Linear Prediction

In this paper, the probability distribution functions (pdf's) of the formant spaces of three major accents of the English language, namely, British Received Pronunciation (RP), General American, and Broad Australian, are modeled and compared. The statistical differences across the formant spaces of these accents are employed for accent conversion. An improved formant tracking method, based on linear prediction (LP) feature analysis and a twodimensional hidden Markov model (2-D-HMM) of format trajectories, is used for estimation of the formant trajectories of vowels and diphthongs of each accent. Comparative analysis of the formant spaces of the three accents indicates that these accents are partly conveyed by the differences of the formants of vowels. The estimates of the probability distributions of the formants for each accent are used in a speech synthesis system for accent conversion. Accent synthesis, through modification of the acoustic parameters of speech, provides a means of assessing the perceptual contribution of each formant parameter on conveying an accent. The results of perceptual evaluations of accent conversion illustrate that formants play an important role in conveying accents. Index Terms-Formant, hidden Markov model (HMM), linear prediction (LP).

In this work a new algorithm for multiple emitter direction finding by using a uniform circular array is proposed. The algorithm is based on single snapshot processing, and therefore, it has no restriction on the coherency of the sources. The problem formulation is based on the transformation of the snapshot. The transformed sequence is formed by taking the discrete Fourier transform of the snapshot and weighting it suitably. It contains the so-called distortion terms, which are taken into account by using an iterative correction scheme to improve the estimation accuracy. The convergence is achieved in a few steps, and a significant performance improvement is observed when the distortion terms are taken into account. The proposed bearing estimation algorithm is based on the linear prediction method developed in this study, in which the prediction filter coefficients are found by replacing the weighted data matrix by a specified rank approximation, which is obtained by its singular-value decomposition. The direction of arrival estimates are obtained from the angular locations of the prediction-error filter zeros. It is observed through computer simulations that the algorithm performance is improved as compared to that of the forward-backward linear prediction (FBLP) and the modified FBLP methods by choosing an appropriate rank for the approximating matrix. The root-mean-square errors are close to the CramCr-Rao bounds in most cases, where the aforementioned methods fail to work. @ 1997 Elsevier Science B.V.

The standard conjugate gradient (CG) method uses orthogonality of the residues to simplify the formulas for the parameters necessary for convergence. In adaptive filtering, the sample-by-sample update of the correlation matrix and the cross-correlation vector causes a loss of the residue orthogonality in a modified online algorithm, which, in turn, results in loss of convergence and an increase of the filter quadratic mean error. This letter extends a recently proposed control Liapunov function analysis of the CG method viewed as a dynamic system in the standard feedback configuration to the case of adaptive filtering.

This paper presents a method for lane boundaries detection which is not affected by the shadows, illumination and un-even road conditions. This method is based upon processing grayscale images using local gradient features, characteris-tic spectrum of lanes, and linear prediction. Firstly, points on the adjacent right and left lane are recognized using the local gradient descriptors. A simple linear prediction model is deployed to predict the direction of lane markers. The contribution of this paper is the use of vertical gradient image without converting into binary image(using suitable thre-shold), and introduction of characteristic lane gradient spectrum within the local window to locate the preciselane marking points along the horizontal scan line over the image. Experimental results show that this method has greater tolerance to shadows and low illumination conditions. A comparison is drawn between this method and recent methods reported in the literature.

This paper addresses the design, implementation and evaluation of ecient low bit-rate speech coding algorithms based on an improved sinusoidal model. A series of algorithms were developed for speech classi®cation and pitch frequency determination, modeling of sinusoidal amplitudes and phases, and frame interpolation. An improved paradigm for sinusoidal phase coding is presented, where short-time sinusoidal phases are modeled using a combination of linear prediction, spectral sampling, linear phase alignment and all-pass phase error correction components. A classdependent split vector quantization scheme is used to encode the sinusoidal amplitudes. The masking properties of the human auditory system are eectively exploited in the algorithms. The algorithms were successfully integrated into a 2.4 kbps sinusoidal coder. The performance of the 2.4 kbps coder was evaluated in terms of informal subjective tests such as the mean opinion score (MOS) and the diagnostic rhyme test (DRT), as well as some perceptually motivated objective distortion measures. Performance analysis on a large speech database indicates considerable improvement in short-time signal matching both in the time and the spectral domains. In addition, subjective quality of the reproduced speech is considerably improved. Ó

