We present an empirical model of the upstream end-to-end Voice-over-IP (VoIP) delay over a mobile, multi-hop wireless network towards a single gateway. First, we define the “VoIP regime” as the regime of network operation in which a fraction 1 - ϵ of the packets are received by the gateway within the maximum tolerable VoIP networking delay y voip , and such that e is less than a maximum tolerable outage probability. We show that within the VoIP regime, the upstream VoIP delay is well-modeled by an exponential distribution whose parameter λ i depends on the number of hops i to the gateway. Second, we show that the coherence time of the VoIP regime is large enough such that the estimation of the {λ i } can be performed by the gateway, and distributed to the nodes such that each node can utilize the {λ i } in estimating the end-to-end delay from its current location for autonomous call admission decisions. Third, we validate the empirical model across scenarios that range from a flat deployment region, to a deployment region with holes, and to the case where there is background User Datagram Protocol (UDP) data traffic. The results are significant for enabling VoIP over high-mobility, multi-hop wireless networks, and in aiding node-based call admission decisions.

In the pursuit of a sparse signal model, mismatches between the signal and the dictionary, as well as atoms poorly selected by the decomposition process, can diminish the efficiency and meaningfulness of the resulting representation. These problems increase the number of atoms needed to model a signal for a given error, and they obscure the relationships between signal content and the elements of the model. To increase the efficiency and meaningfulness of a signal model built by an iterative descent pursuit, such as matching pursuit (MP), we propose integrating into its atom selection criterion a measure ofinterferencebetween an atom and the model. We define interference and illustrate how it describes the contribution of an atom to modeling a signal. We show that for any nontrivial signal, the convergent model created by MP must have as much destructive as constructive interference, i.e., MP cannot avoid correction in the signal model. This is not necessarily a shortcoming of orthogonal variants of MP, such as orthogonal MP (OMP). We derive interference-adaptive iterative descent pursuits and show how these can build signal models that better fit the signal locally, and reduce the corrections made in a signal model. Compared with MP and its orthogonal variants, our experimental results not only show an increase in model efficiency, but also a clearer correspondence between the signal and the atoms of a representation.

We present a correlation-based algorithm for the agglomerative clustering of atoms in sparse atomic decompositions of audio signals. Our goal is to demonstrate useful relationships between elements of the decomposition and the content of the original signal, for such purposes as analysis and modification. We evaluate the performance of the agglomeration algorithm using decompositions of synthetic and real audio signals, and discuss possible extensions of this work.

We describe an adaptive beamforming algorithm for time- division multiple-access (TDMA) signals that utilizes a modified least-squares (LS) cost function, and analyze its performance using a stochastic model. The beamformer weights are computed via a two-step procedure: initial weights are calculated from the training sequence, and these are refined by a semi-blind algorithm using the modified LS cost function. The main goal of the paper is to analyze this algorithm using a stochastic model and Wiener filter theory for the case when the look-direction vector is mismatched. The performance of the proposed adaptive beamformer is also evaluated using simulated TDMA data.

Sparse overcomplete methods, such as matching pursuit, attempt to find an efficient estimation of a signal using terms (atoms) selected from an overcomplete dictionary. In some cases, atoms can be selected that have energy in regions of the signal that have no energy. Other atoms are then used to destructively interfere with these terms in order to preserve the original waveform. Because some terms may even ldquodisappearrdquo in the reconstruction, we refer to the destructive and constructive interference between the atoms of a sparse atomic estimation as ldquodark energy.rdquo In this paper, we formally define dark energy for matching pursuit, explore its properties, and present empirical results for decompositions of audio signals. This paper demonstrates that dark energy is a useful measure of the interference between the terms of a sparse atomic estimation and might provide information for the decomposition process.

In this paper, we describe amplitude estimation algorithms for the Walsh traffic channels in the downlink of Interim Standard 95 (IS-95). The parameter estimate is designed to improve the performance of a successive interference canceller (SIC) by providing greater reconstruction accuracy. A feature of the IS-95 downlink that makes amplitude estimation difficult is that during lowered voice activity levels, bit repetition occurs with a corresponding drop in the symbol energy for a frame of data. As a result, the amplitude level cannot be assumed to remain constant and should be taken into account during signal reconstruction in the SIC. We explore various algorithms for estimating the nominal Walsh traffic channel amplitude level. The distinguishing characteristic of the different techniques is the type of a priori knowledge employed in the estimation. For example, one parameter that may need to be estimated is the bit repetition multiple using a rate determination algorithm.

