This work presents a general framework for blindly estimating the sensor parameters of decision-fusion systems over wireless sensor networks (WSNs). The sensors report their binary decisions to a fusion center (FC) through parallel binary symmetric channels. Then, the FC makes the final decision by combining the noisy sensor decisions according to a certain fusion rule. We present an algorithm for the FC to blindly estimate the sensor parameters from the noisy sensor decisions received after a number of sensing periods. The algorithm covers a wide variety of situations that may arise in WSNs. For example, the algorithm is applicable when the FC knows in advance some of the parameters of some sensors, when it knows the true hypothesis for a subset of sensing periods, or when only a subset of sensors communicates their decisions in each sensing period. Based on the estimates of the system parameters, optimal channel-aware fusion rules are derived considering the minimum Bayes risk criterion. Simulation results show that, after sufficient sensing periods, the estimates of the WSN parameters are accurate enough for the fusion rule to exhibit near-optimal detection performance.

The performance of modern wireless communication systems is typically limited by interference. The impact of interference can be even more severe in ultra-reliable and low-latency communication (URLLC) use cases. A powerful tool for managing interference is rate splitting multiple access (RSMA), which encompasses many multiple-access technologies like non-orthogonal multiple access (NOMA), spatial division multiple access (SDMA), and broadcasting. Another effective technology to enhance the performance of URLLC systems and mitigate interference is constituted by reconfigurable intelligent surfaces (RISs). This paper develops RSMA schemes for multi-user multiple-input multiple-output (MIMO) RIS-aided broad-cast channels (BCs) based on finite block length (FBL) coding. We show that RSMA and RISs can substantially improve the spectral efficiency (SE) and energy efficiency (EE) of MIMO RIS-aided URLLC systems. Additionally, the gain of employing RSMA and RISs noticeably increases when the reliability and latency constraints are more stringent. Furthermore, RISs impact RSMA differently, depending on the user load. If the system is underloaded, RISs are able to manage the interference sufficiently well, making the gains of RSMA small. However, when the user load is high, RISs and RSMA become synergetic.

Flag manifolds encode nested sequences of subspaces and serve as powerful structures for various computer vision and machine learning applications. Despite their utility in tasks such as dimensionality reduction, motion averaging, and subspace clustering, current applications are often restricted to extracting flags using common matrix decomposition methods like the singular value decomposition. Here, we address the need for a general algorithm to factorize and work with hierarchical datasets. In particular, we propose a novel, flag-based method that decomposes arbitrary hierarchical real-valued data into a hierarchy-preserving flag representation in Stiefel coordinates. Our work harnesses the potential of flag manifolds in applications including denoising, clustering, and few-shot learning.

Modern wireless communication systems are expected to provide improved latency and reliability. To meet these expectations, a short packet length is needed, which makes the first-order Shannon rate an inaccurate performance metric for such communication systems. A more accurate approximation of the achievable rates of finite-block-length (FBL) coding regimes is known as the normal approximation (NA). It is therefore of substantial interest to study the optimization of the FBL rate in multi-user multiple-input multiple-output (MIMO) systems, in which each user may transmit and/or receive multiple data streams. Hence, we formulate a general optimization problem for improving the spectral and energy efficiency of multi-user MIMO-aided ultra-reliable low-latency communication (URLLC) systems, which are assisted by reconfigurable intelligent surfaces (RISs). We show that an RIS is capable of substantially improving the performance of multi-user MIMO-aided URLLC systems. Moreover, the benefits of RIS increase as the packet length and/or the tolerable bit error rate are reduced. This reveals that RISs can be even more beneficial in URLLC systems for improving the FBL rates than in conventional systems approaching Shannon rates.

In this paper, we propose a robust algorithm for designing unstructured Grassmannian constellations for noncoherent MIMO communications that accounts for the effect of hardware impairments (HWIs) such as I/Q imbalance (IQI) and carrier frequency offset (CFO). The algorithm uses the minimum diversity product as a cost function to ensure full-diversity constellations. The constellation points in the Grassmannian are optimized to be robust against any value of the HWIs belonging to a given uncertainty set, the values of which are determined by the characteristics of the hardware used. The cost function is optimized by means of a gradient ascent algorithm on the Grassmann manifold. Simulation results suggest that the constellations designed with the robust algorithm show a significant improvement in symbol-error-rate (SER) performance over the HWI-unaware algorithm optimized for ideal devices.

In this paper, we propose a new structured Grassmannian constellation for noncoherent communications over single-input multiple-output (SIMO) Rayleigh block-fading channels. The constellation, which we call Grass-Lattice, is based on a measure preserving mapping from the unit hypercube to the Grassmannian of lines. The constellation structure allows for on-the-fly symbol generation, low-complexity decoding, and simple bit-to-symbol Gray-like coding. Simulation results show that Grass-Lattice has symbol and bit error rate performance close to that of a numerically optimized unstructured constellation, and is more power efficient than other structured constellations proposed in the literature and a coherent pilot-based scheme.

This paper proposes a general optimization framework for rate splitting multiple access (RSMA) in beyond diagonal (BD) reconfigurable intelligent surface (RIS) assisted ultra-reliable low-latency communications (URLLC) systems. This framework can provide a suboptimal solution for a large family of optimization problems in which the objective and/or constraints are linear functions of the rates and/or energy efficiency (EE) of users. Using this framework, we show that RSMA and RIS can be mutually beneficial tools when the system is overloaded, i.e., when the number of users per cell is higher than the number of base station (BS) antennas. Additionally, we show that the benefits of RSMA increase when the packets are shorter and/or the reliability constraint is more stringent. Furthermore, we show that the RSMA benefits increase with the number of users per cell and decrease with the number of BS antennas. Finally, we show that RIS (either diagonal or BD) can highly improve the system performance, and BD-RIS outperforms regular RIS.

This paper proposes schemes to improve the spectral efficiency of a multiple-input multiple-output (MIMO) broadcast channel (BC) with I/Q imbalance (IQI) at transceivers by employing a combination of improper Gaussian signaling (IGS), non-orthogonal multiple access (NOMA) and simultaneously transmit and reflect (STAR) reconfigurable intelligent surface (RIS). When there exists IQI, the output RF signal is a widely linear transformation of the input signal, which may make the output signal improper. To compensate for IQI, we employ IGS, thus generating a transmit improper signal. We show that IGS alongside with NOMA can highly increase the minimum rate of the users. Moreover, we propose schemes for different operational modes of STAR-RIS and show that STAR-RIS can significantly improve the system performance. Additionally, we show that IQI can highly degrade the performance especially if it is overlooked in the design.

We consider the design of multiuser constellations for a multiple access channel (MAC) with K users, with M antennas each, that transmit simultaneously to a receiver equipped with N antennas through a Rayleigh block-fading channel, when no channel state information (CSI) is available to either the transmitter or the receiver. In full-diversity scenarios where the coherence time is at least T ≥ (K + 1)M, the proposed constellation design criterion is based on the asymptotic expression of the multiuser pairwise error probability (PEP) derived by Brehler and Varanasi in [1]. Although this PEP expression was previously considered intractable for optimization, in this work we derive a closed-form formula for its unconstrained gradient and perform Riemannian optimization in the Grassmannian manifold to design multiuser constellations for the MIMO MAC with state-of-the-art performance in terms of symbol error rate (SER).

This paper addresses the passive detection of a common signal in two multi-sensor arrays. For this problem, we derive a detector based on likelihood theory for the case of one-antenna transmitters, independent Gaussian noises with arbitrary spatial structure, Gaussian signals, and known channel subspaces. The detector uses a likelihood ratio where all but one of the unknown parameters are replaced by their maximum likelihood (ML) estimates. The ML estimation of the remaining parameter requires a numerical search, and it is therefore estimated using a sample-based estimator. The performance of the proposed detector is illustrated by means of Monte Carlo simulations and compared with that of the detector for unknown channels, showing the advantage of this knowledge.

