Factorability of lossless time-varying filters and filter banks

We study the factorability of linear time-varying (LTV) lossless filters and filter banks. We give a complete characterization of all, degree-one lossless LTV systems and show that all degree-one lossless systems can be decomposed into a time-dependent unitary matrix followed by a lossless dyadic-based LTV system. The lossless dyadic-based system has several properties that make it useful in the factorization of lossless LTV systems. The traditional lapped orthogonal transform (LOT) is also generalized to the LTV case. We identify two classes of TVLOTs, namely, the invertible inverse lossless (IIL) and noninvertible inverse lossless (NIL) TVLOTs. The minimum number of delays required to implement a TVLOT is shown to be a nondecreasing function of time, and it is a constant if and only if the TVLOT is IIL. We also show that all IIL TVLOTs can be factorized uniquely into the proposed degree-one lossless building block. The factorization is minimal in terms of the delay elements. For NIL TVLOTs, there are factorable and unfactorable examples. Both necessary and sufficient conditions for the factorability of lossless LTV systems are given. We also introduce the concept of strong eternal reachability (SER) and strong eternal observability (SEO) of LTV systems. The SER and SEO of an implementation of LTV systems imply the minimality of the structure. Using these concepts, we are able to show that the cascade structure for a factorable IIL LTV system is minimal. That implies that if a IIL LTV system is factorable in terms of the lossless dyadic-based building blocks, the factorization is minimal in terms of delays as well as the number of building blocks. We also prove the BIBO stability of the LTV normalized IIR lattice     

Adaptive blind source separation of multiple-input multiple-output linearly time-varying FIR system

A new adaptive blind separation scheme for sources mixed by a multiple-input multiple-output (MIMO) linearly time-varying (LTV) FIR system is proposed. First, by dividing measured samples into a series of short segments, time-varying coefficients of the mixing system are approximated by polynomials in time over each segment. Then, a two-step BSS scheme is presented for the approximated system. The first step is to estimate the time variation and convolution effects of the mixing system, and reduce the LTV-FIR mixing system to a linearly time-invariant (LTI) instantaneous system using the conventional input/output system identification scheme. The second step uses the mutual independence knowledge of the sources to further separate the sources from the LTI instantaneous system. The theoretical and experimental studies show that the new BSS scheme has an improved performance in separating sources mixed by an LTV-FIR system.     

On the mobile‐to‐mobile linear time‐variant shallow‐water acoustic channel response

We expose some concepts concerning the channel impulse response (CIR) of linear time‐varying (LTV) channels to give a proper characterization of the mobile‐to‐mobile underwater channel. We find different connections between the linear time‐invariant (LTI) CIR of the static channel and 2 definitions of LTV CIRs of the dynamic mobile‐to‐mobile channel. These connections are useful to design a dynamic channel simulator from the static channel models available in the literature. Such feature is particularly interesting for overspread channels, which are hard to characterize by a measuring campaign. Specifically, the shallow water acoustic (SWA) channel is potentially overspread because of the signal low velocity of propagation, which prompts long delay spread responses and great Doppler effect. Furthermore, from these connections between the LTI static CIRs and the LTV dynamic CIRs, we find that the SWA mobile‐to‐mobile CIR does not only depend on the relative speed between transceivers, but also on the absolute speed of each of them referred to the velocity of propagation. Nevertheless, publications about this topic do not consider it and formulate their equations in terms of the relative speed between transceivers. We illustrate our find using 2 couples of examples where, even though the relative speed between the mobiles is the same, their CIRs are not.     

A new normalized relatively stable lattice structure

This paper proposes a new lattice filter structure that has the following properties. When the filter is linear time invariant (LTI), it is equivalent to the celebrated Gray-Markel lattice. When the lattice parameters vary with time, it sustains arbitrary rates of time variations without sacrificing a prescribed degree of stability, provided that the lattice coefficients are magnitude bounded in a region where all LTI lattices have the same degree of stability. We also show that the resulting LTV lattice obeys an energy contraction condition. This structure thus generalizes the normalized Gray-Markel lattice, which has similar properties but only with respect to stability as opposed to relative stability     

Representations of Linear Dual-Rate System Via Single SISO LTI Filter, Conventional Sampler and Block Sampler

In this brief, it is proved that a linear dual-rate system can be represented via a series cascade of: 1) a conventional expander, a single-input single-output (SISO) linear time-invariant (LTI) filter and a block decimator, or 2) a block expander, an SISO LTI filter and a conventional decimator. Hence, incompatible nonuniform filter banks could achieve perfect reconstruction via LTI filters, conventional samplers and block samplers without expanding the input-output dimension of a subsystem of linear dual-rate systems or converting the nonuniform filter banks to uniform filter banks. The main advantage of the proposed representations is to avoid complicated design of the circuit layout caused by connecting subsystems with large input-output dimension or a lot of subsystems together.     

