Phase Noise In Systems Research Articles

On the Statistics of Intrachannel Four-Wave Mixing in Phase-Modulated Optical Communication Systems

We have analytically derived the correlation functions of intrachannel four-wave mixing (IFWM)-induced phase and amplitude noises in phase-modulated optical communication systems. The phase and amplitude noises are correlated with each other for binary phase-shift keying (PSK) systems but uncorrelated for <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</i> -ary PSK systems with <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</i> > 2. We have also derived analytical approximations to the probability distribution of IFWM-induced phase noise for PSK and differential PSK systems. Furthermore, we have studied the performance of an optimal linear phase-noise predictor derived from the IFWM-induced phase-noise autocorrelation function. This yields a performance improvement of 1.8 dB when IFWM-induced phase noise is the dominant impairment, and an improvement of 0.8 to 1.2 dB in the presence of amplified spontaneous emission noise and nonlinear phase noise in typical terrestrial links.

Performance Limits of Optical Clock Recovery Systems Based on Two-Photon Absorption Detection Scheme

In this paper, we analyze and discuss the performance limits of optical clock recovery systems using a phase-locked loop (PLL) structure with nonlinear two-photon absorption (TPA) phase detection scheme. The motivation in analyzing the aforementioned optical PLL with TPA receiver structure is due to a recent successful experiment reported in . We characterize the mathematical structure of PLLs with TPA, so as to evaluate the performance limits on optical clock recovery mechanism. More specifically, we identify two intrinsic sources of phase noise in the system namely, the on- off nature of the incoming data pulses and the detector's shot noise that ultimately limit the performance of the aforementioned optical clock recovery system. In our characterization of the clock recovery system, we obtain the power spectral densities (PSDs) of the signals involved in the PLL and use the PSDs to obtain a mathematical expression for the variance of the timing jitter inherently associated with the recovered clock. We examine the variance of the introduced timing jitter as a function of different system parameters such as power, bit rate, and pulsewidth of the data and clock signals. An interesting result is that the duty cycle factor near 4 in return to zero optical pulses is optimal in the sense that it minimizes the variance of the system phase noise.

Probability density functions for intensity induced phase noise in CW phase demodulation systems

This paper discusses two probability density functions related to continuous wave (CW) phase demodulation systems such as those used in optical sensing. In the first case, we show that if the input intensity noise in the quadrature streams of the demodulator is Gaussian, then the induced phase noise is approximately Gaussian. If, however, the noise in both in-phase and quadrature streams is correlated, then the intensity induced phase noise exhibits a periodic dependence on the input phase and follows new asymmetric density distributions. We give expressions for the mean and variance for both processes.

Analog Impairments in MIMO-OFDM Systems

MIMO-OFDM is being considered for communication systems where high throughput and spectral efficiency are important factors. Analog impairments like I/Q mismatch and phase noise significantly degrade and limit the performance of communication systems. In this paper, we analyze the impact of I/Q mismatch and phase noise in MIMO-OFDM systems as a function of the number of antennas. We show the improvement in performance that is possible when these impairments are cancelled. We also discuss the impact of correlated and uncorrelated phase noise in MIMO-OFDM systems. Finally, we show the results of I/Q mismatch and phase noise cancellation in wireless measurements performed using a 2times2 MIMO-OFDM testbed

Reduction of Gordon-Mollenauer phase noise in dispersion-managed systems using in-line spectral inversion

The influence of spectral inversion on the phase jitter of a soliton propagating in single-channel arbitrary dispersion-managed systems is studied with a semianalytic moment method. The results are similar to those previously observed in constant-dispersion links and show that the transmission-system reach can significantly be increased.

Analysis and comparison of impairments in differential phase-shift keying and on-off keying transmission systems based on the error probability

The effect of nonlinear phase noise in dispersion-managed optical transmission systems is studied. The variance of the nonlinear phase noise in systems based on differential phase-shift keying (DPSK) in the presence of dispersion is examined analytically, and a semianalytical expression to calculate the error probability including intrachannel four-wave mixing, linear phase noise, and nonlinear phase noise for systems based on DPSK is derived. In addition, for the on-off keying (OOK) format, the formula for the error probability including amplified spontaneous emission noise and intrachannel nonlinear effects has been given. On the basis of the semianalytical expressions, we have compared the error probability of systems based on DPSK and OOK, and the results show that, to reach a given bit error rate of 10(-9) for a specific long-haul system, the difference between the signal-to-noise ratio required by the DPSK format and that required by the OOK format is around 6 dB for the launch power of 0 dBm, and the difference becomes larger as the launch power increases.

