Functional magnetic resonance imaging (fMRI) is one of the most popular methods for studying the human brain. Task-related fMRI data processing aims to determine which brain areas are activated when a specific task is performed and is usually based on the Blood Oxygen Level Dependent (BOLD) signal. The background BOLD signal also reflects systematic fluctuations in regional brain activity which are attributed to the existence of resting-state brain networks. We propose a new fMRI data generating model which takes into consideration the existence of common task-related and resting-state components. We first estimate the common task-related temporal component, via two successive stages of generalized canonical correlation analysis and, then, we estimate the common task-related spatial component, leading to a task-related activation map. The experimental tests of our method with synthetic data reveal that we are able to obtain very accurate temporal and spatial estimates even at very low Signal to Noise Ratio (SNR), which is usually the case in fMRI data processing. The tests with real-world fMRI data show significant advantages over standard procedures based on General Linear Models (GLMs).

We consider the problem of nonnegative tensor factorization. Our aim is to derive an efficient algorithm that is also suitable for parallel implementation. We adopt the alternating optimization (AO) framework and solve each matrix nonnegative least-squares problem via a Nesterov-type algorithm for strongly convex problems. We describe a parallel implementation of the algorithm and measure the speedup attained by itsMessage Passing Interface implementation on a parallel computing environment. It turns out that the attained speedup is significant, rendering our algorithm a competitive candidate for the solution of very large-scale dense nonnegative tensor factorization problems.

Most tensor decomposition algorithms were developed for in-memory computation on a single machine. There are a few recent exceptions that were designed for parallel and distributed computation, but these cannot easily incorporate practically important constraints, such as nonnegativity. A new constrained tensor factorization framework is proposed in this paper, building upon the Alternating Direction method of Multipliers (ADMoM). It is shown that this simplifies computations, bypassing the need to solve constrained optimization problems in each iteration, yielding algorithms that are naturally amenable to parallel implementation. The methodology is exemplified using nonnegativity as a baseline constraint, but the proposed framework can incorporate many other types of constraints. Numerical experiments are encouraging, indicating that ADMoM-based nonnegative tensor factorization (NTF) has high potential as an alternative to state-of-the-art approaches.

We assess the impact of the channel and carrier frequency offset (CFO) estimation errors on the performance of single-carrier systems with MMSE linear equalizers. Performance degradation is caused by the fact that a mismatched MMSE linear equalizer is applied to channel output samples with imperfectly canceled CFO. We develop asymptotic expressions for the excess mean square error (EMSE) induced by the channel and CFO estimation errors. Under some realistic assumptions, we derive a simple EMSE approximation which reveals that performance degradation is mainly caused by the imperfectly canceled CFO. Furthermore, the EMSE is approximately proportional to the CFO estimation error variance, with the proportionality factor being independent of the training sequence. Thus, optimal training sequence (TS) design for CFO estimation is also highly relevant for joint channel and CFO estimation.

The maximization of a full-rank quadratic form over the binary alphabet can be performed through exponential-complexity exhaustive search. However, if the rank of the form is not a function of the problem size, then it can be maximized in polynomial time. By introducing auxiliary spherical coordinates, we show that the rank-deficient quadratic-form maximization problem is converted into a double maximization of a linear form over a multidimensional continuous set, the multidimensional set is partitioned into a polynomial-size set of regions which are associated with distinct candidate binary vectors, and the optimal binary vector belongs to the polynomial-size set of candidate vectors. Thus, the size of the candidate set is reduced from exponential to polynomial. We also develop an algorithm that constructs the polynomial-size candidate set in polynomial time and show that it is fully parallelizable and rank-scalable. Finally, we demonstrate the efficiency of the proposed algorithm in the context of adaptive spreading code design.

Cooperative communications is a rapidly evolving research area. Most of the cooperative protocols that have appeared in the literature assume slow flat fading channels and Gaussian codebooks. In many cases the relays must fully decode their input. It is well known that cooperation is most effective at low SNR where binary input is optimal. Furthermore, energy and cost effectiveness make simple relays most attractive. Motivated by these two facts, we consider a half-duplex orthogonal cooperation protocol with binary input and relays that simply forward their symbol-by-symbol decisions to the destination which performs algebraic decoding; we call it demodulate-and-forward (DmF). We assume independent slow Rayleigh flat fading channels with full channel state information (CSI) at the destination and compute an upper bound for the outage capacity of the DmF protocol. For low SNR and small outage probability, we derive a simple approximation to this bound. For comparison purposes, we compute the outage capacity of direct binary transmission and a simple low-SNR small-outage-probability approximation. We observe that for very small outage probability the DmF protocol significantly outperforms direct transmission. However, for (relatively) high outage probability, the opposite may happen.