On compensating nonlinear distortions of an OFDM system using anefficient adaptive predistorter

This paper presents an efficient adaptive predistortion technique compensating for nonlinear distortions caused by a high-power amplifier (HPA) cascaded with a linear filter in an OFDM system. In the proposed approach, the memoryless HPA, preceded by a linear filter with memory in OFDM systems, is modeled by the Wiener system, which is then precompensated by the proposed adaptive predistorter with a minimum number of filter taps. It is confirmed by computer simulation that the proposed approach produces a faster convergence speed than the previous adaptive predistortion technique, and provides a small output backoff as low as 5.5 dB for an OFDM system employing an HPA with a linear filter     

Statistical pulse compression

The seismic method in petroleum exploration is an echo-location technique to detect interfaces between the subsurface sedimentary layers of the earth. The received seismic reflection record (field trace), in general, may be modeled as a linear time-varying (LTV) system. However, in order to make the problem tractable, we do not deal with the entire field trace as a single unit, but instead subdivide it into time gates. For any time gate on the trace, there is a corresponding vertical section of rock layers within the earth, such that the primary (direct) reflections from these layers all arrive within the gate. Each interface between layers is characterized by a local (or Fresnel) reflection coefficient, which physically must be less than unity in magnitude. Under the hypothesis that the vertical earth section has small reflection coefficients, then within the corresponding time gate the LTV model of the seismic field trace reduces to a linear time-invariant (LTI) system. This LTI system, known as the convolutional model of the seismic trace, says that the field trace is the convolution of a seismic wavelet with the reflection coefficient series. If, in addition, the reflection coefficient series is white, then all the spectral shape of the trace within the gate can be attributed to the seismic wavelet. Thus the inverse wavelet can be computed as the prediction error operator (for unit prediction distance) by the method of least squares. The convolution of this inverse wavelet with the field trace yields the desired reflection coefficients. This statistical pulse compression method, known as predictive deconvolution with unit prediction distance, is also called spike deconvolution. Alternatively, predictive deconvolution with greater prediction distance can be used, and it is known as gapped deconvolution. Other pulse compression methods used in seismic processing are signature deconvolution, wavelet processing, and minimum entropy deconvolution.     

LTV controller design for vehicle lateral control under fault in rear sensors

This work focuses on vehicle lateral control for automated highway systems (AHSs) studied as a part of the California Partners for Advanced Transit and Highways (PATH) Program. In the PATH lateral control system, magnetometers are installed under both front and rear bumpers of the vehicle; these magnetometers measure the lateral deviation of the vehicle relative to the magnets buried along the centerline of each automated lane. Lateral controllers have been designed and tested successfully provided that there is no fault in magnetometers. It has been argued that these controllers are NOT tolerant to the fault in magnetometers. The focus of This work is the degraded-mode lateral control under fault in rear magnetometers. The aim of the controller design is to accomplish adequate performance with the remaining set of magnetometers, the front magnetometers. The effects of the fault are examined, and the significance of the linear time-varying (LTV) property of the front-magnetometer-based vehicle lateral dynamics is recognized. Popular control methods for LTV systems generally involve gain scheduling by switching between several linear time-invariant (LTI) controllers. Such methods are complicated and it is difficult to prove the stability of the switching mechanism. To derive a simple effective LTV controller, feedback linearization is applied to approximately cancel out the time-varying terms in the plant and to function as a gain scheduler. However, due to the weakly damped zeroes of the plant, feedback linearization with state feedback or matched observer state feedback results in weakly damped internal dynamics. In order to tune the internal dynamics, a mismatched observer is designed based on H-infinity optimal control techniques. Experimental results are presented to show the effectiveness of the controller design.     

A New Digital Echo Canceler for Two-Wire Full-Duplex Data Transmission

A new approach to echo canceling for two-wire fullduplex data transmission is proposed. The canceling signal is directly synthesized from the binary data, using a transversal filter approach, and the usual multiplications are replaced by additions and subtractions, thus allowing efficient operation of a large number of taps as required for the canceling of distant echoes. As a specific application, a system processing one sample per baud is discussed where timing signals at both communicating stations are assumed to be synchronized. A stochastic adjustment gradient-type algorithm is used for both training and adaptive tracking of the canceler. It is shown that convergence does not depend on intersymbol interference, timing phase, carrier phase, or the energy ratio of the local to the received signal, but is a function only of the number of taps. Convergence time is proportional to that number, and the optimum step size for fastest convergence is equal to the reciprocal of the number of taps. The residual fluctuation noise is proportional to that part of the mean-square (MS) error which cannot be reduced by the canceler and is a simple function of the product of the tap signal and the step size. The predicted convergence properties are verified by simulation results. Finally, it is shown how such an echo canceler might be used to allow two-wire full-duplex transmission for data rates as high as 4800 bit/s.     