We address the problem of interference leakage (IL) minimization in the K-user multiple-input multiple-output (MIMO) interference channel (IC) assisted by a reconfigurable intelligent surface (RIS). We describe an iterative algorithm based on block coordinate descent to minimize the IL cost function. A reformulation of the problem provides a geometric interpretation and shows interesting connections with envelope precoding and phase-only zero-forcing beamforming problems. As a result of this analysis, we derive a set of necessary (but not sufficient) conditions for a phase-optimized RIS to be able to perfectly cancel the interference on the K-user MIMO IC.

Reconfigurable intelligent surface (RIS) architectures not limited to diagonal phase shift matrices have recently been considered to increase their flexibility in shaping the wireless channel. One of these beyond-diagonal RIS or BD-RIS architectures leads to a unitary and symmetric RIS matrix. In this letter, we consider the problem of maximizing the signal-to-noise ratio (SNR) in single and multiple antenna links assisted by a BD-RIS. The Max-SNR problem admits a closed-form solution based on the Takagi factorization of a certain complex and symmetric matrix. This allows us to solve the max-SNR problem for SISO, SIMO, and MISO channels.

In this paper, we propose an algorithm for designing unstructured Grassmannian constellations for noncoherent multiple-input multiple-output (MIMO) communications over Rayleigh block-fading channels. Unlike the majority of existing unitary space-time or Grassmannian constellations, which are typically designed to maximize the minimum distance between codewords, in this work we employ the asymptotic pairwise error probability (PEP) union bound (UB) of the constellation as the design criterion. In addition, the proposed criterion allows the design of MIMO Grassmannian constellations specifically optimized for a given number of receiving antennas. A rigorous derivation of the gradient of the asymptotic UB on a Cartesian product of Grassmann manifolds, is the main technical ingredient of the proposed gradient descent algorithm. A simple modification of the proposed cost function, which weighs each pairwise error term in the UB according to the Hamming distance between the binary labels assigned to the respective codewords, allows us to jointly solve the constellation design and the bit labeling problem. Our simulation results show that the constellations designed with the proposed method outperform other structured and unstructured Grassmannian designs in terms of symbol error rate (SER) and bit error rate (BER), for a wide range of scenarios.

We consider the design of multiuser constellations for a multiple access channel (MAC) with$K$users, with$M$antennas each, that transmit simultaneously to a receiver equipped with$N$antennas through a Rayleigh block-fading channel when no channel state information (CSI) is available to either the transmitter or the receiver. In full-diversity scenarios where the coherence time is at least$T\geq (K+1)M$, the proposed constellation design criterion is based on the asymptotic expression of the multiuser pairwise error probability (PEP) derived by Brehler and Varanasi (2001). In non-full diversity scenarios, for which the previous PEP expression is no longer valid, the proposed design criteria are based on proxies of the PEP recently proposed by Ngo and Yang (2021). Although both the PEP expression and its bounds or proxies were previously considered intractable for optimization, in this work we derive their respective unconstrained gradients. These gradients are in turn used in the optimization of the proposed cost functions in different Riemannian manifolds representing different power constraints. In particular, in addition to the standard unitary space-time modulation (USTM) leading to optimization on the Grassmann manifold, we consider a more relaxed per-codeword power constraint leading to optimization on the so-calledoblique manifold, and an average power constraint leading to optimization on the so-calledtrace manifold. Equipped with these theoretical tools, we design multiuser constellations for the MIMO MAC in full-diversity and non-full-diversity scenarios with state-of-the-art performance in terms of symbol error rate (SER).

In this paper, we propose a new structured Grassmannian constellation for noncoherent communications over single-input multiple-output (SIMO) Rayleigh block-fading channels. The constellation, which we call Grass-Lattice, is based on a measure preserving mapping from the unit hypercube to the Grassmannian of lines. The constellation structure allows for on-the-fly symbol generation, low-complexity decoding, and simple bit-to-symbol Gray coding. Simulation results show that Grass-Lattice has symbol error rate performance close to that of a numerically optimized unstructured constellation, and is more power efficient than other structured constellations proposed in the literature.

This letter addresses the problem of order estimation for uniform linear arrays (ULAs) with multi-switch antenna selection in the small-sample regime. Multi-switch antenna selection results in a data matrix with missing entries, a scenario for which existing order estimation methods that build on the eigenvalues of the sample covariance matrix do not perform well. A direct application of the Davis-Kahan theorem allows us to show that the signal subspace is quite robust in the presence of missing entries. Based on this finding, this letter proposes a matrix completion (MC) subspace-based order estimation criterion that exploits the shift-invariance property of ULAs. A recently proposed shift-invariant matrix completion (SIMC) method is used for reconstructing the data matrix, and the proposed order estimation criterion is based on the chordal subspace distance between two submatrices extracted from the reconstructed matrix for increasing values of the dimension of the signal subspace. Our simulation results show that the method provides accurate order estimates with percentages of missing entries higher than 50%.

Despite the numerous results in the literature about the eigenvalue distributions of Wishart matrices, the existing closed-form probability density function (pdf) expressions do not allow for efficient sampling schemes from such densities. In this letter, we present a stochastic representation for the eigenvalues of$2 \times 2$complex central uncorrelated Wishart matrices with an arbitrary number of degrees of freedom (referred to as dual Wishart matrices). The draws from the joint pdf of the eigenvalues are generated by means of a simple transformation of a chi-squared random variable and an independent beta random variable. Moreover, this stochastic representation allows a simple derivation, alternative to those already existing in the literature, of some eigenvalue function distributions such as the condition number or the ratio of the maximum eigenvalue to the trace of the matrix. The proposed sampling scheme may be of interest in wireless communications and multivariate statistical analysis, where Wishart matrices play a central role.

This paper addresses the problem of source enumeration by an array of sensors in the presence of noise whose spatial covariance structure is a diagonal matrix with possibly different variances, referred to non-iid noise hereafter, when the sources are uncorrelated. The diagonal terms of the sample covariance matrix are removed and, after applying Toeplitz rectification as a denoising step, the signal covariance matrix is reconstructed by using a low-rank matrix completion method adapted to enforce the Toeplitz structure of the sought solution. The proposed source enumeration criterion is based on the Frobenius norm of the reconstructed signal covariance matrix obtained for increasing rank values. As illustrated by simulation examples, the proposed method performs robustly for both small and large-scale arrays with few snapshots, i.e. small-sample regime.

This paper considers improper Gaussian signaling (IGS) in an overlay cognitive radio scenario. We follow a protocol in which the secondary user (SU) uses part of its power to relay the message for the primary user (PU) and consider a simple yet illustrative 2-user scenario. We analyze two communication schemes depending on whether or not the PU cooperates with the SU and derive closed-form expressions for the optimal transmission parameters that maximize the SU rate while ensuring a specified minimum performance of the PU. Our numerical results show that IGS may significantly outperform proper signaling and that, interestingly, the cooperative approach provides negligible performance gains over its non-cooperative counterpart.

In this paper we present an algorithm to minimize transmit power in multiple-input multiple-output (MIMO) heterogeneous networks (HetNets) with flexible duplexing, a promising strategy that allows the coexistence of uplink and downlink cells within the same time and frequency resource block. First, the proposed algorithm minimizes transmit power for a given uplink/downlink (UL/DL) combination, and afterwards, the optimal solution out of the explored UL/DL combinations is selected. To reduce the computational cost of exploring all the UL/DL settings, we propose a hierarchical switching (HS) approach that considers a reduced subset of transmit directions. By means of Monte Carlo simulations, we show that the proposed technique provides significant power savings with respect to a conventional time-division duplex (TDD) scheme.

Improper Gaussian signaling (IGS) has been shown to enlarge the rate region achievable by conventional proper Gaussian signaling (PGS) schemes in several interference-limited multiuser networks. In this work, we consider the 2-user broadcast channel (BC) when treating interference as noise "TIN" at every receiver. For this scenario, we derive a closed-form characterization of the rate region boundary with IGS. The Pareto-optimal points are achieved when at least one of the users employs maximally improper (rectilinear) signals. Differently from other interference-limited networks, our results show that IGS always outperforms PGS for the 2-user BC with TIN. Furthermore, IGS also enlarges the PGS rate region with time-sharing for this scenario.

