Carrier Phase Jitter Research Articles

Assessment of high-rate GPS using a single-axis shake table

The developments in GNSS receiver and antenna technologies, especially the increased sampling rate up to 100 sps, open up the possibility to measure high-rate earthquake ground motions with GNSS. In this paper we focus on the GPS errors in the frequency band above 1 Hz. The dominant error sources are mainly the carrier phase jitter caused by thermal noise and the stress error caused by the dynamics, e.g. antenna motions. To generate a large set of different motions, we used a single-axis shake table, where a GNSS antenna and a strong motion seismometer were mounted with a well-known ground truth. The generated motions were recorded with three different GNSS receivers with sampling rates up to 100 sps and different receiver baseband parameters. The baseband parameters directly dictate the carrier phase jitter and the correlations between subsequent epochs. A narrow loop filter bandwidth keeps the carrier phase jitter on a low level, but has an extreme impact on the receiver response for motions above 1 Hz. The amplitudes above 3 Hz are overestimated up to 50 % or reduced by well over half. The corresponding phase errors are between 30 and 90 degrees. Compared to the GNSS receiver response, the strong motion seismometer measurements do not show any amplitude or phase variations for the frequency range from 1 to 20 Hz. Due to the large errors for dynamic GNSS measurements, it is essential to account for the baseband parameters of the GNSS receivers if high-rate GNSS is to become a valuable tool for seismic displacement measurements above 1 Hz. Fortunately, the receiver response can be corrected by an inverse filter if the baseband parameters are known.

Improved pilot data aided feed forward based on maximum likelihood for carrier phase jitter recovery in coherent optical orthogonal frequency division multiplexing

Pilot data aided feed forward (PAFF) carrier recovery is essential for phase noise tracking in coherent optical receivers. This paper describes a new PAFF system based on new pilot arrangement and maximum likelihood (ML) to estimate the phase jitter in coherent receiver-induced by local oscillator’s lasers and sampling clock errors. Square M-ary quadrature amplitude modulation (M-QAM) (4, 16, 64, and 256) schemes were used. A detailed mathematical description of the method was presented. The system performance was evaluated through numerical simulations and compared to those with noise-free receiver (ideal receiver) and feed forward without ML. The simulation results show that PAFF performs near the expected ideal phase recovery. Results clearly suggest that ML significantly improves the tolerance of phase error variance. From bit error rate (BER) sensibility evaluation, it was clearly observed that the new estimation method performs better with a 4-QAM (or quadrature phase shift keying (QPSK)) format compared to three others square QAM schemes. Analog to digital converter (ADC) resolution effect on the system performance was analyzed in terms of Q-factor. Finite resolution effect on 4-QAM is negligible while it negatively affects the system performance when M increases.

Cramer-Rao lower bound and EM algorithm for envelope-based SNR estimation of nonconstant modulus constellations

Signal-to-noise ratio (SNR) estimation for linearly modulated signals is addressed in this letter, focusing on envelope-based estimators, which are robust to carrier offsets and phase jitter, and on the challenging case of nonconstant modulus constellations. For comparison purposes, the true Cramer-Rao lower bound is numerically evaluated, obtaining an analytical expression in closed form for the asymptotic case of high SNR values, which quantifies the performance loss with respect to coherent estimation. As the maximum-likelihood algorithm is too complex for practical implementation, an expectation-maximization (EM) approach is proposed, achieving a good tradeoff between complexity and performance for medium-to-high SNRs. Finally, a hybrid scheme based on EM and moments-based estimates is suggested, which performs close to the theoretical limit over a wide SNR range.

Performance comparison of MRC and EGC on a MC-CDMA system with synchronization errors over fading channels

This work derives the average bit error rate (BER) of the uplink and downlink multicarrier code division multiple access (MC-CDMA) systems using maximum ratio combining (MRC) and equal gain combining (EGC) with synchronization errors over fading channels. The derived equation can simultaneously incorporate the parameters of the fading channel and all of the synchronization errors, including frequency offset, carrier phase jitter, and timing jitter. Numerical results indicate that those two combining schemes on the uplink and downlink MC-CDMA systems are degraded by all of the normalized synchronization errors over 10?2. The comparison outcomes between MRC and EGC reveal that the MRC generally outperforms EGC in the uplink MC-CDMA system. However, EGC achieves better performance when the number of users is small, the normalized synchronization errors are low and the signal to noise ratio (SNR) is high. In the downlink system, EGC mainly outperforms MRC when the SNR and the number of users are gradually increased and the normalized synchronization errors are low. Therefore, the selection of MRC or EGC depends on the SNR, the synchronization errors and the number of users in uplink and downlink MC-CDMA systems.

