Sparse Bayesian learning (SBL) associates to each weight in the underlying linear model a hyperparameter by assuming that each weight is Gaussian distributed with zero mean and precision (inverse variance) equal to its associated hyperparameter. The method estimates the hyperparameters by marginalizing out the weights and performing (marginalized) maximum likelihood (ML) estimation. SBL returns many hyperparameter estimates to diverge to infinity, effectively setting the estimates of the corresponding weights to zero (i.e., pruning the corresponding weights from the model) and thereby yielding a sparse estimate of the weight vector. In this letter, we analyze the marginal likelihood as function of a single hyperparameter while keeping the others fixed, when the Gaussian assumptions on the noise samples and the weight distribution that underlies the derivation of SBL are relaxed. We derive sufficient conditions that lead, on the one hand, to f inite hyperparameter estimates and, on the other, to infinite ones. Finally, we show that in the Gaussian case, the two conditions are complementary and reduce to the pruning condition of fast SBL (F-SBL). Thereby, our results offer a novel insight into the fundamental internal features that lead to the pruning mechanism of F-SBL.

In this paper, we present an iterative algorithm that detects and estimates the specular components (SCs) and estimates the dense component (DC) of single-input—multiple-output (SIMO) ultra-wide-band (UWB) multipath channels. Specifically, the algorithm super-resolves the SCs in the delay–angle-of-arrival domain and estimates the parameters of a parametric model of the delay-angle power spectrum characterizing the DC. Channel noise is also estimated. In essence, the algorithm solves the problem of estimating spectral lines (the SCs) in colored noise (generated by the DC and channel noise). Its design is inspired by the sparse Bayesian learning (SBL) framework. As a result the iteration process contains a threshold condition that determines whether a candidate SC shall be retained or pruned. By relying to results from extreme-value analysis the threshold of this condition is suitably adapted to ensure a prescribed probability of detecting spurious SCs. Studies using synthetic and real channel measurement data demonstrate the virtues of the algorithm: it is able to still detect and accurately estimate SCs, even when their separation in delay and angle is down to half the Rayleigh resolution limit (RRL) of the equipment; it is robust in the sense that it tends to return no more SCs than the actual ones. Finally, the algorithm is demonstrated to outperform a state-of-the-art super-resolution channel estimator in terms of robustness in the estimation of the amplitudes of specular components closely spaced in the dispersion domain.

We develop a unified Bayesian framework for optical flow (OF) estimation that uses a variational lower bound to obtain a variational approximation of the posterior probability distribution. Our framework enables the incorporation of domain-specific knowledge as well as a quantification of the uncertainty of OF estimation, and it encompasses existing maximum a posteriori (MAP) and variational Bayes (VB) methods as special cases. We leverage this flexibility for the ultrasound modality by using ultrasound-specific likelihood functions within both MAP and VB methods. Numerical results for the problem of cardiac motion estimation demonstrate that VB methods outperform MAP methods, in addition to providing a more faithful uncertainty measure.

We investigate the capacity scaling of multiple-input-multiple-output systems with the system dimensions. To that end, we quantify how the mutual information varies when the number of antennas (at either the receiver or transmitter side) is altered. For a system comprising R receive and T transmit antennas with R > T, we find the following: by removing as many receive antennas as needed to obtain a square system (provided the channel matrices before and after the removal have full rank) the maximum resulting loss of mutual information over all signal-to-noise ratios (SNRs) depends only on R, T, and the matrix of left-singular vectors of the initial channel matrix, but not on its singular values. In particular, if the latter matrix is Haar distributed the ergodic rate loss is given by Σt=1TΣr=T+1R1/r-t nats. Under the same assumption, if T, R → ∞ with the ratio φ=ΔT/R fixed, the rate loss normalized by R converges almost surely to H(φ) bits with H(·) denoting the binary entropy function. We also quantify and study how the mutual information as a function of the system dimensions deviates from the traditionally assumed linear growth in the minimum of the system dimensions at high SNR.

We design an algorithm for OFDM receivers operating in co-channel interference conditions, where the serving and interfering transmitters are synchronized in time. The channel estimation problem is formulated as one of sparse signal reconstruction using multiple measurement vectors. The proposed design harnesses the sparse common support of, respectively, the desired and interfering MIMO sub-channels by adopting a Bernoulli-Gaussian prior for the weights of the impulse responses of these sub-channels. Then, applying a variational Bayesian inference method we derive an algorithm that performs joint channel estimation, interference cancellation and decoding. Simulation results show how the performance of the proposed receiver depends on its knowledge of the interfering signals' modulation and code. When these are known, our receiver approaches the performance of a genie-aided receiver with perfect interference cancellation. Even with mismatched assumptions on the modulation, our proposed implementation still outperforms receivers which neglect the interference.

We introduce a theoretical approach for designing generalizations of the approximate message passing (AMP) algorithm for compressed sensing which are valid for large observation matrices that are drawn from an invariant random matrix ensemble. By design, the fixed points of the algorithm obey the Thouless-Anderson-Palmer (TAP) equations corresponding to the ensemble. Using a dynamical functional approach we are able to derive an effective stochastic process for the marginal statistics of a single component of the dynamics. This allows us to design memory terms in the algorithm in such a way that the resulting fields become Gaussian random variables allowing for an explicit analysis. The asymptotic statistics of these fields are consistent with the replica ansatz of the compressed sensing problem.

A source traffic model for machine-to-machine communications is presented in this paper. We consider a model in which devices operate in a regular mode until they are triggered into an alarm mode by an alarm event. The positions of devices and events are modeled by means of Poisson point processes, where the generated traffic by a given device depends on its position and event positions. We first consider the case where devices and events are static and devices generate traffic according to a Bernoulli process, where we derive the total rate from the devices at the base station. We then extend the model by defining a two-state Markov chain for each device, which allows for devices to stay in alarm mode for a geometrically distributed holding time. The temporal characteristics of this model are analyzed via the autocovariance function, where the effect of event density and mean holding time are shown.