Design of inline amplifier gains and spacings to minimize the phase noise in optical transmission systems

In optical fiber transmission systems using inline amplifiers, the interaction of a signal and an amplifier noise through the Kerr effect leads to a nonlinear phase noise that can impair detection of phase-modulated signals. The authors show how to minimize the variance of the total phase noise (linear plus nonlinear) by a choice of the number of inline amplifiers N and their spacings and gains, assuming a fixed total system length L and an overall compensation of the fiber loss. In the case of a uniform amplifier spacing and a per-span loss compensation, there exists a finite N that minimizes the total phase noise. This contrasts with the well-known observation that a linear phase noise alone is minimized by a choice of an infinite N. Relaxing the constraints of the uniform spacing and/or the per-span loss compensation leads to further reduction of the total phase noise. The optimization of the spacings and the gains can be approximately formulated as a convex problem. In typical terrestrial and transoceanic systems, the total-phase-noise variance can be reduced by up to 45% and 83%

Convergence of phase noise in DPSK transmission systems by novel phase noise averagers

This investigation proposes a novel all-optical phase noise averager to reduce residual phase noise in the differential phase-shift keying (DPSK) transmission system with phase-preserving amplitude regenerators. The proposed phase noise averager is based on a phase-sensitive amplifier but does not require an extra phase-locking optical pump beam. It can increase the correlation between the phase noises of neighboring bits and greatly reduce the differential phase noise in the transmission system. Independently of the cascaded spans, analytical analysis demonstrates that, in the DPSK system with repeated averagers, the total differential phase noise will be less than that before the first averager. Theoretical analysis and numerical simulation are carried out and confirm the significant improvement of DPSK signals using the proposed novel phase noise averagers.

Effect of dispersion on nonlinear phase noise in optical transmission systems

An analytic expression for the variance of nonlinear phase noise that uses a first-order perturbation technique is obtained. The results show that for highly dispersive transmission systems, amplified spontaneous emission-induced phase noise due to self-phase modulation becomes much smaller than that for the systems with no dispersion.

Full Time-Varying Phase Noise Analysis for MOS Oscillators Based on Floquet and Sylvester Theorems

In this paper a set of full time-varying analyzing methods of phase noise for oscillators based on Floquet and Sylvester theorems are established, it provides a good idea for designing oscillators with perfect phase noise performance. The periodic state solution space of a linear periodic time-varying system is constructed with Floquet and Sylvester theorems, and the phase noise perturbation vectors of an oscillator autonomous system are characterized on this space. The analytical expressions of the phase noise spectrums, both 1/(Δf)2 and Lorentzian forms, are obtained, and the contributions to the phase noise of each noise sources are determined. With a generator approach and some modification, the method could be extended to the flicker noise. For RF front-end oscillators composed of MOS active devices, planar inductors and MOS varactors, the time-varying model parameters of the small signal equivalent circuits are constructed according to the periodic varying working-points. By the means of automatic small-signal equivalent-circuit construction, state-variable selection and periodic time-varying state-matrix generation, the system perturbation vectors and phase noise power spectrums are efficiently calculated. For a 10 GHz MOS oscillator, the 1/(Δf)2 and Lorentzian spectrums are calculated. Comparing with the results of SpectreRF, it indicates the proposed methods are accurate and reliable, especially the Lorentzian spectrum close to the carrier is more reasonable than previous methods. Every noise source contributions to the phase noise are listed and the results are analyzed. At last the applications of the methods to designing low phase noise oscillators and to analyzing the phase noise of composite systems, as well as the difficulty of flicker noise analysis, are addressed.

Compensation of IQ imbalance and phase noise in OFDM systems

Nowadays, a lot of effort is spent on developing inexpensive orthogonal frequency-division multiplexing (OFDM) receivers. Especially, zero intermediate frequency (zero-IF) receivers are very appealing, because they avoid costly IF filters. However, zero-IF front-ends also introduce significant additional front-end distortion, such as IQ imbalance. Moreover, zero-IF does not solve the phase noise problem. Unfortunately, OFDM is very sensitive to the receiver nonidealities IQ imbalance and phase noise. Therefore, we developed a new estimation/compensation scheme to jointly combat the IQ imbalance and phase noise at baseband. In this letter, we describe the algorithms and present the performance results. Our compensation scheme eliminates the IQ imbalance based on one OFDM symbol and performs well in the presence of phase noise. The compensation scheme has a fast convergence and a small residual degradation: even for large IQ imbalance, the overall system performance for an OFDM-wireless local area network (WLAN) case study is within 0.6 dB of the optimal case. As such, our approach greatly relaxes the mismatch specifications and thus enables low-cost zero-IF receivers.

Phase noise characterization by carrier suppression techniques in RF photonic systems

We propose and demonstrate a novel approach to measure the phase noise in radio-frequency photonic systems by employing a suppressed carrier technique. With this technique, the flicker phase noise floor is reduced by 36 dB. To the best of our knowledge, this is the first time that the phase noise of a photodetector is measured, and found to be -126 dBc/Hz at 1 Hz from the carrier at 8.4 GHz.

