In this study we introduce Logarithmic Frequency Shift Keying (Log-FSK), a novel frequency modulation for over-the-air computation (AirComp). Log-FSK leverages non-linear signal processing to produce AirComp in the frequency domain, this is, the maximum frequency of the received signal corresponds to the sum of the individual transmitted frequencies. The demodulation procedure relies on the inverse Discrete Cosine Transform (DCT) and the extraction of the maximum frequency component. Log-FSK enables the computation of functions beyond the sum by incorporating nomographic function representation. Furthermore, unlike existing AirComp modulations, Log-FSK allows to compute several functions in a single transmission. We evaluate the capabilities of the scheme in an additive white Gaussian noise (AWGN) and flat-fading channels. To demonstrate its practicality, we present specific applications and experimental results showcasing the effectiveness of Log-FSK AirComp within linear Wireless Sensor Networks (WSN). Our numerical results show that Log-FSK outperform linear analog modulations in terms of MSE and power consumption.

Federated edge learning (FEEL) is a framework for training models in a distributed fashion using edge devices and a server that coordinates the learning process. In FEEL, edge devices periodically transmit model parameters to the server, which aggregates them to generate a global model. To reduce the burden of transmitting high-dimensional data by many edge devices, a broadband analog transmission scheme has been proposed. The devices transmit the parameters simultaneously using a linear analog modulation, which are aggregated by the superposition nature of the wireless medium. However, linear analog modulations incur in an excessive power consumption for edge devices and are not suitable for current digital wireless systems. To overcome this issue, in this paper we propose a digital frequency broadband aggregation. The scheme integrates a Multiple Frequency Shift Keying (MFSK) at the transmitters and a type-based multiple access (TBMA) at the receiver. Using concurrent transmission, the server can recover the type (i.e., a histogram) of the transmitted parameters and compute any aggregation function to generate a shared global model. We provide an extensive analysis of the communication scheme in an additive white Gaussian noise (AWGN) channel and compare it with linear analog modulations. Our experimental results show that the proposed scheme achieves no drop in performance up to -10 dB and outperforms the analog counterparts, while requiring 14 dB less in peak-to-average power ratio (PAPR) than linear analog modulations.

This work presents an orthonormal transform that splits the Orthogonal Frequency Division Multiplex (OFDM) symbol into slices with ranked rate and decoding complexity. The advantage over the existing carrier or time segmentation is that the proposed technique does not depend on the frequency channel to produce slices of equal rate. Also, the encoding and the decoding complexity is kept simple.

The use of multi-antenna transmitters is emerging as an essential technology of the future wireless communication systems. While Zero-Forcing Beamforming (ZFB) has become the most popular low-complexity transmit beamforming design, it has some drawbacks basically related to the effort of "trying" to invert the channel coefficients towards the interfered users. In particular, ZFB performs poorly in the low Signal-to-Noise Ratio (SNR) regime and does not work when the interfered users outnumber the transmit antennas. In this paper, we study in detail an alternative transmit beamforming design framework, where we allow some residual received-interference power instead of trying to null it completely out. Subsequently, we provide a close-form non-iterative optimal solution that avoids the use of sophisticated convex optimization techniques that compromise its applicability onto practical systems. Supporting results based on numerical simulations show that the proposed transmit beamforming is able to perform close to the optimal with much lower computational complexity.

This paper proposes a transmit beamforming technique to cope with the problem of the Multiple Input Single Output Interference Channel (MISO IC). In this scenario, the achievable sum-rate is highly conditioned by the inter-user interference. Furthermore, optimizing the sum-rate is known to be a cumbersome problem. In order to deal with this problem, we approximate the sum-rate when the desired received signal power level is higher than the multiuser interference power level (i.e. when the Signal-to-Interference Ratio (SIR) is high). For that case, the sum-rate expression can be optimized distributively and it leads to a transmit beamformer that outperforms the existing decentralized techniques when the channel gains are asymmetric. Numerical simulations show the performance of the proposed technique which improves the existing decentralized designs for the MISO IC.

This paper addresses the problem of transmit beam-forming in open spectrum communication systems. In these scenarios, the operator or the data communication provider delivers a set of base stations to the final users under no radio planning strategy. In order to deal with such an uncoordinated communication system, this work presents a centralized algorithm for calculating the optimal precoding strategy the via semidefinite relaxation technique. The problem to be solved is a novel design of minimum norm beamformers under QoS and received power constraints. Numerical results will show the performance of the method.

