This work formulates a collaborative decision-making framework that exploits over-the-air computation to efficiently aggregate soft information from distributed sensors. This new AirCompFDM protocol approximates the sufficient statistic (SS) of optimum binary hypothesis testing at a server node in this distributed sensing environment under different operation constraints. Leveraging pre/post-processing functions on over-the-air aggregation of sensor log-likelihood ratios, Air-CompFDM significantly improves bandwidth efficiency with little detection loss, even from modest numbers of participating sensors and imperfect phase pre-compensation. Without phase pre-compensation, the benefit of over-the-air sensor aggregation diminishes but still can mitigate the effect of channel noise. Importantly, AirCompFDM outperforms the traditional bandwidth-hungry polling scheme, even under low SNR. Furthermore, we analyze the Chernoff information and obtain the approximate effect of sensor aggregation on the probability of detection error that can help develop advanced detection strategies.

We propose an over-the-air learning framework for collaborative decision making in wireless sensor networks. The low complexity framework leverages low-latency sensor transmission for a decision server to coordinate measurement sensors for hypothesis testing through over-the-air aggregation of sensor data over a multiple-access channel. We formulate several collaborative over-the-air hypothesis testing problems under different practical protocols for collaborative learning and decision making. We develop hypothesis tests for these network protocols and deployment scenarios including channel fading. We provide performance benchmark for both basic likelihood ratio test and generalized likelihood ratio test under different deployment conditions. Our results clearly demonstrate gain provided by increasing number of collaborative sensors.

3GPP has recently accelerated the standardization process for Device-to-Device communications. Sidelink, which refers to the radio link between two user equipments (UEs), is a major update in 3GPP Release 12. In this paper, we will first introduce sidelink related structures and procedures in Release 12. Based on basic LTE signaling schemes, we propose methods of using demodulation reference signal (DMRS), which is used as reference signal in both uplink and sidelink, for advance D2D neighbor discovery and resource scheduling of D2D transmissions. Our study shows that reference signal of normal LTE channels can be well exploited to facilitate the newly proposed sidelink communications.

We propose a blind calibration algorithm for removing the distortion created by timing mismatches in time-interleaved analog-to-digital converters (TIADCs). A polyphase domain model of the TIADC which is parameterized by the timing mismatches is introduced. The model is used to derive correction and estimation methods which work in tandem. The adaptive blind estimation method only requires a slight amount of oversampling. Further the overall calibration method has a low complexity, can track drifting timing mismatches, and has an easily updateable correction network.

This paper presents a method to calibrate the gain and memory errors of a pipelined analog-to-digital converter (ADC) used in an adaptively equalized baseband receiver. Both types of errors degrade ADC linearity, which significantly limits overall system performance. Adaptive finite-impulse-response filters at the output of each pipeline stage correct gain and memory errors and also perform channel equalization. The least-mean-square (LMS) algorithm is used to adapt the filter coefficients. The objective is to minimize the mean square error across the sheer in the receiver. Simulation results are presented to demonstrate improved performance with calibration.

This paper considers the design of a minimax test for two hypotheses where the actual probability densities of the observations are located in neighborhoods obtained by placing a bound on the relative entropy between actual and nominal densities. The minimax problem admits a saddle point which is characterized. The robust test applies a nonlinear transformation which flattens the nominal likelihood ratio in the vicinity of one. Results are illustrated by considering the transmission of binary data in the presence of additive noise.

Mismatches between sample-and-hold (S/H) circuits in a time-interleaved analog-to-digital data converter (ADC) cause undesirable distortions in the output spectrum. To reduce these undesired spectral components, we introduce a hybrid filter-bank model of a two channel time-interleaved ADC. The model allows the development of a digital domain correction technique that removes the first-order effects of S/H mismatches. A single FIR correction filter is required, and simulations demonstrate the effectiveness of the proposed correction method

This paper considers a robust mean-square error (MSE) equalizer design problem for flat-fading multiple-input multiple-output (MIMO) channels with imperfect channel and noise information at the receiver. When the channel state information (CSI) and the noise covariance are known exactly at the receiver, a minimum mean square error (MMSE) equalizer can be employed to estimate the transmitted signal. However, in actual systems, it is necessary to take into account channel and noise estimation errors. We consider here a worst-case equalizer design problem where the goal is to find the equalizer minimizing the equalization MSE for the least favorable channel model within a neighborhood of the estimated model. Lagrangian optimization is used to convert this min-max problem into a convex min-min problem over a convex domain which is solved by interchanging the minimization order.

