Designing energy-efficient beamformers is a major challenge to the deployment of battery-powered devices transmitting short data packets at millimeter-wave frequencies. In general, directly maximizing energy efficiency will not meet the stringent reliability requirements of certain Internet-of-Things applications. We focus on designing analog beamformers in a device-to-device setting under short packets, a finite encoder set, and imperfect channel knowledge. To guarantee the required error decoding performance, a two-step procedure is proposed such that beamformers are designed to minimize the power consumption subject to reliability constraints under worst-case channel estimation errors, and then the channel encoder maximizing the energy efficiency is selected. The proposed design enjoys a moderate loss under practical low-resolution phase shifters, and exhibits robustness to inaccurate channel estimators, which is crucial to the tradeoff between energy efficiency and error decoding performance.

This paper deals with scenario-aware, uncoordinated, and distributed signaling techniques in the context of feedforward opportunistic communications, that is, when the opportunistic transmitting node does not cooperate with any other node in a heterogeneous communication context. In this signaling technique, each network node individually follows a transmission strategy based on the locally sensed occupied and unused physical-layer network resources to minimize the induced interference onto other coexisting networks, taking into account the impact of the sensing errors and the locality of the sensing information. The paper identifies and characterizes critical invariance properties of the transmitted pulse shaping waveforms that guarantee the detectability of the feedforward transmitted signal by the uncoordinated receiving nodes, irrespective of the sensing signal space basis. The paper also shows that, under mild operating conditions, the proposed transmission scheme asymptotically defines efficient alternatives in the frequency domain, such as the circulant-shaping TDMA (CS-TDMA) modulation, and all of them admit a direct adaptation to frequency-selective channels. Numerical evaluation of the proposed schemes validates the provided theoretical models.

Inter-system interference may limit the performance of co-existing systems in dense heterogeneous wireless networks. Context-aware waveform design can profitably overcome this limitation. However, the latter substantially depends on degrees-of-freedom (DoF) sensing mechanisms. In this work, we show that total least-squares (TLS)-based waveform design is robust against sensing uncertainties. Given the equivalence of minimum norm and TLS, the latter exhibits the good properties of linear predictors, which are of paramount importance to guarantee minimum inter-system interference and detectability by neighboring nodes. Additionally, since derived solution relies on orthogonal projector onto the so- called noise subspace, we can efficiently and iteratively construct an orthogonal waveform-book enabling the presented transmission scheme in multi-carrier scenarios. Simulation results are presented to support our theoretical contributions, and to highlight any potential advantage of proposed solution in crowded heterogenous wireless networks.

The uncoordinated design of pulse shaping filters for opportunistic communications is addressed. We show that under degrees-of-freedom sensing uncertainties the waveform design problem can be cast as a minimum-norm optimization, admitting hence a closed-form expression. Because designed waveforms are adapted to scenario working conditions, proposed design scheme may be considered in pilot reference signals design to achieve orthogonality, regardless the traditionally considered pilot symbols orthogonality. Hence, the effect of interferences such as pilot contamination is diminished. However, a crucial aspect relies on their detectability. Since each node uses only local observations from the wireless network, the sensed degrees-of-freedom may slightly differ from one node to others. In this paper we prove that, thanks to the existence of some invariances, designed waveforms can be detected by neighboring nodes. Even though degrees-of-freedom sensing uncertainties may incur in a performance loss, we propose a least-squares constrained basis pursuit algorithm to reduce the effect of uncertainties by considering only the degrees-of-freedom subspace intersection.

A generic software tool to evaluate the impact of ionospheric disturbances is presented, including low and high latitude physically-based models, and low and high frequency fluctuations. This tool has been developed specifically to assess the performance of navigation receivers, but it is ready to simulate other frequencies and even receivers in dynamic conditions, which allows it to be used in other applications such as communications, GNSS-R, radar altimetry or SAR.

This paper revisits the model order selection problem in the context of second-order spectrum sensing in cognitive radio. Taking advantage of the recent interest on the generalized likelihood ratio (GLR), the asymptotic performance of the minimum description length (MDL) rule under unknown noise variance is addressed. In particular, by exploiting the asymptotically Chi-squared distribution of the GLR, a complete characterization of the error probability is reported, instead of approximating only the missed-detection probability as done in the literature.

