Joint Maximum Likelihood Research Articles

On the Hybrid TOA/RSS Range Estimation in Wireless Sensor Networks

Distance estimation, which arises in many applications and especially in range-based localization, is addressed for joint received signal strength (RSS) and time of arrival (TOA) data. A statistical characterization of the joint maximum likelihood estimator, which is unavailable in closed-form, is provided together with a full performance assessment in terms of the actual mean squared error (MSE), in order to establish when hybrid estimation is superior compared to RSS-only or TOA-only estimation. Furthermore, a novel closed-form estimator is proposed based on an ad-hoc relaxation of the likelihood function, which removes the need to adopt iterative methods for hybrid TOA/RSS ranging and strikes a better bias-variance tradeoff for improved performance. A thorough theoretical analysis, corroborated by numerical simulations, shows the effectiveness of the proposed approach, which outperforms state-of-the-art solutions.

Analysis of Detection Methods for Space Frequency Block Code MIMO-OFDM System in Fast Fading Channels

Multiple antennae with the multicarrier trans-receiver system have increased diversity gain and higher data rates. For high performance 4G wireless communication, the multiple inputs and multiple outputs with orthogonal frequency division multiplexing (MIMO-OFDM) employing Space Frequency Block Codes which provides frequency and spatial diversity in fast fading environments to provide reliability of transmission. Space Frequency Block Code technique encodes data by using frequency diversity on multiple antennae. The challenge of these space-frequency diversity transmitted signal is a detection of original symbols at receiver in a fast fading environment. In this paper, it has been analyzed four detection methods, Simple maximum-likelihood, Joint maximum-likelihood, Zero-forcing and Decision-feedback. The evaluation of the detection methods is done on the basis of the Signal to Noise Ratio, Bit Error Rate and complexity of implementation in fast fading channels under three vehicular speeds i.e. 3km/hr, 60km/hr, and 120km/hr.

Joint Estimation of MIMO-OTH Radar Measurements and Ionospheric Parameters

To avoid the disadvantage of the traditional over-the-horizon (OTH) radar, which uses only the measurements of ionospheric parameters obtained from an ionosonde to estimate the target parameters, this paper proposes a new multiple-input multiple-output skywave OTH radar, which estimates the ionospheric and target parameters jointly by exploiting the data received by both the ionosonde and the radar receivers. First, we consider the scenario where the prior distribution of ionospheric parameters is unknown, the joint maximum likelihood estimator is developed and the Cramer–Rao bound (CRB) is derived to analyze the estimation performance. Then, the case with known Gaussian ionospheric prior distribution is analyzed, we develop the hybrid maximum likelihood and maximum a posteriori estimator, and the hybrid CRB (HCRB) is derived for analyzing the estimation performance. Finally, we show that the proposed joint estimation approaches lead to better accuracy for the ionospheric and target parameters estimation. We prove that both the CRB and the HCRB vary with the ionosonde measurement error covariance, and the corresponding upper and lower bounds are derived.

Multiple carrier frequency offsets and multipath channels estimation for coordinated multi-point FBMC systems

Filter bank multicarrier (FBMC) systems are active candidates for the physical layer of the fifth generation of wireless communication networks (5G). The combination of FBMC system with the coordinated multipoint (CoMP) has been proposed to improve the performance of mobile terminals (MT) located at the cell edge. Accurate estimation of carrier frequency offset (CFO) and channel has great importance in communication systems. In this paper, a data-aided joint maximum likelihood (ML) CFO and channel estimation is proposed for the downlink of CoMP. Notably choosing the proper training sequences from Hadamard matrix for different base stations (BSs) reduces the complexity of estimator. Additionally joint CFO correction and channel equalization has been studied at the MT. Finally, we evaluate the efficacy of the presented algorithms using simulation.

Hunting high and low: disentangling primordial and late-time non-Gaussianity with cosmic densities in spheres

Non-Gaussianities of dynamical origin are disentangled from primordial ones using the formalism of large deviation statistics with spherical collapse dynamics. This is achieved by relying on accurate analytical predictions for the one-point probability distribution function (PDF) and the two-point clustering of spherically-averaged cosmic densities (sphere bias). Sphere bias extends the idea of halo bias to intermediate density environments and voids as underdense regions. In the presence of primordial non-Gaussianity, sphere bias displays a strong scale dependence relevant for both high and low density regions, which is predicted analytically. The statistics of densities in spheres are built to model primordial non-Gaussianity via an initial skewness with a scale-dependence that depends on the bispectrum of the underlying model. The analytical formulas with the measured nonlinear dark matter variance as input are successfully tested against numerical simulations. For local non-Gaussianity with a range from $f_{\rm NL}=-100$ to $+100$ they are found to agree within 2\% or better for densities $\rho\in[0.5,3]$ in spheres of radius 15 Mpc$/h$ down to $z=0.35$. The validity of the large deviation statistics formalism is thereby established for all observationally relevant local-type departures from perfectly Gaussian initial conditions. The corresponding estimators for the amplitude of the nonlinear variance $\sigma_8$ and primordial skewness $f_{\rm NL}$ are validated using a fiducial joint maximum likelihood experiment. The influence of observational effects and the prospects for a future detection of primordial non-Gaussianity from joint one- and two-point densities-in-spheres statistics are discussed.