Analysis of ICI Cancellation Scheme in OFDM Systems With Phase Noise

Phase noise in orthogonal frequency division multiplexing (OFDM) systems destroys the orthogonality of the subcarriers and inter-carrier interference (ICI) is caused. In this paper, the ICI self-cancellation scheme is adopted to combat the ICI caused by phase noise in OFDM systems. Moreover, the error coefficients are defined and the theoretical expressions of carrier to interference ratio (C/I) with and without the ICI self-cancellation scheme are separately derived. From the simulation results, it is verified that the ICI self-cancellation scheme obviously decreases the amount of the ICI caused by phase noise and the improvement of C/I could reach 10 dB when the normalized 3 dB bandwidth of phase noise is 0.4. However, the convolutional coding OFDM (COFDM) system could supply more performance gain at the expense of increasing decoder complexity compared to OFDM system with the ICI self-cancellation scheme in the frequency-selective channel.

Cross-phase-modulation-induced nonlinear phase noise in WDM direct-detection DPSK systems

In direct-detection differential-phase-shift-keying (DPSK) systems, the signal-spontaneous emission beat noise introduces phase noise due to Kerr nonlinearity. In wavelength-division-multiplexed (WDM) systems, this nonlinear phase noise comes not only from the channel itself through self-phase modulation (SPM) but also from the other channels through cross-phase modulation (XPM). In this paper, we theoretically and experimentally investigate XPM-induced nonlinear phase noise. We calculate the performance degradation of DPSK systems caused by XPM-induced nonlinear phase noise in addition to SPM-induced phase noise and experimentally verify it using a 600-km nonzero-dispersion-shifted-fiber link.

A low-power integrated tuner for cable telephony applications

This paper describes an integrated tuner for cable telephony in a 0.35 /spl mu/m, 27 GHz SOI BiCMOS technology. The IC integrates a complete dual-conversion signal path including upconverter, downconverter, variable-gain amplifier, LO synthesizers with fully integrated voltage-controlled oscillators, gain control circuitry, as well as digital calibration and interface circuits. It accepts signals in the 200-880 MHz band and produces a 44 MHz IF. Drawing 168 mA from a 3 V supply, the tuner system has a worst case noise factor of 7.3 dB, system phase noise below -78 dBc/Hz at a 10 kHz offset, spurs below -42 dBc for 137 5 dBmV input channels, a gain of 60 dB, and gain control range of 68 dB. The 13 mm/sup 2/ IC meets specifications across an outdoor temperature range of -40/spl deg/C to 100/spl deg/C in production lots.

Offset phase locking of Er,Yb:glass laser eigenstates for RF photonics applications

An optical source of microwaves with very low phase noise for communications and radar systems is realized and tested. It is obtained by dual-frequency operation of a diode pumped Er,Yb:glass laser. An electrooptic crystal inserted inside the resonator permits both to tune the frequency difference between orthogonally polarized eigenstates, and to turn the laser into a voltage controlled oscillator. An optical phase-locked loop is then implemented in the GHz range, resulting in a measured instrument limited 3 dB-linewidth of 10 Hz. The phase noise is shown to be -100 dBc/Hz at 10-kHz offset.

Analytical modeling and simulation of phase noise interference in OFDM-based digital television terrestrial broadcasting systems

This paper deals with the problem of modeling of phase noise in OFDM systems and the impact it may have on the bit error rate performance of such systems subject to a number of system variables and to a number of channel conditions which may be encountered when such systems are deployed for certain applications such as high speed wireless LANs and Digital Television Terrestrial Broadcasting (DTTB). The phase noise processes, the sources of which are the transmitter's and receiver's local oscillator, are modeled using what is believed to be commercially realizable phase noise masks. Such masks represent the long-term averaged power spectral densities of the local oscillator output signal.

An approximation of filtered signal envelope with phase noise in coherent optical systems

We examine the approximation of the probability density of a filtered signal envelope in the presence of phase noise. The probability density function (pdf) is of practical interest, especially for the performance evaluation of coherent optical systems employing envelope detection. We consider a few possibilities for approximate pdf construction, and develop simple, yet very accurate, expressions to describe the envelope of a filtered signal influenced by phase noise. To check the accuracy, we use the approximation for performance evaluation of a coherent optical frequency-shift keying (FSK) receiver, and compare the results with those obtained from existing methods.

On a recursive formula for the moments of phase noise

We present a recursive formula for the moments of phase noise in communication systems. The phase noise is modeled using continuous Brownian motion. The recursion is simple and valid for an arbitrary initial phase value. The moments obtained bp the recursion are used to calculate approximations to the probability density function of the phase noise, using orthogonal polynomial series expansions and a maximum entropy criterion.

Analysis of the effect of phase noise in OFDM systems

AbstractMulticarrier systems are gaining much attention for their possible application to the transmission of asynchronous transfer mode (ATM) data packets over indoor radio channels. Due to the high frequency selectivity of these channels, at data rate of some tens of Mbits/s multicarrier modulation appears a convenient technique to reduce the intersymbol interference produced by multipath propagation. However, multicarrier modulation exhibits a significant sensitivity to the phase noise of the oscillator used for frequency down‐conversion at the receiver. In order to give a quantitative measure of such impairment, in this paper we evaluate the impact of the oscillator phase noise on the system performance and, in particular, four modulation schemes are compared.