Propagation channels with maximum excess delay exceeding the duration of the cyclic prefix (CP) in OFDM systems cause intercarrier and intersymbol interference which, unless accounted for, degrade the receiver performance. Using tools from Bayesian inference and sparse signal reconstruction, we derive an iterative algorithm that estimates an approximate representation of the channel impulse response and the noise variance, estimates and cancels the intrinsic interference and decodes the data over a block of symbols. Simulation results show that the receiver employing our algorithm outperforms receivers applying traditional interference cancellation and pilot-based schemes, and it approaches the performance of an ideal receiver with perfect channel state information and perfect interference cancellation capabilities. We highlight the relevance of our algorithm in the context of both current and future wireless communications systems. By enabling the OFDM receiver experiencing these harsh conditions to locally cancel the interference, our design circumvents the spectral efficiency loss incurred by extending the CP duration, otherwise a straightforward solution. Furthermore, it sets the premises for the development of receivers for multicarrier systems like 5G, in which the subcarrier orthogonality may be relaxed or the frame duration shortened, at the expense of cutting down the CP or even removing it altogether.

We propose a hybrid message passing method for distributed cooperative localization and tracking of mobile agents. Belief propagation and mean field message passing are employed for, respectively, the motion-related and measurement-related parts of the factor graph. Using a Gaussian belief approximation, only three real values per message passing iteration have to be broadcast to neighboring agents. Despite these very low communication requirements, the estimation accuracy can be comparable to that of particle-based belief propagation.

Bayesian hierarchical modelling is a well-established branch of Bayesian inference. In this letter, we derive and study the estimation performance for the Bayesian hierarchical linear model (BHLM). Specifically, we consider a linear model with hierarchical priors for the involved amplitude and noise vectors. We provide closed-form expressions of the Bayesian Cramér-Rao bound (BCRB) for the following settings: (i) an arbitrary prior and hyperprior and (ii) a Gaussian-Y prior for the amplitudes, while the prior of noise is a Gaussian-X in both cases. Gaussian-X means that the conditional prior given the hyperparameter is Gaussian and X is the hyperprior. For the hierarchical distribution associated with spherical invariant random variables, the BCRB has a compact closed-form expression and enjoys several interesting properties that are discussed. Finally, we provide a theoretical analysis of the statistical efficiency of the linear minimum mean square error (MMSE) estimator in the low- and high-noise variance regimes when the hyperparameters are stochastically dominant.

This letter deals with turbo equalization for coded data transmission over intersymbol interference (ISI) channels. We propose a message-passing algorithm that uses the expectation propagation rule to convert messages passed from the demodulator and decoder to the equalizer and computes messages returned by the equalizer by using a partial Gaussian approximation (PGA). We exploit the specific structure of the ISI channel model to compute the latter messages from the beliefs obtained using a Kalman smoother/equalizer. Doing so leads to a significant complexity reduction compared to the initial PGA implementation. Results from Monte Carlo simulations show that the proposed approach leads to a significant performance improvement compared to state-of-the-art turbo equalizers and allows for trading performance with complexity.

Recently we presented the S-AMP approach, an extension of approximate message passing (AMP), to be able to handle general invariant matrix ensembles. In this contribution we extend S-AMP to non-linear observation models. We obtain generalized AMP (GAMP) as the special case when the measurement matrix has zero-mean iid Gaussian entries. Our derivation is based upon 1) deriving expectation-propagation-(EP)-like equations from the stationary-points equations of the Gibbs free energy under first- and second-moment constraints and 2) applying additive free convolution in free probability theory to get low-complexity updates for the second moment quantities.

In this letter, a message-passing algorithm that combines belief propagation and expectation propagation is applied to design an iterative receiver for intersymbol interference channels. We detail the derivation of the messages passed along the nodes of a vector-form factor graph representing the underlying probabilistic model. We also present a simple but efficient method to cope with the “negative variance” problem of expectation propagation. Simulation results show that the proposed algorithm outperforms, in terms of bit-error-rate and convergence rate, a LMMSE turbo-equalizer based on Gaussian message passing with the same order of computational complexity.

In this letter, we design iterative receiver algorithms for joint frequency-domain equalization and decoding in a single carrier system assuming perfect channel state information. Based on an approximate inference framework that combines belief propagation (BP) and the mean field (MF) approximation, we propose two receiver algorithms with, respectively, parallel and sequential message-passing schedules in the MF part. A recently proposed receiver based on generalized approximate message passing (GAMP) is used as a benchmarking reference. The simulation results show that the BP-MF receiver with sequential passing of messages achieves the best BER performance at the expense of higher computational complexity compared to that of the GAMP receiver. The parallel BP-MF receiver has complexity similar to that of GAMP, but its low convergence rate yields poor performance, especially under high signal-to-noise ratio conditions.

We propose a novel iterative estimation algorithm for linear observation models called S-AMP. The fixed points of S-AMP are the stationary points of the exact Gibbs free energy under a set of (first- and second-) moment consistency constraints in the large system limit. S-AMP extends the approximate message-passing (AMP) algorithm to general matrix ensembles with a well-defined large system size limit. The generalization is based on the S-transform (in free probability) of the spectrum of the measurement matrix. Furthermore, we show that the optimality of S-AMP follows directly from its design rather than from solving a separate optimization problem as done for AMP.

We study the problem of interference alignment in the multiple-input multiple-output interference channel. Aiming at minimizing the interference leakage power relative to the receiver noise level, we use the deterministic annealing approach to solve the optimization problem. In the corresponding probabilistic formulation, the precoders and the orthonormal bases of the desired signal subspaces are variables distributed on the complex Stiefel manifold. To enable analytically tractable computations, we resort to the variational mean field approximation and thus obtain a novel iterative algorithm for interference alignment. We also show that the iterative leakage minimization algorithm by Gomadam et al. and the alternating minimization algorithm by Peters and Heath, Jr. are instances of our method. Finally, we assess the performance of the proposed algorithm through computer simulations.

