1,084 research outputs found
Optimal and Approximate Methods for Detection of Uncoded Data with Carrier Phase Noise
Previous results in the literature have shown that derivation of the optimum \textit{maximum-likelihood} (ML) receiver for \textit{symbol-by-symbol} (SBS) detection of an uncoded data sequence in the presence of \textit{random phase noise} is an intractable problem, since it involves the computation of the conditional \textit{probability distribution function} (PDF) of the phase noise process. In this paper, we seek to minimize \textit{symbol error probability} (SEP), which is achieved by SBS detection of the sequence based on all received signals. We show that the ML detector for this problem can be formulated as a weighted sum of central moments of the conditional PDF of phase noise. Given that the central moments of the conditional PDF of phase noise can be estimated, this new optimal structure is tractable with respect to the previously known optimal ML receiver. Furthermore, based on the new receiver structure, we propose a simple approximate method for SBS detection and investigate its scope and applicability. Simulation results demonstrate that SEP performance close to optimality can be obtained through the proposed method for scenarios of low phase noise variance and low \textit{signal-to-noise ratio} (SNR)
Soft metrics and their Performance Analysis for Optimal Data Detection in the Presence of Strong Oscillator Phase Noise
In this paper, we address the classical problem of maximum-likelihood (ML)
detection of data in the presence of random phase noise. We consider a system,
where the random phase noise affecting the received signal is first compensated
by a tracker/estimator. Then the phase error and its statistics are used for
deriving the ML detector. Specifically, we derive an ML detector based on a
Gaussian assumption for the phase error probability density function (PDF).
Further without making any assumptions on the phase error PDF, we show that the
actual ML detector can be reformulated as a weighted sum of central moments of
the phase error PDF. We present a simple approximation of this new ML rule
assuming that the phase error distribution is unknown. The ML detectors derived
are also the aposteriori probabilities of the transmitted symbols, and are
referred to as soft metrics. Then, using the detector developed based on
Gaussian phase error assumption, we derive the symbol error probability (SEP)
performance and error floor analytically for arbitrary constellations. Finally
we compare SEP performance of the various detectors/metrics in this work and
those from literature for different signal constellations, phase noise
scenarios and SNR values
Constellation Optimization in the Presence of Strong Phase Noise
In this paper, we address the problem of optimizing signal constellations for
strong phase noise. The problem is investigated by considering three
optimization formulations, which provide an analytical framework for
constellation design. In the first formulation, we seek to design
constellations that minimize the symbol error probability (SEP) for an
approximate ML detector in the presence of phase noise. In the second
formulation, we optimize constellations in terms of mutual information (MI) for
the effective discrete channel consisting of phase noise, additive white
Gaussian noise, and the approximate ML detector. To this end, we derive the MI
of this discrete channel. Finally, we optimize constellations in terms of the
MI for the phase noise channel. We give two analytical characterizations of the
MI of this channel, which are shown to be accurate for a wide range of
signal-to-noise ratios and phase noise variances. For each formulation, we
present a detailed analysis of the optimal constellations and their performance
in the presence of strong phase noise. We show that the optimal constellations
significantly outperform conventional constellations and those proposed in the
literature in terms of SEP, error floors, and MI.Comment: 10 page, 10 figures, Accepted to IEEE Trans. Commu
Channel, Phase Noise, and Frequency Offset in OFDM Systems: Joint Estimation, Data Detection, and Hybrid Cramer-Rao Lower Bound
Oscillator phase noise (PHN) and carrier frequency offset (CFO) can adversely
impact the performance of orthogonal frequency division multiplexing (OFDM)
systems, since they can result in inter carrier interference and rotation of
the signal constellation. In this paper, we propose an expectation conditional
maximization (ECM) based algorithm for joint estimation of channel, PHN, and
CFO in OFDM systems. We present the signal model for the estimation problem and
derive the hybrid Cramer-Rao lower bound (HCRB) for the joint estimation
problem. Next, we propose an iterative receiver based on an extended Kalman
filter for joint data detection and PHN tracking. Numerical results show that,
compared to existing algorithms, the performance of the proposed ECM-based
estimator is closer to the derived HCRB and outperforms the existing estimation
algorithms at moderate-to-high signal-to-noise ratio (SNR). In addition, the
combined estimation algorithm and iterative receiver are more computationally
efficient than existing algorithms and result in improved average uncoded and
coded bit error rate (BER) performance
Feedforward pilot-aided carrier synchronization using a DCT basis expansion
This contribution deals with phase noise estimation from pilot symbols. The phase noise process is approximated by an expansion of Discrete Cosine-Transform (DCT) basis functions containing only a few terms. We propose a feedforward algorithm that estimates the DCT coefficients without requiring detailed knowledge about the phase noise statistics. We demonstrate that the resulting (linearized) mean-square phase estimation error consists of two contributions: a contribution from the additive noise, that equals the Cramer-Rao lower bound, and a noise-independent contribution that results from the phase noise modeling error. We investigate the effect of the symbol sequence length and the number of estimated DCT coefficients on the estimation accuracy and on the corresponding bit error rate (BER). We propose a pilot symbol configuration allowing to estimate any number of DCT coefficients not exceeding the number of pilot symbols. For large block sizes, the DCT-based estimation algorithm substantially outperforms algorithms that estimate only the time-average or the linear trend of the carrier phase
ML Detection in Phase Noise Impaired SIMO Channels with Uplink Training
The problem of maximum likelihood (ML) detection in training-assisted
single-input multiple-output (SIMO) systems with phase noise impairments is
studied for two different scenarios, i.e. the case when the channel is
deterministic and known (constant channel) and the case when the channel is
stochastic and unknown (fading channel). Further, two different operations with
respect to the phase noise sources are considered, namely, the case of
identical phase noise sources and the case of independent phase noise sources
over the antennas. In all scenarios the optimal detector is derived for a very
general parametrization of the phase noise distribution. Further, a high
signal-to-noise-ratio (SNR) analysis is performed to show that
symbol-error-rate (SER) floors appear in all cases. The SER floor in the case
of identical phase noise sources (for both constant and fading channels) is
independent of the number of antenna elements. In contrast, the SER floor in
the case of independent phase noise sources is reduced when increasing the
number of antenna elements (for both constant and fading channels). Finally,
the system model is extended to multiple data channel uses and it is shown that
the conclusions are valid for these setups, as well.Comment: (To appear in IEEE Transactions on Communications, 2015), Contains
additional material (Appendix B. T-slot Detectors
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