This article is focused on speech coding methods for achieving communication quality speech at bit rates of 4 kbit/s and lower. The speech coding techniques are based on an all-pole model of the vocal tract which may be implemented in the time domain with appropriately selected excitation functions or else may be fit to a spectral analysis of the speech signal. Three main types of coders are described below. Code-excited linear prediction (CELP) coders select their excitation from waveform codebooks using analysis-by-synthesis closed-loop techniques, which need to be supplemented by speech classification and open-loop parametric techniques for keeping up with quality at lower rates. The prototypical sinusoidal coder (SC) has a bank of oscillators for signal synthesis, driven by a model of the magnitude spectrum. However, phase regeneration is important in enhancing speech reconstruction at low rates. Waveform interpolation (WI) coders afford a wider timefrequency footprint for the representation of the excitation, showing a good potential for achieving toll quality at bit rates below 4 kbit/s.

We present an algorithm for lossy compression of hyperspectral images for implementation on field programmable gate arrays (FPGA). To greatly reduce the bit rate required to code images, we use linear prediction between the bands to exploit the large amount of inter-band correlation. The prediction residual is compressed using the Set Partitioning in Hierarchical Trees algorithm. To reduce the complexity of the predictive encoder, we propose a bit plane-synchronized closed loop predictor that does not require full decompression of a previous band at the encoder. The new technique achieves almost the same compression ratio as standard closed loop predictive coding and has a simpler on-board implementation.

Abstract—We model a segment of filtered speech signal as a product of elementary signals as opposed to a sum of sinusoidal signals. Using this model, one can better appreciate the basic relationships between envelopes and phases or instantaneous frequencies (IF's) of ...

Cet article pr~sente une nouvelle mdthode de codage audionum6rique h faible retard et & d~bit rdduit pour des applications ~mergentes en tdldcommunication telles que l'audioconfgrence ou la vidgoconf(rence. Le codeur dgveloppd permet de traiter des signaux g~n&iques (parole, musique, sons d'accompagnement, sons d'ambiance,...) un d~bit de 64 kbit/s avec un retard de codage et d~codage aux environs de 5 ms dans la bande de fr6quence 20-15000 Hz. Ce codeur s'articule sur une d~composition en sous-bandes du signal d'entrde assocMe g~ un codage de la parole de type LD-r L'introduction d' un modkle psychoacoustique permet de d~terminer le d~bit optimal gt allouer g~ chacune des sous-bandes en fonction des caractdristiques propres de l'audition humaine. Pour satisfaire la demande de ddbit requise par le modkle psychoacoustique et pour rdduire la complexit~ algorithmique induite par cette structure de codage, nous avons prdsentd une nouvelle mdthode de quantification vectorielle bas~e sur les rYseaux rdguliers de points. Cette mdthode pennet de quantifier le signal rdsiduel au sein du codeur LO-CELP sans effectuer de recherche trop complexe du meilleur quantificateur. Des tests objectifs et subjectifs ont dt# r~alisds sur des sYquences sonores critiques utilis~es par l'tso. Des tests formels ont montrY que la qualit6 du codeur proposd est comparable aux meilleures implantations de la norme MPEG-I, touche 11, avec l'avantage, pour la solution propos6e, d'avoir un retard de codage et d6codage beaucoup plus faible (5 ms).

In this paper we present a generalization of the geometry coder by Touma and Gotsman [34] to polygon meshes. We let the polygon information dictate where to apply the parallelogram rule that they use to predict vertex positions. Since polygons tend to be fairly planar and fairly convex, it is beneficial to make predictions within a polygon rather than across polygons. This, for example, avoids poor predictions due to a crease angle between polygons. Up to 90 percent of the vertices can be predicted this way. Our strategy improves geometry compression by 10 to 40 percent depending on (a) how polygonal the mesh is and (b) on the quality (planarity/convexity) of the polygons.