In this paper, we present a Bayesian channel estimation algorithm for multicarrier receivers based on pilot symbol observations. The inherent sparse nature of wireless multipath channels is exploited by modeling the prior distribution of multipath components' gains with a hierarchical representation of the Bessel K probability density function; a highly efficient, fast iterative Bayesian inference method is then applied to the proposed model. The resulting estimator outperforms other state-of-the-art Bayesian and non-Bayesian estimators, either by yielding lower mean squared estimation error or by attaining the same accuracy with improved convergence rate, as shown in our numerical evaluation.

Existing methods for sparse channel estimation typically provide an estimate computed as the solution maximizing an objective function defined as the sum of the log-likelihood function and a penalization term proportional to the ℓ1-norm of the parameter of interest. However, other penalization terms have proven to have strong sparsity-inducing properties. In this work, we design pilot-assisted channel estimators for OFDM wireless receivers within the framework of sparse Bayesian learning by defining hierarchical Bayesian prior models that lead to sparsity-inducing penalization terms. The estimators result as an application of the variational message-passing algorithm on the factor graph representing the signal model extended with the hierarchical prior models. Numerical results demonstrate the superior performance of our channel estimators as compared to traditional and state-of-the-art sparse methods.

We design iterative receiver schemes for a generic communication system by treating channel estimation and information decoding as an inference problem in graphical models. We introduce a recently proposed inference framework that combines belief propagation (BP) and the mean field (MF) approximation and includes these algorithms as special cases. We also show that the expectation propagation and expectation maximization (EM) algorithms can be embedded in the BP-MF framework with slight modifications. By applying the considered inference algorithms to our probabilistic model, we derive four different message-passing receiver schemes. Our numerical evaluation in a wireless scenario demonstrates that the receiver based on the BP-MF framework and its variant based on BP-EM yield the best compromise between performance, computational complexity and numerical stability among all candidate algorithms.

In this paper, we present a thorough investigation on the impact of spatial smoothing and forward-backward averaging techniques for subspace-based channel estimation. The spatial smoothing technique requires the selection of a window size, which, if not selected properly, leads to dramatically performance breakdown of the subspace-based methods. We aim to provide an explanation of the performance drop for certain window sizes and subsequently an understanding of a proper window size selection. In particular, we describe the behavior of the magnitude of the least signal eigenvalue as a function of the window size employed. Through simulations we show that the magnitude of this eigenvalue is of particular importance for estimating the subspace and the entailing performance of the channel estimator.

We propose a novel algorithm for sensor self-localization in cooperative wireless networks where observations of relative sensor distances are available. The variational message passing (VMP) algorithm is used to implement a mean field solution to the estimation of the posterior probabilities of the sensor positions in an R2scenario. Extension to R3is straight-forward. Compared to non-parametric methods based on belief propagation, the VMP algorithm features significantly lower communication overhead between sensors. This is supported by performance simulations which show that the estimated mean localization error of the algorithm stabilizes after approximately 30 iterations.

A general path loss model for in-room radio channels is proposed. The model is based on experimental observations of the behavior of the delay-power spectrum in closed rooms. In such a room, the early part of the spectrum observed at different positions typically consists of a dominant component (peak) that vanishes as the transmitter-receiver distance increases; the late part decays versus distance according to the same exponential law in delay regardless of the distance. These observations motivate the proposed model of the delay-power spectrum with an early dominant component and a reverberant component. The dominant component is modeled as a Dirac delta function weighted with a factor decaying according to an inverse distance power law (d-n). The reverberant component is an exponentially decaying function versus delay with distance-dependent onset. Its power decays exponentially with distance. The proposed model allows for the prediction of path loss, mean delay, and rms delay spread versus distance. We use measurements to validate the model. We observe good agreement of the model prediction for mean delay and rms delay spread.

In this contribution, a multi-user receiver for M-QAM MIMO-OFDM operating in time-varying and frequency-selective channels is derived. The proposed architecture jointly performs semi-blind estimation of the channel weights and noise inverse variance, serial interference cancellation and decoding in an iterative manner. The scheme relies on a variational message-passing approach, which enables a joint design of all these functionalities or blocks but the last one. Decoding is performed using the sum-product algorithm. This is in contrast to nowadays proposed approaches in which all these blocks are designed and optimized individually. Simulation results show that the proposed receiver outperforms in coded bit-error-rate a state-of-the- art iterative receiver of same complexity, in which all blocks are designed independently. Joint block design and, as a result, the fact that the uncertainty in the channel estimation is accounted for in the proposed receiver explain this better performance.

In this paper we present a refined model of the wireless multipath channel along with a thorough analysis on the impact of spatial smoothing techniques when used for improved channel estimation. The state-of-the-art channel estimation algorithm for pilot-aided OFDM systems is robustly designed and operates without knowledge of the time-varying multipath propagation delays in the wireless channel. However, algorithms exploiting knowledge of these time-varying delay parameters can outperform the state-of-the-art solution. We demonstrate from simulations how the Unitary ESPRIT algorithm together with spatial smoothing techniques exhibit a promising potential for multipath propagation delay estimation. Furthermore, we show that the optimum smoothing parameters depend notably on the channel model assumed, specifically in terms of the dynamical behavior of the multipath delays.

In this paper, we present a novel iterative receiver for MIMO-OFDM systems with synchronous interferers. The receiver is derived based on the Kullback-Leibler divergence minimization framework, and combines channel estimation, interference cancellation and residual noise estimation in an iterative manner. By using both the pilot and data symbols, the channel estimator improves the accuracy of the estimates in each iteration, which leads to a more effective interference cancellation and data detection process. A performance evaluation based on Monte-Carlo simulations shows that the proposed scheme can effectively mitigate the effect of interferers, and operates very close to the single-user performance even in severe interference scenarios.

In this paper, we present a novel approach for pilot-aided channel estimation in OFDM systems with synchronous co-channel interference. The estimator is derived based on the Kullback-Leibler divergence minimization framework. The obtained solution iteratively updates both the desired user's and the interferer's channels, using a combination of linear minimum mean squared-error (LMMSE) filtering and interference cancellation, avoiding the complex matrix inversions involved in the full LMMSE channel estimation approach. Estimation of the noise variance is also included in the iterative algorithm, accounting for Gaussian noise and residual interference after each iteration. The estimates of both channels are used at the equalizer to reject the interfering signal, thus mitigating the degradation due to co-channel interference. Simulation results show that the receiver using the proposed estimator performs as good as the one employing the full LMMSE estimator and very closely to a receiver having perfect knowledge of the channel coefficients.