Improper Gaussian signaling (IGS) has been used as an effective interference management tool in interference limited systems. Improper Gaussian signals are correlated with their complex conjugates. In this paper, we investigate the optimality of IGS from an energy efficiency (EE) perspective. First, we obtain closed form optimality conditions for IGS. We then leverage these conditions to devise a bisection method that finds the optimal transmission parameters. Our results show that IGS can improve the EE of an underlay cognitive radio system.

Digital constellations formed by hexagonal or other non-square two-dimensional lattices are often used in advanced digital communication systems. The integrals required to evaluate the symbol error rate (SER) of these constellations in the presence of Gaussian noise are in general difficult to compute in closed form, and therefore Monte Carlo simulation is typically used to estimate the SER. However, naive Monte Carlo simulation can be very inefficient and requires very long simulation runs, especially at high signal-to-noise ratios. In this letter, we adapt a recently proposed multiple importance sampling technique, called ALOE (for “at least one rare event”), to this problem. Conditioned to a transmitted symbol, an error (or rare event) occurs when the observation falls in a union of half-spaces or, equivalently, outside a given polytope. The proposal distribution for ALOE samples the system conditionally on an error taking place, which makes it more efficient than other importance sampling techniques. ALOE provides unbiased SER estimates with simulation times orders of magnitude shorter than conventional Monte Carlo.

This paper considers an unlicensed multiple-access channel (MAC) that coexists with a licensed point-to-point user, following the underlay cognitive radio paradigm. We assume that every transceiver except the secondary base station has one antenna and that the primary user (PU) is protected by a minimum rate constraint. In contrast to the conventional assumption of proper Gaussian signaling, we allow the secondary users to transmit improper Gaussian signals, which are correlated with their complex conjugate. When the secondary base station performs zero-forcing, we show that improper signaling is optimal if the sum of the interference channel gains (in an equivalent canonical model) is above a certain threshold. Additionally, we derive an efficient algorithm to compute the transmission parameters that attain the rate region boundary for this scenario. The proposed algorithm exploits a single-user representation of the secondary MAC along with new results on the optimality of improper signaling in the single-user case when the PU is corrupted by an improper noise.

This paper addresses the problem of designing asymptotically optimal improper constellations with a given circularity coefficient (correlation coefficient between the constellation and its complex conjugate). The designed constellations are optimal in the sense that, at high signal-to-noise-ratio (SNR) and for a large number of symbols, yield the lowest probability of error under an average power constraint for additive white Gaussian noise channels. As the number of symbols grows, the optimal constellation is the intersection of the hexagonal lattice with an ellipse whose eccentricity determines the circularity coefficient. Based on this asymptotic result, we propose an algorithm to design finite improper constellations. The proposed constellations provide significant SNR gains with respect to previous improper designs, which were generated through a widely linear transformation of a standard M-ary quadrature amplitude modulation constellation. As an application example, we study the use of these improper constellations by a secondary user in an underlay cognitive radio network.

It has been shown that improper Gaussian signaling (IGS) can improve the performance of wireless interference-limited systems when perfect channel-state information (CSI) is available. In this paper, we investigate the robustness of IGS against imperfect CSI on the transmitter side in a two-user single-input single-output (SISO) interference channel (IC) as well as in a SISO Z-IC, when interference is treated as noise. We assume that the true channel coefficients belong to a known region around the channel estimates, which we call the uncertainty region. Following a worst-case robustness approach, we study the rate-region boundary of the IC for the worst channel in the uncertainty region. For the two-user IC, we derive a robust design in closed form, which is independent of the phase of the channels by allowing only one of the users to transmit IGS. For the Z-IC, we provide a closed-form design for the transmission parameters by considering an enlarged uncertainty region and allowing both users to employ IGS. In both cases, the IGS-based designs are ensured to perform no worse than proper Gaussian signaling. Furthermore, we show, through numerical examples, that the proposed robust designs significantly outperform non-robust solutions.

Hardware non-idealities are among the main performance restrictions for upcoming wireless communication systems. Asymmetric hardware distortions (HWD) happen when the impairments of the I/Q branches are correlated or imbalanced, which in turn generate improper additive interference at the receiver side. When the interference is improper, as well as in other interference-limited scenarios, improper Gaussian signaling (IGS) has been shown to provide rate and/or power efficiency benefits. In this paper, we investigate the rate benefits of IGS in a two-user interference channel (IC) with additive asymmetric HWD when interference is treated as noise. We propose two iterative algorithms to optimize the parameters of the improper transmit signals. We first rewrite the rate region as an pseudo-signal-to-interference-plus-noise-ratio (PSINR) region and employ majorization minimization and fractional programming to find a suboptimal solution for the achievable user rates. Then, we propose a simplified algorithm based on a separate optimization of the powers and complementary variances of the users, which exhibits lower computational complexity. We show that IGS can improve the performance of the two-user IC with additive HWD. Our proposed algorithms outperform proper Gaussian signaling and competing IGS algorithms in the literature that do not consider asymmetric HWD.

In this work we propose a new adaptive algorithm for cooperative spectrum sensing in dynamic environments where the channels are time varying. We assume a centralized spectrum sensing procedure based on the soft fusion of the signal energy levels measured at the sensors. The detection problem is posed as a composite hypothesis testing problem. The unknown parameters are estimated by means of an adaptive clustering algorithm that operates over the most recent energy estimates reported by the sensors to the fusion center. The algorithm does not require all sensors to report their energy estimates, which makes it suited to be used with any sensor selection strategy (active sensing). Simulation results show the feasibility and efficiency of the method in realistic slow-fading environments.

This work addresses the problem of determining whether two multivariate random time series have the same power spectral density (PSD), which has applications, for instance, in physical-layer security and cognitive radio. Remarkably, existing detectors for this problem do not usually provide any kind of optimality. Thus, we study here the existence under the Gaussian assumption of optimal invariant detectors for this problem, proving that the uniformly most powerful invariant test (UMPIT) does not exist. Thus, focusing on close hypotheses, we show that the locally most powerful invariant test (LMPIT) only exists for univariate time series. In the multivariate case, we prove that the LMPIT does not exist. However, this proof suggests two LMPIT-inspired detectors, one of which outperforms previously proposed approaches, as computer simulations show.

In this paper, we study the problem of locating a predefined sequence of patterns in a time series. In particular, the studied scenario assumes a theoretical model is available that contains the expected locations of the patterns. This problem is found in several contexts, and it is commonly solved by first synthesizing a time series from the model, and then aligning it to the true time series through dynamic time warping. We propose a technique that increases the similarity of both time series before aligning them, by mapping them into a latent correlation space. The mapping is learned from the data through a machine-learning setup. Experiments on data from nondestructive testing demonstrate that the proposed approach shows significant improvements over the state of the art.

The transmission of improper Gaussian signals, instead of the conventional proper ones, has been shown to improve the performance in interference-limited networks. In this work we analyze the performance of a multiple-antenna user that transmits maximally improper signals and whose transmit covariance matrix satisfies a set of constraints that limit the harmfulness of the interference caused by this user. As opposed to the single-antenna case, there are different possible improper spatial signatures, which provide different performance. We first obtain new results for maximally improper random vectors based on majorization theory. We then apply these results to derive the improper spatial signatures that either maximize or minimize the performance. Numerical examples show that the performance difference between these two extreme cases can be surprisingly large.

This paper provides a complete characterization of the boundary of an achievable rate region, called the Pareto boundary, of the single-antenna Z interference channel (Z-IC), when interference is treated as noise and users transmit complex Gaussian signals that are allowed to be improper. By considering the augmented complex formulation, we derive a necessary and sufficient condition for improper signaling to be optimal. This condition is stated as a threshold on the interference channel coefficient, which is a function of the interfered user rate and which allows insightful interpretations into the behavior of the achievable rates in terms of the circularity coefficient (i.e., degree of impropriety). Furthermore, the optimal circularity coefficient is provided in closed form. The simplicity of the obtained characterization permits interesting insights into when and how improper signaling outperforms proper signaling in the single-antenna Z-IC. We also provide an in-depth discussion on the optimal strategies and the properties of the Pareto boundary.

