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The maximally flat variable-delay (VD) digital filter can be derived by using the discrete-Pascal-transform (DPT) and the DPT-based Pascal-polynomial interpolation. In this paper, we develop an efficient structure for the low-complexity and high-modularity implementation of this Pascal-type VD filter. As compared to other existing filter structures, this new structure greatly reduces the multiplication operations required in the filtering process. Roughly speaking, the proposed new structure can reduce the multiplication operations by almost one-third. Thus, this new filter structure has the lowest filter complexity among all the existing filter structures for the implementation of the maximally flat VD filter. As a result, signal interpolation can be efficiently performed through utilizing this new filter structure. As opposed to other existing structure with transient problem, we will show that the proposed new structure does not involve any transient problem. That is, it is a transient-free structure. Consequently, the proposed new filter structure can achieve more accurate signal-interpolation results than other structures that have the transient problem. Finally, we show that this proposed structure also has high modularity and it is suited for modularized hardware implementation. [ABSTRACT FROM PUBLISHER]

The unceasing demand for continuous situational awareness calls for innovative and large-scale signal processing algorithms, complemented by collaborative and adaptive sensing platforms to accomplish the objectives of layered sensing and control. Towards this goal, the present paper develops a spline-based approach to field estimation, which relies on a basis expansion model of the field of interest. The model entails known bases, weighted by generic functions estimated from the field's noisy samples. A novel field estimator is developed based on a regularized variational least-squares (LS) criterion that yields finite-dimensional (function) estimates spanned by thin-plate splines. Robustness considerations motivate well the adoption of an overcomplete set of (possibly overlapping) basis functions, while a sparsifying regularizer augmenting the LS cost endows the estimator with the ability to select a few of these bases that “better” explain the data. This parsimonious field representation becomes possible, because the sparsity-aware spline-based method of this paper induces a group-Lasso estimator for the coefficients of the thin-plate spline expansions per basis. A distributed algorithm is also developed to obtain the group-Lasso estimator using a network of wireless sensors, or, using multiple processors to balance the load of a single computational unit. The novel spline-based approach is motivated by a spectrum cartography application, in which a set of sensing cognitive radios collaborate to estimate the distribution of RF power in space and frequency. Computer simulations and tests on real data corroborate that the estimated power spectrum density atlas yields the desired RF state awareness, since the maps reveal spatial locations where idle frequency bands can be reused for transmission, even when fading and shadowing effects are pronounced. [ABSTRACT FROM PUBLISHER]

This paper presents an analysis of the performance and behavior of a blind adaptive carrier phase offset recovery scheme based on dispersion minimization (DM). The algorithm, called the DM-derotator, is a kind of simple equalizer that attempts to correct the carrier phase offset by minimizing the dispersion of the projection of the real part of the (complex) data signal. The recent application of this algorithm to digital broadcasting signals motivates our analysis. This paper classifies the stationary points of the DM-derotator for a variety of source signals including digital vestigial side band (VSB) and quadrature amplitude modulation (QAM) and discusses initialization strategies. The analysis is extended to a variety of situations including i) its behavior in the presence of intersymbol interference, ii) its behavior when there is statistical dependence between the in-phase and quadrature components, and iii) its tracking ability. [ABSTRACT FROM AUTHOR]

Hyperspectral unmixing (HU) is a crucial signal processing procedure to identify the underlying materials (or endmembers) and their corresponding proportions (or abundances) from an observed hyperspectral scene. A well-known blind HU criterion, advocated by Craig during the early 1990s, considers the vertices of the minimum-volume enclosing simplex of the data cloud as good endmember estimates, and it has been empirically and theoretically found effective even in the scenario of no pure pixels. However, such kinds of algorithms may suffer from heavy simplex volume computations in numerical optimization, etc. In this paper, without involving any simplex volume computations, by exploiting a convex geometry fact that a simplest simplex of N vertices can be defined by N associated hyperplanes, we propose a fast blind HU algorithm, for which each of the N hyperplanes associated with the Craig’s simplex of N vertices is constructed from N-1 affinely independent data pixels, together with an endmember identifiability analysis for its performance support. Without resorting to numerical optimization, the devised algorithm searches for the N(N-1) active data pixels via simple linear algebraic computations, accounting for its computational efficiency. Monte Carlo simulations and real data experiments are provided to demonstrate its superior efficacy over some benchmark Craig-criterion-based algorithms in both computational efficiency and estimation accuracy. [ABSTRACT FROM PUBLISHER]