Non wide-sense stationary (WSS) uncorrelated-scatterering (US) fading processes are observed in vehicular communications. To estimate such a process under additive white Gaussian noise we use the local scattering function (LSF). In this paper we present an optimal parametrization of the multitaper-based LSF estimator. We do this by quantizing the mean square error (MSE). For that purpose we use the structure of a two-dimensional Wiener filter and optimize the parameters of the estimator to obtain the minimum MSE (MMSE). We split the observed fading process in WSS regions and analyze the influence of the estimator parameters on the MMSE under different lengths of the stationarity regions and signal-to-noise ratio values. The analysis is performed considering three different scenarios representing different scattering properties. We show that there is an optimal combination of estimator parameters for different lengths of stationarity region and signal-to-noise ratio values which provides a minimum MMSE.

Due to the significantly reduced cost and effort for system calibration time-division multiplexing (TDM) is a commonly used technique to switch between the transmit and receive antennas in multiple-input multiple-output (MIMO) radio channel sounding. Nonetheless, Baum et al. have shown that phase noise of the transmitter and receiver local oscillators, when it is assumed to be a white Gaussian random process, can cause large errors of the estimated channel capacity of a low-rank MIMO channel when the standard channel matrix estimator is used. Experimental evidence shows that consecutive phase noise samples affecting measurement samples collected with real TDM-MIMO channel sounders are correlated. In this contribution a capacity estimator that accounts for the phase noise correlation is proposed. The estimator is based on a linear minimum mean square error estimate of the MIMO channel matrix. It is shown by means of Monte Carlo simulations assuming a measurement- based phase noise model, that the MIMO channel capacity can be estimated accurately for signal-to-noise ratios up to about 35 dB.

We investigate link quality metrics (LQMs) based on mutual information (MI) for fast link adaptation (FLA) in IEEE 802.11n wireless local area network (WLAN) with convolutional coding and higher order modulations. The LQMs are scalar quantities that map the receiver's post-decoding behaviour in a frequency-selective channel into an equivalent behaviour in an AWGN channel. From this metric the expected packet error rate (PER) can be predicted. Two LQMs are presented that are derived from the SINRs of all sub-carriers and streams: the effective SNR and the effective mutual information. The effective mutual information is the mean mutual information including a correction factor which improves the PER estimation accuracy in various highly frequency-selective channels. The FLA algorithm dynamically selects a modulation and coding scheme (MCS) that maximizes the throughput (TP), while keeping the average PER over time below a target value. Furthermore, we present methods of searching for the most suitable MCS. Practical performance bounds are obtained by means of simulations. We show that both investigated LQMs yield accurate PER estimates and that the resulting TP of the FLA algorithm used in a 2 x 2 MIMO bit-interleaved coded modulation (BICM) OFDM system that performs channel estimation is only 1.7 dB from the performance bound of the TP.

In this contribution a low-complexity particle filtering algorithm is proposed to track the parameters of time-variant propagation paths in multiple-input multiple-output (MIMO) radio channels. A state-space model is used to describe the path evolution in delay, azimuth of arrival, azimuth of departure, Doppler frequency and complex amplitude dimensions. The proposed particle filter (PF) has an additional resampling step specifically designed for wideband MIMO channel sounding, where the posterior probability density functions of the path states is usually highly concentrated in the multi-dimensional state space. Preliminary investigations using measurement data show that the proposed PF can track paths stably with a small number of particles, e.g. 5 per path, even in the case where the paths are undetected by the conventional SAGE algorithm.

The wireless hybrid enhanced mobile radio estimators (WHERE) consortium researches radio positioning techniques to improve various aspects of communications systems. In order to provide the benefits of position information available to communications systems, hybrid data fusion (HDF) techniques estimate reliable position information. Within this paper, we first present the scenarios and radio technologies evaluated by the WHERE consortium for wireless positioning. We compare conventional HDF approaches with two novel approaches developed within the framework of WHERE. Yet, HDF may still provide insufficient localization accuracy and reliability. Hence, we will research and develop new cooperative positioning algorithms, which exploit the available communications links among mobile terminals of heterogeneous wireless networks, to further enhance the positioning accuracy and reliability.

In this paper, a theoretical framework of divergence minimization (DM) is applied to derive iterative receiver algorithms for coded CDMA systems. The DM receiver obtained performs joint channel estimation, multiuser decoding, and noise- covariance estimation. While its structure is similar to that of many ad-hoc receivers in the literature, the DM receiver is the result of applying a formal framework for optimization without further simplifications, namely the DM approach with a factorizable auxiliary model distribution. The well-known expectation- maximization (EM) algorithm and space-alternating generalized expectation-maximization (SAGE) algorithm are special cases of degenerate model distributions within the DM framework. Furthermore, many ad-hoc receiver structures from literature are shown to represent approximations of the proposed DM receiver. The DM receiver has four interesting properties that all result directly from applying the formal framework: (i) The covariances of all estimates involved are taken into account, (ii) The residual interference after interference cancellation is handled by the noise-covariance estimation as opposed to by LMMSE filters in other receivers, (iii) Posterior probabilities of the code symbols are employed rather than extrinsic probabilities, (iv) The iterative receiver is guaranteed to converge in divergence. The theoretical insights are illustrated by simulation results.