An integrated analysis for MC‐CDMA system with synchronization errors over fading channels

Synchronization errors and fading channels are individually considered in many previous studies. This study derives the average bit error rate (BER) of the uplink and downlink MC‐CDMA systems using equal gain combining (EGC) with synchronization errors over the fading channels. The obtained average BER of the uplink and downlink MC‐CDMA systems simultaneously considers most of the synchronization errors and the parameters of the fading channel. Since it is difficult to acquire the closed‐form of average BER, the Chernoff bound is adopted to derive the upper bound of the average BER instead. Computer simulation results show that the performance of the uplink and downlink MC‐CDMA systems are degraded by the fading channel and synchronization errors such as frequency offset, carrier phase jitter and timing jitter. This fully corresponds to theoretical derivations. Also, by comparing the uplink to the downlink systems, we conclude that the average BER of the downlink MC‐CDMA system degrades faster due to the increasing value of synchronization errors.

Decimal Frequency Offset Estimation in COFDM Wireless Communications

Timing jitter, frequency offset, carrier phase jitter and sampling clock frequency offset are the main synchronization errors encountered by OFDM systems. As many literature studies have proved, OFDM systems are very sensitive to frequency errors. In this paper, an improved method for decimal frequency offset estimation in time domain is proposed. In addition, lots of simulations have proved that when the decimal frequency offset in data streams approaches 0.5 of the subcarrier spacing, a wrong estimated frequency offset with inverse polarity will be presented, and therefore, a novel adjusting model to deal with this problem is also proposed in this paper. Simulation results show that the mean square error (MSE) can be significantly improved by over three orders of magnitude at high SNR with the proposed method compared with the conventional method. The corresponding field programmable gate array (FPGA) circuit through test in HDTV prototype in Team of Engineering Expert Group (TEEG) proves its feasibility and availability.

Synchronization sensitivity of multicarrier systems

AbstractIn this paper, we give an overview of the sensitivity of a number of multicarrier systems to carrier and clock synchronization errors. A comparison is made between orthogonal frequency division multiplexing/multiple access (OFDM(A)) and two combinations of the orthogonal multicarrier technique and the code‐division multiple access (CDMA) technique, i.e. multicarrier CDMA (MC‐CDMA), where the spreading is accomplished in the frequency domain and multicarrier direct‐sequence CDMA (MC‐DS‐CDMA), where the spreading is done in the time domain. We evaluate the effect of small synchronization errors on the BER performance by deriving simple analytical expressions for the BER degradation that are based upon truncated Taylor series expansions. To allow a fair comparison, all considered systems are able to accommodate the same number of users and each user operates at the same data rate. Under these conditions, we show that all multicarrier systems exhibit the same sensitivity to carrier phase jitter and timing jitter. Further, when the number of carriers is equal to the maximum number of users, the different multicarrier systems also are equally affected by a carrier frequency offset or a clock frequency offset. Copyright © 2004 AEI

Frequency offset estimation for OFDM in wireless communications

Timing jitter, frequency offset, carrier phase jitter and sampling clock frequency offset are the main synchronization errors encountered by OFDM systems. As many literatures have proved, OFDM systems are very sensitive to frequency errors. In this paper, three new methods to estimate the integer part of frequency offset are proposed, simulation results show its robustness to mitigate the multi-path effect and its enlarged estimation range for frequency offset. The correspondent field programmable gate array (FPGA) circuit through test in HDTV prototype in Team of Engineering Expert Group (TEEG) proves its feasibility and availability. The proposed method is also suitable for burst mode transmission systems such as wireless local area network (WLAN) and fixed-broadband wireless access (F-BWA).