The frequency diversity exhibited by cyclostationary signals is exploited in this paper. A novel rank-1 frequency-domain representation of a digital waveform is proposed to address the generalized likelihood ratio (GLR) detection of a cyclo-stationary signal with unknown white noise. With the aim of avoiding the well-known sensitivity of cyclostationary-based detectors to frequency-selective fading channels, a parametric channel model based on the coherence bandwidth is adopted and incorporated in the GLR test. The proposed detector outperforms the classical spectral correlation magnitude detectors by exploiting the rank-1 structure of small spectral co-variance matrices.

This study addresses the optimal spectrum sensing detection based on the complete or partial side‐information on the signal and noise statistics. The use of the generalised‐likelihood ratio test (GLRT) involves maximum‐likelihood (ML) estimation of the nuisances. ML estimation of the unknowns is especially challenging for wideband cognitive radio because closed‐form solutions are often not available. Based on the equivalence between the wideband regime and the low‐signal‐to‐noise ratio regime, this study provides a general kernel framework for GLRT spectrum sensing. It is shown that any GLRT detector exclusively depends on the projection of the sample covariance matrix of the data onto a given underlying kernel that reflects the available side‐information in the problem. The kernels in several scenarios of interest are derived, including the widespread single and multi‐frequency channelisation cases. Theoretical interpretations and numerical results show the trade‐off between detection performance and the degree of side‐information on the most informative statistics for detection, that is, the modulation format and spectrum distribution of the primary users.

This paper addresses the problem of blind detection of a wide-sense stationary (WSS) signal over fading channels. We propose a test statistic which is optimal from a correlation-matching perspective that shows invariance with respect to the noise power and the channel gain. In the blind scenario, we derive the quadratic sphericity test (QST) which exploits the structure of the fading channel as a squared mean to arithmetic mean ratio of the eigenvalues of the autocorrelation matrix of the observations. We provide numerical results to assess the performance of the QST in several fading scenarios, as well as the benchmarking to other blind and non-blind detectors.

In this work, we show the existence of sampling walls in signal detection of nonuniformly sampling wideband signals in the presence of noise uncertainty. A sampling wall is the sampling rate below which the target error probabilities (namely the missed detection and false alarm probabilities) cannot be achieved at a given signal to noise ratio (SNR) regardless the number of acquired samples. Contrary to existing works, we address the signal detection as a binary hypotheses testing problem without having to reconstruct neither the signal nor the spectrum from the observations. Specifically, we adopt a Bernoulli distributed sampler as it exhibits good tradeoff properties between complexity and performance. We show that Bernoulli nonuniform sampling suffers from noise enhancement, which translates into a whitening effect in the correlation of the legacy signal. Therefore, in the presence of noise uncertainty, we derive explicit expressions for sampling walls as a function of the legacy signal occupation, the SNR and the noise uncertainty level. Finally, numerical results are further provided to assess the behavior of the sampling walls and signal detection performance.

The performance in signal detection is evaluated by the error (false-alarm and missed-detection) probabilities. However, calculating these probabilities is a difficult task in practice. This paper studies the asymptotic behavior of the energy-detector and the estimator-correlator by means of the Stein's lemma. The Stein's lemma is an information-theory result that provides the best achievable error exponent in the error probabilities when the number of observations goes to infinity. The derived closed-form expressions explain how detection performance is driven by the detector parameters and the second-order statistics of the problem. More specifically, it is shown that the error exponents depend on the signal-to-noise ratio (SNR) and the observation size. The prime focus is to establish a link between the required observation size for a fixed error probability as a function of the SNR. Numerical results show the tightness of the lemma.

The spectrum analysis problem based on the periodogram and Capon estimates from a nonuniformly sampled signal is addressed. The nonuniform sampling process is cast as a linear projection matrix which encompasses several recent sampling strategies such as compressive sampling. A rank-1 correlation- matching approach is proposed to derive a general filter-bank framework that allows the formulation of the nonuniform periodogram and Capon estimates as particular cases. The performance of the novel periodogram and Capon estimates is analyzed in a cognitive radio scenario where the primary system is a multiband signal with sparse spectrum. Both theoretical and numerical results show that the denoising process required by correlation-matching plays an important role in spectral analysis based on nonuniform sampling.

In this paper, we consider a novel compressed correlation-matching (CCM) approach for spectrum sensing of wideband sparse signals. We derive a general closed-form estimate of the wideband sparse signal level from compressed observations, while providing physical interpretation of the problem. The formulation allows straightforward application to signal processing problems of interest, such as generalized likelihood ratio test (GLRT) spectrum sensing for wideband cognitive radio. Simulation results are reported to assess the behavior of the CCM method.