It is well-known that the use of improper signaling schemes can be beneficial in interference-limited networks. Here we consider an underlay cognitive radio scenario, where a multi-antenna primary user is protected by an interference temperature constraint that ensures a prescribed rate requirement. We study how the interference temperature threshold changes when the interference is constrained to be maximally improper. Since the spatial structure of the impropriety is an additional degree of freedom, we provide the maximum value of the interference threshold that ensures the rate requirement. We illustrate the potential payoffs of improper signaling with some numerical examples, which show that a secondary user can significantly improve its achievable rate with respect to the proper signaling case.

We propose a new detector of primary users in cognitive radio networks. The main novelty of the proposed detector in comparison to most known detectors is that it is based on sound statistical principles for detecting cyclostationary signals. In particular, the proposed detector is (asymptotically) the locally most powerful invariant test, i.e. the best invariant detector for low signal-to-noise ratios. The derivation is based on two main ideas: the relationship between a scalar-valued cyclostationary signal and a vector-valued wide-sense stationary signal, and Wijsman's theorem. Moreover, using the spectral representation for the cyclostationary time series, the detector has an insightful interpretation, and implementation, as the broadband coherence between frequencies that are separated by multiples of the cycle frequency. Finally, simulations confirm that the proposed detector performs better than previous approaches.

In this paper, the impact of improper Gaussian signaling is studied for an underlay cognitive radio (CR) scenario comprised of a primary user (PU), which has a rate constraint, and a secondary user (SU), both single-antenna. We first derive expressions for the achievable rate of the SU when it transmits proper and maximally improper Gaussian signals (assuming that the SU is solely limited by the CR constraint). These expressions depend on the channel gains to and from the SU through a single variable. Thereby, we observe that improper signaling is beneficial whenever the SU rate is below a threshold, which depends on the signal-to-noise ratio (SNR) and rate requirement of the PU. Furthermore, we provide bounds on the achievable gain that also depend only on the PU parameters. Then, the achievable rate is studied from a statistical viewpoint by deriving its cumulative distribution function considering a constant received SNR at the PU. In addition, we specialize this expression for the Z interference channel, for which the expected achievable rate is also derived. Numerical examples illustrate our claims and show that the SU may significantly benefit from using improper signaling.

In this paper, we study the number of different interference alignment (IA) solutions in a K-user multiple-input multiple-output (MIMO) interference channel, when the alignment is performed via beamforming and no symbol extensions are allowed. We focus on the case where the number of IA equations matches the number of variables. In this situation, the number of IA solutions is finite and constant for any channel realization out of a zero-measure set and, as we prove in this paper, it is given by an integral formula that can be numerically approximated using Monte Carlo integration methods. More precisely, the number of alignment solutions is the scaled average of the determinant of a certain Hermitian matrix related to the geometry of the problem. Interestingly, while the value of this determinant at an arbitrary point can be used to check the feasibility of the IA problem, its average (properly scaled) gives the number of solutions. For single-beam systems, the asymptotic growth rate of the number of solutions is analyzed and some connections with classical combinatorial problems are presented. Nonetheless, our results can be applied to arbitrary interference MIMO networks, with any number of users, antennas, and streams per user.

In this paper we propose an algorithm to design interference alignment (IA) precoding and decoding matrices for MIMO X networks (XN). The proposed algorithm is rooted in the homotopy continuation techniques commonly used to solve systems of nonlinear equations. Homotopy methods find the solution of a target system by smoothly deforming the known solutions of a start system which can be trivially solved. The key observation leading to a simple start system is realizing that the inverse IA problem, i.e., finding the channels that satisfy the IA conditions given a set of precoders and decoders, is linear and, therefore, a convenient trivial system. Once the start system has been solved, standard prediction and correction techniques are applied to track the solution all the way to the target system. Our results show that the proposed algorithm is able to consistently find solutions achieving the maximum number of degrees of freedom (DoF) whereas alternating minimization techniques, which typically work well for the interference channel (IC), repeatedly fail for the XN. Further, the algorithm provides insights into the feasibility of alignment in MIMO X networks for which theoretical results are scarce.

In this paper, a cognitive radio (CR) scenario comprised of a secondary interference channel (IC) and a primary point-to-point link (PPL) is studied, when the former interferes the latter. In order to satisfy a given rate requirement at the PPL, typical approaches impose an interference temperature constraint (IT). When the PPL transmits multiple streams, however, the spatial structure of the interference comes into play. In such cases, we show that spatial interference shaping constraints can provide higher sum-rate performance to the IC while ensuring the required rate at the PPL. Then, we extend the interference leakage minimization algorithm (MinIL) to incorporate such constraints. An additional power control step is included in the optimization procedure to improve the sum-rate when the interference alignment (IA) problem becomes infeasible due to the additional constraint. Numerical examples are provided to illustrate the effectiveness of the spatial shaping constraint in comparison to IT when the PPL transmits multiple data streams.

We derive the generalized likelihood ratio test (GLRT) for detecting cyclostationarity in scalar-valued time series. The main idea behind our approach is Gladyshev's relationship, which states that when the scalar-valued cyclostationary signal is blocked at the known cycle period it produces a vector-valued wide-sense stationary process. This result amounts to saying that the covariance matrix of the vector obtained by stacking all observations of the time series is block-Toeplitz if the signal is cyclostationary, and Toeplitz if the signal is wide-sense stationary. The derivation of the GLRT requires the maximum likelihood estimates of Toeplitz and block-Toeplitz matrices. This can be managed asymptotically (for large number of samples) exploiting Szegö's theorem and its generalization for vector-valued processes. Simulation results show the good performance of the proposed GLRT.

Physical-layer authentication techniques exploit the unique properties of the wireless medium to enhance traditional higher-level authentication procedures. We propose to reduce the higher-level authentication overhead by using a state-of-the-art multi-target tracking technique based on Gaussian processes. The proposed technique has the additional advantage that it is capable of automatically learning the dynamics of the trusted user's channel response and the time-frequency fingerprint of intruders. Numerical simulations show very low intrusion rates, and an experimental validation using a wireless test bed with programmable radios demonstrates the technique's effectiveness.

Alternating minimization and steepest descent are commonly used strategies to obtain interference alignment (IA) solutions in the K-user multiple-input multiple-output (MIMO) interference channel (IC). Although these algorithms are shown to converge monotonically, they experience a poor convergence rate, requiring an enormous amount of iterations which substantially increases with the size of the scenario. To alleviate this drawback, in this letter we resort to the Gauss-Newton (GN) method, which is well-known to experience quadratic convergence when the iterates are sufficiently close to the optimum. We discuss the convergence properties of the proposed GN algorithm and provide several numerical examples showing that it always converges to the optimum with quadratic rate, reducing dramatically the required computation time in comparison to other algorithms, hence paving a new way for the design of IA algorithms.

In this paper, we consider the feasibility of linear interference alignment (IA) for multiple-input-multiple-output (MIMO) channels with constant coefficients for any number of users, antennas, and streams per user, and propose a polynomial-time test for this problem. Combining algebraic geometry techniques with differential topology ones, we first prove a result that generalizes those previously published on this topic. In particular, we consider the input set (complex projective space of MIMO interference channels), the output set (precoder and decoder Grassmannians), and the solution set (channels, decoders, and precoders satisfying the IA polynomial equations), not only as algebraic sets, but also as smooth compact manifolds. Using this mathematical framework, we prove that the linear alignment problem is feasible when the algebraic dimension of the solution variety is larger than or equal to the dimension of the input space and the linear mapping between the tangent spaces of both smooth manifolds given by the first projection is generically surjective. If that mapping is not surjective, then the solution variety projects into the input space in a singular way and the projection is a zero-measure set. This result naturally yields a simple feasibility test, which amounts to checking the rank of a matrix. We also provide an exact arithmetic version of the test, which proves that testing the feasibility of IA for generic MIMO channels belongs to the bounded-error probabilistic polynomial complexity class.