Sensitivity of orthogonal frequency-division multiplexed systems to carrier and clock synchronization errors

In this contribution, we present an overview of research results pertaining to the sensitivity of orthogonal frequency-division multiplexed (OFDM) systems to synchronization errors. We show that OFDM systems are quite sensitive to carrier frequency offset and clock frequency offset: in the presence of these impairments, the signal-to-noise ratio (SNR) at the input of the decision device is a decreasing function of the number of carriers. On the other hand, carrier phase jitter and timing jitter give rise to a degradation of the SNR at the input of the decision device which does not depend on the number of carriers; as compared to traditional single-carrier systems, OFDM systems have the same sensitivity to carrier phase jitter and a somewhat larger sensitivity to timing jitter.

The Sensitivity of MC‐CDMA to Synchronisation Errors

AbstractIn this contribution, we investigate the sensitivity of MC‐CDMA systems to synchronisation errors. We show that the signal‐to‐noise ratio (SNR) of the MC‐CDMA system at the input of the decision device in the presence of a carrier frequency offset or a clock frequency offset is a rapidly decreasing function of the number of carriers. For a maximal load, carrier phase jitter and timing jitter give rise to a degradation that is independent of the spectral content of the jitter; moreover, the degradation caused by carrier phase jitter is independent of the number of carriers. A constant carrier phase offset and a constant timing offset cause no degradation of the MC‐CDMA system performance.

The effect of carrier phase jitter on MC-CDMA performance

We investigate the influence of the carrier phase jitter of a phase-locked local oscillator on the performance of a multicarrier code-division multiple-access (MC-CDMA) system in a nondispersive channel. This carrier phase jitter degrades the signal-to-noise ratio at the input of the decision device. When all users have the same power level and phase jitter spectrum, it is shown that for the highest load, the degradation only depends on the jitter variance but not on the specific shape of the jitter spectrum nor on the number of carriers.

The effect of carrier phase jitter on the performance of orthogonal frequency-division multiple-access systems

We investigate the sensitivity to carrier phase jitter of an orthogonal frequency-division multiple-access (OFDMA) system. When all OFDMA carriers have the same power level and jitter spectrum, the degradation caused by the jitter is shown to be equal to the degradation of an OFDM system. Also, traditional FDMA is found to be slightly more robust than OFDMA.

Comparison of Single-Carrier and Multi-Carrier QAMSystem Performance in the Presence of Carrier Phase Jitter

In this contribution, we investigate how the carrier phase jitter of a phase-locked oscillator for IF-to-baseband conversion affects the performance of single-carrier QAM (SC-QAM) and multi-carrier QAM (MC-QAM); the considered multi-carrier system is of the OFDM (orthogonal frequency-division multiplexed) type. This phase jitter reduces the signal-to-noise ratio (SNR) at the input of the decision device, and therefore gives rise to an increase of the bit error rate. We show that, for a given jitter variance, SC-QAM and MC-QAM yield the same SNR degradation. However, when the synchronization for MC-QAM is derived from a pilot tone, we point out that the resulting jitter variance is considerably larger than for SC-QAM, in which case MC-QAM is degraded much more than SC-QAM.

Convergence properties of optimal adaptive carrier phase jitter predictors for sinusoidal jitter

Carrier recovery systems in high performance digital modem receivers must remove carrier phase jitter as well as track carrier phase and frequency offsets. A popular approach to removing periodic phase jitter is to use an adaptive LMS FIR linear predictor with baud spaced taps to predict the jitter angle one baud in the future. Experimentally, the convergence rates for such predictors were found to depend heavily on the jitter frequency. It is well known in adaptive filter theory that the predictor convergence rate depends on the eigenvalues of the correlation matrix of the input signal. By allowing jitter predictors with a given number of taps to have tap spacings greater than one baud and by deriving a general formula for the eigenvalues of the appropriate correlation matrix, it is shown how to design predictors exhibiting optimal convergence rates over a range of commonly observed jitter frequencies.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Performance of 256-QAM system in the presence of phase jitter and co-channel interference

The symbol error rates (SERs) for a 256-QAM system in the presence of sinusoidal co-channel interference, noise and non-perfect carrier recovery are determined. Ii is shown lhai the combined effect is a significant increase in SERs, and lhe SERs are shown as a function of carrier-phase jitter variance (σ2 ψ) and signal-to-noise ratio, parametrized by a carrier-to-inierference raiio.