The advance of cognitive radio (CR) technology put in evidence the need of new spectral estimation methods for proper labeling of licensed and un-licensed users. We present a new spectral estimation procedure for monitoring the radio spectrum. The estimate is derived from a different view point of traditional filter bank approach. The resulting method is able to detect a predetermined spectral shape forming part or contributing to a given data record, providing at the same time an estimate of its power level and its frequency location. We prove that traditional filter-bank spectral estimation reduces to a particular case of our procedure. The specific spectral shape to detect is named hereafter as the candidate spectrum. The major motivation for this procedure was the proper spectrum labeling of licensed users in cognitive radio scenarios. The performance of the spectral monitoring procedure is demonstrated in the detection of a BPSK primary user in a wireless scenario containing DVB-T emissions.

An interesting but apparently forgotten auto-regressive moving-average (ARMA) parameter estimation method, introduced by one of us in 1984, and refined later on by others, is revisited. In the process, we provide a new simpler derivation of the method as well as an enhanced version of its cepstrum-based step. We argue that this method has an appealing advantage over Durbin's method, which is probably the most frequently used non-iterative method for ARMA parameter estimation.

In this paper, we study the design of the transmitter in the downlink of a multiuser and multiantenna wireless communications system, considering the realistic scenario where only an imperfect estimate of the actual channel is available at both communication ends. Precisely, the actual channel is assumed to be inside an uncertainty region around the channel estimate, which models the imperfections of the channel knowledge that may arise from, e.g., estimation Gaussian errors, quantization effects, or combinations of both sources of errors. In this context, our objective is to design a robust power allocation among the information symbols that are to be sent to the users such that the total transmitted power is minimized, while maintaining the necessary quality of service to obtain reliable communication links between the base station and the users for any possible realization of the actual channel inside the uncertainty region. This robust power allocation is obtained as the solution to a convex optimization problem, which, in general, can be numerically solved in a very efficient way, and even for a particular case of the uncertainty region, a quasi-closed form solution can be found. Finally, the goodness of the robust proposed transmission scheme is presented through numerical results. Robust designs, imperfect CSI, multiantenna systems, broadcast channel, convex optimization.

In this letter, we study spatial Tomlinson-Harashima precoding (STHP) from an information theoretic point of view encompassing both the single and the multiuser scenarios. Since the performance of any communications preceding scheme relies on the quality of the channel state information (CSI) that is made available at the transmitter side, in this work we focus our attention on the analysis of the robustness of STHP in terms of rate loss when the CSI is imperfect. Precisely, we present a robust design of the set of moduli used in STHP and, consequently, of the corresponding power allocation, that maximizes the achievable rates for the worst-case errors in the CSI in the small errors regime.

We are interested in studying different capacity formulations in linear vector Gaussian channels where the transmitter is only informed with the magnitude of the complex channel matrix coefficients and the receiver has perfect channel knowledge. Initially, we give the general expressions for the ergodic, compound, and outage capacities for our particular model of channel state information. Next, focusing on the compound formulation, we find that the optimal transmitter strategy consists in independent signaling through the transmit dimensions. Finally, we present a new result on the power allocation for the maximization of the outage mutual information.

We present the optimum design of a linear transmitter for a multi-input multi-output communication system when the input data consists of two QPSK streams and the receiver performs maximum likelihood detection. The transmitter design is optimal in the sense that it minimizes the worst-case pairwise error probability. We prove that the resulting linear transmitter constructs, as a function of the two input QPSK streams, a new signal constellation. Moreover, we show that this new signal constellation is such that the minimum distance among the points of the received constellation is maximized and, indirectly, the number of neighbors at minimum distance is also maximized.

In this paper repetition-based cooperative diversity technique has been taken into consideration. For this technique there exists a trade off between the gains achieved by diversity reception and the decrease in bandwidth efficiency. Both effects have a hard dependence on the number of cooperating terminals. Here an analysis based on the average bit error rate (BER) of multilevel signaling MQAM modulation is presented to characterize the optimal achievable end-to-end throughput. In this way it is shown that threshold decisions can be taken to find out the optimal choice for the number of relays and modulation size. Thanks to that, efficient protocols can be designed using this information.