The problem of spectrum sensing in multi-frequency cognitive radio systems is addressed. We show that as the sensed bandwidth increases, the primary user detection is governed by a low signal-to-noise ratio (low-SNR) regime. By means of low-SNR approximations, we show that the optimal generalized likelihood ratio test (GLRT) only depends on the second order statistics of the observations and on a shaping kernel that highlights the relevant parameters required for detection. Furthermore, the ML estimates of the unknown model parameters are derived for multi-frequency systems, which allow closed-form expressions for the GLRT statistic. The detection performance and the kernel interpretation are supported with simulation results.

This letter focuses on the design of an adaptive bit-interleaved coded modulation (BICM) scheme for frequency selective slow fading channels where the transmitter has certain knowledge of the channel response. In particular, we consider the design of the interleaver stage for a specific convolutional code operating with OFDM modulation. The adaptive interleaver uses the puncturing tables of the rate-compatible punctured convolutional codes (RCPC codes) to rearrange the bits as a function of the fading values and the specific constellation. The performance of different interleavers are compared, revealing that the adaptive RCPC-based interleaver produces larger Euclidean distances between the received codewords and reduces the packet error rate (PER), specially when the number of deep-faded subcarriers increases. Numerical results also evidence the importance of the interleaver choice when comparing the performance of different power allocation strategies.

This paper focuses on the evaluation of performance limits for ultra-wideband communications in terms of constellation-constrained capacity. The major drawback of most of the existing capacity measures is that an exact and closed-form expression cannot be easily obtained. As a result, evaluation of these capacity measures must resort to numerical methods. In this paper, however, closed-form upper bounds for the constellation-constrained capacity of PPM modulation are proposed for both coherent and non-coherent receivers. The tightness of the proposed bounds is evaluated under the IEEE 802.15.3a/4 channel models where a good match is observed, in particular, for the low-SNR regime.

The paper presents a cyclostationary approach to the non-data-aided (NDA) phase and timing estimation problem for staggered modulations. The problem is addressed under the low-SNR unconditional maximum likelihood (UML) framework, and modulation schemes, such as offset quadrature amplitude modulation (OQAM) and minimum shift keying (MSK), are considered. It is found that not only the timing parameter but also the phase, can be jointly obtained from the asymptotic UML cost function based on spectral line generation after a second-order non-linearity.

In this paper we study from a theoretical and practical perspective the problem of nondata-aided (NDA) carrier phase recovery with MSK-type modulations. As suggested in previous works, the optimal ML estimator for low SNRs is quadratic on the received data. However, self-noise limits its performance in the medium-to-high SNR interval. To overcome this limitation, we have deduced optimal second-order schemes for the whole SNR range. The proposed estimator is asymptotically efficient when the SNR is low and cancels out the self-noise at high SNRs. Closed-form expressions are obtained for the high-SNR asymptotic case and a complete discussion is provided on its applicability in closed-loop and feed-forward schemes.

This paper addresses the problem of non-data-aided (NDA) symbol timing error estimation in presence of unknown deterministic carrier frequency errors. A general framework for the stochastic low-SNR ML estimation is derived considering a prior distribution for the carrier frequency error, and exploiting the cyclostationary properties of linear modulations. Finally, the well-known Oerder and Meyr (square timing) method is shown to become a particular case of this general solution.

A beamforming for OFDM modulation is proposed that allocates power over subchannels and subcarriers. The design follows a minimum BER criterion taking into account the different reliability of CSI estimates at both ends of the transmitter link. The transmitter design is based on a generalized exponential BER bound that is tighter than the Chernoff bound, whereas the receiver that minimizes the BER is implemented by the MAP detector. The resulting design reconfigures itself, from the known solution, when perfect CSI is available to the open-loop solution depending on the channel uncertainty.

The paper presents a novel approach to parameter estimation based on sample covariance matrix linear processing. The originality of this framework relies upon two facts: (1) the Gaussian assumption about the nuisance parameters is avoided; (2) quadratic feed-forward schemes are designed saving the complexity and delay of conventional ML-based algorithms that carry out an exhaustive search throughout the whole parameter range. This second aim is achieved by adopting a Bayesian perspective in which the parameter of interest is modeled as a random variable of known a priori distribution. The Bayesian approach allows us to establish certain optimality criteria (mean squared error, bias and variance) yielding to estimation schemes with the best performance on the average, that is, with respect to the assumed prior of the parameter. In order to illustrate the proposed theory, we address the problem of frequency estimation in digital communications. This example has been chosen because its formulation encompasses several problems of special interest such as non-data-aided open-loop carrier synchronization, direction-of-arrival estimation in narrow-band uniform linear arrays and, if the signal is processed in the frequency domain, timing recovery and time-of-arrival estimation in positioning systems, as well.