This paper proposes a decoupling method for low complexity turbo equalization of frequency selective multiple-input multiple-output (MIMO) wireless systems. A coded MIMO system can be viewed as a serially concatenated coding (SCC) system where the encoder for the transmitted signals and the MIMO channel take on the roles of inner code and outer code, respectively. Several MIMO turbo equalization methods have been proposed for detecting coded signals transmitted by multiple antennas in the presence of interchannel interference (ICI) and intersymbol interference (ISI). However these methods use MAP or MMSE-based MIMO inner equalizers in the turbo iteration. The complexity of such equalizers grows rapidly as the number of transmit or receive antennas increases, or as the order of the MIMO channel increases. To overcome this difficulty, we propose to use a MIMO FIR decoupler on either the transmit or receive side in order to transform the MIMO channel into parallel single-input single-output (SISO) subchannels. Turbo equalization can then be applied separately to each scalar subchannel, resulting in a low complexity receiver. Transmit or noise power constraints can be included in the decoupler design. Simulations demonstrating the effectiveness of the proposed low-complexity turbo equalizer are presented.

A blind maximum-likelihood equalization algorithm is described and its convergence behavior is analyzed. Since the algorithm employs the Viterbi algorithm (VA) to execute the expectation step of the expectation-maximization (EM) iteration, we call it the expectation-maximization Viterbi algorithm (EMVA). An EMVA-based blind channel-acquisition technique which achieves a high global convergence probability is developed. The performance of the method is evaluated via numerical simulations under static and fading channel conditions.

This paper considers the turbo equalization of trellis-coded modulated (TCM) broadband wireless signals that are affected by both intersymbol interference (ISI) due to multipath propagation and cochannel interference (CCI) due to the presence of adjacent users. Long channel dispersion causing both impediments to be severe makes the direct application of trellis-based turbo equalizers impossible, particularly for high-order signal modulations. For this reason, we present two computationally feasible space-time turbo receiver architectures employing linear antenna arrays and broadband beamformers. The first receiver uses a beamformer for joint rejection of interfering signals and shortening of the channel corresponding to the desired signal so that a scalar trellis-based turbo equalizer can be applied to its output. At each beamformer branch, the composite effect of the CCI and the white channel noise is viewed as colored noise. Because trellis search algorithms are limited to cases where the observation noise is white, this imposes quadratic noise whitening constraints on the beamformer design that is solved by a Lagrangian relaxation approach. The second receiver architecture removes the dependence on trellis search techniques for equalization by implementing the turbo equalizer directly with a soft-information-aided broadband beamformer at its front end and a soft-input soft-output (SISO) decoder at its back end. We outline the design considerations associated with each receiver and present bit error rate (BER) simulations for the turbo equalization of 8-phase-shift keying (PSK) TCM signals.

The paper considers a robust precoder design problem for multiple-input multiple-output (MIMO) flat-fading channels with imperfect channel knowledge at the transmitter. The robust design problem requires finding the optimal precoder minimizing the equalization mean-square error (MSE) for the least favorable channel located in a ball centered about the estimated channel. Lagrangian optimization is used to convert this min-max problem into a min-min convex minimization problem over a convex domain which is solved by interchanging the minimization order. The robust precoder and associated least favorable channel have an intuitive interpretation since the least-favorable channel zeroes out the weakest subchannels, and the robust precoder implements a pseudo-inverse only for the remaining subchannels.

We address the doubly-iterative space-time equalization of broadband wireless signals for frequency selective multiple-input multiple-output (MIMO) systems employing M-ary modulation through bit to symbol mapping. The proposed receiver consists of a soft-information aided MMSE space-time equalizer processing antenna array observations at the front-end, followed by the serial concatenation of two soft-input soft-output (SISO) modules: a symbol-to-bit demapper and a channel decoder. In the proposed scheme, a new equalization stage is started only after several inner demapping/decoding iterations are applied to improve the soft decisions. The doubly iterative structure offers not only a reduced overall computational complexity but also a significant equalization gain as illustrated by the results.

This paper considers a robust FIR precoder design problem for frequency-selective multiple-input multiple-output (MIMO) wireless systems under transmit power constraints with imperfect channel knowledge at the transmitter. The robust design problem requires finding the optimal power constrained FIR precoder for the worst-case channel model within a neighborhood of the estimated channel. The neighborhood is formed by placing a bound on Kullback-Leibler (KL) divergence between the actual and estimated channels. We show that the optimal power constrained FIR precoder designed for the estimated channel under the assumption of perfect channel knowledge is robust when channel uncertainties are measured by the KL divergence "metric".