Digital systems dedicated to audio and speech processing usually require sample rate conversion units in order to adapt the sample rate from different signal flows: for instance 8 and 16 kHz for speech, 32 kHz for the broadcast rate, 44.1 kHz for CDs, and 48 kHz for studio work. The designer chooses the sample rate conversion (SRC) technology based on objective criteria, such as figures of complexity, development or integration cycle and of course performance characterization. The performances of the fractional SRC system include the in-band and the aliasing characterization plus its distortion behavior due to internal rounding errors. The paper shows the existence of a new compound time-invariant system made of multiple instances of the same SRC system. The characterization of the original SRC is obtained from the linear and distortion characteristics of this time-invariant system. Regular methods for characterizing time-invariant systems apply. The SRC system can be analyzed in black box conditions, either in batch processing or in real-time processing. Examples illustrate the capability of the method to fully recover characteristics and rounding noise behavior from actual SRC implementations. [ABSTRACT FROM PUBLISHER]

This paper introduces a tensor framework to solve the problem of nonunitary joint block diagonalization (JBD) of a set of real or complex valued matrices. We show that JBD can be seen as a particular case of the block-component-decomposition (BCD) of a third-order tensor. The resulting tensor model fitting problem does not require the block-diagonalizer to be a square matrix: the over- and underdetermined cases can be handled. To compute the tensor decomposition, we build an efficient nonlinear conjugate gradient (NCG) algorithm. In the over- and exactly determined cases, we show that exact JBD can be computed by a closed-form solution based on eigenvalue analysis. In approximate JBD problems, this solution can be used to efficiently initialize any iterative JBD algorithm such as NCG. Finally, we illustrate the performance of our technique in the context of independent subspace analysis (ISA) based on second-order statistics (SOS). [ABSTRACT FROM PUBLISHER]

One of the most commonly used data analysis tools, principal component analysis (PCA), since is based on variance maximization, assumes a circular model, and hence cannot account for the potential noncircularity of complex data. In this paper, we introduce noncircular PCA (ncPCA), which extends the traditional PCA to the case where there can be both circular and noncircular Gaussian signals in the subspace. We study the properties of ncPCA, introduce an efficient algorithm for its computation, and demonstrate its application to model selection, i.e., the detection of both the signal subspace order and the number of circular and noncircular signals. We present numerical results to demonstrate the advantages of ncPCA over regular PCA when there are noncircular signals in the subspace. At the same time, we note that since a noncircular model has more degrees of freedom than a circular one, there are cases where a circular model might be preferred even though the underlying problem is noncircular. In particular, we show that a circular model is preferred when the signal-to-noise ratio (SNR) is low, number of samples is small, or the degree of noncircularity of the signals is low. Hence, ncPCA inherently provides guidance as to when to take noncircularity into account. [ABSTRACT FROM PUBLISHER]

There is a fundamental tradeoff between power consumption, data transmission rates, and congestion levels in a wireless network. These three elements influence the performance of rate and power control strategies, and they need to be coordinated judiciously. This paper proposes dynamic rate and power control algorithms for distributed wireless networks that also account for the congestion levels in a network. The design is pursued by formulating state-space models with and without uncertain dynamics and by determining control signals that help meet certain performance criteria (such as robustness and desired levels of signal-to-interference ratio). Simulation results illustrate the performance of the proposed control schemes. [ABSTRACT FROM AUTHOR]