This paper introduces a high-performance concealment algorithm for packetized PCM-coded speech as in ITU-T Recommendation G.711. The proposed prediction algorithm implements a combination of linear prediction model and reverse-order replicated pitch period technique as implemented in the ITU-T G.711 Appendix A (ITUT Recommendation G.117, November 2000). The new algorithm is compared to the ITU-T G.711 Appendix A standard and to the commercial tool of packet repetition. It is shown to produce better concealment quality in almost all cases. ?

This paper describes a robust feature extraction technique for continuous speech recognition. Central to the technique is the minimum variance distortionless response (MVDR) method of spectrum estimation. We consider incorporating perceptual information in two ways: 1) after the MVDR power spectrum is computed and 2) directly during the MVDR spectrum estimation. We show that incorporating perceptual information directly into the spectrum estimation improves both robustness and computational efficiency significantly. We analyze the class separability and speaker variability properties of the features using a Fisher linear discriminant measure and show that these features provide better class separability and better suppression of speaker-dependent information than the widely used mel frequency cepstral coefficient (MFCC) features. We evaluate the technique on four different tasks: an in-car speech recognition task, the Aurora-2 matched task, the Wall Street Journal (WSJ) task, and the Switchboard task. The new feature extraction technique gives lower word-error-rates than the MFCC and perceptual linear prediction (PLP) feature extraction techniques in most cases. Statistical significance tests reveal that the improvement is most significant in high noise conditions. The technique thus provides improved robustness to noise without sacrificing performance in clean conditions. Index Terms-Distortionless response, minimum variance, robust feature extraction for continuous speech recognition, spectral analysis, speech analysis.

This paper discusses six most frequent methods used to extract different features in Electrocardiograph (ECG) signals namely Autoregressive (AR), Wavelet Transform (WT), Eigenvector, Fast Fourier Transform (FFT), Linear Prediction (LP), and Independent Component Analysis (ICA). The study reveals that Eigenvector method gives better performance in frequency domain for the ECG feature extraction. © 2012 IEEE.

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Some useful services in cellular radio networks and also a class of handover algorithms require knowledge of the present position and velocity of mobiles. This paper deals with a method to track mobiles by on-line monitoring of field strength data of surrounding base stations at successive time points. Such data is available in present global system for mobile communication (GSM) systems each 0.48 s and also in code-division multiple-access (CDMA) systems for transmission control. Because of strong random fluctuations of the signals, appropriate smoothing is the key point of the procedure. We develop a locally linear prediction model of successive positions as a basis for Kalman filtering. This approach turns out to be extremely successful, achieving average mislocations of 70 m in simulated test runs. Further improvement is possible by using external geographical information.

Many transform-based compression techniques, such as Fourier, Walsh, Karhunen-Loeve (KL), wavelet, and discrete cosine transform (DCT), have been investigated and devised for electrocardiogram (ECG) signal compression. However, the recently introduced Burrows-Wheeler Transformation has not been completely investigated.

This paper describes a novel spectral envelope estimation technique which adapts to the characteristics of the observed signal. This is possible via the introduction of a second bilinear transformation into warped minimum variance distortionless response (MVDR) spectral envelope estimation. As opposed to the first bilinear transformation, however, which is applied in the time domain, the second bilinear transformation must be applied in the frequency domain. This extension enables the resolution of the spectral envelope estimate to be steered to lower or higher frequencies, while keeping the overall resolution of the estimate and the frequency axis fixed. When embedded in the feature extraction process of an automatic speech recognition system, it provides for the emphasis of the characteristics of speech features that are relevant for robust classification, while simultaneously suppressing characteristics that are irrelevant for classification. The change in resolution may be steered, for each observation window, by the normalized first autocorrelation coefficient.