Correlation Reduction Precoding for Joint Decoding in Overloaded MIMO-OFDM System on Rician Channel

This paper presents a correlation reduction precoding scheme for joint decoding in an overloaded multiple input multiple output (MIMO)-orthogonal frequency division multiplexing system. In the overloaded MIMO system, the number of receive antenna elements is less than that of transmit antenna elements. Through joint maximum likelihood (ML) decoding a frequency diversity suppresses the BER degradation owing to the spatial multiplexing of signal streams. On a Rician channel, the correlation among coded symbols deteriorates the performance of the joint ML decoding. Thus, this paper proposes the precoding scheme that reduces the correlation on the Rician channel. Numerical results obtained through computer simulation show that the proposed scheme improves the BER by a factor of 1/10 on the Rician channel with a Rician factor of 10.

Space-Time Coding for Aeronautical Telemetry: Part I—Estimators

This paper derives and analyzes the estimators required for detection and decoding of Alamouti-encoded-shaped offset QPSK version TG (SOQPSK-TG). The joint maximum likelihood (ML) estimators for the frequency offset, channel delays, and channel gains are derived and analyzed. As a complexity-reducing technique, a sequential version of the ML estimators is developed. The Cramer–Rao bound for the parameters is derived and used to analyze the performance of the estimators to determine pilot sequence length. The complexity of the frequency estimator is reduced by applying the Zoom FFT algorithm in the coarse search. The complexity of the channel delay estimator was reduced by developing a novel version of the simplex search algorithm that operated on a discrete two-dimensional grid. These estimation algorithms were implemented in a prototype demodulator that was field tested at Edwards AFB.

Efficient Transmission and Detection Based on RNS for Generalized Space Shift Keying

We propose an efficient transmission scheme for the generalized space shift keying (GSSK) based on the residue number system (RNS). The proposed scheme increases the number of active transmit antenna combinations (TACs), resulting in a higher throughput than that of the conventional GSSK systems. The received signals can be detected by a joint maximum likelihood (ML) detection, whose complexity, however, grows exponentially with the number of active TACs. To solve this problem, we propose a new detection method based on the RNS, whose complexity is much lower than that of the joint ML detection with negligible performance loss.

Spurious Latent Class Problem in the Mixed Rasch Model: A Comparison of Three Maximum Likelihood Estimation Methods under Different Ability Distributions

Recent research has shown that over-extraction of latent classes can be observed in the Bayesian estimation of the mixed Rasch model when the distribution of ability is non-normal. This study examined the effect of non-normal ability distributions on the number of latent classes in the mixed Rasch model when estimated with maximum likelihood estimation methods (conditional, marginal, and joint). Three information criteria fit indices (Akaike information criterion, Bayesian information criterion, and sample size adjusted BIC) were used in a simulation study and an empirical study. Findings of this study showed that the spurious latent class problem was observed with marginal maximum likelihood and joint maximum likelihood estimations. However, conditional maximum likelihood estimation showed no overextraction problem with non-normal ability distributions.

Inference in a two-parameter generalized order statistics model

ABSTRACTAs a submodel of generalized order statistics with two unknown model parameters, m-generalized order statistics may serve as a simple model for ordered quantities in a given application. It is shown that the joint distribution of m-generalized order statistics has a representation as a regular exponential family in the model parameters, as it is the case for the comprising model. Utilizing this finding, a minimal sufficient and complete statistic is obtained along with distributional properties. Joint maximum likelihood estimation of the parameters is considered, and strong consistency and asymptotic efficiency of the estimator are established. A test is provided to decide whether a restriction to the submodel is reasonable.

The logarithmic vector multiplicative error model: an application to high frequency NYSE stock data

We develop a general form logarithmic vector multiplicative error model (log-vMEM). The log-vMEM improves on existing models in two ways. First, it is a more general form model as it allows the error terms to be cross-dependent and relaxes weak exogeneity restrictions. Second, the log-vMEM specification guarantees that the conditional means are non-negative without any restrictions imposed on the parameters. We further propose a multivariate lognormal distribution and a joint maximum likelihood estimation strategy. The model is applied to high frequency data associated with a number of NYSE-listed stocks. The results reveal empirical support for full interdependence of trading duration, volume and volatility, with the log-vMEM providing a better fit to the data than a competing model. Moreover, we find that unexpected duration and volume dominate observed duration and volume in terms of information content, and that volatility and volatility shocks affect duration in different directions. These results are interpreted with reference to extant microstructure theory.