In this paper we provide an efficient procedure to compute the total number of degrees of freedom (DoF), achievable by linear beamforming, of the K-user multiple-input multiple-output (MIMO) interference channel with an arbitrary number of Tx-Rx antennas at each link. Firstly, we derive an analytical outer bound that generalizes the results that exist for the symmetric K-user M × N interference channel. Secondly, we obtain a tighter bound by solving a convex optimization problem that includes as constraints the DoF characterizations for point-to-point MIMO links and for 2-user interference channels. The solution to this convex problem admits an interesting waterfilling interpretation. Finally, exploiting this outer bound and using a recently proposed feasibility test, we show that it is possible to obtain the DoF for any interference channel in an efficient way. Some simulations results are included to illustrate the tightness of the derived bounds, as well as to study the DoF achievable for the 4-user channel when we distribute the total number of antennas among users and between transmitters and receivers in different ways.

We describe two formulations of the kernel canonical correlation analysis (KCCA) problem for multiple data sets. The kernel-based algorithms, which allow one to measure nonlinear relationships between the data sets, are obtained as nonlinear extensions of the classical maximum variance (MAX-VAR) and minimum variance (MINVAR) canonical correlation analysis (CCA) formulations. We then show how adaptive versions of these algorithms can be obtained by reformulating KCCA as a set of coupled kernel recursive least-squares algorithms. We illustrate the performance of the proposed algorithms on a nonlinear identification application and a cognitive radio detection problem.

It has been recently shown that for the 3-user single-input single-output (SISO) interference channel with constant channel coefficients, a maximum of 1.2 degrees-of-freedom (DoF) are achievable using linear interference alignment schemes when improper (a.k.a. asymmetric) Gaussian signaling is applied. In this paper, we study the 4-user SISO interference channel and provide inner and outer bounds for the total number of DoF achievable for this channel. We prove that at least 4/3 DoF are achievable for the 4-user channel using also linear interference alignment techniques and improper signaling. A simple converse proof shows that no more than 8/5 DoF are achievable for this scheme. Simulation results seem to indicate that the inner bound is in fact tight for this channel, and serve to illustrate the sum-rate improvement with respect to time division multiple access (TDMA) techniques.

In this paper, we study how many different solutions exist for a feasible interference alignment (IA) problem. We focus on linear IA schemes without symbol extensions for the K-user multiple-input multiple-output (MIMO) interference channel. When the IA problem is feasible and the number of variables matches the number of equations in the polynomial system, the number of solutions is known to be finite. Unfortunately, the exact number of solutions is only known for a few particular cases, mainly single-beam MIMO networks. In this paper, we prove that the number of IA solutions is given by an integral formula that can be numerically approximated using Monte Carlo integration methods. More precisely, the number of solutions is the scaled average over a subset of the solution variety (formed by all triplets of channels, precoders and decoders satisfying the IA polynomial equations) of the determinant of certain Hermitian matrix related to the geometry of the problem. Our results can be applied to arbitrary interference MIMO networks, with any number of users, antennas and streams per user.

In this paper, we study the existence of locally most powerful invariant tests (LMPIT) for the problem of testing the covariance structure of a set of Gaussian random vectors. The LMPIT is the optimal test for the case of close hypotheses, among those satisfying the invariances of the problem, and in practical scenarios can provide better performance than the typically used generalized likelihood ratio test (GLRT). The derivation of the LMPIT usually requires one to find the maximal invariant statistic for the detection problem and then derive its distribution under both hypotheses, which in general is a rather involved procedure. As an alternative, Wijsman's theorem provides the ratio of the maximal invariant densities without even finding an explicit expression for the maximal invariant. We first consider the problem of testing whether a set ofN-dimensional Gaussian random vectors are uncorrelated or not, and show that the LMPIT is given by the Frobenius norm of the sample coherence matrix. Second, we study the case in which the vectors under the null hypothesis are uncorrelated and identically distributed, that is, the sphericity test for Gaussian vectors, for which we show that the LMPIT is given by the Frobenius norm of a normalized version of the sample covariance matrix. Finally, some numerical examples illustrate the performance of the proposed tests, which provide better results than their GLRT counterparts.

An alternating optimization algorithm was recently proposed for the K-user multiple-input multiple-output (MIMO) interference channel. For flat-fading channels and feasible problems, this algorithm successfully aligns the interfering signals exploiting the spatial dimensions. In this paper, we consider the case in which all pairwise MIMO channels are frequency-selective (convolutive), and the users transmit broadband signals using a single-carrier scheme. Unlike the flat-fading case, for frequency-selective channels it is necessary to add a spectral mask in the frequency response of the precoders and decoders to avoid trivial solutions. We show in the paper that each step of the alternating minimization algorithm can be reformulated as a convex optimization problem in which the autocorrelation function of the precoders or decoders is obtained. Upon convergence, a final spectral factorization stage must be applied to obtain the precoders and decoders from their autocorrelation functions. Simulation results are provided to illustrate the performance of the proposed algorithm.

Spectrum sensing is a key component of the cognitive radio (CR) paradigm. Among CR detectors, multiantenna detectors are gaining popularity since they improve the detection performance and are robust to noise uncertainties. Traditional approaches to multiantenna spectrum sensing are based on the generalized likelihood ratio test (GLRT) or other heuristic detectors, which are not optimal in the Neyman-Pearson sense. In this work, we derive the locally most powerful invariant test (LMPIT), which is the optimal detector, among those preserving the problem invariances, in the low SNR regime. In particular, we apply Wijsman's theorem, which provides us an alternative way to derive the ratio of the distributions of the maximal invariant statistic. Finally, numerical simulations illustrate the performance of the proposed detector.

In this paper, we propose a test for checking the feasibility of linear interference alignment (IA) for multiple-input multiple-output (MIMO) channels with constant coefficients for any number of users, antennas and streams per user. We consider the compact complex manifold formed by those channels, pre-coders and decoders that satisfy the polynomial IA equations (the so-called solution variety), and study its projection onto the input space formed by the interference channels. When the derivative of this projection is surjective, namely when the tangent space of the solution variety is projected into the whole tangent space of the inputs space, the linear alignment problem is feasible; otherwise is infeasible. Building on these results, a general feasibility test, which amounts to check whether a given matrix is full-rank or not, is proposed.

In this paper, we introduce a kernel recursive least-squares (KRLS) algorithm that is able to track nonlinear, time-varying relationships in data. To this purpose, we first derive the standard KRLS equations from a Bayesian perspective (including a sensible approach to pruning) and then take advantage of this framework to incorporate forgetting in a consistent way, thus enabling the algorithm to perform tracking in nonstationary scenarios. The resulting method is the first kernel adaptive filtering algorithm that includes a forgetting factor in a principled and numerically stable manner. In addition to its tracking ability, it has a number of appealing properties. It is online, requires a fixed amount of memory and computation per time step, incorporates regularization in a natural manner and provides confidence intervals along with each prediction. We include experimental results that support the theory as well as illustrate the efficiency of the proposed algorithm.

In this paper we consider the application of a homotopy-continuation based method for finding interference alignment (IA) solutions for the deterministic K-user multiple-input multiple-output (MIMO) channel, when all users wish to send one stream of data. Homotopy continuation is based on the idea of deforming a start system, whose solution can easily be found, to reach the target system that we want to solve. For the IA problem we show that a good initial system is obtained by considering a rank-one approximation of the original MIMO interference channels. Specifically, as long as the original system is feasible, a rank-one approximation of the MIMO channels allow us to find a closed-form interference-free solution. The proposed algorithm is shown to have a lower complexity than previous methods with comparable sum-rate performance. Furthermore, it is also shown that the trivial system (rank-one MIMO channels) and target system (full-rank MIMO channels) have exactly the same number of solutions. Exploiting this equivalence, an efficient method to enumerate all the IA solutions that exist in a single-beam MIMO network is proposed.