The maximization of a full-rank quadratic form over a finite alphabet is NP-hard in both a worst-case sense and an average sense. Interestingly, if the rank of the form is not a function of the problem size, then it can be maximized in polynomial time. An algorithm for the efficient computation of the binary vector that maximizes a rank-deficient quadratic form is developed based on an analytic procedure. Auxiliary spherical coordinates are introduced and the multi-dimensional space is partitioned into a polynomial-size set of regions; each region corresponds to a distinct binary vector. The binary vector that maximizes the rank-deficient quadratic form is shown to belong to the polynomial-size set of candidate vectors. Thus, the size of the feasible set is efficiently reduced from exponential to polynomial.

We consider the maximization of a quadratic form over the binary alphabet. By introducing auxiliary spherical coordinates, we show that if the rank of the form is not a function of the problem size, then (i) the multidimensional space is partitioned into a polynomial-size set of regions which are associated with distinct binary vectors and (ii) the binary vector that maximizes the rank-deficient quadratic form belongs to the polynomial-size set of candidate vectors. Thus, the size of the feasible set of candidate vectors is efficiently reduced from exponential to polynomial. We also develop an algorithm that constructs the polynomial-size feasible set in polynomial time and show that it is fully parallelizable and rank-scalable. Finally, we examine the efficiency of the proposed algorithm in the context of multiple-input multiple-output signal detection.

We consider the behavior of the transmit Wiener filter for broadcast channels with non-cooperating users under channel uncertainties. We derive a second-order approximation to the excess mean-square error (EMSE) induced by using a channel estimate as if it were the true channel. In the high SNR cases, we develop a simple approximation to the EMSE. It turns out that the EMSE is proportional to the minimum mean square error with the proportionality factor determined by the total transmit power and the length of the training block.

Water-filling is the technique that computes the input data covariance matrix that achieves capacity in Gaussian parallel or block channels. A suboptimal precoding scheme, that has been observed to perform quite close to water-filling in some cases of great interest, is when all "active" eigenvectors of the input data covariance matrix receive the same power. Both techniques require perfect channel knowledge at the transmitter. We consider the suboptimal precoding scheme when, at the transmitter, we use a channel estimate as if it were the true channel and we derive a closed form expression relating the channel estimation error covariance matrix with a mean mutual information decrease. We observe that serious error magnification may happen if the channel matrix is badly conditioned and the SNR is high.

We consider minimum mean-square error Tomlinson-Harashima (MMSE-TH) precoding for time-varying frequency-selective channels. We assume that the receiver estimates the channel and sends the channel state information (CSI) estimate to the transmitter through a lossless feedback channel that introduces a certain delay. Thus, the CSI mismatch at the receiver is due to estimation errors, while the CSI mismatch at the transmitter is due to both estimation errors and channel time variations. We exploit a priori statistical channel knowledge, and we derive an optimal TH precoder, adopting a Bayesian approach. We use simulations to compare the performance of the so-derived TH precoder with that of the same-complexity MMSE decision-feedback equalizer (DFE). We observe that for low signal-to-noise ratios (SNRs) and sufficiently slow channel time variations, the optimal TH precoder outperforms the DFE, while at high SNR, the opposite happens.

Water-filling is the precoding scheme that achieves capacity in Gaussian parallel or block-based channels. A suboptimal precoding scheme, which has been observed to perform quite close to water-filling, in some cases of great interest, is when all "active" eigenvectors of the input data covariance matrix receive the same power. Both techniques require perfect channel knowledge at the transmitter. In this work, we consider the sensitivity of the suboptimal scheme when a channel estimate is used at the transmitter as if it were the true channel. Using tools from matrix perturbation theory, we derive closed-form expressions and bounds relating the channel estimation error covariance matrix with the mean mutual information decrease. We thus uncover the factors that determine the behavior of the suboptimal precoding scheme under channel uncertainties. Simulations are in agreement with our theoretical results

In cases where the signal-to-noise ratio (SNR) in ECGs is very poor, the correct definition of characteristics such as the isoelectric line and the J-point (beginning of the ST segment) is difficult. Inaccurate definition of those ECG characteristics can lead an automated ischemia detector to an incorrect diagnosis. We propose a method capable of extracting from noisy long duration ECG recordings those ECG characteristics that can be used for myocardial ischemia detection and analysis. We tested the performance of the method using noisy ECGs from the European Society of Cardiology ST-T database (ESC ST-T database). The results were more than satisfactory and the performance of our ischemia detector was improved in all cases. The proposed technique has low computational effort and can be executed in real time.

The continuous use of adaptive algorithms is strongly dependent on their behavior in finite-precision environments. We study the nonlinear round-off error accumulation system of the conventional RLS algorithm and we derive bounds for the relative precision of the computations and the accumulated round-off error, which guarantee the numerical stability of the finite-precision implementation of the algorithm. The bounds depend on the conditioning of the problem and the exponential forgetting factor. Simulations agree with our theoretical results.