The adaptive successive interference canceler (ASIC) is a multistage nonlinear detector that sequentially estimates multiple users in a direct-sequence code-division multiple-access (DS/CDMA) system. In order to successfully regenerate the multiple access interference and subtract it from the received signal, the ASIC requires accurate estimates of the users' received amplitudes. In this paper, we analyze the bit-error-rate performance of the ASIC employing a single antenna element in a synchronous DS/CDMA system. Computer simulations verify the accuracy of the analysis, and a numerical example illustrates the sensitivity of the SIC to incorrect amplitude estimates.

We describe an adaptive algorithm that uses a subspace method for separating cochannel time-division multiple-access (TDMA) signals impinging on an antenna array. A frame synchronization algorithm is initially employed to identify the cochannel scenario. The adaptive algorithm uses a subspace decomposition of the array signals to constrain the beamformer weights for the signal of interest to be in a specific subspace. This subspace corresponds to the orthogonal complement of the subspace spanned by the direction vectors of the interferers. A follow-on linear equalizer removes the intersymbol interference (ISI) introduced by the transmit filter.

Cochannel interference occurs when two or more signals overlap in frequency and are present concurrently. Unlike in spread-spectrum multiple-access systems where the different users necessarily share the same channel, cochannel interference is a severe hindrance to frequency- and time-division multiple-access communications, and is typically minimized by interference rejection/suppression techniques. Rather than using interference suppression, we are interested in the joint estimation of the information-bearing narrow-band cochannel signals. Novel joint estimators are proposed that employ a single-input demodulator with oversampling to compensate for timing uncertainties. Assuming finite impulse-response channel characteristics, maximum likelihood (ML) and maximum a posteriori (MAP) criteria are used to derive cochannel detectors of varying complexities and degrees of performance. In particular, a (suboptimal) two-stage joint MAP symbol detector (JMAPSD) is introduced that has a lower complexity than the single-stage estimators while accruing only a marginal loss in error-rate performance at high signal-to-interference ratios. Assuming only reliable estimates of the primary and secondary signal powers, a blind adaptive JMAPSD algorithm for a priori unknown channels is also derived. The performance of these nonlinear joint estimation algorithms is studied through example computer simulations for two cochannel sources.

This paper analyzes the perceptron mean weight learning behavior for a system identification model with Gaussian input training data and fixed non zero biases for both the perceptron and the unknown system. The analysis is based upon the partial evaluation of certain expectations using Price's (1958) theorem followed by numerical integration in the mean weight recursions. The mean weight vector is shown to be in the same direction as that of the unknown system. A scalar recursion is derived for the length of the mean weights. The recursion is shown to yield weight vector predictions that are in close agreement with Monte Carlo simulations of the perceptron learning behavior. The stationary points are also accurately predicted by the theoretical model.

In this paper, we present a stochastic analysis of the constant modulus (CM) array for time-varying channels. An expression for the mean-square error is derived, which is based on a recursion for the weight-error correlation matrix. The analysis yields an accurate model of the tracking behavior of the CM array provided the array maintains capture on the same source. Computer simulations are presented to illustrate the tracking behavior of the CM array and to verify the theoretical model.

Dual-mode adaptive algorithms with rapid convergence properties are presented for the equalization of frequency selective fading channels and the recovery of time-division multiple access (TDMA) mobile radio signals. The dual-mode structure consists of an auxiliary adaptive filter that estimates the channel during the training cycle. The converged filter weights are used to initialize a parallel bank of filters that are adapted blindly during the data cycle. When the symbol timing is known, this filter bank generates error residuals that are used to perform approximate maximum a posteriori symbol detection (MAPSD) and provide reliable decisions of the transmitted signal. For channels with timing jitter, joint estimation of the channel parameters and the symbol timing using an extended Kalman filter algorithm is proposed. Various methods are described to reduce the computational complexity of the MAP detector, usually at the cost of some performance degradation. Also, a blind MAPSD algorithm for combining signals from spatially diverse receivers is derived. This diversity MAPSD (DMAPSD) algorithm, which can be easily modified for the dual-mode TDMA application, maintains a global set of MAP metrics even while blindly tracking the individual spatial channels using local error estimates. The performance of these single-channel and diversity MAPSD dual-mode algorithms are studied via computer simulations for various channel models, including a mobile radio channel simulator for the IS-54 digital cellular TDMA standard.