This paper addresses the problem of non-data-aided (NDA) symbol timing estimation in presence of carrier frequency errors. For that purpose, a novel stochastic maximum likelihood (ML) estimator is derived following a Bayesian approach by considering the carrier frequency error an unknown deterministic parameter constrained within a certain range. Further on, it will be exploited the cyclostationary nature of the received data for obtaining an ML symbol timing estimator. In this way, it is found that the weighted cyclic autocorrelation function of the received data is sufficient statistic of the problem and thus, an optimal ML symbol timing estimator is derived for low signal-to-noise ratios (SNR). As a consequence of the study, the well-known Oerder and Meyr ("square timing") method becomes a particular case of this new general solution.

This paper deals with closed-loop schemes in OFDM modulation systems. A Bayesian approach is presented to design minimum BER prefiltering matrices in the presence of channel uncertainties. This formulation leads to a robust algorithm that exhibits lower sensitivity to channel estimation errors than classical schemes. The proposed design encompasses the single antenna transmission, the beamforming schemes and the frequency flat fading channels as particular cases.

In this paper we develop a new, versatile framework for the design of optimal non-data-aided (NDA) parameter estimators based on the exploitation of the received signal sample covariance matrix. The estimator coefficients are optimized in. order to yield minimum mean squared error (MSE) estimates of the parameter. Some linear constraints are introduced into the optimization process allowing the designer to have control over the estimator characteristic response. For those scenarios where bias is forbidden, as it happens in ranging applications, we provide the optimal solution minimizing the estimates bias within the range of the received parameter. The adopted approach is Bayesian as we treat the wanted parameter as a random variable with a known a priori probability distribution (prior). This modeling allows us to unify the design of both open- and closed-loop estimators. The proposed formulation encompasses all the linear modulations as well as the binary continuous phase modulation (CPM). The new approach supplies optimal estimation schemes without the need of assuming a given statistics for the unknown symbols, that is, avoiding the common adoption of the Gaussian assumption, which does not apply in digital communications. Special attention is paid to those low-complexity implementations for which the maximum likelihood efficiency is not guaranteed.

The design of accurate equalization schemes, optimizing the transmission strategy, can be achieved if channel status information is available not only at the receiver but also at the transmitter side. Accordingly, we propose a feasible scheme to track the channel response by the transmitter based on channel prediction, becoming a suitable solution in time-varying channels. Moreover, to follow faithfully the channel variability, the receiver can estimate the channel prediction error and next update the transmitter predictor through a return link. This paper provides an accurate study of the predictor design, and analyzes the way to minimize the amount of information exchanged through the feedback channel concerning the differential entropy of channel evolution. Furthermore, the prediction error is quantified focusing on the rate-distortion function, and it is shown that a low throughput is enough for tracking the channel coefficients even in the presence of fast time-varying channels.

Estimation of frequency and symbol timing in continuous phase modulated (CPM) signals is investigated. Several well-known statistical approaches, classically applied to the sensor array problem, are used to derive non-data-aided (NDA) algorithms under a unifying general framework (estimation-directed). A new cost function is proposed which is shown to provide a good compromise between additive and pattern noise cancellation, when the additive noise power is unknown.

The study of parameter estimation under additive and multiplicative noise terms constitutes an interesting signal processing research topic with important consequences in the development of high-performance digital communication receivers. In this sense, the paper addresses the analysis of non-assisted digital synchronizers based on up to fourth-order moments and it shows how this alternative outperforms the conventional second-order techniques. The study is performed for MSK (minimum shift keying) as a particular case of the binary CPM modulations. This transmission scheme is adopted because it allows a simple extension to any linear digital modulation and to any multiple access modulation, as well. Simulation results show that the higher-order techniques exhibit a parameter estimation variance closer to the so-called modified Cramer-Rao bound for moderate-to-high SNR if compared to second-order techniques.

The use of (spectrally efficient) CPM modulations may lead to a serious performance degradation of the classical non-data-aided (NDA) frequency and timing estimators due to the presence of self noise. The actual performance of these estimators is usually much worse than that predicted by the classical modified Cramer-Rao bound. We apply some well known results in the field of signal processing to these two important problems of synchronization. In particular we propose and explain the meaning of the unconditional CRB in the synchronization task. Simulation results for MSK and GMSK, along with the performance of some classical and previously proposed synchronizers, show that the proposed bound (along with the MCRB) is useful for a better prediction of the ultimate performance of the NDA estimators.