In this paper, we investigate a cross-layer approach to transmit antenna selection capable of adapting the number of active antennas to varying channel conditions. We address a cross-layer methodology in the sense that the criterion for the selection of antenna subsets is the maximization of link layer throughput which takes into account characteristics both at the physical and link layers. In order to enhance system performance, adaptive modulation is included to jointly perform antenna selection and rate adaptation. Performance assessment is conducted in terms of link layer throughput and transmission delay

The performance of any communications precoding scheme relies on the quality of the channel state information that is made available at the transmitter side. In this paper, we study the robustness of spatial Tomlinson-Harashima precoding (STHP) in terms of rate loss when errors are considered in the feedback link. We will evaluate the performance degradation of the uniform power allocation with antenna selection strategy for STHP (which is quasioptimal when there are no feedback errors) and compare it with a robust power allocation designed to maximize the achievable rates for the worst-case feedback noise. It is shown that the performance difference between both approaches is very small. Consequently, uniform power allocation with antenna selection arises as a good solution for STHP even in the presence of feedback errors.

Theoretical investigation have shown that multiple antenna schemes can improve link reliability and provide high spectral efficiency. Space-time block coding (STBC) and vertical Bell Labs layered space time (V-BLAST) systems are capable of meeting these requirements by using multiple antenna strategies,respectively. However, in order to achieve largely improved performance they need precise channel information at the receiver, which is difficult to be guaranteed in some specific scenarios. In this paper, independent component analysis (ICA) technique is exploited to detect the transmitted signals blindly, which needs not the channel estimation. By analyzing the essential structures of STBC and V-BLAST systems, the specific models suitable to ICA are established. The robustness against channel estimation error and flexibility of system design can be acquired by using the ICA based scheme. Simulation results demonstrate the validity of proposed approach and the feasibility of ICA based scheme is also discussed.

We address the problem of the design of a transmitter in a multi-input-multi-output (MIMO) space diversity system. We consider a design which is robust to errors in the channel estimate available at the transmitter. The design is based on the minimization of the necessary transmit power while guaranteeing a minimum and specified quality of service (QoS) in terms of signal to noise ratio (SNR) with a certain probability. According to this objective, the transmitter exploits all the eigenmodes of the MIMO channel estimate, distributing the transmit power in a robust way among the channel modes by using orthonormal temporal signatures. In order to guarantee a full rate transmission, the orthonormal temporal signatures designed for real constellations in orthogonal space-time block codes (OSTBC) are used, leading to a system structure based on a combination of OSTBC and orthogonal weighted beamforming.

In this paper, we study the ergodic capacity of a multiple input multiple output (MIMO) uncorrelated flat fading channel with perfect channel state information at the receiver and partial channel state information at the transmitter. We focus our attention on the case where the transmitter is informed only with the modulus of the channel matrix coefficients. First, we prove that a simple power allocation strategy among transmitting antennas is the optimal scheme, in the sense that is a capacity achieving architecture. Next, for the particular case where only two antennas are used at each communication end, we derive closed form expressions for the ergodic capacity and the optimal power assigned to each antenna.

Orthogonal frequency division multiplexing (OFDM) has been recently established for several systems such as HiperLAN/2 and Digital video/audio broadcasting, due the easy implementation of the modulator/demodulator and the equalizer. Moreover, also increasing interest is currently being put on multiple-input multiple-output (MIMO) channels, based on the use of antenna arrays at both the transmitter and the receiver. Here, we propose two joint beamforming strategies of low computational load for systems combining OFDM and MIMO. The ultimate objective is the maximization of the signal-to-noise and interference ratio (SNIR) over the carriers subject to a total transmit power constraint. Specifically, the maximization of the harmonic SNIR mean and the minimum SNIR over the subcarriers are proposed. The asymptotic behavior of the proposed methods is analyzed to provide a complete comparative and general view of the most relevant and already known transmit power allocation strategies. Finally, a theoretical analysis of the performance degradation of these techniques is carried out for the case in which the channel state information (CSI) is not perfect. Monte Carlo simulation results for the system bit-error rate and performance degradation with imperfect CSI are provided.