GPS空时自适应阵列干扰仿真研究

在分析了GPS空时自适应处理(STAP)抗干扰技术的基本原理与自适应时域滤波器带宽特性的基础上,提出了可大幅度减少对抗STAP所需干扰源数量的方法。仿真试验表明,对于天线单元为M,延时抽头数为N的STAP,如果全部采用窄带干扰信号,所需干扰源的数量约等于N(M-1)+1;如果采用宽带干扰信号,则有效对抗STAP所需的干扰源数量仅等于阵列单元数M。     

Adaptive channel partitioning and modulation for linear time-varying channels

We present a novel channel partitioning and modulation technique for linear time-varying (LTV) channels using adaptive bases of localized complex exponentials. We show that localized complex exponentials are approximate eigenfunctions of underspread LTV channels. A basis of localized complex exponentials that approximately diagonalizes the LTV channel is selected adaptively by the receiver during a training period. The basis selection process is equivalent to matching the support intervals of the localized complex exponentials to the rate of the channel time variation. The receiver sends information regarding the selected basis to the transmitter which modulates the subsequent data stream in this basis. The adaptive modulation technique performs significantly better than conventional orthogonal frequency-division multiplexing systems for rapidly varying LTV channels such as time-frequency-selective mobile radio channels.     

Adaptive bit rate maximizing time-domain equalizer design for DMT-based systems

The classical discrete multitone receiver as used in, e.g., digital subscriber line (DSL) modems, combines a channel shortening time-domain equalizer (TEQ) with one-tap frequency-domain equalizers (FEQs). In a previous paper, the authors proposed a nonlinear bit rate maximizing (BM) TEQ design criterion and they have shown that the resulting BM-TEQ and the closely related BM per-group equalizers (PGEQs) approach the performance of the so-called per-tone equalizer (PTEQ). The PTEQ is an attractive alternative that provides a separate complex-valued equalizer for each active tone. In this paper, the authors show that the BM-TEQ and BM-PGEQ, despite their nonlinear cost criterion, can be designed adaptively, based on a recursive Levenberg-Marquardt algorithm. This adaptive BM-TEQ/BM-PGEQ makes use of the same second-order statistics as the earlier presented recursive least-squares (RLS)-based adaptive PTEQ. A complete range of adaptive BM equalizers then opens up: the RLS-based adaptive PTEQ design is computationally efficient but involves a large number of equalizer taps; the adaptive BM-TEQ has a minimal number of equalizer taps at the expense of a larger design complexity; the adaptive BM-PGEQ has a similar design complexity as the BM-TEQ and an intermediate number of equalizer taps between the BM-TEQ and the PTEQ. These adaptive equalizers allow us to track variations of transmission channel and noise, which are typical of a DSL environment.     

Fourier series based nonminimum phase model for statistical signalprocessing

In this paper, a parametric Fourier series based model (FSBM) for or as an approximation to an arbitrary nonminimum-phase linear time-invariant (LTI) system is proposed for statistical signal processing applications where a model for LTI systems is needed. Based on the FSBM, a (minimum-phase) linear prediction error (LPE) filter for amplitude estimation of the unknown LTI system together with the Cramer-Rao (CR) bounds is presented. Then, an iterative algorithm for obtaining the optimum LPE filter with finite data is presented that is also an approximate maximum-likelihood algorithm when data are Gaussian. Then three iterative algorithms using higher order statistics (HOS) with finite non-Gaussian data are presented to estimate parameters of the FSBM followed by some simulation results as well as some experimental results with real speech data to support the efficacy of the proposed algorithms using the FSBM. Finally, we draw some conclusions     

The relationship between tapped delay-line and FFT processing inadaptive arrays

The use of fast Fourier transform (FFT) processing behind the elements in adaptive arrays is often considered as a means of improving the nulling bandwidth of such arrays. However, it is shown that the output signal-to-interference-plus-noise ratio obtained from an adaptive array with FFTs behind the elements is identical to that of an equivalent adaptive array with tapped delay-line processing. The equivalent tapped delay-line array has the same number of taps in each delay line as the number of time samples in the FFTs, and has a delay between taps equal to the delay between samples in the FFTs. Thus, while the bandwidth performance of an adaptive array can be improved by using time-delayed samples of each element signal, no further improvement results from taking FFTs of these sampled signals. The same bandwidth performance is obtained by simply weighting and combining the time-domain samples directly     

Convergence properties of optimal adaptive carrier phase jitterpredictors 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     

