True Cramer-Rao bounds for carrier and symbol synchronization

This contribution considers the Cramer-Rao bound (CRB) related to estimating the synchronization parameters (carrier phase, carrier frequency and time delay) of a noisy linearly modulated signal with random data symbols. We explore various scenarios, involving the estimation of a subset of the parameters while the other parameters are either considered as nuisance parameters or a priori known to the receiver. In addition, some results related to the CRB for coded transmission will be presented

Blind Phase Recovery in Cross QAM Communication Systems with the Reduced Constellation Eigth-Order Estimator (RCEOE)

The eighth-order (EOE) phase estimator [4] is modified to work for an eight-symbol symmetrical constellation, so that the large signal-to-noise (SNR) performance is not limited by self-noise. By using only the eight highest energy points of cross- QAM constellations, a reduced constellation eighth-order estimator (RCEOE) is proposed. Computer simulations for 128-QAM show that this new method performs substantially better than the recently introduced APP phase estimator of Wang et al. [8]. However, simulations with 32-QAM show little performance advantage of the RCEOE over the APP estimator, for SNR values normally of interest, whereas for low SNR, the improvement is significant. Application to any constellation which can be reduced to an 8-symbol quadrant symmetrical sub-constellation is straightforward

The true Cramer-Rao bound for estimating the carrier phase of a convolutionally encoded PSK signal

This contribution considers the true Cramer-Rao bound (CRB) related to estimating the carrier phase of a noisy linearly modulated signal in the presence of encoded data symbols. Timing delay and frequency offset are assumed to be known. A generall expression and computational method is derived to evaluate the CRB in the presence of codes for which a trellis diagram can be drawn (block codes, trellis codes, convolutional codes,...). Results are obtained for several minimum free distance non-recursive convolutional (NRC) codes, and are compared with the CRB obtained with random (uncoded) data [1] and with the modified Cramer-Rao bound (MCRB) from [2]. We find that for small signal-to-noise ratio (SNR) the CRB is considerably smaller for coded transmission than for uncoded transmission. We show that the SNR at which the CRB is close to the MCRB decreases as the coding gain increases, and corresponds to a bit error rate (BER) of about 0.001. We also compare the new CRBs with the simulated performance of (i) the (code-independent) Viterbi & Viterbi phase estimator [3] and (ii) the recently developed turbo synchronizer [4,5]

A Simple Improvement to the Viterbi and Viterbi Monomial-Based Phase Estimators

It is well known that the Viterbi and Viterbi Monomial- Based Phase Estimator, which includes the Mth Power Estimator, performs poorly for cross QAM signals. However, it is shown here that by allowing the power of the monomial to be negative, much improved performance can be realized at medium to high signalto- noise ratios (SNR). Monte Carlo simulations are used to demonstrate the efficacy of this novel simple extension, for 32- and 128-QAM systems. In principle, this extension can also be applied to other constellations, e.g., (4,12)-PSK

Carrier Phase Estimation Through the Rotation Algorithm for 64-QAM Optical Systems

A novel low-complexity two-stage digital feedforward carrier phase estimation algorithm based on the rotation of constellation points to remove phase modulation for a 64-ary quadrature amplitude modulation (QAM) system is proposed and analyzed both experimentally and through numerical simulations. The first stage is composed of a Viterbi and Viterbi (V&V) block, based on either the standard quadrature phase shift keying (QPSK) partitioning algorithm using only Class-1 symbols or a modified QPSK partitioning scheme utilizing both Class-1 and outer most triangle-edge (TE) symbols. The second stage applies the V&V algorithm after the removal of phase modulation through rotation of constellation points. Comparison of the proposed scheme with constellation transformation, blind phase search (BPS) and BPS+MLE (maximum likelihood estimation) algorithm is also shown. For an OSNR penalty of 1 dB at bit error rate of 1e−2 , the proposed scheme can tolerate a linewidth times symbol duration product (Δν · Ts) equal to 3.7 × 1e−5 , making it possible to operate 32-GBd optical 64-QAM systems with current commercial tunable laser

Cramer-Rao Lower Bounds for the Synchronization of UWB Signals

We present Cramér-Rao lower bounds (CRLBs) for the synchronization of UWB signals which should be tight lower bounds for the theoretical performance limits of UWB synchronizers. The CRLBs are investigated for both single-pulse systems and time-hopping systems in AWGN and multipath channels. Insights are given into the relationship between CRLBs for different Gaussian monocycles. An approximation method of the CRLBs is discussed when nuisance parameters exist. CRLBs in multipath channels are studied and formulated for three scenarios depending on the way multipath interference is treated. We find that a larger number of multipaths implies higher CRLBs and inferior performance of the synchronizers, and multipath interference on CRLBs cannot be eliminated completely except in very special cases. As every estimate of time delay could not be perfect, the least influence of the synchronization error on the performance of receivers is quantified

Deep learning versus spectral techniques for frequency estimation of single tones: Reduced complexity for software-defined radio and iot sensor communications

Despite the increasing role of machine learning in various fields, very few works considered artificial intelligence for frequency estimation (FE). This work presents comprehensive analysis of a deep-learning (DL) approach for frequency estimation of single tones. A DL network with two layers having a few nodes can estimate frequency more accurately than well-known classical techniques can. While filling the gap in the existing literature, the study is comprehensive, analyzing errors under different signal-to-noise ratios (SNRs), numbers of nodes, and numbers of input samples under missing SNR information. DL-based FE is not significantly affected by SNR bias or number of nodes. A DL-based approach can properly work using a minimal number of input nodes N at which classical methods fail. DL could use as few as two layers while having two or three nodes for each, with the complexity of O{N} compared with discrete Fourier transform (DFT)-based FE with O{Nlog2 (N)} complexity. Furthermore, less N is required for DL. Therefore, DL can significantly reduce FE complexity, memory cost, and power consumption, which is attractive for resource-limited systems such as some Internet of Things (IoT) sensor applications. Reduced complexity also opens the door for hardware-efficient implementation using short-word-length (SWL) or time-efficient software-defined radio (SDR) communications

Low-complexity and phase noise tolerant carrier phase estimation for dual-polarization 16-QAM systems

2011-2012 > Academic research: refereed > Publication in refereed journalVersion of RecordPublishe