In this paper, we introduce the one-two descriptor. The one-two descriptors is the sum of the vertex contributions such that each pendant vertex contributes 1, each vertex of degree two adjacent to pendant vertex contributes 2, and each vertex of degree higher than two also contributes 2. We test this descriptor on the benchmark data set of the octane isomers proposed by the International Academy of Mathematical Chemistry. We show that this descriptor is a good predictor of the heat capacity at P constant (CP) and of the total surface area (TSA). Linear model predictions for both these properties are better then predictions of any of the benchmark descriptors proposed by International Academy of Mathematical Chemistry. Linear model predictions of TSA are also better then predictions of any of Adriatic descriptors, while linear model predictions of CP are not as good as predictions by Adriatic descriptor called inverse sum lordeg index. We also analyze the mathematical properties of this descriptor and we find tight upper and lower bounds in the families of the trees with n vertices and the chemical trees with n vertices.

In this paper we consider the problem of building a linear prediction model when the number d of candidate covariates is large and the data possibly contains anomalies that are difficult to visualize and clean. We aim at predicting the non-outlying cases. Therefore, we need a method that is robust and scalable at the same time.

This thesis deals with developing improved techniques for speech coding based on the recent developments in sparse signal representation. In particular, this work is motivated by the need to address some of the limitations of the wellknown linear prediction (LP) model currently applied in many modern speech coders. In the first part of the thesis, we provide an overview of Sparse Linear Prediction, a set of speech processing tools created by introducing sparsity constraints into the LP framework. This approach defines predictors that look for a sparse residual rather than a minimum variance one with direct applications to coding but also consistent with the speech production model of voiced speech, where the excitation of the all-pole filter can be modeled as an impulse train, i.e., a sparse sequence. Introducing sparsity in the LP framework will also bring to develop the concept of high-order sparse predictors. These predictors, by modeling efficiently the spectral envelope and the harmonics components with very few coefficients, have direct applications in speech processing, engendering a joint estimation of short-term and long-term predictors. We also give preliminary results of the effectiveness of their application in audio processing. The second part of the thesis deals with introducing sparsity directly in the linear prediction analysis-by-synthesis (LPAS) speech coding paradigm. We first propose a novel near-optimal method to look for a sparse approximate excitation using a compressed sensing formulation. Furthermore, we define a novel re-estimation procedure to adapt the predictor coefficients to the given sparse excitation, balancing the two representations in the context of speech coding. Finally, the advantages of the compact parametric representation of a segment of speech, given by the sparse linear predictors and the use of the reestimation procedure, are analyzed in the context of frame independent coding for speech communications over packet networks.

In this paper, we define an algorithm with low complexity which performs a new use of the linear prediction analysis (covariance method) to retrieve the maximum-phase component of speech signals. First, we study the mixed-phase model of speech through a new representation named the Zeros of Z-Transform (ZZT) in the z-plane, which is an all-zero representation of the ztransform of a discrete time signal. Then, based on the properties of the mixed-phase model, we introduce an algorithm to estimate the anticausal glottal flow component from speech signals. LP-covariance analysis is used to estimate a pole pair outside the unit circle corresponding to the anticausal poles of the source signal component in the mixed-phase speech model. Given the pair of anticausal poles, a procedure to resynthesize the anticausal part of the glottal flow, and then an open quotient estimation method, are proposed. Evaluations show that the method is high quality for analyzing synthetic speech but lacks robustness in analysis of natural speech.

This paper presents lossless compression schemes for ECG signals based on neural network predictors and entropy encoders. Decorrelation is achieved by nonlinear prediction in the first stage and encoding of the residues is done by using lossless entropy encoders in the second stage. Different types of lossless encoders, such as Huffman, arithmetic, and runlength encoders, are used. The performances of the proposed neural network predictor-based compression schemes are evaluated using standard distortion and compression efficiency measures. Selected records from MIT-BIH arrhythmia database are used for performance evaluation. The proposed compression schemes are compared with linear predictor-based compression schemes and it is shown that about 11% improvement in compression efficiency can be achieved for neural network predictor-based schemes with the same quality and similar setup. They are also compared with other known ECG compression methods and the experimental results show that superior performances in terms of the distortion parameters of the reconstructed signals can be achieved with the proposed schemes.