This paper deals with a novel design approach for a converging iterative receiver for coded CDMA that estimates both the channel coefficients and the transmitted symbols. The receiver design is based on the variational Bayesian space-alternating generalized expectation-maximization (VB-SAGE) method. Conceptually, the probability distribution of each user's code sequence and the probability distribution of all channel coefficients are updated in an iterative fashion. The obtained receiver, which we refer to as VB-SAGE receiver, performs iterative channel estimation, interference cancellation and single-user decoding. Even though the design is based on code sequence probabilities, only the soft decisions (mean values) and the variances of the code symbols are required for channel estimation and interference cancellation; moreover, the variances are functions of the soft decisions. These soft decisions are computed by the single-user decoders based on the outputs of the interference cancellation device. The iterative process of the VB-SAGE receiver is guaranteed to converge in the free energy. The VB-SAGE method proposed in this paper may also be used for other applications.

Time-division multiplexing (TDM) is commonly used to switch between the elements of the transmit and receive antenna arrays in multiple-input multiple-output (MIMO) radio channel sounding. However, phase noise of the local phase- locked oscillators at the transmitter (TX) and the receiver (RX) causes measurement errors that can lead to significant impairment of the performance of traditional estimators of the radio channel parameters, like the path parameters (direction of departure, direction of arrival) and the channel capacity. In this paper, we derive a signal model for phase noise on short- term and long-term observation window scales. The short-term and long-term behaviours of phase noise are modelled as an autoregressive moving average (ARMA) and an autoregressive integrated moving average (ARIMA) model respectively. We focus the investigations on the characterization of the short-term component of phase noise, as this component predominates on the scale of the duration of the measurement cycles in MIMO channel sounding. All pair of TX and RX array elements are switched once in a measurement cycle. The ARMA model for the short-term phase noise component is validated by contrasting the sample autocorrelation function, the periodogram, and the sample Allan variance obtained from phase-noise measurement data with those computed from the estimated ARMA model. Finally, the impact of phase noise on the traditional estimate of MIMO channel capacity is analyzed. We show that the performance impairment is less than that shown in [5] under the hypothesis of uncorrelated phase-noise samples. The difference is due to the non-vanishing correlation between temporally nearby phase-noise samples. In addition, we show that the length of the period of the sounding signal affects the channel capacity estimate as well. This can be explained by the fact that the correlation between phase noise samples corresponding to different sounding periods decreases as the period length increases.

In this contribution, the Fisher-Bingham-5 (FB5) probability density function (pdf) is used to model the shape of the direction power spectral density function (psdf) of individual path components in the radio channel. The FB5 distribution is selected because, among all direction distributions, it maximizes the entropy under the constraints that the first and second distribution moments are specified. A SAGE (space-alternating generalized expectation-maximization) algorithm is derived based on this model for estimation of the parameters characterizing the direction psdf of each path component in a multi-path scenario. The performance of the SAGE algorithm is evaluated using measurement data. Preliminary results show that the estimated direction psdfs of individual path components exhibit different ovalnesses and tilt angles. These density functions are noticeably more concentrated than the corresponding footprints in the Bartlett spectrum.

In this contribution the radio channel model proposed in [1] is extended to include multiple transmitters and receivers. The propagation environment is modelled using random graphs where vertices of a graph represent scatterers and edges model the wave propagation between scatterers. Furthermore, we develop a closed form analytical expression for the transfer matrix of the propagation graph. It is shown by simulation that impulse response and the delay-power spectrum of the graph exhibit exponentially decaying power as a result of the recursive scattering structure of the graph. The impulse response exhibits a transition from specular to diffuse signal contributions as observed in measurements.

In this paper, the space alternating generalized expectation-maximization (SAGE) method is applied to derive receivers for coded CDMA systems. In the so-called SAGE receiver, hard decision code symbols are fed back from the single user decoders to the joint channel estimator and interference canceler. Using multivariate Gaussian approximations, the SAGE receiver is then modified such that soft values of code symbols are fed back from the single user decoders. We refer to this modified receiver as SAGE-based receiver. Compared to the SAGE receiver, the SAGE-based receiver considers the statistical properties of the code symbols, thus the channel estimation and the interference cancellation take symbol estimation errors into account. A performance improvement in terms of bit error rate (BER) and system load of the SAGE-based receiver compared to the SAGE receiver and other receivers is shown by means of Monte Carlo simulations.

This paper deals with the derivation and optimization of an iterative receiver architecture performing joint multiuser decoding and channel estimation. We consider an asynchronous multirate convolutional coded DS-CDMA system that communicates over quasi-static flat Rayleigh fading channels. The proposed receiver is derived within the space-alternating generalized expectation-maximization (SAGE) framework in connection with the noise-splitting approach. The used theoretical framework guarantees convergence of the receiver, as opposed to many other iterative receiver structures. Furthermore, the noise-splitting approach provides a set of noise-weighting coefficients that can be optimized under weak constraints. The inputs to the single-user decoders are linear combinations of two kinds of soft values with weights determined by the noise-weighting coefficients. These two kinds of soft values can be interpreted as a priori information and extrinsic information, respectively, if the channels are known. In the case of unknown channels, they are asymptotically a priori and asymptotically extrinsic, i.e., they become a priori and extrinsic when the length of the observed frame tends to infinity. In most cases, the optimum coefficients lead to extrinsic or asymptotically extrinsic values fed to the input of the single-user decoders. Monte Carlo simulations show that the proposed receiver is resistant to channel estimation errors and supports high system loads.

Essential parameters of physical, propagation-based MIMO channel models are the fading statistics and the directional spread of multipath clusters. In this paper we determine these parameters in the azimuth-of-arrival/azimuth-of-departure (AoA/AoD) domain based on comprehensive indoor MIMO measurements at 5.2 GHz in a cluttered office environment using the SAGE algorithm for parameter estimation. Due to cluster identification in AoA/AoD-domain we found a greater number of clusters than those reported in previous publications. Regarding the fading statistics of clusters, so far not studied, strong (obstructed-)line-of-sight clusters show Rician fading, corresponding to few dominant propagation paths, whereas most clusters exhibit Rayleigh fading, corresponding to many paths with approximately equal powers and uncorrelated phases. Root-mean-square cluster azimuth spreads (CASs) were estimated with a novel method by appropriately restricting the support of the cluster azimuth distribution. We found that the estimated CASs are different when seen from transmitter or receiver, i.e. their ranges are from 2deg to 9deg and from 2deg to 7deg at the transmitter side and the receiver side, respectively

In this paper, a unified framework for Ultra-Wideband channel (UWB channel) modeling based on the maximum entropy approach is provided. For a given set of constraints, a consistent model which takes into account the information at hand is obtained. Two cases are considered: channel power knowledge and knowledge of the covariance matrix. The channel power delay spectrum is also derived and the impact of the channel bandwidth is assessed through information theoretic considerations. The information variation slope with respect to the bandwidth is also studied, based on wideband measurements performed at Institut Eurecom1.