Spectrum sensing is a challenging key component of the Cognitive Radio paradigm, since primary signals must be detected in the face of noise uncertainty and at signal-to-noise ratios (SNRs) well below decodability levels. Multiantenna detectors exploit spatial independence of receiver thermal noise to boost detection performance and robustness. Here, we study the problem of detecting Gaussian signals with unknown rank-P spatial covariance matrix when the noise at the receiver is independent across the antennas and with unknown power. A generic diagonal noise covariance matrix is allowed to model calibration uncertainties in the different antenna frontends. We derive the generalized likelihood ratio test (GLRT) for this detection problem. Although, in general, the corresponding statistic must be obtained by numerical means, in the low SNR regime the GLRT does admit a closed form. Numerical simulations show that the proposed asymptotic detector offers good performance even for moderate SNR values.

This work addresses the problem of deciding whether a set of realizations of a vector-valued time series with unknown temporal correlation are spatially correlated or not. Specifically, the spatial correlation is induced by a colored source over a frequency-flat single-input multiple-output (SIMO) channel distorted by independent and identically distributed noises with temporal correlation. The generalized likelihood ratio test (GLRT) for this detection problem does not have a closed-form expression and we have to resort to numerical optimization techniques. In particular, we apply the successive convex approximations approach which relies on solving a series of convex problems that approximate the original (non-convex) one. The proposed solution resembles a power method for obtaining the dominant eigenvector of a matrix, which changes over iterations. Finally, the performance of the proposed detector is illustrated by means of computer simulations showing a great improvement over previously proposed detectors that do not fully exploit the temporal structure of the source.

We propose a novel semi-supervised classifier for handwritten digit recognition problems that is based on the assumption that any digit can be obtained as a slight transformation of another sufficiently close digit. Given a number of labeled and unlabeled images, it is possible to determine the class membership of each unlabeled image by creating a sequence of such image transformations that connect it, through other unlabeled images, to a labeled image. In order to measure the total transformation, a robust and reliable metric of the path length is proposed, which combines a local dissimilarity between consecutive images along the path with a global connectivity-based metric. For the local dissimilarity we use a symmetrized version of the zero-order image deformation model (IDM) proposed by Keysers et al. in [1]. For the global distance we use a connectivity-based metric proposed by Chapelle and Zien in [2]. Experimental results on the MNIST benchmark indicate that the proposed classifier out-performs current state-of-the-art techniques, especially when very few labeled patterns are available.

This work considers the independent component analysis (ICA) of quaternion random vectors. In particular, we focus on the Gaussian case, and therefore the ICA problem is solved by exclusively exploiting the second-order statistics (SOS) of the observations. In the quaternion case, the SOS of a random vector are given by the covariance matrix and three complementary covariance matrices. Thus, quaternion ICA amounts to jointly diagonalizing these four matrices. Following a maximum likelihood (ML) approach, we show that the ML-ICA problem reduces to the minimization of a cost function, which can be interpreted as a measure of the entropy loss due to the correlation among the estimated sources. In order to solve the non-convex ML-ICA problem, we propose a practical quasi-Newton algorithm based on quadratic local approximations of the cost function. Finally, the practical performance and potential application of the proposed technique is illustrated by means of numerical examples.

Alternating minimization algorithms are typically used to find interference alignment (IA) solutions for multiple-input multiple-output (MIMO) interference channels with more than K=3 users. For these scenarios many IA solutions exit, and the initial point determines which one is obtained upon convergence. In this paper, we propose a new iterative algorithm that aims at finding the IA solution that maximizes the average sum-rate. At each step of the alternating minimization algorithm, either the precoders or the decoders are moved along the direction given by the gradient of the sum-rate. Since IA solutions are defined by a set of subspaces, the gradient optimization is performed on the Grassmann manifold. The step size of the gradient ascent algorithm is annealed to zero over the iterations in such a way that during the last iterations only the interference leakage is being minimized and a perfect alignment solution is finally reached. Simulation examples are provided showing that the proposed algorithm obtains IA solutions with significant higher throughputs than the conventional IA algorithms.

One of the key problems in cognitive radio (CR) is the detection of primary activity in order to determine which parts of the spectrum are available for opportunistic access. This detection task is challenging, since the wireless environment often results in very low SNR conditions. Moreover, calibration errors and imperfect analog components at the CR spectral monitor result in uncertainties in the noise spectrum, making the problem more difficult. In this work, we present a new multiantenna detector which is based on the fact that the observation noise processes are spatially uncorrelated, whereas any primary signal present should result in spatial correlation. In particular, we derive the generalized likelihood ratio test (GLRT) for this problem, which is given by the quotient between the determinant of the sample covariance matrix and the determinant of its block-diagonal version. For stationary processes the GLRT tends asymptotically to the integral of the logarithm of the Hadamard ratio of the estimated power spectral density matrix. Additionally, we present an approximation of the frequency domain detector in the low SNR regime, which results in computational savings. The performance of the proposed detectors is evaluated by means of numerical simulations, showing important advantages over existing detectors.

We present a kernel-based recursive least-squares (KRLS) algorithm on a fixed memory budget, capable of recursively learning a nonlinear mapping and tracking changes over time. In order to deal with the growing support inherent to online kernel methods, the proposed method uses a combined strategy of growing and pruning the support. In contrast to a previous sliding-window based technique, the presented algorithm does not prune the oldest data point in every time instant but it instead aims to prune the least significant data point. We also introduce a label update procedure to equip the algorithm with tracking capability. Simulations show that the proposed method obtains better performance than state-of-the-art kernel adaptive filtering techniques given similar memory requirements.

In this paper the two main definitions of quaternion properness (or second order circularity) are reviewed, showing their connection with the structure of the optimal quaternion linear processing. Specifically, we present a rigorous generalization of the most common multivariate statistical analysis techniques to the case of quaternion vectors, and show that the different kinds of quaternion improperness require different kinds of widely linear processing. In general, the optimal linear processing is full-widely linear, which requires the joint processing of the quaternion vector and its involutions over three pure unit quaternions. However, in the case of jointly ℚ-proper and ℂη-proper vectors, the optimal processing reduces, respectively, to the conventional and semi-widely linear processing, with the latter only requiring to operate on the quaternion vector and its involution over the pure unit quaternion η. Finally, a simulation example poses some interesting questions for future research.

Society demands access to high capacity wireless communications and to the services that can be provided on top of them. To satisfy these demands, engineers are constantly developing new technologies. These developments have to be selectively transferred to the university curricula. The student has to be familiar not only with the basic theory and techniques, but also with those of the more advanced techniques that provide a more profound insight. One of these techniques is based on Multiple-Input Multiple-Output (MIMO) systems. In this paper we show how to build a web platform for learning advanced digital communications based on a MIMO testbed. Using as starting point a 4 × 4 flexible dual band (2.4/5 GHz), we first develop a webservice interface to provide remote access to the services offered by the testbed and then implement a virtual laboratory where the students can parameterize and perform advanced experiments.

In this paper, we propose a general beamforming criterion for pre-FFT processing in orthogonal frequency division multiplexing (OFDM) systems with multiple transmit and receive antennas. The proposed criterion depends on a single parameter α, which establishes a tradeoff between the energy of the equivalent SISO channel (after Tx-Rx beamforming) and its spectral flatness. The proposed cost function embraces most reasonable criteria for designing Tx-Rx pre-FFT beamformers. Hence, for particular values of α the proposed criterion reduces to the minimization of the mean square error (MSE), the maximization of the system capacity, or the maximization of the received signal-to-noise ratio (SNR). In general, the proposed criterion results in a non convex optimization problem. However, we show that the problem can be approximately solved by semidefinite relaxation (SDR) techniques. Additionally, since the computational cost of SDR for this problem is rather high, we propose a simple yet efficient gradient search algorithm which provides satisfactory solutions with a moderate computational cost for OFDM-based WLAN standards such as 802.11a. Finally, the good performance of the proposed technique is illustrated by means of some numerical results.