In this paper we address the design of a multiple transmit antenna system in which the channel state information (CSI) at the transmitter is not perfect. Two different approaches are analyzed: one based on the minimization of the mean square error (MMSE) and the other based on the application of the maximum likelihood sequence estimation (MLSE). In both cases a Bayesian criterion is used in order to take into account the error between the CSI and the real channel. Finally, some simulation results and conclusions are provided, showing the gain of these approaches when the error between the CSI and the real channel is either Gaussian or uniform, where this last case corresponds to a quantization of the channel time response in order to transmit the CSI through a feedback channel from the receiver to the transmitter.

This paper addresses the joint design of transmit and receive beamvectors for a multicarrier MIMO channel within the general and powerful framework of convex optimization theory. From this perspective, a great span of design criteria can be easily accommodated and efficiently solved even though closed-form expressions may not be available. Among other criteria, we consider the minimization of the average bit error rate (BER) and also of the maximum BER among all carriers for a given signal constellation. We show how to include additional constraints to control the peak-to-average ratio (PAR) in the system design.

In this paper we address the problem of the design of a power allocation strategy for an orthogonal frequency division multiplexing (OFDM) system. We assume no spatial diversity at the transmitter and receiver, that is, a single-input-single-output (SISO) channel is considered. The goal is to allocate all the available power at the transmitter among the different carriers according to a minimum mean bit error rate (BER) criterion. When designing this strategy, we assume that channel state information (CSI) is available at the transmitter. Two different approaches are taken. The first one considers that the channel estimates are perfect, whereas the second approach assumes that there is some estimation error, and therefore, this approach is robust in nature. Finally, we propose an efficient algorithm for computing the power allocated to the carriers for both approaches, and show some simulation results in order to compare them.

Multi-input multi-output (MIMO) channels have been shown in the literature to present a significant capacity increase over single-input single-output ones in some situations. To achieve this theoretical capacity, the constituent parallel subchannels arising from the MIMO channel have to be properly used. Many practical schemes are being currently developed to achieve this goal. We first show that, from an information-theoretic point of view, beamforming becomes asymptotically optimal as the spatial correlation of the channel fading increases. In light of this result, wideband beamvectors are jointly derived for both transmission and reception. We allow a controlled partial response and design zero-forcing and minimum mean-squared error transmit-receive filters. Conceptually, the beamforming scheme is shown to decompose into two stages: the first one corresponds to a spatial flattening of the MIMO channel, i.e., choosing the subchannel with the highest gain at each frequency; the second stage depends on the particular design criterion and performs a power distribution at the transmitter and defines the equalizer at the receiver. These methods are further extended to the general case of multiple beamforming, i.e., when more than one subchannel are used. An exact and practical implementation of a modified "waterfilling" solution required for the filter design is proposed. All derived methods are assessed and compared in terms of capacity and bit-error rate.

When transmitting over multiple-input-multiple-output (MIMO) channels, there are additional degrees of freedom with respect to single-input-single-output (SISO) channels: the distribution of the available power over the transmit dimensions. If channel state information (CSI) is available, the optimum solution is well known and is based on diagonalizing the channel matrix and then distributing the power over the channel eigenmodes in a "water-filling" fashion. When CSI is not available at the transmitter, but the channel statistics are a priori known, an optimal fixed power allocation can be precomputed. This paper considers the case in which not even the channel statistics are available, obtaining a robust solution under channel uncertainty by formulating the problem within a game-theoretic framework. The payoff function of the game is the mutual information and the players are the transmitter and a malicious nature. The problem turns out to be the characterization of the capacity of a compound channel which is mathematically formulated as a maximin problem. The uniform power allocation is obtained as a robust solution (under a mild isotropy condition). The loss incurred by the uniform distribution is assessed using the duality gap concept from convex optimization theory. Interestingly, the robustness of the uniform power allocation also holds for the more general case of the multiple-access channel.

A particular property of the matched desired impulse response receiver is introduced, namely, the fact that full exploitation of the diversity is obtained with multiple beamformers when the channel is spatially and timely dispersive. This particularity makes the receiver specially suitable for mobile and underwater communications. The new structure provides better performance than conventional and weighted VRAKE receivers, and a diversity gain with no need for additional radio frequency equipment. The baseband hardware needed for this new receiver may be obtained through reconfigurability of the RAKE architectures available at the base station. The proposed receiver is tested through simulations assuming UTRA frequency-division-duplexing mode.