In this paper, the problem of blind equalization of constant modulus (CM) signals is formulated within the support vector regression (SVR) framework. The quadratic inequalities derived from the CM property are transformed into linear ones, thus yielding a quadratic programming (QP) problem. Then, an iterative reweighted procedure is proposed to blindly restore the CM property. The technique is suitable for real and complex modulations, and it can also be generalized to nonlinear blind equalization using kernel functions. We present simulation examples showing that linear and nonlinear blind SV equalizers offer better performance than cumulant-based techniques, mainly in applications when only a small number of data samples is available, such as in packet-based transmission over fast fading channels. [ABSTRACT FROM AUTHOR]

The analytical performance of the subspace-based blind linear minimum mean-square error (MMSE) multiuser detection algorithm in general multipath multi-antenna code-division multiple-access (CDMA) systems is investigated. In blind multiuser detection, the linear MMSE detector of a given user is estimated from the received signals, based on the knowledge of only the spreading sequence of that user. Typically, the channel of that user must be estimated first, based on the orthogonality between the signal and noise subspaces. An asymptotic limit theorem for the estimate of the blind linear detector (when the received signal sample size is large) is obtained, based on which approximate expressions of the average output signal-to-inference plus noise ratios (SINRS) and bit error rates (BERs) for both binary phase-shift keying (BPSK) and quaternary phase-shift keying (QPSK) modulations are given. Corresponding results for group-blind multiuser detectors are also obtained. Examples are provided to demonstrate the excellent match between the theory developed in this paper and the simulation results. [ABSTRACT FROM AUTHOR]

In orthogonal frequency division multiplexing (OFDM) systems, for every block of K data samples, an overhead of L samples of cyclic prefix (CP) or zero padding (ZP) is added to combat frequency selective channels. The code rate, which is defined as the ratio K/(K + L), is a measure of the efficiency of transmitting user information. In this paper, a new system is proposed to increase the code rate without increasing the number of subcarriers and without increasing the bandwidth. The proposed system considers appending the L zeros (ZP) once for every P blocks of data samples, which would increase the code rate to PK/(PK + L). It is assumed that the channel is not varying over the transmission of P consecutive data blocks In order to recover the P data blocks in a computationally efficient manner, an interleaving scheme is proposed, and the proposed system is called the interleaved OFDM (IOFDM) system. Various issues such as computational complexity, peak-to-average power ratio (PAPR), and the effect of synchronization errors on the performance of the IOFDM system are also presented. Based on a numerical simulation study, the average bit-error-rate (BER) performance of the IOFDM system is shown to be very close to that of the OFDM system for a moderate increase in computational complexity and delay. [ABSTRACT FROM AUTHOR]

The eigenstructure based characterization of M-channel finite impulse response perfect reconstruction (FIR PR) filterbanks in a previous paper by the authors is extended here to the linear-phase case. Some results relating to linear-phase filterbanks is derived by finding appropriate restrictions on the eigenstructure of the analysis polyphase matrix. Consequently, a complete and minimal characterization for such filterbanks with all analysis length 2M and any synthesis length is developed. Parameterization and design examples are also presented. [ABSTRACT FROM AUTHOR]

In this paper we present a deterministic worst-case approach for reconstructing discrete-valued signals that have been filtered via dispersive and noisy systems ("channels"). This approach, which is explored based on robust control ideas and makes no assumption on the noise (distribution or structure) other than a requirement that its magnitude be bounded, can serve as a complement to existing approaches that attempt to reconstruct discrete-valued signals by optimizing probabilistic criteria. The particular problems touched upon are: (i) necessary and sufficient conditions for causal (possibly delayed) perfect reconstruction under deterministic magnitude bounded noise for single-input single-output (SISO) and multi-input multi-output (MIMO) channels; (ii) perfect reconstruction based on decision feedback (DF) structures; and (iii) necessary and sufficient conditions for perfect reconstruction with DF structures in the presence of uncertainties in the channel. The l¹ control theory emerges as the natural key player for analysis and synthesis of perfect reconstructing strategies in this framework. [ABSTRACT FROM AUTHOR]