The probability of error in AM-PM systems due to noncoherent demodulation, interference and noise

The symbol error rates (SER) of different 16-level AM-PM systems (16-QAM, 8-8, 4-90, 1-5-10, 1-6-9, 5-11) in the presence of sinusoidal interference, Gaussian noise and imperfect carrier recovery are determined. The SER are shown as functions of the carrier phase jitter variance (/spl sigma//sub /spl Psi///sup 2/) and parametrized by the signal-to-noise ratio (SNR) and carrier-to-interference ratio (CIR). The performance is evaluated numerically by the cubature rule. This method requires only the possibility to calculate the values of the probability density function (PDF) of the demodulated output signal, and it can also be used easily in other problems when the received signal is a function of two variables. >

On the effects of phase jitter on QPSK lock detection

The performance of a QPSK (quadrature phase-shift keying) lock detector is described, taking into account the degradation due to carrier phase jitter. Such an analysis is necessary for accurate performance prediction purposes in scenarios where both the loop SNR is low and the estimation period is short. The derived formulas are applicable to several QPSK loops and are verified using computer simulations.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Phase jitter sensitivity of rotationally invariant 8 and 16 point trellis codes

Prabhu examined the sensitivity of uncoded PSK modulations to carrier phase jitter. A Gaussian phase jitter model was assumed. The same study is conducted for trellis coded PSK and QAM modulations. Rotationally invariant codes are considered and an explicit design procedure is included. Through digital computer simulation it was found that for practical values of rms phase jitter coding gains for rotationally invariant codes are either maintained or enhanced through trellis coding. Four examples are presented which represent the design procedure. The phase jitter sensitivity is given in each case. Analytic expressions are also derived for the differential encoding rules to be used in the 8 and 16 point examples presented.

A systematic approach to carrier recovery and detection of digitally phase modulated signals of fading channels

The problem of optimal carrier recovery and detection of digitally phase modulated signals on fading channels by using a nonstructured approach is presented, i.e. no constraint is placed on the receiver structure. First, the optimal receiver is derived for digitally phase-modulated signals when transmitted over a frequency-nonselective fading channel with memory. The memory results from the fact that usually the coherence time of the channel is larger than the symbol period. Symbols adjacent in time cannot be detected independently and therefore the well-known quadratic receiver is not optimal in this case. A maximum a posteriori (MAP) detector is derived and explicitly utilizes the channel memory for carrier recovery. The derivation shows that the optimal carrier recovery is, under certain conditions, a Kalman filter. Some attractive properties of this carrier recovery unit (including the absence of hang up) are discussed. Then the error rate of several digital modulation schemes is calculated taking the performance of the filter into account. The differences in susceptibility of the modulation schemes to carrier phase jitter are specified. >

Influence of coding and hardware imperfections on the bit error structure of multilevel QAM systems

When putting together 140-Mb/s 16-ary quadrature amplitude modulation (16-QAM) modems, radio-relay sets, and the appertaining total multiplex/demultiplex equipment, different and even higher bit error rates (BERs) have been measured at the primary low-level 64-kb/s outputs as compared to that at 140 Mb/s. The authors show that this error multiplex effect is mainly caused by the coding of signal points and by hardware imperfections such as carrier and clock phase jitter, nonideal regenerator threshold voltages, etc. They derive the mathematical tools necessary for calculation of the bit error structure at the modem output under optimum and nonoptimum receiver conditions. It is shown how the errors are distributed among the demultiplexer channels. QAM space diagrams of distorted signals are used for calculation of the BERs in the subsystems. Some experimental results emphasize the fact that the multiplex equipment must not be excluded from design considerations for QAM modems. The 16- and 64-QAM systems are compared with respect to their susceptibility to the error multiplex effect, and a scrambling technique is proposed as a possible means to reduce the BER differences. >