@article {367,
	title = {Testing blind separability of complex Gaussian mixtures},
	journal = {Signal Processing},
	volume = {95},
	year = {2014},
	month = {February},
	pages = {49{\textendash}57},
	abstract = {The separation of a complex mixture based solely on second-order statistics can be achieved using the Strong Uncorrelating Transform (SUT) if and only if all sources have distinct circularity coefficients. However, in most problems we do not know the circularity coefficients, and they must be estimated from observed data. In this work, we propose a detector, based on the generalized likelihood ratio test (GLRT), to test the separability of a complex Gaussian mixture using the SUT. For the separable case (distinct circularity coefficients), the maximum likelihood (ML) estimates are straightforward. On the other hand, for the non-separable case (at least one circularity coefficient has multiplicity greater than one), the ML estimates are much more difficult to obtain. To set the threshold, we exploit Wilks{\textquoteright} theorem, which gives the asymptotic distribution of the GLRT under the null hypothesis. Finally, numerical simulations show the good performance of the proposed detector and the accuracy of Wilks{\textquoteright} approximation.},
	doi = {10.1016/j.sigpro.2013.08.010},
	author = {Ram{\'\i}rez, David and Schreier, Peter J. and V{\'\i}a, Javier and Santamar{\'\i}a, Ignacio}
}
@article {547,
	title = {Robust Improper Signaling for Two-user SISO Interference Channels},
	journal = {IEEE Transactions on Communications},
	volume = {67},
	year = {2019},
	month = {July},
	pages = {4709-4723},
	abstract = {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.},
	keywords = {Achievable rate region, imperfect CSI, improper Gaussian signaling, two-user interference channel, worst-case robustness.},
	doi = {10.1109/TCOMM.2019.2910549},
	author = {Mohammad Soleymani and Lameiro, Christian and Santamar{\'\i}a, Ignacio and Schreier, Peter J.}
}
@article {487,
	title = {Rate Region Boundary of the SISO Z-interference Channel with Improper Signaling},
	journal = {IEEE Transactions on Communications},
	volume = {65},
	year = {2017},
	month = {March},
	pages = {1022-1024},
	abstract = {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 singleantenna Z-IC. We also provide an in-depth discussion on the
optimal strategies and the properties of the Pareto boundary.},
	issn = {0090-6778},
	doi = {10.1109/TCOMM.2016.2641948},
	author = {Lameiro, Christian and Santamar{\'\i}a, Ignacio and Schreier, Peter J.}
}
@article {565,
	title = {Maximally improper signaling in underlay MIMO cognitive radio networks},
	journal = {IEEE Transactions on Signal Processing},
	year = {2019},
	abstract = {In this paper we address the problem of subspace averaging, with special emphasis placed on the question of estimating the dimension of the average. The results suggest that the enumeration of sources in a multi-sensor array, which is a problem of estimating the dimension of the array manifold, and as a consequence the number of radiating sources, may be cast as a problem of averaging subspaces. This point of view stands in contrast to conventional approaches, which cast the problem as one of identifiying covariance models in a factor model. We present a robust formulation of the proposed order fitting rule based on majorization-minimization algorithms. A key element of the proposed method is to construct a bootstrap procedure, based on a newly proposed discrete distribution on the manifold of projection matrices, for stochastically generating subspaces from a function of experimentally-determined eigenvalues. In this way, the proposed subspace averaging (SA) technique determines the order based on the eigenvalues of an average projection matrix, rather than on the likelihood of a covariance model, penalized by functions of the model order. By means of simulation examples, we show that the proposed SA criterion is especially effective in high-dimensional scenarios with low sample support.},
	doi = {10.1109/TSP.2019.2953665},
	author = {Lameiro, Christian and Santamar{\'\i}a, Ignacio and Schreier, Peter J. and Utschick, Wolfgang}
}
@article {506,
	title = {Information-Theoretic Analysis of a Family of Improper Discrete Constellations},
	journal = {Entropy},
	volume = {20},
	year = {2018},
	doi = { doi:10.3390/e20010045},
	url = {http://www.mdpi.com/1099-4300/20/1/45/pdf},
	author = {Santamar{\'\i}a, Ignacio and Crespo, P. and Lameiro, Christian and Schreier, Peter J.}
}
@article {559,
	title = {Improper Signaling for SISO Two-user Interference Channels with Additive Asymmetric Hardware Distortion},
	journal = {IEEE Transactions on Communications},
	volume = {67},
	year = {2019},
	month = {December},
	pages = {8624-8638},
	abstract = {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-noiseratio (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.},
	doi = {10.1109/TCOMM.2019.2939310},
	author = {Mohammad Soleymani and Lameiro, Christian and Santamar{\'\i}a, Ignacio and Schreier, Peter J.}
}
@article {620,
	title = {Improper Signaling for Multicell MIMO RIS-assisted Broadcast Channels with I/Q Imbalance},
	journal = {IEEE Transactions on Green Communications and Networking},
	volume = {6},
	year = {2022},
	month = {June},
	pages = {723-738},
	doi = {10.1109/TGCN.2021.3140150},
	author = {Mohammad Soleymani and Santamar{\'\i}a, Ignacio and Schreier, Peter J.}
}
@article {574,
	title = {Improper Gaussian Signaling for the K-user MIMO Interference Channels with Hardware Impairments},
	journal = {IEEE Transactions on Vehicular Technology},
	volume = {69},
	year = {2020},
	month = {October},
	pages = {11632-11645},
	doi = { 10.1109/TVT.2020.3015558},
	author = {Mohammad Soleymani and Santamar{\'\i}a, Ignacio and Schreier, Peter J.}
