates in subthreshold during reset, and the nonlinearity of the charge to voltage conversion, which is becoming more pronounced as CMOS technology scales. The paper presents a detailed and rigorous analysis of temporal noise due to thermal and shot noise sources in CMOS active pixel sensor (APS) that takes into consideration these complicating factors. Performing time-domain analysis, instead of the more traditional frequency-domain analysis, we find that the reset noise power due to thermal noise is at most half of its commonly quoted kT/C value. This result is corroborated by several published experimental data including data presented in this paper. The lower reset noise, however, comes at the expense of image lag. We find that alternative reset methods such as overdriving the reset transistor gate or using a pMOS transistor can alleviate lag, but at the expense of doubling the reset noise power. We propose a new reset method that alleviates lag without increasing reset noise.

Performance Optimization and Laser Linewidth Requirement Evaluation for a Coherent Optical Psk System With DDL

This paper presents the exact requirement laser linewidth evaluation for both heterodyne and homodyne receivers with a Decision-Driven Loop (DDL). Taking the laser phase noise and photodetector shot noise into account, the Probability Density Function (p.d.f.) of the phase error is determined. The optimal normalized loop bandwidth is determined by minimizing the Bit-Error Rate (BER). The power penalty dependence on laser linewidth is also determined. All calculations are based on the nonlinear Phase-Locked Loop (PLL) model. The laser phase noise and photodiode shot noise are described through loop parameter variations. The laser phase noise is presented specifically through frequency variations of both the transmitter laser and the local laser instead of phase fluctuations. Finally, the comparison between nonlinear phase loop model results determined here and linear phase loop model results obtained in [1, 2] is presented.

Direct detection optical overlapping PPM-CDMA communication systems with double optical hardlimiters

Direct detection optical code-division multiple-access (CDMA) communication systems involving overlapping pulse-position modulation (OPPM) is considered. Double optical hardlimiters placed before and after the correlator at the receiver side is proposed for this system. The performance (in terms of the bit error probability) of this system is evaluated taking into account the effect of both the multiple-user interference and the photodetector shot noise. Both the receiver dark current and thermal noise are ignored in our analysis since their effect is very minor. The performance of the above receiver is compared to that of the OPPM-CDMA correlator receiver without hardlimiters, OPPM-CDMA optimum receiver, and OOK-CDMA optimum receiver. Our results reveal that, for given pulsewidth and throughput constraints, significant improvement in the performance is acquired when adding double optical hardlimiters to the correlator of the OPPM-CDMA receiver. Moreover the performance of this system is asymptotically close to the optimum OPPM-CDMA system and is considerably superior to the optimum OOK-CDMA system. It is also reported that the capacity of the proposed system is about 5.3 times greater than that of the optimum OOK-CDMA system.

Error Rate Analysis of Optical Receivers with Fabry-Perot Optical Filter and Equalizing Postdetection Filtering

A complete analytic solution in form of the moment-generating function is presented for the statistical distribution of the decision variable of an on-off system with a Fabry-Perot optical filter. The results include ASE noise, photodetector shot noise and dark current together with thermal noise in the decision circuit. The influence of intersymbol interference is incorporated into the analysis and the optimal bandwidth of the optical filter is determined. It is shown that an equalizing electrical postdetection filter may make a significant improvement in performance. The analysis is extended to cover receivers with an arbitrary optical filter and arbitrary postdetection filtering by making use of a Gaussian approximation.

Error probability evaluation of optical systems disturbed by phase noise and additive noise

A direct and efficient method for evaluation of the error probability of optical heterodyne receivers in the presence of phase noise is presented. A closed form expression for the statistics of the decision variable, including photodetector shot noise and thermal noise from electronic circuitry, is derived. The analysis assumes simple integrating filters in the receiver and is based on a power series expansion of the filtered phase noise. The error probability is calculated using a saddle point approximation which is numerically simple and gives accurate results. The optimal prefilter bandwidth for best phase noise rejection is easily determined. >

On the bit error rate of lightwave systems with optical amplifiers

The problem of evaluating the performances of communication systems with optical amplifiers and a wideband optical filter is addressed. Exact probability of error expressions for optical signals in presence of amplifier spontaneous noise and photodetector shot noise are given and compared with those predicted by Gaussian approximations for amplitude shift keying (ASK), frequency shift keying (FSK), or differential phase shift keying (DPSK) modulations, both for ideal photodetectors and for the case where shot noise is significant. >