Adaptive-FRESH Filters for Compensation of Cycle-Frequency Errors

This paper deals with the problem of uncertainties in the periodicities of linear almost-periodically time-variant (LAPTV) filters. These filters are usually implemented as a set of branches, each consisting of a frequency shifter followed by a linear time-invariant (LTI) filter. This implementation is also known as FRESH filters. This paper is motivated by the fact that, when there exist errors in the frequency shifts, the optimum set of LTI filters is obtained by canceling the outputs of the corresponding branches. The purpose of this paper is to analyze the nonstationary behavior of adaptive filters in order to mitigate this problem. Our results show that an adaptive filter can offset the errors in the frequency shifts. The reason is that the coefficients of the adaptive filter are updated so that the filter actually performs as a linear periodically time-variant filter for each branch. This allows to track the errors in the frequency shifts when the rate of convergence of the adaptive algorithm is suitably selected. An analytical study of the convergence is presented, which allows to compute the optimal rate of convergence and the mean squared-error attained by the adaptive filter.     

Real-valued maximum likelihood decoder for quasi-orthogonal space-time block codes

In this letter, we propose a low complexity Maximum Likelihood (ML) decoding algorithm for quasi-orthogonal space-time block codes (QOSTBCs) based on the real-valued lattice representation and QR decomposition. We show that for a system with rate r = n_s/T, where n_s is the number of transmitted symbols per T time slots; the proposed algorithm decomposes the original complex-valued system into a parallel system with n_s 2 × 2 real-valued components, thus allowing for a simple joint decoding of two real symbols. For a square QAM constellation with L points (L-QAM), this algorithm achieves full diversity by properly incorporating two-dimensional rotation using the optimal rotation angle and the same rotating matrix for any number of transmit antennas (N ⩾4). We show that the complexity gain becomes greater when N or L becomes larger. The complexity of the proposed algorithm is shown to be linear with the number of transmitted symbols n_s.     

Application of Fast Kalman Estimation to Adaptive Equalization

Very rapid initial convergence of the equalizer tap coefficients is a requirement of many data communication systems which employ adaptive equalizers to minimize intersymbol interference. As shown in recent papers by Godard, and by Gitlin and Magee, a recursive least squares estimation algorithm, which is a special case of the Kalman estimation algorithm, is applicable to the estimation of the optimal (minimum MSE) set of tap coefficients. It was furthermore shown to yield much faster equalizer convergence than that achieved by the simple estimated gradient algorithm, especially for severely distorted channels. We show how certain "fast recursive estimation" techniques, originally introduced by Morf and Ljung, can be adapted to the equalizer adjustment problem, resulting in the same fast convergence as the conventional Kalman implementation, but with far fewer operations per iteration (proportional to the number of equalizer taps, rather than the square of the number of equalizer taps). These fast algorithms, applicable to both linear and decision feedback equalizers, exploit a certain shift-invariance property of successive equalizer contents. The rapid convergence properties of the "fast Kalman" adaptation algorithm are confirmed by simulation.     

Blind identification of linear subsystems of LTI-ZMNL-LTI modelswith cyclostationary inputs

Discrete-time nonlinear models consisting of two linear time invariant (LTI) filters separated by a finite-order zero memory nonlinearity (ZMNL) of the polynomial type (the LTI-ZMNL-LTI model) are appropriate in a large number of practical applications. We discuss some approaches to the problem of blind identification of such nonlinear models, It is shown that for an Nth-order nonlinearity, the (possibly non-minimum phase) finite-memory linear subsystems of LTI-ZMNL and LTI-ZMNL-LTI models can be identified using the N+1th-order (cyclic) statistics of the output sequence alone, provided the input is cyclostationary and satisfies certain conditions. The coefficients of the ZMNL are not needed for identification of the linear subsystems and are not estimated. It is shown that the theory presented leads to analytically simple identification algorithms that possess several noise and interference suppression characteristics     

A low complexity reduced-rank MMSE receiver for DS/CDMA communications

The minimum mean squared error (MMSE) receiver is a linear filter which can achieve optimal near-far resistance in direct-sequence code-division multiple-access communications. However, one of the main problems of this receiver is the required number of filter taps, which is typically large. This is especially true in systems with a large processing gain in which case the receiver's computation burden becomes very high. As a result, methods for reducing the complexity of the MMSE receiver have been of great interest in recent years. We propose an efficient partitioned MMSE receiver based on a classification algorithm. It is shown that the computational complexity (in terms of the filter taps) of the proposed receiver can be reduced significantly while good performance is maintained. Based on the special structure of our proposed receiver, we also propose a release-merge adaptive partition algorithm which can update the partition and the receiver's coefficients simultaneously. In particular, it is demonstrated that the proposed receiver can perform much better than previously proposed reduced-rank MMSE receivers, such as the partial despreading MMSE receiver and the cyclically shifted filter bank receiver, with even a smaller number of taps.