Orthogonal Frequency Division Multiplexing (OFDM) has been recently established for several systems such as HIPERLAN/2 and Digital Video and Audio Broadcasting. The success of this modulation is due to the easy implementati9n of the modulator and demodulator, including the equalization process. Moreover, in last years also increasing interest has been put on the study of Multi-Input-Multi-Output (MIMO) channels, based on the use of arrays of antennas at both the transmitter and the receiver. In this paper we propose two new and low computational cost joint beamforming strategies for communication systems that combine OFDM and MIMO channels. An asymptotic analysis of the proposed methods is carried out, providing a complete comparative study among other classical strategies. To demonstrate the potential of the proposed techniques, we present MonteCarlo simulation results of the system BER and make comparisons with other methods.

The Bayesian or maximum a posteriori (MAP) symbol-by-symbol detector allows minimum BER single user detection in CDMA systems with less memory requirements than the multiuser maximum likelihood sequence estimator. This work proposes a further complexity reduction by developing a fuzzy recursive implementation of the Bayesian detector. Simulation studies demonstrate the almost optimal performance of the developed fuzzy detector. The resulting system offers a performance v.s. complexity trade-off very appealing for detection in a 3/sup rd/ generation mobile handset.

Multi-input multi-output (MIMO) channels arising from the use of multi-element antenna (MEA) systems both in transmission and reception have been shown to support a considerable amount of bit rate. The information-theoretic capacity of such channels is severely affected by the spatial correlation. In this paper, we evaluate the ergodic and outage capacity of typical MIMO channels appearing in UMTS indoor scenarios. The frequency-selectivity and the spatial correlation of the MIMO channel are taken into account using realistic models obtained from field measurements performed within the IST project METRA (http://www.ist-metra.org). For capacity assessment, we use the transmission schemes considered by the 3GPP for UMTS. In particular, we analyze the cases of having and not having channel state information (CSI) at the transmitter, and also the case in which beamforming is used for transmission.

A self-reference beamforming algorithm, based on the inherent temporal redundancy structure presented by the spreading codes of direct sequence code division multiple access (DS-CDMA) systems, is proposed. It is derived from a novel perspective of chip level cross-correlation properties. The algorithm is shown to give the optimal solution in the sense of maximum signal to interference plus noise ratio (SINR). Block and adaptive approaches to solve the problem are given. The method is tested against the well-known temporal reference beamformer (TRB) combined with a decision-directed approach, showing a performance similar to it, despite no side information is being used.

The well-known structure of an array combiner along with a maximum likelihood sequence estimator (MLSE) receiver is the basis for the derivation of a space-time processor presenting good properties in terms of co-channel and intersymbol interference rejection. The use of spatial diversity at the receiver front-end together with a scalar MLSE implies a joint design of the spatial combiner and the impulse response for the sequence detector. This is faced using the MMSE criterion under the constraint that the desired user signal power is not cancelled, yielding an impulse response for the sequence detector that is matched to the channel and combiner response. The procedure maximizes the signal-to-noise ratio at the input of the detector and exhibits excellent performance in realistic multipath channels.

The use of spatial diversity at the receiver front-end together with a sequence detector implies a joint design problem of the spatial combiner and the sequence detector impulse response. This joint design is usually faced under the constraint that the impulse response of the sequence detector is matched to the channel plus combiner response. This procedure maximizes the signal to noise ratio at the input of the detector but does not guarantee that the so-called effective signal to noise ratio is maximized. This work presents a procedure that, starting from the matched criteria, faces directly the maximization of the effective signal to noise ratio, yet preserving all the features of the spatial processor in terms of co-channel and high order intersymbol interference rejection.

This paper addresses a new architecture for blind adaptive beamforming when dealing with frequency hopping (FH) modulation in cellular mobile communications systems. The proposed code reference beamformer (CRB) takes advantage of the inherent frequency diversity to estimate beforehand the noise plus interference correlation matrix, which is employed as the first part of the framework. Then, a second stage is adaptively obtained without any a priori knowledge of either the direction of arrival or the array manifold. Using this information, the first stage is in turn readjusted and, as a result, the scheme is able to track non-stationary scenarios following the channel variations with no previous references.

This work develops a novel dynamic fuzzy logic system that, based on a fuzzy basis function expansion, successfully solves the non-linear problem of narrowband interference prediction and rejection in DS-SS. A fuzzy basis function representation provides a natural framework for combining both numerical and linguistic information in a uniform fashion. The result is a low complexity non-linear adaptive line enhancer, which offers a faster convergence rate and an overall better performance over other well-known non-linear line enhancers.