Given a nominal statistical model, we consider the minimax estimation problem consisting of finding the best least-squares estimator for the least favorable statistical model within a neighborhood of the nominal model. The neighborhood is formed by placing a bound on the Kullback-Leibler (KL) divergence between the actual and nominal models. For a Gaussian nominal model and a finite observations interval, or for a stationary Gaussian process over an infinite interval, the usual noncausal Wiener filter remains optimal. However, the worst case performance of the filter is affected by the size of the neighborhood representing the model uncertainty. On the other hand, standard causal least-squares estimators are not optimal, and a characterization is provided for the causal estimator and the corresponding least favorable model. The causal estimator takes the form of a risk-sensitive estimator with an appropriately selected risk sensitivity coefficient.

This paper presents a space-time turbo (iterative) equalization method for trellis-coded modulation (TCM) signals over broadband wireless channels. For fixed wireless systems operating at high data rates, the multipath delay spread becomes large, making it impossible to apply trellis-based equalization methods. The equalizer proposed here consists of a broadband beamformer which processes antenna array measurements to shorten the observed channel impulse response, followed by a conventional scalar turbo equalizer. Since the applicability of trellis-based equalizers is limited to additive white noise channels, the beamformer is required to preserve the whiteness of the noise at its output. This constraint is equivalent to requiring that the finite-impulse response (FIR) beamforming filters must have a power complementarity property. The power complementarity property imposes nonnegative definite quadratic constraints on the beamforming filters, so the beamformer design is expressed as a constrained quadratic optimization problem. The composite channel impulse response at the beamformer output is shortened significantly, making it possible to use a turbo equalizer for the joint equalization and decoding of trellis modulated signals. The proposed receiver structure is simulated for two-dimensional TCM signals such as 8-PSK and 16-QAM and the results indicate that the use of antenna arrays with only two or three elements allows a large decrease in the channel signal-to-noise ratio needed to achieve a 10/sup -4/ bit-error rate.

We propose a low-complexity turbo space-time equalizer for signals transmitted over broadband wireless channels. The transmitter employs trellis coded modulation (TCM) for its bandwidth and power efficiency, and the broadband transmission is severely impaired by both intersymbol interference (ISI), due to multipath dispersion of the wireless channel, and cochannel interference (CCI), due to the presence of adjacent users. The proposed turbo equalizer consists of a broadband beamformer, which performs soft interference cancellation and space-time minimum mean-square error (MMSE) equalization, followed by a soft-in, soft-out (SISO) TCM decoder. A priori expected symbol values are used as soft inputs in the soft interference cancellation stage and then, after beamforming, the elements of the output sequence are mapped onto extrinsic log-likelihoods or probabilities using a Gaussian assumption. Because these two operations make the beamformer a SISO processor, the front-end of the space-time receiver is suitable for iterative processing. The proposed structure is implemented with small antenna arrays and simulated for turbo equalization of 8-PSK TCM signals, and simulation results indicate a relatively close performance to "no interference" bounds after only a small number of turbo iterations.

We propose a blind maximum-likelihood (ML) equalization method for synchronous and asynchronous spread-spectrum code-division multiple access (CDMA) signals in intersymbol interference channels. Our method employs an expectation-maximization Viterbi algorithm (EMVA) capable of joint channel identification and signal estimation for transmission systems that admit a hidden Markov model description. By modelling the observed signal as a finite-state hidden Markov process, it is possible to use the Viterbi algorithm (VA) to execute the M-phase of the expectation-maximization iteration. When the parameter estimate converges to a stationary point, the best survivor of the VA is selected as the ML estimate of the transmitted sequence. Simulations show that the EMVA performs almost as well as the ML detector based on exact channel knowledge and that it is near-far resistant in the presence of large power disparities among users. We then devise an EMVA-based quasi-maximum-likelihood successive cancellation (QML-SC) method which reduces the trellis complexity by first ignoring weak users, equalizing the stronger users, subtracting off their contributions from the observed signal, equalizing and cancelling the weak users, and repeating the procedure until convergence. Though not near-far resistant, the QML-SC method tends to resist the near-far effect for a wide range of power disparities.

We propose a blind maximum-likelihood (ML) detection algorithm for continuous-phase modulated (CPM) signals transmitted over a noisy linear FIR channel. This is referred to as the Expectation-Maximization-Viterbi algorithm (EMVA) [1, 2]. The EMVA is a blind algorithm capable of simultaneously performing system identification and signal estimation whenever the transmission system can be modeled as a finite-state machine with unknown parameters, a scenario frequently encountered in signal processing for communications. We specifically focus on CPM, but t he algorithm is equally applicable to any other modulation type, linear or nonlinear. The channel estimate obtained via the EMVA is shown via simulations to, asymptotically (as the SNR increases) attain the most optimistic Cramér-Rao bo und and to have an error performance close to that of the true channel; a 0.5 dB difference is seen at BER equal to 10−4.