In this paper, the second-order circularity of quaternion random vectors is analyzed. Unlike the case of complex vectors, there exist three different kinds of quaternion properness, which are based on the vanishing of three different complementary covariance matrices. The different kinds of properness have direct implications on the Cayley-Dickson representation of the quaternion vector, and also on several well-known multivariate statistical analysis methods. In particular, the quaternion extensions of the partial least squares (PLS), multiple linear regression (MLR) and canonical correlation analysis (CCA) techniques are analyzed, showing that, in general, the optimal linear processing is full-widely linear. However, in the case of jointly Q-proper or Cη-proper vectors, the optimal processing reduces, respectively, to the conventional or semi-widely linear processing. Finally, a measure for the degree of improperness of a quaternion random vector is proposed, which is based on the Kullback-Leibler divergence between two zero-mean Gaussian distributions, one of them with the actual augmented covariance matrix, and the other with its closest proper version. This measure quantifies the entropy loss due to the improperness of the quaternion vector, and it admits an intuitive geometrical interpretation based on Kullback-Leibler projections onto sets of proper augmented covariance matrices.

Abstract In this paper, a new technique for the blind estimation of frequency and/or time‐selective multiple‐input multiple‐output (MIMO) channels under space‐time block coding (STBC) transmissions is presented. The proposed method relies on a basis expansion model (BEM) of the MIMO channel, which reduces the number of parameters to be estimated, and includes many practical STBC‐based transmission scenarios, such as STBC‐orthogonal frequency division multiplexing (OFDM), space‐frequency block coding (SFBC), time‐reversal STBC, and time‐varying STBC encoded systems. Inspired by the unconstrained blind maximum likelihood (UML) decoder, the proposed criterion is a subspace method that efficiently exploits all the information provided by the STBC structure, as well as by the reduced‐rank representation of the MIMO channel. The method, which is independent of the specific signal constellation, is able to blindly recover the MIMO channel within a small number of available blocks at the receiver side. In fact, for some particular cases of interest such as orthogonal STBC‐OFDM schemes, the proposed technique blindly identifies the channel using just one data block. The complexity of the proposed approach reduces to the solution of a generalized eigenvalue (GEV) problem and its computational cost is linear in the number of sub‐channels. An identifiability analysis and some numerical examples illustrating the performance of the proposed algorithm are also provided. Copyright © 2009 John Wiley & Sons, Ltd.

In this paper, we study transmission schemes for a novel OFDM-based MIMO system which performs adaptive signal combining in radio-frequency (RF). Specifically, we consider the problem of selecting the linear precoder and the transmit and receive RF weights (or beamformers) for minimizing the bit error rate (BER) under the assumption of perfect channel knowledge and linear receivers. Firstly, it is shown that the optimal precoder amounts to uniformly distribute the overall mean square error (MSE) among the information symbols. Secondly, we propose a gradient search algorithm to obtain the optimal pair of beamformers. Interestingly, in the case of low signal to noise ratios (SNR), the proposed beamforming criterion is equivalent to the maximization of the received SNR. However, for moderate and high SNRs, part of the received SNR is sacrificed in order to improve the channel response of the worst subcarriers, which translates into significant advantages over other previously proposed approaches. Finally, the performance of the proposed scheme is illustrated by means of some numerical examples.

In this paper, we study beamforming schemes for a novel MIMO transceiver, which performs adaptive signal combining in the radio-frequency domain. Assuming perfect channel knowledge at both the transmit and receive sides, we consider the problem of selecting the transmit and receive RF beamformers that maximize the capacity (MaxCAP criterion) of the system under orthogonal frequency division multiplexing (OFDM) transmissions. This problem is non-convex and has no closed-form solution, therefore the maximum capacity beamformers are found using a gradient search algorithm. Furthermore, it is shown in the paper that, for low signal-to-noise ratios (SNR), the MaxCAP criterion is equivalent to maximizing the received SNR (MaxSNR criterion). However, for moderate and high SNRs, the maximum capacity beamformers sacrifice part of the received SNR in order to improve the worst subcarriers and, in this way, they increase the overall capacity of the multicarrier channel. Finally, by means of numerical examples we show that the MaxCAP criterion significantly outperforms the MaxSNR criterion in terms of bit error rate and outage probability.

The coherence spectrum is a well-known measure of the linear statistical relationship between two time series. In this paper, we extend this concept to several processes and define the generalized magnitude squared coherence (GMSC) spectrum as a function of the largest eigenvalue of a matrix containing all the pairwise complex coherence spectra. The GMSC is bounded between zero and one, and attains its maximum when all the processes are perfectly correlated at a given frequency. Furthermore, three different GMSC spectrum estimators, extending those previously proposed for the MSC of two processes, are presented. Specifically, we compare the Welch method, the minimum variance distortionless response (MVDR) estimator and a new estimator based on canonical correlation analysis (CCA).

In this paper, the conditions for blind identifiability from second-order statistics (SOS) of multiple-input multiple-output (MIMO) channels under orthogonal space-time block coded (OSTBC) transmissions are studied. The main contribution of the paper consists in the proof that, assuming more than one receive antenna, any OSTBC with a transmission rate higher than a given threshold, which is inversely proportional to the number of transmit antennas, permits the blind identification of the MIMO channel from SOS. Additionally, it has been proven that any real OSTBC with an odd number of transmit antennas is identifiable, and that any OSTBC transmitting an odd number of real symbols permits the blind identification of the MIMO channel regardless of the number of receive antennas, which extends previous identifiability results and suggests that any nonidentifiable OSTBC can be made identifiable by slightly reducing its code rate. The implications of these theoretical results include the explanation of previous simulation examples and, from a practical point of view, they show that the only nonidentifiable OSTBCs with practical interest are the Alamouti codes and the real square orthogonal design with four transmit antennas. Simulation examples and further discussion are also provided.

Abstract In this paper we employ a 2 × 2 Multiple‐Input Multiple‐Output (MIMO) hardware platform to evaluate, in realistic indoor scenarios, the performance of different space‐time block coded (STBC) transmissions at 2.4 GHz. In particular, we focus on the Alamouti orthogonal scheme considering two types of channel state information (CSI) estimation: a conventional pilot‐aided supervised technique and a recently proposed blind method based on second‐order statistics (SOS). For comparison purposes, we also evaluate the performance of a Differential (non‐coherent) space‐time block coding (DSTBC). DSTBC schemes have the advantage of not requiring CSI estimation but they incur in a 3 dB loss in performance. The hardware MIMO platform is based on high‐performance signal acquisition and generation boards, each one equipped with a 1 GB memory module that allows the transmission of extremely large data frames. Upconversion to RF is performed by two RF vector signal generators whereas downconversion is carried out with two custom circuits designed from commercial components. All the baseband signal processing is implemented off‐line in MATLAB®, making the MIMO testbed very flexible and easily reconfigurable. Using this platform we compare the performance of the described methods in line‐of‐sight (LOS) and non‐line‐of‐sight (NLOS) indoor scenarios. Copyright © 2007 John Wiley & Sons, Ltd.

In this paper, a new technique for the estimation of the magnitude squared coherence (MSC) spectrum is proposed. The method is based on the relationship between the MSC and the canonical correlation analysis (CCA) of stationary time series. Particularly, the canonical correlations coincide asymptotically with the squared roots of the MSC, which is exploited in the paper to obtain an estimate of the MSC based on a reduced-rank version of the estimated coherence matrix. The proposed technique provides a higher spectral resolution than the well-known Welch's method, and it also avoids the signal mismatch problem associated to the minimum variance distortionless response (MVDR) based approach. Finally, the performance of the proposed method is evaluated by means of some numerical examples.