Joint Maximum Likelihood Estimation for Diagnostic Classification Models.

Joint maximum likelihood estimation (JMLE) is developed for diagnostic classification models (DCMs). JMLE has been barely used in Psychometrics because JMLE parameter estimators typically lack statistical consistency. The JMLE procedure presented here resolves the consistency issue by incorporating an external, statistically consistent estimator of examinees' proficiency class membership into the joint likelihood function, which subsequently allows for the construction of item parameter estimators that also have the consistency property. Consistency of the JMLE parameter estimators is established within the framework of general DCMs: The JMLE parameter estimators are derived for the Loglinear Cognitive Diagnosis Model (LCDM). Two consistency theorems are proven for the LCDM. Using the framework of general DCMs makes the results and proofs also applicable to DCMs that can be expressed as submodels of the LCDM. Simulation studies are reported for evaluating the performance of JMLE when used with tests of varying length and different numbers of attributes. As a practical application, JMLE is also used with "real world" educational data collected with a language proficiency test.

Antenna Reliability Ordering Technique for Unequal Error Protection in Jointly Detected MIMO Systems

In this paper, we address the ordering of transmit antennas according to reliability for unequal error protection (UEP) in spatially multiplexed (SM) multiple-input multiple-output (MIMO) systems with joint detection at the receiver. When zero-forcing (ZF) detection is adopted, the reliabilities of transmit antennas are explicitly expressed as postequalization signal-to-noise ratios (SNRs). Thus, multiantenna UEP can be implemented by assigning data of high priority to transmit antennas with a high postequalization SNR. Unfortunately, the overall error performance is generally unsatisfactory. Various joint signal detection techniques that achieve maximum likelihood (ML) or near-ML performance have been developed as alternatives to ZF, but it is not obvious how to discriminate the reliabilities of the transmit antennas or the jointly detected symbols. Recently, an ordering technique for antenna reliabilities was proposed that exploits the structure of the previous near-optimal QR-decomposition-based least-reliable-layer joint detection. In this paper, we divide the log-likelihood ratio of each symbol into collaborative and individual components, assuming joint ML detection. We derive a statistical connection between the magnitude order of each component of the multiple symbols (or the corresponding transmit antennas) and the post-ZF-equalization SNRs. Based on the statistical connections, we propose the use of post-ZF-equalization SNR as a criterion for antenna reliability ordering of SM MIMO with various near-optimal, as well as optimal, joint detections. The differentiated error performance of transmit antennas is also shown to be mainly attributed to the difference of individual components, and the tendency becomes stronger as the constellation size increases. Simulations demonstrate that the proposed ordering technique better meets the UEP requirement with lower computational complexity than the conventional ordering. Assuming $N_t \times N_t$ MIMO systems, the previous ordering and the proposed ordering require $\mathcal{O}(N_t^3)+\sum_{N=2}^{N_t-1}\mathcal{O}(NN_t^2+N^3)$ and $\mathcal{O}(N_t^3)$ , respectively.

ML modulation classification in presence of unreliable observations

Joint detection and maximum-likelihood (ML) classification of linear modulations based on observations collected over an unknown flat-fading additive Gaussian noise channel is considered. It is assumed that some of the observations are subject to data failures, in which case the receiver acquires only noise. Expectation–maximisation algorithm is employed to compute the ML estimates of the unknown channel parameters, which are then substituted into the corresponding likelihood expressions to perform hypothesis testing. Numerical simulations indicate that a suboptimal classifier, which is ignorant to data failures, exhibits extremely poor performance in the presence of high failure rates. On the other hand, the proposed classifier demonstrates comparable performance with that of the clairvoyant classifier which is assumed to have a priori knowledge of the channel parameters and data failures.

Joint Maximum Likelihood Detection in Far User of Non-Orthogonal Multiple Access

Joint Maximum Likelihood Detection in Far User of Non-Orthogonal Multiple Access

Joint Maximum Likelihood Time Delay Estimation of Unknown Event-Related Potential Signals for EEG Sensor Signal Quality Enhancement.

Electroencephalograms (EEGs) measure a brain signal that contains abundant information about the human brain function and health. For this reason, recent clinical brain research and brain computer interface (BCI) studies use EEG signals in many applications. Due to the significant noise in EEG traces, signal processing to enhance the signal to noise power ratio (SNR) is necessary for EEG analysis, especially for non-invasive EEG. A typical method to improve the SNR is averaging many trials of event related potential (ERP) signal that represents a brain’s response to a particular stimulus or a task. The averaging, however, is very sensitive to variable delays. In this study, we propose two time delay estimation (TDE) schemes based on a joint maximum likelihood (ML) criterion to compensate the uncertain delays which may be different in each trial. We evaluate the performance for different types of signals such as random, deterministic, and real EEG signals. The results show that the proposed schemes provide better performance than other conventional schemes employing averaged signal as a reference, e.g., up to 4 dB gain at the expected delay error of 10°.