We present the basic methodology for minimum-energy bandlimited prediction of time-variant flat Rayleigh-fading channels. This predictor is based on a subspace spanned by time-concentrated and bandlimited sequences. The concept of time-variant channel estimation using time-concentrated and band-limited sequences was introduced recently by Zemen et al. We extend this concept to the problem of time-variant channel prediction. Slepian showed that discrete prolate spheroidal (DPS) sequences can be used to calculate the minimum-energy bandlimited continuation of a finite sequence. DPS sequences are optimal for a time-variant channel with flat Doppler spectrum. We generalize the concept of time-concentrated and band-limited sequences to arbitrary Doppler spectra approaching closely the lower prediction error limit defined by the Wiener filter. In practical systems detailed channel covariance information is not available. We design a set of subspaces spanned by DPS sequences with fixed time-concentration but growing bandwidth. The best DPS subspace is selected dynamically for each observation interval using a Doppler bandwidth estimate allowing for low complexity channel prediction. The performance of the new predictor is compared to that of the Wiener filter by means of Monte Carlo simulations.

This contribution provides a fresh look at the asymptotic (in terms of number of antennas) design of multiple-antenna wireless systems, with the goal of giving useful insights on the deployment of future MIMO systems. For the i.i.d. Gaussian and double-directional models, we provide guidelines in terms of the repartition of the antennas between the transmitter and the receiver, and study the influence of array geometry on the ergodic mutual information per antenna. Furthermore, we compare the LOS and NLOS situations, and evaluate the relative importance of the LOS component and path loss in Ricean fading, as well as in the low-rank Ricean component case.

An iterative receiver for joint multiuser-decoding and channel-estimation of coded CDMA is derived by applying the noise-splitting approach within the space alternating generalized expectation-maximization (SAGE) framework. We consider asynchronous single-rate DS/CDMA over flat Rayleigh fading channels. The resulting receiver structure comprises partial successive interference-cancellation (SIC), channel estimation, and soft-input/hard-output maximum likelihood sequence decoding (MLSD) for each user. Additionally, one obtains a set of noise-weighting coefficients that can be freely chosen within weak constraints. These coefficients determine the amount of feedback from the decoder output to the decoder input in the subsequent iteration, and thus, "how extrinsic" the decoder output values are. The noise-weighting coefficients strongly influence the system performance. Their optimization within the SAGE framework leads to extrinsic output values in most of the cases. The proposed receiver is evaluated by Monte-Carlo simulations, and it shows two major advantages: high load is supported and convergence is guaranteed.

This paper addresses application of the Bayesian evidence procedure to the analysis of wireless channels. We use relevance vector machines, a kernel-based technique to locally maximize evidence that turns out to be promising in the context of the wireless channel estimation. This approach not only allows to estimate channel parameters, but also provides a tool to assess the number of multipath components. We show that in the case of channel sounding using a pulse-compression technique, it is possible to design an optimal kernel, as well as to estimate parameters of the additive noise and base on it a thresholding level to implement model order estimation. The applicability of the proposed scheme is demonstrated with synthetic as well as real channel measurements.

An important parameter of MIMO channel models is the cluster root-mean-square (rms) directional spread. In this paper we determine this parameter in the azimuth-of-arrival/azimuth-of-departure (AoA/AoD) domain based on comprehensive indoor MIMO measurements at 5.2 GHz in a cluttered office environment. This is done in a four-step procedure: (i) the SAGE algorithm is used to extract propagation paths, (ii) clusters of estimated paths in the double-azimuth domain are defined, (iii) the estimated propagation paths are allocated to the clusters, (iv) the cluster directional spreads are estimated based solely on propagation paths within the clusters. We found that the spreads are different when seen from transmitter or receiver due to different propagation conditions resulting in AoD rms cluster spreads lying in the range from 2 to 9 degrees and AoA rms cluster spreads in the range from 2 to 7 degrees.

In this paper, an azimuth spread estimator (ASE) for slightly distributed scatters (SDSs) is derived based on the generalized-array-manifold (GAM) approximation model [1]. To improve the performance of this estimator we propose an array size adaptation (ASA) technique that adjusts the array aperture selectively for each SDS by modifying the number of antennas. This technique is applied to uniform linear arrays but can be extended to two or three dimensional arrays. Simulation results demonstrate the improvement achieved with the combined ASA-ASE scheme. In particular, it is shown that this scheme outperforms the conventional Spread-ESPRIT technique.

To save hardware and reduce the effort to calibrate the system, channel sounding with Tx and Rx antenna arrays is commonly performed in TDM mode where the array elements are successively switched. We refer to this technique as TDM-MIMO channel sounding. The ISI-SAGE algorithm (Fleury, B.H. et al., 2003; Yin, X. et al., 2003), applied in combination with TDM-MIMO channel sounding, makes it possible to extend the Doppler frequency estimation range (DFER) (Yin, X. et al., 2003). The extension is significant when arrays with large element numbers are employed. We derive the signal model for TDM-MIMO channel sounding and report analytical investigations showing that this DFER extension requires selection of switching modes (SMs) tailored to the array characteristics. The SM of a switched array is the temporal order in which the array elements are switched. In fact, the traditionally used SMs of uniform linear and planar arrays, where the elements are switched according to their natural spatial ordering, prove to be inappropriate as they lead to an ambiguity in the joint estimation of DF and directions. We also introduce the concept of normalized sidelobe level (NSL) associated to the SM of a switched array. We show that minimizing the NSL is a sensible criterion for the identification of SM, leading to DF and direction estimates with nearly optimum performance in terms of root mean square estimation error. Finally experimental investigations illustrate the impact of the SM of a uniform planar array on the behaviour of the DF and direction of arrival estimates computed with the ISI-SAGE algorithm.