The conditional maximum likelihood (CML) principle, well known in the context of sensor array processing, is applied to the problem of timing recovery. A new self-noise free CML-based timing error detector is derived. Additionally, a new (conditional) Cramer-Rao bound (CRB) for timing estimation is obtained, which is more accurate than the extensively used modified CRB (MCRB).

Linear block codes in the complex field can be applied in spatial and/or temporal diversity receivers in order to develop high performance schemes for (almost-) blind equalization in mobile communications. The proposed technique uses the structure of the encoded transmitted information (with redundancy) to achieve equalization schemes based on a deterministic criterion. Simulations show that the proposed technique is more efficient than other schemes that follow similar equalizer structures. The result is an algorithm that provides the design of channel equalizers in low EbNo scenarios.

The use of spectrally efficient continuous phase modulations for mobile communications may lead to a serious performance degradation of the classical frequency error detectors (FEDs) due to the presence of self-noise. This article presents a new statistically efficient frequency estimation algorithm for staggered modulations. The cancellation of the self-noise is accomplished by the use of the conditional ML principle, well known in the context of array processing, as an alternative to the unconditional ML, typically applied in the communications field. The paper also provides a new Cramer Rao bound (CRB) which is more accurate than the so-called modified CRB (MCRB) extensively applied to synchronization problems.

Linear block codes can be applied in spatial and/or temporal diversity receivers in order to develop high performance schemes for blind equalization in mobile communications. The proposed technique uses the structure of the encoded transmitted information (with redundancy) to achieve equalization schemes based on a deterministic criterion. Simulations show that the proposed technique is more efficient than other schemes that follow similar equalizer structures. The result is an algorithm that provides the design of blind channel equalizers in low EbNo scenarios.

This paper addresses the use of multichannel receivers for blind equalization in TDMA under frequency selective channels and OFDM systems in frequency flat fading channels. A new criteria is proposed for blind equalization of finite length mobile channels.

A new modulation scheme called transform modulations is proposed which improves the system performance in frequency-flat fading mobile channels. They ameliorate the effect of the fadings over the transmitted signal by spreading the information in time, using a linear transform operator. The design of this scheme is discussed and its advantages are shown by means of simulations. The relationship of this scheme with OFDM modulation is also analyzed.

A blind algorithm for channel distortion compensation is presented which can be employed in spatial or temporal diversity receivers. The proposed technique can be used in frequency selective and frequency flat fading mobile channels, using burst transmission schemes in the first case and OFDM modulation in the second one. The algorithm is base on a deterministic criteria and is suited for estimation when short sets of data are available.

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 cost function for adaptive filtering is proposed, based on the statistical reference criterion. The purpose of this criterion is to enforce a given probability density function at the output of a system. The only aprioristical knowledge utilized is that of the target PDF. This makes it particularly suitable for blind adaptation in the context of arrays in contrast to temporal or spatial reference techniques. Applications that are foreseen are: blind channel equalization, adaptive beamforming for single or multiple signals and source separation. The main goal is blind signal recovery in unfavourable wanted signal-to-inference power ratios.

We present a new method for recursively estimating the frequency and timing parameters of a second order cyclostationary signal with known cyclic autocorrelation matrix (CAM). This problem appears in the context of radar as well as asynchronous communications in highly non-stationary environments (e.g. telemetry) due to the Doppler effect. The parameters evolution is modelled by a zero-order random walk. The estimates are obtained from the instantaneous CAM (ICAM) of the signal. While nonlinear Kalman filter theory is a possible approach to this problem, Bayes risk theory is used instead. In this way the Riccati equation and gain matrices become independent of the estimates, thus allowing a look-up table solution. The folded normal density (FND) is assumed as parameters' prior. The prior is recursively updated in mean (estimates) and variance. By comparing the obtained equations with linear Kalman filter equations we show that with few modifications a first-order random walk model can be easily incorporated to cope with highly non-stationary frequency evolution.>

In this paper we derive the optimum linear algorithm for the separation by an array of a given number of cyclostationary signals of the type encountered in digital communications. Spatially and temporally uncorrelated noise is considered at the input to each sensor. It is proved that the optimum signal separator can be expressed as a matrix transfer function in the z-domain. It is intended that this algorithm be used as a benchmark to test the performance of adaptive schemes. Therefore, bounds on the noise estimation covariance are obtained assuming perfect knowledge of the number of sources as well as of their timing and DOA.>

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.>

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.>