The standard conjugate gradient (CG) method uses orthogonality of the residues to simplify the formulas for the parameters necessary for convergence. In adaptive filtering, the sample-by-sample update of the correlation matrix and the cross-correlation vector causes a loss of the residue orthogonality in a modified online algorithm, which, in turn, results in loss of convergence and an increase of the filter quadratic mean error. This letter extends a recently proposed control Liapunov function analysis of the CG method viewed as a dynamic system in the standard feedback configuration to the case of adaptive filtering.

Representations and statistical properties of the process F defined by F,+l = A(E, + E,), are given. Here X(u): = Ub. sign(u) + m and {En}:z is Gaussian white noise. The process E represents the binary quantizer error in a model for single-loop Sigma-Delta modulation. The innovations variables are found and the existence and uniqueness of an invariant probability measure, ergodicity properties, as well as the existence of the exponential moment with respect to the invariant probability are proved using Markov process theory. We consider also E as a random perturbation, for small values of the variance of En, of the orbits of sn+l = X(sn). Here sn has the uniform invariant distribution on the interval [mb, m + b]. Analytical approximations to the structure of the power spectrum of F are obtained using a linear prediction in terms of the innovations variables and the perturbation approach.

We consider the on-line predictive version of the standard problem of linear regression; the goal is to predict each consecutive response given the corresponding explanatory variables and all the previous observations. We are mainly interested in prediction intervals rather than point predictions. The standard treatment of prediction intervals in linear regression analysis has two drawbacks: (1) the classical prediction intervals guarantee that the probability of error is equal to the nominal significance level ǫ, but this property per se does not imply that the long-run frequency of error is close to ǫ; (2) it is not suitable for prediction of complex systems as it assumes that the number of observations exceeds the number of parameters. We state a general result showing that in the on-line protocol the frequency of error for the classical prediction intervals does equal the nominal significance level, up to statistical fluctuations. We also describe alternative regression models in which informative prediction intervals can be found before the number of observations exceeds the number of parameters. One of these models, which only assumes that the observations are independent and identically distributed, is popular in machine learning but greatly underused in the statistical theory of regression.

Let X X T 2 3 w x C be a positive hermitian X P 0 matrix-valued function on the bitorus with T 2 log det X b ÀI and T 2 kXk`I. Then X is the v 1-limit of p j p à j , where p j is a x  x j rectangular bi-analytic matrix function. A continuous and strictly positive hermitian X X T 2 3 w x may be factored as pp à with p an x  I analytic operator function.

In this paper an audio coding scheme based on the Empirical Mode Decomposition (EMD) in association with the Hilbert transform is presented. The audio signal is decomposed adaptively into intrinsic oscillatory components by EMD called Intrinsic Mode Functions (IMFs) and the associated instantaneous amplitudes and the instantaneous phases calculated. The basic principle of the proposed approach consists in encoding the instantaneous amplitudes and the instantaneous phases. The decoder recovers the original signal after IMFs reconstruction by demodulation, and their summation. The compression method is applied to different audio signals, and results compared to MP3 and to wavelet approaches.

This paper describes and discusses the 'STBU' speaker recognition system, which performed well in the NIST Speaker Recognition Evaluation 2006 (SRE). STBU is a consortium of 4 partners: Spescom DataVoice (South Africa), TNO (The Netherlands), BUT (Czech Republic) and University of Stellenbosch (South Africa). The STBU system was a combination of three main kinds of subsystems: (1) GMM, with shorttime MFCC or PLP features, (2) GMM-SVM, using GMM mean supervectors as input to an SVM, and (3) MLLR-SVM, using MLLR speaker adaptation coefficients derived from an English LVCSR system. All subsystems made use of supervector subspace channel compensation methods-either eigenchannel adaptation or nuisance attribute projection. We document the design and performance of all subsystems , as well as their fusion and calibration via logistic regression. Finally, we also present a cross-site fusion that was done with several additional systems from other NIST SRE-2006 participants.