In this paper, the conditions for blind identifiability from second order statistics (SOS) of multiple-input multiple-output (MIMO) channels under orthogonal space-time block coded (OSTBC) transmissions are studied. The main contribution of the paper is to show that, assuming more than one receive antenna, any OSTBC with a transmission rate higher than a given threshold, which is inversely proportional to the number of transmit antennas, permits the blind identification of the MIMO channel from SOS. Additionally, some previous identifiability results have been extended. The implications of these theoretical results include the explanation of previous simulation examples found in the literature and, from a practical point of view, they show that the only non-identifiable OSTBC codes with practical interest are the Alamouti codes and the real square orthogonal design with four transmit antennas. Further discussion and empirical analysis are also provided.

In this letter we derive a simple and tight closed-form approximation for the ergodic capacity of orthogonal space-time block coding in arbitrary fading channels. The expression is an analytical function of the power covariance matrix of the channel. In the case of uncorrelated channels the expression only depends on the variances of the channel power gains. These channel statistics can be easily obtained from both analytical and physical fading channel models. Simulations results show the accuracy of the proposed expression

In this paper we apply the structural risk minimization (SRM) principle to derive a blind single-input multiple-output (SIMO) channel estimation algorithm, which is robust to channel order overestimation. Specifically, the blind estimation is formulated as a support vector regression (SVR) problem in which the channel coefficients are the Lagrange multipliers of the dual problem. In this paper, we show that the SRM principle pushes to zero the small leading and trailing terms of the channel impulse response even when its order is highly overestimated. The main drawback of this approach is the high computational cost of the resulting quadratic programming (QP) problem. To alleviate this, in this paper we propose to use a simple and fast algorithm called the Adatron to solve the QP problem. Simulation results are provided to demonstrate the performance of our channel estimator.

In this paper we propose a new kernel-based version of the recursive least-squares (RLS) algorithm for fast adaptive nonlinear filtering. Unlike other previous approaches, we combine a sliding-window approach (to fix the dimensions of the kernel matrix) with conventional L2-norm regularization (to improve generalization). The proposed kernel RLS algorithm is applied to a nonlinear channel identification problem (specifically, a linear filter followed by a memoryless nonlinearity), which typically appears in satellite communications or digital magnetic recording systems. We show that the proposed algorithm is able to operate in a time-varying environment and tracks abrupt changes in either the linear filter or the nonlinearity

In this paper, a new second-order statistics (SOS) based method for blind decoding of orthogonal space time block coded (OSTBC) systems with only one receive antenna is proposed. To avoid the inherent ambiguities of this problem, the spatial correlation matrix of the source signals must be non-white and known at the receiver. In practice, this can be achieved by a number of simple linear precoding techniques at the transmitter side. More specifically, it is shown in the paper that if the source correlation matrix has different eigenvalues, then the decoding process can be formulated as the problem of maximizing the sum of a set of weighted variances of the signal estimates. Exploiting the special structure of OSTBCs, this problem can be reduced to a principal component analysis (PCA) problem, which allows us to derive computationally efficient batch and adaptive blind decoding algorithms. The algorithm works for any OSTBC (including the popular Alamouti code) with a single receive antenna. Some simulation results are presented to demonstrate the potential of the proposed procedure

We consider the application of kernel canonical correlation analysis (K-CCA) to the supervised equalization of Wiener systems. Although a considerable amount of research has been carried out on identification/equalization of Wiener models, in this paper we show that K-CCA is a particularly suitable technique for the inversion of these nonlinear dynamic systems. Another contribution of this paper is the development of an online K-CCA algorithm which combines a sliding-window approach with a recently proposed reformulation of CCA as an iterative regression problem. This online algorithm permits fast equalization of time-varying Wiener systems. Simulation examples are added to illustrate the performance of the proposed method.

This letter proposes a clustering-based approach for solving the underdetermined (i.e., fewer mixtures than sources) postnonlinear blind source separation (PNL BSS) problem when the sources are sparse. Although various algorithms exist for the underdetermined BSS problem for sparse sources, as well as for the PNL BSS problem with as many mixtures as sources, the nonlinear problem in an underdetermined scenario has not been satisfactorily solved yet. The method proposed in this letter aims at inverting the different nonlinearities, thus reducing the problem to linear underdetermined BSS. To this end, first a spectral clustering technique is applied that clusters the mixture samples into different sets corresponding to the different sources. Then, the inverse nonlinearities are estimated using a set of multilayer perceptrons (MLPs) that are trained by minimizing a specifically designed cost function. Finally, transforming each mixture by its corresponding inverse nonlinearity results in a linear underdetermined BSS problem, which can be solved using any of the existing methods.

Canonical correlation analysis (CCA) is a classical tool in statistical analysis that measures the linear relationship between two data sets. In this paper we show that CCA can be reformulated as a pair of coupled least squares (LS) problems. By exploiting this idea, we first present an iterative batch procedure to extract all the canonical vectors through a regression procedure. Then, we derive a recursive least squares (RLS) algorithm for on-line CCA. This algorithm can be further improved to increase its robustness against outliers and impulsive noise. The proposed algorithm is applied to blind identification of multichannel FIR systems, and its performance is illustrated through simulations.

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

A novel technique for blind identification of multichannel FIR systems is derived from the learning paradigm of support vector machines (SVMs). Specifically, blind identification is formulated as a support vector regression problem and an iterative procedure, which avoids a trivial solution, is proposed to solve it. The SVM-based approach can be viewed as a regularized version of the least squares method for blind identification. We show that minimizing the complexity of the solution, as suggested by the structural risk minimization (SRM) principle, increases the robustness of the proposed SVM-based technique to channel order overestimation as well as to poor diversity channels (i.e., when a pair of subchannels have close zeros). The performance of the method is demonstrated through some simulation examples.

Recent work has shown how the support vector machine (SVM) framework can be used for blind equalization of constant modulus (CM) signals. The basic idea consists of exploiting the CM property of the input signals to reformulate the blind equalization problem as a regression problem. We extend this idea to encompass the problem of separating and estimating multiple CM signals mixed through an unknown matrix (i.e., blind beamforming). The quadratic inequalities derived from the CM property are transformed into linear ones, thus yielding a quadratic programming (QP) problem. Then an iterative reweighted procedure is proposed to blindly restore the CM property. Once a signal is recovered, its contribution to the original observations is removed and the iterative procedure can be applied again to extract another CM signal. Simulation results show that this SVM-based algorithm offers better performance than the algebraic constant modulus algorithm (ACMA), mainly when only a small number of snapshots is available.

MIMO systems based on dual-polarized antennas at transmitter and receiver constitute an interesting alternative to conventional MlMO configurations. This paper analyzes the ergodic capacity of such systems in urban micro- and pico-cellular environments. The MIMO channel is modeled by using a site-specific ray-tracing propagation tool. This technique permits to analyze the impact of environmental parameters, like antennas location and orientation, on the system performance. Ergodic capacity estimations in a specific urban environment are presented.

A new approach to the design of prototype filters for conventional nearly perfect reconstruction (N-PR) cosine-modulated filter banks is presented. The new method is based on the frequency sampling approach for the design of finite-impulse response filters. In the proposed approach, the magnitude response values of samples in the transition band of the prototype filter are the only parameters to be optimized. The analytical and simulation results show that despite there being no direct control over the stopband attenuation of the prototype filter, the performance of the filter bank is extremely good, and in several cases, the whole system closely satisfies the PR property.

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

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

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

In this paper the problem of blind equalization of constant modulus (CM) signals is formulated within the support vector (SV) regression framework. The quadratic inequalities derived from the CM property are transformed into linear ones, thus yielding a quadratic programming (QP) problem. Then an iterative reweighted procedure is proposed to blindly restore the CM property. The technique can be generalized to nonlinear blind equalization using kernel functions. We present simulation examples showing that linear and nonlinear blind SV equalizers offer better performance than cumulant-based techniques, mainly in applications when only a small number of data samples is available, such as in packet-based transmission over fast fading channels.

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

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

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

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

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

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

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

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

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

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

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

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