In this paper we investigate and propose two methods for pilot-tone-aided carrier recovery in space-time coded systems with transmit and receive diversity for high-rate applications. We assume that due to mismatches in local oscillators, there is a small relative frequency and phase offset between the two transmit antennas. The first approach relies on an FFT for initial carrier frequency and phase recovery at the receiver, plus a simple decision-directed circuit for estimating initial phase error and canceling accumulative phase error due to carrier frequency estimation. This is a non-tracking technique that prevents accumulation of phase error and has no burst length limitation. The second technique also uses an FFT for initial estimation, but uses a DPLL for tracking at the receiver, and thus requires lower FFT resolution (as few as 64 points). Simulations results are shown for a (2,2) spatial DEMUX system with two transmit and two receive antennas. The simulation results show that the latter technique is more robust. With smaller FFT and shorter pilot duration, the estimated phase error due to low resolution is resolved by use of a reduced constellation algorithm. All simulations assume a narrow-band channel for simplicity, but these results can also apply to broadband channels, using a different space-time coding algorithm.

This paper presents a turbo (iterative) equalization method for complex TCM (trellis-coded modulation) signals over broadband wireless channels based on receiver antenna array measurements. The channel is highly dispersive at high data rates causing a severe intersymbol interference (ISI) effect and making the direct application of any trellis based equalization algorithm infeasible. The problem of reducing this excess interference is solved by receiver diversity combining, i.e. using a linear antenna array and a broadband beamformer in the receiver. The beamformer output that contains less ISI is viewed as the output of a serial concatenated coding system and optimum symbol detection is achieved by a turbo equalization and decoding scheme. The proposed receiver structure is simulated for two dimensional TCM signals such as 8-16 PSK and 16-QAM and the results indicate an improved performance of the diversity receiver.

In this paper we study and compare critical Markov random fields (CMRFs) and fractional Brownian motions (FBMs). Both of these classes of models can be used to describe self-similar phenomena. Their characteristics, namely the index of similarity of a FBM, and the critical exponents of a CMRF, are defined and contrasted. We argue that CMRFs provide a more flexible mechanism for generating self-similar patterns, since the parameters of a CMRF can be selected to generate anisotropic patterns, while FBM models are inherently isotropic.>

We have designed a 4-channel 10/spl times/10 nonseparable orthogonal linear phase perfect reconstruction filter bank (PRFB), hereafter NSEP, and examined its performance in image compression applications. It is shown that, in addition to the orthogonality property, NSEP offers an excellent compression performance. Because of their limited spatial support, the nonseparable filters can be implemented at a reasonable computational cost. The orthogonality property also allows the use of image compression algorithms which exploit orthogonality for bit allocation purposes. We demonstrate that the NSEP filters have superior spatial localization properties when compared to filters arising in a 2-D separable PRFB generated from a l-D Daubechies FB of length 10. This superior spatial localization results in less visible ringing distortion in compressed images. In addition, the linear phase property of NSEP distributes the ripples located at image edges evenly on both sides of each edge, thus reducing further their visibility. Because of these advantages, NSEP is a viable and attractive candidate for high quality, low bit rate image compression applications.>

Efficient recursive smoothing algorithms are developed for isotropic random fields that can be obtained by passing white noise through rational filters. The estimation problem is shown to be equivalent to a countably infinite set of 1-D separable two-point boundary value smoothing problems. The 1-D smoothing problems are solved using a Markovianization approach followed by a standard 1-D smoothing algorithm. The desired field estimate is then obtained as properly weighted sum of the 1-D smoothed estimates. The 1-D two-point boundary value problems are also shown to have the same asymptotic properties and yield a stable spectral factorization of the power spectrum of the isotropic random fields.>

Multidimensional inverse scattering problems of elastics are formulated as generalized tomographic problems. The 2-D elastic problem for wideband plane P-wave illumination is considered with emphasis on the inversion of the PS mode. Using the Born approximation and filtering the observed scattered field, generalized elliptic projections of the perturbations to the Lame parameters and density are obtained. The resulting integral geometric problem is solved in the frequency domain, deriving the projection slice theorem associated with this problem. The reconstructed image is a linear combination of the unknown parameter perturbations, where the coefficients depend on the angle of incidence of the probing wave.>