Volatility risk premium implications of GARCH option pricing models

In this paper we explore important implications of capturing volatility risk premium (VRP) within a parametric GARCH setting. We study the transmission mechanism of shocks from returns to risk-neutral volatility by providing an examination of the news-impact curves and impulse–response functions of risk-neutral volatility, in order to better understand how option prices respond to return innovations. We report a value of −3% for the magnitude of the average VRP and we recover the empirical densities under physical and risk-neutral measures. Allowing for VRP is crucial for adding flexibility to the shape of the two distributions. In our estimation procedure, we adopt a MLE approach that incorporates both physical return and risk-neutral VIX dynamics. By introducing volatility - instead of variance - innovations in the joint likelihood function and by allowing for contemporaneous correlation between innovations in returns and the VIX we show that we may critically reduce the bias and improve the efficiency of the joint maximum likelihood estimator, especially for the parameters of the volatility process. Modeling returns and the VIX as a bi-variate normal permits identification of a contemporaneous correlation coefficient of approximately −30% between returns and risk-neutral volatility.

Frequency Estimation in OFDM Direct-Conversion Receivers Using a Repeated Preamble

This paper investigates the problem of carrier frequency offset (CFO) recovery in an OFDM receiver affected by frequency-selective in-phase/quadrature (I/Q) imbalances. The analysis is based on maximum-likelihood (ML) methods and relies on the transmission of a training preamble with a repetitive structure in the time domain. After assessing the accuracy of the conventional ML (CML) scheme in a scenario characterized by I/Q impairments, we review the joint ML (JML) estimator of all unknown parameters and evaluate its theoretical performance. In order to improve the estimation accuracy, we also present a novel CFO recovery method that exploits some side-information about the signal-to-interference ratio. It turns out that both CML and JML can be derived from this scheme by properly adjusting the value of a design parameter. The accuracy of the investigated methods are compared with the relevant Cramer–Rao bound. Our results can be used to check whether conventional CFO recovery algorithms can work properly or not in the presence of I/Q imbalances and also to evaluate the potential gain attainable by more sophisticated schemes.

Fully distributed clock synchronization in wireless sensor networks under exponential delays

In this paper, we study the global clock synchronization problem for wireless sensor networks under unknown exponential delays in the two-way message exchange mechanism. The joint maximum likelihood estimator of clock offsets, clock skews and fixed delays for the network is formulated as a linear programming (LP) problem. Then, based on the alternating direction method of multipliers (ADMM), we propose a fully distributed synchronization algorithm which has low communication overhead and computation cost. Simulation results show that the proposed algorithm achieves better accuracy than consensus algorithm and the distributed least squares algorithm, and can always converge to the centralized optimal solution.

Channel Sounding and Parameter Estimation for a Wideband Correlation-Based MIMO Model

Previous correlation-based wideband multiple-input-multiple-output (MIMO) channel models have been limited to non-line-of-sight (NLoS) scenarios where simple antenna correlation measurements are sufficient to describe the correlated Gaussian process representing the fading statistics. However, in the presence of line-of-sight (LoS) or specular reflections, simple antenna correlation measurements unfortunately do not lead to accurate fading characterizations. In this paper, we propose a trend-stationary correlation-based analytical model for wideband LoS and NLoS MIMO channels and design and validate a wideband multitone MIMO channel sounder and estimator to, respectively, measure channel impulse responses (CIRs) and estimate channel parameters for this model. Joint maximum-likelihood (ML) estimation of the LoS component and the NLoS complex correlation matrix is presented. In addition to enabling the estimation of the path correlation matrix of a wireless channel in the presence of LoS components, the modeling approach also provides tools to evaluate the validity of the assumption of uncorrelated scattering (US), even in LoS environments, which is commonly used in channel modeling. A more general model that does not assume US is also presented, which can likewise be estimated using the proposed estimator. To validate the channel sounding/model estimator techniques, we employ channel sounding waveforms and collect snapshots from the outputs of a state-of-the-art hardware MIMO channel emulator capable of emulating multipath channels under the US assumption. Receiver signal processing and channel parameter estimation are performed on the collected data, and the results are compared with the emulated channel parameters. The work is unique in that it provides a correlation-based multipath MIMO channel modeling approach that addresses LoS environments, it describes corresponding estimation techniques to extract the full complex correlation matrix, and the model estimators are backed using channel sounding with emulation-based validation.