Cubic spline interpolation is commonly applied in signal reconstruction problems. However, overshooting between samples is normally observed, and typically the reconstructed signal does not preserve the statistical properties of the original data or other desired properties such as monotonicity or convexity. These undesirable effects are minimized in the case of piecewise linear (PWL) interpolation, of course with a discontinuous derivative. In this paper we use a parameterized family of splines, named /spl alpha/splines, that allows a smooth transition from PWL (/spl alpha/ = 0) to cubic spline interpolation (/spl alpha/ = 1). Closed-form expressions that relate /spl alpha/ to the smoothness and variance of the interpolation are derived. Moreover, a fast interpolation technique based on digital filtering can be applied.

In this letter, we present a simple expression for the optimization of the threshold detection performance for direct-sequence spread-spectrum code acquisition in the presence of carrier-frequency offset. The proposed scheme divides the total integration time into subintervals, and the results of the coherent integrations performed over these subintervals are noncoherently combined prior to detection. The proposed expression allows obtaining the optimum number of coherent-integration subintervals for a given total integration time.

Modem digital communications are DSP based. We present a DSP-based digital communications lab. Although based on very simple hardware, we try to show that most practical situations that we can find in the design of digital communication systems can be reproduced in our setting. The main idea in our approach is to give the same importance to discrete-time and continuous-time communication signals. Looking for student motivation, the lab is based on a problem solving approach making the students develop from simple to more complex communications systems from the very beginning. It needs very simple equipment already known to the students, so most of the time is devoted to digital communications work, and it is low cost. Personal and team work is combined in the lab, pursuing student motivation.

In this paper, a new blind equalization algorithm for multilevel modulations is proposed. It is based on maximizing the correlation between the probability density function (pdf) of the signal at the output of the equalizer and the desired pdf. The algorithm employs the Parzen window method to estimate the pdf of the squared modulus of the equalizer output. A stochastic gradient-based algorithm is used to maximize the correlation between this pdf and the pdf of the corresponding modulation. The proposed algorithm shows an excellent performance when compared with conventional adaptive blind algorithms, such as CMA, in quadrature amplitude modulation (QAM) schemes.

In this paper the problem of blind equalization of constant modulus (CM) signals is formulated within the support vector (SV) regression 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 can 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.

We address the blind identification of single-input-multiple output (SIMO) finite impulse response systems when the input signal is sparse. The problem is equivalent to underdetermined blind source separation (BSS), but with temporal correlation among the sources. Exploiting the sparse character of the input signal, the algorithm solves three different problems: first, to estimate the directions of the columns of the channel matrix; second, to estimate the L/sub 2/-norm of the columns; and finally, to find the correct ordering of the columns of the mixing matrix. The last step is not required for the blind source separation (BSS) problem, since any permutation of the columns is admissible for BSS. The performance and computational cost of the algorithm in a noiseless situation is compared against subspace-based techniques.

Maximum-likelihood estimation of chaotic signal generated by iterating piecewise-linear maps on the unit interval exhibits an exponential increase in computational cost with the register length. This paper considers iterative estimation algorithms based on the Expectation-Maximization (EM) algorithm and related space alternating methods. This approach is inspired in the parallelism that may be drawn between chaotic estimation and multiuser detection, which also becomes prohibitively complex as the number of users increases. The resulting algorithms are based on an iterative updating of estimates of the chaotic signal itinerary. Computer simulations show that the proposed algorithms achieve the performance of the ML estimator for short data registers and improve the computationally feasible (suboptimal) estimators for long records.

In this paper a novel blind equalization algorithm based on stochastic gradient descent minimization of order-α Renyi's entropy and designed for constant modulus signals is introduced. The algorithm applies a new nonparametric estimator for Renyi's entropy, which has been recently proposed and allows to compute any order of entropy. In comparison with conventional adaptive blind techniques, such us CMA, the proposed algorithm shows a remarkable increase in convergence speed with only a moderate increase in computational cost.

The problem of estimating n source signals from m measurements that are an unknown mixture of the sources is known as blind source separation. In the underdetermined —less measurements than sources— linear case, the solution process can be conveniently divided in three stages: represent the signals in a sparse domain, find the mixing matrix, and estimate the sources. In this paper we adhere to that approach and parametrize the performance of these stages as a function of the sparsity of the signals. To find the mixing matrix and track its variations in the dynamic case a nonparametric maximum-likelihood approach based on Parzen windowing is presented. To invert the underdetermined linear problem we present an estimator that chooses the “best” demixing matrix in a sample by sample basis by using some previous knowledge of the statistics of the sources. The results are validated by Montecarlo simulations.