In this paper a new method, based on linear prediction, is proposed for wind speed forecasting. The method utilizes the 'linear prediction' method in conjunction with 'filtering' of the wind speed waveform. The filtering eliminates the undesired parts of the frequency spectrum (i.e. smoothing) of the measured wind speed which is less effective in an application, for example, in a wind energy conversion system. The linear prediction method is intuitively explained with some easy to follow case studies to clarify the complex underlying mathematics. For verification purposes, the proposed method is compared with real wind speed data based on experimental results. The results show the effectiveness of the linear prediction method.

This paper presents and evaluates an inverse filtering technique of the speech signal which is based on the Stabilized Weighted Lin-ear Prediction (SWLP) of speech [1]. SWLP emphasizes the speech samples that fit the underlying speech production model well, by imposing temporal weighting of the square of the residual signal. The performance of SWLP is compared to the conventional Linear Prediction based inverse filtering techniques, such as the Autocorre-lation and Closed Phase Covariance method. All the inverse filtering approaches are evaluated on a database of speech signals generated by a physical model of the voice production system. Results show that the estimated glottal flows using SWLP are closer to the original glottal flow than those estimated by the Autocorrelation approach, while its performance is comparable to the Closed Phase Covariance approach.

This article is focused on speech coding methods for achieving communication quality speech at bit rates of 4 kbit/s and lower. The speech coding techniques are based on an all-pole model of the vocal tract which may be implemented in the time domain with appropriately selected excitation functions or else may be fit to a spectral analysis of the speech signal. Three main types of coders are described below. Code-excited linear prediction (CELP) coders select their excitation from waveform codebooks using analysis-by-synthesis closed-loop techniques, which need to be supplemented by speech classification and open-loop parametric techniques for keeping up with quality at lower rates. The prototypical sinusoidal coder (SC) has a bank of oscillators for signal synthesis, driven by a model of the magnitude spectrum. However, phase regeneration is important in enhancing speech reconstruction at low rates. Waveform interpolation (WI) coders afford a wider timefrequency footprint for the representation of the excitation, showing a good potential for achieving toll quality at bit rates below 4 kbit/s.

This paper reports on the specific contribution of the Wavelet Transform (WT) in the TCX coding model for audio signals. TCX, or "Transform Coded excitation", is a frame based coding algorithm that uses both time domain (linear prediction) and frequency domain (transform coding) approaches to exploit signal redundancies as well as frequency masking. While previous work on TCX used the Discrete Fourier Transform (DFI'), the quality for highly non-stationary signals such as percussions was less than satisfactory. The WT has: therefore been investigated as a compromise between time and frequency resolution.

An artificial neural network (ANN) based helicopter identification system is proposed. The feature vectors are based on both the tonal and the broadband spectrum of the helicopter signal. ANN pattern classifiers are trained using various parametric spectral representation techniques. Specifically, linear prediction, reflection coefficients, cepstrum, and line spectral frequencies (LSF) are compared in terms of recognition accuracy and robustness against additive noise. Finally, an 8-helicopter ANN classifier is evaluated, It is also shown that the classifier performance is dramatically improved if it is trained using both clean data and data corrupted with additive noise.

In this paper, we propose a method of estimating the reflection coefficients of an adaptive lattice filter. In this method, conventional adaptive algorithms, for example, the normalized least mean square (NLMS) algorithm, are used for the estimation. In general, the reflection coefficients are estimated as cross-correlation coefficients between forward and backward prediction errors in each stage of the adaptive lattice filter. Accordingly, two divisions in each stage, and effectively doubling the number of stages, are required. A problem is that the processing cost of division is higher than that of multiplication, especially in cheap digital signal processors (DSPs). Hence, the reduction of the number of divisions is strongly desired in practical use. The proposed technique can decrease the number of divisions to one, provided that the NLMS algorithm is used. Moreover, in the application of the adaptive lattice filter, system identification is also important. In this paper, we present a technique for the application. The technique is derived from the proposed method.