A digital signal processing (DSP) approach is used to study numerical methods for discretizing and solving linear elliptic partial differential equations (PDEs). Whereas conventional PDE analysis techniques rely on matrix analysis and on a space-domain point of view to study the performance of solution methods, the DSP approach described here relies on frequency-domain analysis and on multidimensional DSP techniques. Both discretization schemes and solution methods are discussed. In the area of discretization, mode-dependent finite-difference schemes for general second-order elliptic PDEs are examined, and are illustrated by considering the Poisson, Helmholtz, and convection-diffusion equations as examples. In the area of solution methods, the authors focus on methods applicable to self-adjoint positive definite elliptic PDEs. Both direct and iterative methods are discussed, including fast Poisson solvers, elementary and accelerated relaxation methods, multigrid methods, preconditioned conjugate gradient methods and domain-decomposition techniques. In addition to describing these methods in a DSP setting, an up-to-date survey of recent developments is also provided.>

A novel linear maximum-entropy method (MEM) spectral-estimation algorithm for 2-D isotropic random fields is presented. This procedure differs from pervious 2-D MEM algorithms by the fact that maximum advantage is taken of the symmetries implied by isotropy. It is shown that the isotropic MEM problem has a linear solution and that it is equivalent to the problem of constructing the optimal linear filter for estimating the underlying isotropic field at a point on the boundary of a disk of radius R, given noisy measurements of the field inside the disk. A fast algorithm for computing the estimation filter is then used to obtain the MEM spectral estimate.>

An efficient algorithm for computing the maximum-likelihood estimates of multiple signals observed by an array of sensors is presented. The algorithm provides estimates of parameters related to the directional patterns of the sources as well as estimates of the location parameters of the sources. Furthermore, the algorithm is equally applicable to wideband sources and narrowband sources and does not require a knowledge of the statistical properties of the signals.>

Sampling theorems are developed for isotropic random fields and their associated Fourier coefficient processes. A wave-number-limited isotropic random field z(r) is considered whose spectral density function is zero outside a disk of radius B centered at the origin of the wavenumber plane. z(r) can be reconstructed in the mean-square sense from its observation on the countable number of circles with radius r/sub i/=i pi /B, i in N, or of radius r/sub i/=a/sub i,n//B, i in N, where a/sub 1,n/ denotes the ith zero of the nth-order Bessel function J/sub n/(x), and n is arbitrary.>

The inverse scattering problem for an acoustic medium is considered within the homogeneous background Born approximation. A constant-density acoustic medium is probed by a wide-band plane-wave source. The scattered field is observed along a receiver array located outside the medium. Two methods for partial reconstruction of the medium velocities are presented. In the first method (the slant-stack method), the projections of the velocity potential at a range of angles are obtained from the plane-wave components of the scattered field. The range of available projection angles is determined by the receiver array aperture and the incidence direction of the probing plane wave. The medium velocities are, then, partially reconstructed from available projections via well-known methods of straight-line tomography. In the second method (the imaging-filtering method), the observed traces are filtered, back-propagated into the medium, and imaged at the source traveltimes, in the same way as in migration. The resulting image is, then, filtered by a linear space-invariant filter to obtain a partial reconstruction of the medium velocities. Both reconstruction methods are illustrated by some synthetic examples for several receiver geometries.

Martingale decomposition techniques are used to derive Markovian models for the error in smoothed estimates of processes described by linear models driven by white noise. These models, together with some simple Hilbert space decomposition ideas, provide a simple unified framework for examining a variety of problems involving the efficient assimilation of spatial data, which we refer to as mapping problems. Algorithms for several different mapping problems are derived. A specific example of map updating for a two-dimensional random field is included.

The problem considered involves estimating a two-dimensional isotropic random field given noisy observations of this field over a disk of finite radius. By expanding the field and observations in Fourier series, and exploiting the covariance structure of the resulting Fourier coefficient processes, recursions are obtained for efficiently constructing the linear least-squares estimate of the field as the radius of the observation disk increases. These recursions are similar to the Levinson equations of one-dimensional linear prediction. In the spectral domain they take the form of Schrödinger equations, which are used to give an inverse spectral interpretation of our estimation procedure.

A new implementation is presented for the optimum likelihood ratio detector for stationary Gaussian signals in white Gaussian noise that uses only two causal time-invariant filters. This solution also has the advantage that fast algorithms based on the Levinson and Chandrasekhar equations can he used for the determination of these time-invariant filters. By using a notion of "closeness to stationarity,' there is a natural extension of the above results for nonstationary signal processes.