The use of spatial diversity at the receiver front-end together with a sequence detector implies a joint design problem of the spatial combiner and the sequence detector impulse response. This joint design is usually faced under the constraint that the impulse response of the sequence detector is matched to the channel and combiner response. This procedure maximizes the signal to noise ratio at the input of the detector but, as it is well known, this does not guarantee a minimum probability of error, which is more related to the so-called effective signal to noise ratio. This work presents a procedure that, starting from a simple structure for the space-time receiver aims directly at the maximization of the effective signal to noise ratio, yet preserving all the features of the spatial processor in terms of co-channel and high order intersymbol interference rejection.

An algorithm for the joint tracking of source DOAs and sensor positions is presented to address the problem of DOA tracking in the presence sensor motion. Initial maximum likelihood estimates of source DOAs and sensor positions are refined by Kalman filtering. Spatio-temporally correlated array movement is considered. Source angle dynamics are used to achieve correct data association. The new technique is capable of performing well for the difficult cases of sources that cross in angle, fully coherent sources, as well as sources of identical or vastly different (possibly time-varying) power. Computer simulations show that the approach is robust in the presence of array motion modeling uncertainty and effectively reduces dependence on expensive and possibly unreliable hardware.

This work addresses the problem of spatial reference estimation in mobile scenarios. Novel techniques based on fuzzy logic are introduced to enhance the performance of a tracking system. Specifically, the model-free function approximation capability of fuzzy logic is used to obtain high resolution angle estimates from the spatial spectral density. These estimates are used to improve the resolution of the tracker. To the authors knowledge it is the first time that fuzzy logic is introduced in array spectral estimation. This work also develops a fuzzy controller for acting as an interpolative supervisor of different trackers that apply in different operating conditions of the dynamic nonlinear system. The result is a localization and tracking system that attains a resolution comparable to that of high resolution techniques as the minimum variance or Capon estimator. One of the main features of the proposed technique is its low computational burden. In summary, the presented system supports the expectation of adaptive arrays for obtaining a communication front-end of affordable complexity, developing cost and good performance.

The estimation of probability density functions (PDFs) of a given random variable (r.v.) is involved in topics related to codification, speech or whenever a short record of data is available but a greater amount is needed. Existing methods go from the so-called minimum description-length method, up to others based on the maximisation of the differential entropy imposing constraints on the moments of the r.v. In this paper we propose to estimate a PDF function by means of spectral estimate methods, since the positiveness and the real character of any PDF function allow us to deal with it as a power spectrum density function. Particularly, the minimum variance method is focused on because it can be generalised to multidimensional problems, being used in this paper to estimate the joint-PDF function of a multidimensional r.v.

A new algorithm for signal selective tracking of the directions-of-arrival (DOAs) of multiple moving targets with an array of passive sensors is presented. A new method based on the principles of maximum likelihood estimation and cyclostationarity is used to generate initial angle estimates which, in turn, are refined by a Kalman filter. Source angle dynamics are used to achieve correct data association. High performance is obtained with relatively low computational complexity.

A new architecture for adaptive arrays using frequency hopping modulation is addressed. The resolution of the array and the interference rejection increase substantially applying random processing to the carrier frequency of the signals. The proposed framework is composed of two different stages. The anticipative stage, devoted to minimize the noise and fixed interferences contribution and the GSLC stage which provides cancellation of follower jammers and solves the multiuser collision problem. The developed system requires neither temporal nor spatial reference for its implementation, only the frequency sequence must be known. An adaptive approach has been implemented, allowing a fast convergence to the optimal behavior.

This paper deals with the general problem of separating two independent wideband sources when they are mixed by unknown filters. In order to solve this problem, a backward framework is proposed which is composed of two different stages. The first one consists of two linear predictors devoted to improve the source separation, whitening the input signals. Their coefficients are calculated applying the LMS algorithm, minimizing the mean squared errors between the predicted signals and the output of the separation network. The second stage is formed by decoupling filters that have to be blindly estimated imposing an independence criterion to the outputs.>