The statistical learning behavior of the single-layer backpropagation algorithm was analyzed using a system identification formulation for noise-free training data [Bershad et al. 1993]. Transient and steady-state results were obtained for the mean weight behavior, mean-square error (MSE), and probability of correct classification. The present paper extends these results to the case of noisy training data. Three new analytical results are obtained: 1) the mean weights converge to finite values even when the bias terms are zero, 2) the MSE is bounded away from zero, and 3) the probability of correct classification does not converge to unity. However, over a wide range of signal-to-noise ratios (SNRs), the noisy training data does not have a significant effect on the perceptron stationary points relative to the weight fluctuations. Hence, one concludes that noisy training data has a relatively small effect on the ability of the perceptron to learn the model weight vector F.

We describe an approach to cochannel signal recovery for correlated sources that is based on the the MUSIC (multiple signal classification) algorithm and the constant modulus (CM) array. The MUSIC algorithm provides estimates of the source angles of arrival, which are used to initialize a parallel bank of CM arrays. These adaptive beamformers are updated by the constant modulus algorithm (CMA) to capture and track the source signals, even when they are highly correlated. Computer simulations are presented to illustrate the transient behavior of the proposed algorithm.>

A new blind equalization algorithm based on a suboptimum Bayesian symbol-by-symbol detector is presented. It is first shown that the maximum a posteriori (MAP) sequence probabilities can be approximated using the innovations likelihoods generated by a parallel bank of Kalman filters. These filters generate a set of channel estimates conditioned on the possible symbol subsequences contributing to the intersymbol interference. The conditional estimates and MAP symbol metrics are then combined using a suboptimum Bayesian formula. Two methods are considered to reduce the computational complexity of the algorithm. First, the technique of reduced-state sequence estimation is adopted to reduce the number of symbol subsequences considered in the channel estimation process and hence the number of parallel filters required. Second, it is shown that the Kalman filters can be replaced by simpler least-mean-square (LMS) adaptive filters. A computational complexity analysis of the LMS Bayesian equalizer demonstrates that its implementation in parallel programmable digital signal processing devices is feasible at 16 kbps. The performance of the resulting algorithms is evaluated through bit-error-rate simulations, which are compared to the performance bounds of the maximum-likelihood sequence estimator. It is shown that the Kalman filter and LMS-based algorithms achieve blind start-up and rapid convergence (typically within 200 iterations) for both BPSK and QPSK modulation formats.>

Rosenblatt's algorithm is a recursive method that is often used to adjust the weights of a single-layer perceptron. It is capable of partitioning the input signal space into two regions that are separated by a hyperplane boundary. Thus, when the values of the input signal are linearly separable, the algorithm will converge to a stable stationary point that yields zero mean-square error. The authors examine the stationary points of Rosenblatt's algorithm when the data are not linearly separable. A system identification model is used to generate the data. An expression is also derived for the probability of an incorrect classification of the output signal when the weights are converged at a stationary point.>

The authors present a novel version of low-delay vector excitation coding (LD-VXC) operating at 8 kb/s that provides very good speech quality with a coding delay below that of the CCITT requirement. The coder integrates techniques such as vector quantization and analysis-by-synthesis, without any excessive buffering of speech samples in the encoder, by incorporating backward adaptive linear prediction. Compared with LD-VXC at 16 kb/s which was reported earlier, this version features an increased vector dimension, closed-loop pitch prediction with a three-tap pitch filter, codebook orthogonalization techniques, and dual-mode interframe coding of the pitch trajectory. Informal listening tests demonstrate that its quality is comparable to that of VSELP operating at the same rate, while maintaining a delay constraint an order of magnitude smaller than that of VSELP.>