In this paper, we present an efficient iterative receiver architecture of tractable complexity for joint multiuser detection and channel estimation (JDE) in DS/CDMA based on the EM algorithm. The EM algorithm provides a set of free parameters called weight coefficients which can be selected to optimize its performance. Two optimality criteria are defined and analytical expressions for the corresponding optimized weight coefficients are given. Monte Carlo simulations of an asynchronous multi-rate system operating in flat Rayleigh fading channel show that the proposed receiver is near-far resistant and robust against errors in estimation of the channel parameters.

We proposed (Fleury, B.H. et al., Proc. XXVII Gen. Assy of Int. Union of Radio Scientists, p.2127, 2002; Proc. IEEE Veh. Tech. Conf., VTC 2002, p.522-6, 2002) the ISI-SAGE (improved-search-and-initialization space-alternating generalized expectation-maximization) algorithm for joint estimation of the relative delay, the directions of departure and of incidence, the Doppler frequency (DF) and the complex weight (or attenuation) of waves propagating from the transmitter (Tx) site to the receiver (Rx) site in mobile radio environments. We now present theoretical and simulation results describing the performance of the scheme for DF estimation applied in combination with channel sounding using switched multiple-element Tx and Rx antennas. The maximum absolute DF that can be estimated is shown to be half the switching rate rather than half the measurement cycle rate as commonly believed. The switching rate is the rate with which the pairs of Tx and Rx elements are switched, while the measurement cycle rate is the rate with which any fixed pair of Tx and Rx elements is switched. The ratio of the former rate by the latter is larger than or equal to the product of the numbers of Tx and Rx elements. Hence, the scheme allows for DF estimation in a range much larger than commonly believed. Monte-Carlo simulations also show that above a certain signal-to-noise-ratio (SNR) threshold, depending on the characteristics of the TDM mode, the estimator performs close to optimum. The results make it possible to link the parameter setting of the TDM mode to the operational SNR range for individual waves to be estimated.

We consider semidefinite relaxations of a quadratic optimization problem with polynomial constraints. This is an extension of quadratic problems with Boolean variables. Such combinatorial problems cannot, in general, be solved in polynomial time. Semidefinite relaxation has been proposed as a promising technique to give provable good bounds on certain Boolean quadratic problems in polynomial time. We formulate the extensions from Boolean variables to quarternary variables using (i) a polynomial relaxation or (ii) standard semidefinite relaxations of a linear transformation of Boolean variables. We compare the two different relaxation approaches analytically. The relaxations can all be expressed as semidefinite programs, which can be solved efficiently using e.g. interior point methods. Applications of our results include maximum likelihood estimation in communication systems, which we explore in simulations in order to compare the quality of the different relaxations with optimal solutions.

Joint optimization of both signature sequences and linear receiver filters for a downlink DS-CDMA system with multipath propagation channels is considered. The signature sequences and the receiver filters are optimized in order to minimize the sum of the mean-squared-errors at the output of the receivers while maintaining a fixed total transmitting power. The signature sequences and receiver filters are derived using a filtering approach to accommodate for the multipath propagation effects.

This contribution describes an extension of the ISI-SACR (initialization-and-search-improved space-alternating generalized expectation maximization) algorithm originally published in [B.H. Fleury, et al., 2001] and [2002] to include polarization estimation. The proposed scheme allows for joint estimation of the relative delay, the direction (i.e. azimuth and co-elevation) of departure, the direction of incidence, the Doppler frequency and the complex polarization matrix of propagation paths between the transmitter (Tx) site and the receiver (Rx) site in mobile radio environments. This contribution presents the initialization procedure of the extended ISI-SAGR algorithm and discusses necessary and sufficient conditions regarding the responses of multiple-element Tx and Rx arrays for the system consisting of these two arrays to be able to estimate all coefficients of the polarization matrix. Experimental investigations in a line-of-sight microcellular environment illustrate the application potential of the ISI-SACR algorithm for gaining insight into the polarization states of individual paths. This information is of paramount importance for the design of stochastic and prediction models ut the radio channel for communication systems equipped with multiple Tx and Rx dual-polarized antennae.

We present two efficient iterative receiver structures of tractable complexity for joint multiuser detection and multichannel estimation (JDE) of direct-sequence code-division multiple-access signals. The schemes result from an application of the expectation-maximization (EM) and the space-alternating generalized expectation-maximization (SAGE) algorithms, respectively. The EM-JDE receiver updates the data bit sequences in parallel, while the SAGE-JDE receiver reestimates them successively. The channel parameters are updated in parallel in both schemes. The EM algorithm provides a set of free parameters, called weight coefficients, which can be selected to optimize its performance. Two optimality criteria are defined and analytical expressions for the corresponding optimized weight coefficients are given. Monte-Carlo simulations of a synchronous scenario show that the proposed JDE receivers have excellent multiuser efficiency and are robust against errors in the estimation of the channel parameters. Moreover, very short training sequences are required for the JDE schemes to converge. Simulation results further demonstrate that the SAGE-JDE receiver exhibits a better performance when the users' bit sequences are updated in the order of increasing signal strength, i.e., the bit sequence of the user with the weakest signal strength is updated first at each stage.

This contribution presents results from an application of the SAGE (space-alternating generalized expectation-maximization) algorithm published in Fleury et al. (2002) to measurement data collected in a selected propagation environment. The scheme jointly estimates the delay, the direction (i.e. azimuth and coelevation) of departure, the direction of incidence, as well as the Doppler frequency of waves propagating from the transmitter to the receiver. An improved initialization and search procedure is proposed which enhances the probability of identifying weak paths and therefore allows for a more comprehensive and detailed characterization of the propagation mechanisms. In order to relate the estimated waves to the propagation environment, a simple method based on ray tracing attempts to reconstruct the propagation paths based on the estimated wave parameters while assuming oneand two-bounce scattering. Significant objects can be identified in the environment that coincide with the interaction points of the calculated paths. The same conclusions can be drawn from similar analyses of other environments. The presented results demonstrate the high potential of high-resolution estimation techniques performing true joint estimation of delay, direction of departure, and direction of incidence for detailed investigations of dispersion in the radio channel jointly in delay and in direction at both transmitter and receiver sites. These studies are of paramount importance for an accurate characterization of MIMO (multiple-input multiple-output) systems operating in these channels.