This paper shows a new architecture specially thought to model non-linear systems (NLSs). At first, it was applied only to memoryless systems but then it developed to solve a more general problem, NLSs with memory. The result is a new filter, based on the Fourier transform, that the authors have named "K-filter". Important features of the K-filter are its nonlinear behaviour and second, that it profits from a temporal diversity of the input signal in order to provide itself with memory. At the end of the paper, the K-filter is used to solve an identification problem of a communication system which behaves nonlinearly due to the response of the amplifiers and which also has memory introduced basically by the channel response. The simulation results will provide an evaluation of the K-filter.>

This paper addresses the problem of simultaneous multiuser service. To find a feasible solution to the collision problem, two time reference multibeamformer systems are developed (BPSK TRMB and frequency framing TRMB). Based on a two-stage architecture, they enlarge the potential of existing separating neural networks and the algorithm (EM). Their goal is to perform a low computational simultaneous digital demodulation of users. The results support the frequency framing TRMB as the more robust system, which is able to give service to users in very degradated SNR scenarios; only the decoupling weights and their corresponding High Order Statistics learning is the overhead from a pure superposition of single channel receivers.>

Joint detection of carrier and timing parameters in digital communications is an alternative of recent interest when compared with individual acquisitions of each one of the parameters. The eigenvalue decomposition method of the signal structured covariance matrix is applied to jointly synchronize carrier frequency and timing (symbol transitions) in a full digital receiver. A very fast acquisition stage is obtained when phase shift keying (PSK) and minimum shift keying (MSK) signals are transmitted in an additive Gaussian noise channel. The parameters of interest are estimated from the signal subspace as a fast and computationally efficient alternative to the matched filter technique to estimate the timing parameter and also an alternative to the classic bank of filters technique used to acquire the carrier frequency parameter.>

A multitone tracker is described using two basic principles in optimum frequency estimation: processing bandwidth depending on the distance from the estimate to the actual frequency values, and parallel estimates with inhibitory paths to ensure orthogonality between the enhanced tones. The first feature is provided by extended Kalman filters (EKFs), and the second one is achieved by a high-order rule for the learning of the inhibitory cells. It is shown that the independence between signals is linked to the high-order function of the learning process. The resulting multitone tracker seems to be a potential alternative to adaptive high-resolution methods or time-frequency tools.>

A procedure for carrier-to-inference ratio (CIR) beamforming avoiding single value decomposition and derived from the classic carrier-to-interference-plus-noise ratio (CINR) solution is presented. The resulting nulling, for impinging interferers, is of the same degree as when using noise-subspace procedures. The method is based on the use of a temporal reference, already available in the satellite payload, together with the spatial steered beamvector (the Applebaum solution). The resulting procedure is a valuable alternative to the classic covariance loading methods, since it does not require further matrix inversion, and the noise estimate is derived from the existing hardware. Some results corresponding to a data-relay-satellite scenario are reported.>

Simultaneous frequency and phase acquisition and tracking methods in very short data records are reviewed and studied from a maximum-likelihood (ML)-estimation point of view. The frequency estimate of Tretter and Kay (see A.J. Viterbi and A.M. Viterbi, 1983) is extended to a multiple-parameter estimate. The resulting algorithm uses ML estimates for magnitude and phase prior to the linear regression procedure. The procedure provides good performance even under narrowband interferences and colored background noise. The application of interest is the estimation of Doppler frequency and channel leakage in burst communication systems.>

The potential of a two-dimensional spectral estimation approach to the problem of DOA (direction of arrival) estimation in wideband array beamforming problems is presented. It is shown that the covariance or interspectral matrix does not provide an adequate starting point in order to coherently average the energy of a given source. Angle focusing is envisaged from a prior two-dimensional spectral density. From this prior estimate, basic DFT interpolation may be used to obtain an angle/frequency representation of the wavefield, where source focusing can be done without requiring ad-hoc transformations. The viewpoint of the wideband DOA estimation problem states more clearly the potential, objectives, and fundamental limitations of focusing methods which are carried out at the interspectral matrix level or at the two-dimensional spectral density level.>

The min-norm method is related to the MUSIC bearing estimation method. This relation suggests a weighted version of min-norm method obtained from the eigenvalue method of Johnson and DeGraaf (1982). The method is obtained by weighting the eigenvectors with the inverse of the eigenvalues. Some experimental results illustrate the comparative behavior of the algorithm. Both the weighted and unweighted methods were implemented with a recursive algorithm that performs the spectral decomposition of the correlation matrix and is based on the properties of elemental matrices called dyads. The problem is reduced to an eigendecomposition of the sum of a diagonal matrix with a dyad, which is easily obtained. This computation can be executed in high degree of parallelism.>