The authors present a statistical analysis of the steady-state and transient properties of the single-layer backpropagation algorithm for Gaussian input signals. It is based on a nonlinear system identification model of the desired response which is capable of generating an arbitrary hyperplane decision boundary. It is demonstrated that, although the weights grow unbounded, the mean-square error decreases towards zero. These results indicate that the algorithm, on average, quickly learns the correct hyperplane associated with the system identification model. However, the nature of the mean-square error and the corresponding performance surface are such that the perceptron is prevented from correctly classifying with probability one until the weights converge at infinity.>

A comparative analysis of the stationary points of the constant modulus algorithm (CMA) performance function that is based on two different Gaussian assumptions is presented. In one case, it is assumed that the received signal is unconditionally Gaussian. This approach leads to an infinity of solutions, all of which correspond to a minimum of the performance function. In the second case, it is assumed that the received signal conditioned in one of the transmitted symbols in Gaussian. This approach leads to several possible solutions that depend not only on the channel characteristics, but also on the symbol on which the conditioning is performed.>

An analysis is presented of the stationary points of an adaptive algorithm that adjusts the perceptron weights. This algorithm is identical in form to the least-mean-square (LMS) algorithm, except that a hard limiter is incorporated at the output of the summer. In addition, a momentum term is included in the weight update; this modified algorithm is referred to as the momentum LMS (MLMS) algorithm. It is shown that the stationary points of the MLMS algorithm are not unique; they depend not only on the statistics of the input and the desired response, but also on the specific values used for the algorithm convergence parameters, the step size and convergence constant.>

An analysis of the stationary (convergence) points of an adaptive algorithm that adjusts the perceptron weights is presented. This algorithm is identical in form to the least-mean-square (LMS) algorithm, except that a hard limiter is incorporated at the output of the summer. The algorithm is described in detail, a simple two-input example is presented, and some of its convergence properties are illustrated. When the input of the perceptron is a Gaussian random vector, the stationary points of the algorithm are not unique and they depend on the algorithm step size and the momentum constant. The stationary points of the algorithm are presented, and the properties of the adaptive weight vector near convergence are discussed. Computer simulations that verify the analysis are given.>

A perceptron learning algorithm may be viewed as a steepest-descent method whereby an instantaneous performance function is iteratively minimized. An appropriate performance function for the most widely used perceptron algorithm is described and it is shown that the update term of the algorithm is the gradient of this function. An example is given of the corresponding performance surface based on Gaussian assumptions and it is shown that there is an infinity of stationary points. The performance surfaces of two related performance functions are examined. Computer simulations that demonstrate the convergence properties of the adaptive algorithms are given.

A novel structure for multirate adaptive filtering with lower computational complexity and improved performance of the adaptive algorithm is introduced. It uses auxiliary subbands and a modified filter bank with decimated subbands. It avoids the aliasing distortions encountered in critically decimated overlapping filter banks as well as the spectral gaps in nonoverlapping filter banks. The authors show that this structure has a lower computational complexity than previously reported structures. Computer simulations are included showing the improvement in performance that can be achieved with the new structure operating as an adaptive line enhancer (ALE) compared with the conventional ALE.>

Lattice-form algorithms are described for adaptive IIR (infinite-impulse-response) filtering that are based on the Gauss-Newton search method. Several approximations of the Hessian matrix that have different levels of computational complexity are considered, and the results are compared to a previous IIR lattice algorithm. Computer simulations in a system-identification configuration illustrate their convergence properties. Algorithms for the two-multiplier lattice with distinct coefficients in each section, and the one-multiplier form, are outlined.>

An adaptive pole-zero filter comprised of a bank of bandpass filters is presented. The bandpass filters permit the adaptive filter to be realized in a parallel form of first-order sections. Simple monitoring of the filter poles during adaptation is therefore possible so that stability can be ensured. This paper focuses on bandpass filters which are implemented by a frequency-sampling structure; the use of other types of bandpass filters is briefly discussed. An application in system identification is described and computer simulation results are given.

A parallel form adaptive pole-zero filter implemented in the frequency domain is presented. This filter can exactly model any proper rational system with distinct poles and it permits direct monitoring of pole trajectories during adaptation so that instability of the filter is easily prevented.