We present a method of tractable complexity for joint data detection and channel estimation of DS/CDMA signals. The scheme results from an application of the SAGE algorithm. Monte Carlo simulations of a synchronous scenario show that the method is near-far resistant and that it is robust against estimation errors of the channel parameters. Moreover, very short training sequences are required for the scheme to converge. Simulation results further demonstrate that a better performance is obtained when the users' bit sequences are cyclically updated in the order of increasing strength of the users' signals at the output of the whitening filter in the receiver.

We present analytical results relating to first- and second-moment characterization of direction dispersion and spatial selectivity in the radio channel as well as to the duality between these two effects. Dispersion in direction can be characterized either by the direction power spectrum or by a family of spatial Doppler power spectra at the reception site. Two measures called the direction spread and the maximum spatial Doppler spread are introduced which describe the extent of channel dispersion in direction and in spatial Doppler frequency, respectively. Both measures are analogous to the delay and Doppler spreads, which are commonly employed to describe the extent of dispersion in delay and Doppler frequency, respectively. The relationships between the two approaches for characterizing spatial dispersion and especially between the direction and maximum spatial Doppler spreads are analytically established. The coherence distance at a certain level summarizes certain features of space selectivity in the radio channel which impact on the performance of communication systems. Two uncertainty relations between the direction spread and the coherence distance as well as between the maximum spatial Doppler spread and the coherence distance express the duality between direction dispersion and space selectivity. These relations are analogous to those established previously between the delay spread and the coherence bandwidth and between the Doppler spread and the coherence time. Examples relevant to mobile communications in the case where the waves propagate only horizontally illustrate the theoretical results. An application of these results to the design of uniform linear antenna arrays is also discussed.

This study investigates the application potential of the SAGE (space-alternating generalized expectation-maximization) algorithm to jointly estimate the relative delay, incidence azimuth, Doppler frequency, and complex amplitude of impinging waves in mobile radio environments. The performance, i.e., high-resolution ability, accuracy, and convergence rate of the scheme, is assessed in synthetic and real macro- and pico-cellular channels. The results indicate that the scheme overcomes the resolution limitation inherent to classical techniques like the Fourier or beam-forming methods. In particular, it is shown that waves which exhibit an arbitrarily small difference in azimuth can be easily separated as long as their delays or Doppler frequencies differ by a fraction of the intrinsic resolution of the measurement equipment. Two waves are claimed to be separated when the mean-squared estimation errors (MSEEs) of the estimates of their parameters are close to the corresponding Cramer-Rao lower bounds (CRLBs) derived in a scenario where only a single wave is impinging. The adverb easily means that the MSEEs rapidly approach the CLRBs, i.e., within less than 20 iteration cycles. Convergence of the log-likelihood sequence is achieved after approximately ten iteration cycles when the scheme is applied in real channels. In this use, the estimated dominant waves can be related to a scatterer/reflector in the propagation environment. The investigations demonstrate that the SAGE algorithm is a powerful high-resolution tool that can be successfully applied for parameter extraction from extensive channel measurement data, especially for the purpose of channel modeling.

A demodulation algorithm for a base station receiver in a direct sequence (DS) spread spectrum code division multiple access (CDMA) communication system is proposed which performs joint multiuser detection and estimation using the output signals of an antenna array in the absence of a tight power control. The scheme is a combination of a multistage (MS) detector for data recovery and a space-alternating generalized expectation maximization (SAGE) algorithm for channel parameter estimation. Monte-Carlo simulations show that the scheme is able to overcome the near-far problem while simultaneously combining the signal energy spread over time and space in a nearly optimum fashion.

A stochastic radio channel model (SRCM) for broadband indoor mobile systems operating at 5.2 and 17 GHz has been derived within the ACTS project AC085 Magic WAND. The SRCM accurately describes the dispersive nature of real radio channels in time, frequency, direction, and polarization. These effects are important for the design and performance evaluation of advanced receiver structures that exploit the inherent channel diversity, e.g., by means of adaptive antennas. The wideband SRCM takes into account all relevant propagation effects observed in real indoor environments. For example, it includes large-scale fluctuations such as transitions where waves are emerging and vanishing as well as the delay drift of the waves. In the paper, the modeling approach adopted for the SRCM is described and illustrated by simulation results.

The applicability of the SAGE (space-alternating generalized expectation-maximization) algorithm to the estimation of time variant radio channels is demonstrated. This algorithm allows one to separate the complex multi-dimensional optimization problem required to compute the estimate of the parameters characterizing the impinging waves, i.e. their delay, incidence azimuth, Doppler frequency, and complex amplitude, into separate one dimensional optimization processes that can be performed sequentially. The performance of the scheme, i.e. its convergence behavior and its accuracy, is investigated in synthetic and real channels.

An uncertainty relation of the same kind as the one by Heisenberg is established between the coherence interval and the spectral spread of zero-mean wide-sense-stationary mean-square-continuous processes whose spectrum has a finite second moment. Pairs of estimates of the coherence bandwidth and of the corresponding delay spread which have been obtained from measurements in an indoor radio environment are confined as stated by this uncertainty relation.

New bounds for real, continuous, nonnegative-definite functions are established. As an application it is shown that the variation of a real mean-square-continuous (MSC) wide-sense-stationary (WSS) process is bounded by its Maclaurin polynomials, either from below or from above depending on their degree. The least upper bound for the variation of a real MSC WSS process which depends solely on the process' spectral spread is also obtained. In comparison to previously published results, the new bounds present many advantages which are discussed. The extension of these bounds to complex MSC WSS processes is straightforward.>