Chaotic signals generated by iterating nonlinear difference equations may be useful models for many natural phenomena. We propose a family of chaotic models for signal processing applications. The chaotic signals generated by this family of first-order difference equations have autocorrelations identical to stochastic first-order autoregressive (AR) processes. After considering the huge computational cost and the inconsistency of the optimal model estimator in the maximum-likelihood (ML) sense we propose low-cost, suboptimal estimation approaches. Computer simulations show the good performance of the proposed modeling approach.

Chaotic signals are potentially attractive in a wide range of signal processing applications. This paper deals with Bayesian estimation of chaotic sequences generated by tent maps and observed in white noise. The existence of invariant distributions associated with these sequences makes the development of Bayesian estimators quite natural. Both maximum a posteriori (MAP) and minimum mean square error (MMSE) estimators are derived. Computer simulations confirm the expected performance of both approaches and show how the inclusion of a priori information produces in most cases an increase in performance over the maximum likelihood (ML) case.

We present a modular neural network structure for global modeling of microwave transistors (MESFET/HEMT). The model is able to accurately represent both, the small-signal and the large-signal behavior of the device. This is achieved by means of an original neural architecture, which is composed of two main modules. The first module captures the nonlinear dynamic I/V characteristic of the transistor, which governs the large signal behavior of the device. The second module estimates the derivatives at the operation (bias) point by means of a neural network and then it locally reconstructs the function by means of a third order Taylor series around that point. This second module is able to reproduce the small-signal intermodulation behavior. These two modules are combined into a global model by means of a simple fuzzy controller. In this way the global model represents adequately the device behavior independently of the nature of the applied signals.

We present a simple and very accurate neuronal architecture approach matching, in a wide range of iris aperture, thickness and frequency, the numerical results obtained by using a precise high frequency electromagnetic simulator for symmetrical inductive irises in rectangular waveguide. For this purpose, a smoothed piecewise linear model has been chosen because this approach permits smooth transitions between linear regions through the use of logarithm of hyperbolic cosine functions, well suited for the frequency behavior of these inductive irises and circuit optimization. The model has been easily implemented into MMICAD(R), by using their MDL capability. Comparisons for high order high frequency waveguide filters for satellite applications has been made, showing an excellent agreement with full 3D electromagnetic HP-HFSS(R) simulations.

In this paper we present the Smoothed Piecewise Linear (SPWL) model as a useful tool for device modeling problems. The SPWL model is an extension of the well-known canonical piecewise linear model proposed by Chua, which substitutes the abrupt absolute value function for a smoothing function (the logarithm of hyperbolic cosine). This function makes the model derivable; moreover the smoothness of the global model can be controlled by means of a single smoothing parameter. The parameters of the model are adapted to fit the nonlinear function, while the smoothing parameter is selected according to derivative constraints. The proposed SPWL model is successfully applied to model a microwave HEMT transistor under optical illumination using real measurements.

Chaotic signals generated by iterating piecewise-linear (PWL) maps on the unit interval are highly attractive in a wide range of signal processing applications. In this letter, optimal estimation algorithms for signals generated by iterating PWL maps and observed in white noise are derived based on the method of maximum likelihood (ML). It is shown how the phase space of the map may be decomposed into a number of regions and how the estimation problem is linear in each of these regions. The final ML estimate is obtained as the best performing of these "local" solutions.

Based on a Gaussian mixture model for the reflectivity sequence, the authors present a new technique for blind deconvolution of seismic data. The method obtains a deconvolution filter that maximizes at its output a measure of the relative entropy between the proposed Gaussian mixture and a pure Gaussian distribution. A new updating procedure for the mixture parameters is included in the algorithm: it allows one to apply the algorithm without any prior knowledge about the signal and noise. A simulation example illustrates the performance of the proposed method.

This paper presents a new Bussgang-type technique for blind deconvolution of spiky signals. Based on a Gaussian mixture model for the spiky signal, the method obtains a deconvolution filter and a zero-memory nonlinearity to estimate the signal. A new updating procedure for the mixture parameters (and, therefore, for the nonlinear estimator) is included in the algorithm: it allows to apply the algorithm without any prior knowledge about the signal and noise. A simulation example illustrates the performance of the proposed method.