This paper describes the study on example selection in regression problems using µ-SVM (Support Vector Machine) linear as prediction algorithm. The motivation case is a study done on real data for a problem of bus trip time prediction. In this study we use three different training sets: all the examples, examples from past days similar to the day where prediction is needed, and examples selected by a CART regression tree. Then, we verify if the CART based example selection approach is appropriate on different regression data sets. The experimental results obtained are promising.

Two distinct two-class pattern recognition problems are studied, namely, the detection of male subjects who are diagnosed with vocal fold paralysis against male subjects who are diagnosed as normal and the detection of female subjects who are suffering from vocal fold edema against female subjects who do not suffer from any voice pathology. To do so, utterances of the sustained vowel "ah" are employed from the Massachusetts Eye and Ear Infirmary database of disordered speech. Linear prediction coefficients extracted from the aforementioned utterances are used as features. The receiver operating characteristic curve of the linear classifier, that stems from the Bayes classifier when Gaussian class conditional probability density functions with equal covariance matrices are assumed, is derived. The optimal operating point of the linear classifier is specified with and without reject option. First results using utterances of the "rainbow passage" are also reported for completeness. The reject option is shown to yield statistically significant improvements in the accuracy of detecting the voice pathologies under study.

A new hybrid PSO-EA-DEPSO algorithm based on particle swarm optimization (PSO), evolutionary algorithm (EA), and differential evolution (DE) is presented for training a recurrent neural network (RNN) for multiple-input multiple-output (MIMO) channel prediction. This algorithm is shown to outperform RNN predictors trained off-line by PSO, EA, and DEPSO as well as a linear predictor trained by the Levinson-Durbin algorithm. To explore the effects of channel prediction error at the receiver, new expressions for the received SNR, array gain, and average probability of error are derived and analyzed. These expressions differ from previous results which assume the prediction error is Gaussian and/or independent of the true CSI. The array gain decays with increasing signal-to-noise ratio and is slightly larger for spatially correlated systems. As the prediction error increases in the non-saturation region, the coding gain decreases and the diversity gain remains unaffected.

In the context of randomized clinical trials, multiplicity arises in many forms. One prominent example is when a key endpoint is measured and analyzed both at baseline and after treatment. It is common to analyze each separately, but more efficient to adjust the post-treatment comparisons for the baseline values. Adjustment techniques generally treat the covariate (baseline value, in this case) as either nominal or continuous. Either is problematic when applied to an ordinal covariate, the former because it fails to exploit the natural ordering and the latter because it relies on an artifical notion of linear prediction and differences between values. We propose new methods for adjusting for ordinal covariates without having to treat them as nominal or continuous. Specifically, the information-preserving composite endpoint consists of the pair of values for each patient, one at baseline and one after treatment. Some of these patterns will indicate more improvement than others, yet some pairs of patterns are not comparable. Hence, the ordering is only partial. We develop an approach to testing and deriving estimators of magnitudes of the treatment effect based on comparing each observation in one group to each observation in the other group to which it is comparable.

A variable step-size is necessary in the least-meansquare (LMS) algorithm to achieve both fast convergence and a small final excess mean-square estimation error. As a well-studied area, many variations of the LMS algorithm with variable stepsizes have been proposed in the literature. A common point in these algorithms is that the step-size is computed according to some pre-specified formulas with preset control parameters, and therefore the generated step-size is a predetermined constant at each single time point. In this paper, we propose a novel parameter-free step-size adjustment approach, in which the stepsize is viewed as a variable, and rechosen at each new time point to minimize a least-squares cost function. Experiments for the linear prediction of random processes show the effectiveness of the proposed approach in rapidly driving the mean-square estimation error to a small final steady-state value. The most significant feature of the new approach is that no control parameters need to be set in advance.