The role of the periodogram envelope as a nonparametric approach for spectral estimation and its potential in parametric spectral estimation using variational approaches are examined. The spectral envelope, or its prior estimate the periodogram envelope, represents a very good candidate for starting any approach to spectral estimation due to its smooth character, its robustness against flat noise spectra, and its statistical stability. Setting envelope constraints in variational spectral estimation increases the statistical stability of the resulting estimate while preserving the high resolution of the best reported methods. The case of line spectra is briefly described to demonstrate the potential of the envelope-associated matrix in the line spectrum. This allows the designer to convert SUD and MUSIC methods to the new starting function.>

The author describes how Rayleigh estimates can be viewed as a method which performs singular-value decomposition (SVD) procedure without doing it. As a short cut to get principal-component reduction, Rayleigh quotients allow the resolution of frequency detectors yet preserve the asymptotic behavior of the actual power spectral density. In a filtering framework the estimate is extended to adaptive schemes and 2-D spectral estimation. The resulting estimate provides the means for adaptive processing with low computational complexity. It avoids also the crucial decision between signal subspace and noise subspace which promotes undesired distortion and false peaks in spectral estimation applications.>

This work describes the use of constraints in variational procedures for spectral analysis. It is reported how the designer in a variational approach for spectral estimation has to select a set of constraints. At the same time it is shown that the selected set of constraints becomes more relevant, as concerns with the resulting quality of the estimate, than the objective function minimized or maximized in the procedure. Finally, some examples are presented which are the result of considering correlation and envelope constraints and minimizing the correlation extrapolation energy.

This paper is a first attempt to give formalism to non-linear system design and in which context, related with similar linear processing techniques, they are located. A summary on the relation-ship of linear objectives and classical adaptive algorithms, in non-linear design problems, introduces the paper; giving the potential of random search techniques in order to open the different problems in non-linear objectives that could be handled with them. After, the similarity between probability distribution functions and power spectral density in linear processing is shown. This is supported by a nice example of non-linear system design. Finally, some prospective work is reported in the problem of adaptive companding design.

This work reports how to include general concepts of the one-dimensional MLM procedure in a two-channel problem of cross-spectrum estimation. It is shown in the sequel that there is no any problem in extrapolating the well-known procedures for auto-spectrum estimation to the cross-spectrum, if the original procedure can be explained as a filter bank analysis procedure. The resulting cross-spectrum estimate looks formally to satisfy the excellent features which the normalized maximum likelihood procedure, reported previously by the authors, does in the auto-spectrum problem as concerns with resolution a low-side lobe behavior.

Starting from the classical procedure reported by Capon for power level estimation from ML filters, the authors present how this method can be modifyed in order to obtain a power spectral density estimate. The basic idea is to compute the effective bandwidth of the ML filter, and normalize the power level estimate, at the output of a quadratic detector following the filter, with it. The effective bandwidth has been obtained by an equal area constraint criteria. Furthermore, the above mentioned estimate, we called NMLM, converges in the distributional sense to the true spectral power density. This suggest the use of new estimates, denoted in the text as q-MLM, which improves the mentioned convergence both in 1-D as well as 2-D problems of SPA.

Current trends in spectral estimation techniques follow basicaly two guidelines; by introducing modifications in the objctive function to be minimized or, keeping the objetive, by modifying the set of constraints in the minimization procedure. This work can be encompassed in the second sense, showing the potential of cepstrum constraints in spectral estimation methods. The special features associated with this constraints allow to use raw approximations in order to linearize or simplify the computations involved in the procedure maintaning within margins of adequate quality the resulting estimate.

The use of lattice structures in last years had been generalized in parametric signals analysis methods. There are a broad fan of coefficients calculation procedures not related between them, that seems to Show a different behaviour depending on the signal under analysis, and they are sensitive to the parameters selection. In the present work we try to eliminate the above problems by means an adequate parameters assignation depending on the local and global properties of the signal. This way one can obtain a broad field of applications algorithm that does not need set the parameters initially, allowing to the engineer an easy adaptation of its algorithm to the problem without the risk of a bad decision, with their sometimes bad consecuences in the algorithm evaluation, in setting some concrete values to the algorithm parameters.