}
@article {543,
	title = {Improper Gaussian Signaling for Multiple-Access Channels in Underlay Cognitive Radio},
	journal = {IEEE Transactions on Communications},
	volume = {67},
	year = {2019},
	month = {March},
	pages = {1817-1830},
	abstract = {This  paper considers an unlicensed multiple-accesschannel (MAC) that coexists witha licensed point-to-point user,following  the  underlay  cognitive  radio  paradigm.  We  assumethat  every  transceiver  except  the  secondary  base  station  hasone  antenna  and  that  the  primary  user  (PU)  is  protected  bya   minimum   rate   constraint.  In   contrast   to   the  conventionalassumption of proper Gaussian signaling, we allow the secondaryusers  to  transmit  improper  Gaussian  signals,  which  are  corre-lated  with  their  complex  conjugate.  When  the  secondary  basestation  performs  zero-forcing,  we  show  that  improper  signalingis   optimal   if   the  sum   of   the   interference   channel  gains   (inan  equivalent  canonical  model)  is  above  a  certain  threshold.Additionally,  we  derive  an  efficient  algorithm  to  compute  thetransmission  parameters  that  attain  the  rate  region  boundaryfor  this  scenario.  The  proposed  algorithm  exploits  a  single-userrepresentation of the secondary MAC along with new results onthe optimality of improper signaling in the single-user case whenthe PU is corrupted  by an  improper noise.},
	issn = {1558-0857},
	doi = {10.1109/TCOMM.2018.2880765},
	author = {Lameiro, Christian and Santamar{\'\i}a, Ignacio and Schreier, Peter J.}
}
@article {562,
	title = {Ergodic Rate for Fading  Interference Channels with Proper and Improper Gaussian Signaling},
	journal = {Entropy},
	volume = {21},
	year = {2019},
	month = {September},
	doi = {https://doi.org/10.3390/e21100922},
	author = {Mohammad Soleymani and Santamar{\'\i}a, Ignacio and Lameiro, Christian and Schreier, Peter J.}
}
@article {609,
	title = {Distributed algorithms for spectral and energy-efficiency maximization of K-user interference channels},
	journal = {IEEE Access},
	volume = {9},
	year = {2021},
	month = {July},
	pages = {96948-96963},
	abstract = {In this paper, we propose a cooperative distributed framework to optimize a variety of rate and energy-efficiency (EE) utility functions, such as the minimum-weighted rate or the global EE, in the K-user interference channel. We focus on the single-input multiple-output (SIMO) case, where each user, based solely on local channel state information (CSI), optimizes its transmit power and receive beamformer, although the framework can also be extended to the multiple-output multiple-input (MIMO) case. The distributed framework combines an alternating optimization approach with majorization minimization (MM) techniques, thus ensuring convergence to a stationary point of the centralized cost function. Closed-form power update rules are obtained for some utility functions, thus obtaining very fast convergence algorithms. The receivers treat interference as noise (TIN) and apply the beamformers that maximize the signal-to-interference-plus-noise (SINR). The proposed cooperative distributed algorithms are robust against channel variations and network topology changes and, as our simulation results suggest, they perform close to the centralized solution. As a benchmark, we also study a non-cooperative distributed framework based on the so-called "signal-to-leakage-plus-noise ratio" (SNLR) that further reduces the overhead of the cooperative version.},
	doi = {10.1109/ACCESS.2021.3094976},
	author = {Mohammad Soleymani and Santamar{\'\i}a, Ignacio and Schreier, Peter J.}
}
@article {453,
	title = {Detection of Multivariate Cyclostationarity},
	journal = {IEEE Transactions on Signal Processing},
	volume = {63},
	year = {2015},
	month = {October},
	pages = {5395-5408},
	abstract = {This paper derives an asymptotic generalized likelihood ratio test (GLRT) and an asymptotic locally most powerful invariant test (LMPIT) for two hypothesis testing problems: 1) Is a vector-valued random process cyclostationary (CS) or is it wide-sense stationary (WSS)? 2) Is a vector valued random process CS or is it nonstationary? Our approach uses the relationship between a scalar-valued CS time series and a vector-valued WSS time series for which the knowledge of the cycle period is required. This relationship allows us to formulate the problem as a test for the covariance structure of the observations. The covariance matrix of the observations has a block-Toeplitz structure for CS and WSS processes. By considering the asymptotic case where the covariance matrix becomes block-circulant we are able to derive its maximum likelihood (ML) estimate and thus an asymptotic GLRT. Moreover,
using Wijsman{\textquoteright}s theorem, we also obtain an asymptotic LMPIT.
These detectors may be expressed in terms of the Lo{\`e}ve spectrum, the cyclic spectrum, and the power spectral density, establishing how to fuse the information in these spectra for an asymptotic
GLRT and LMPIT. This goes beyond the state of-the-art, where it is common practice to build detectors of cyclostationarity from ad-hoc functions of these spectra.},
	author = {Ram{\'\i}rez, David and Schreier, Peter J. and V{\'\i}a, Javier and Santamar{\'\i}a, Ignacio and Louis L. Scharf}
}
@article {412,
	title = {Benefits of Improper Signaling for Underlay Cognitive Radio},
	journal = {IEEE Wireless Communications Letters},
	volume = {4},
	year = {2015},
	month = {Ferbuary},
	pages = {22-25},
	author = {Lameiro, Christian and Santamar{\'\i}a, Ignacio and Schreier, Peter J.}
}
@conference {424,
	title = {A Regularized Maximum Likelihood Estimator for the Period of a Cyclostationary Process},
	booktitle = {Asilomar Conference on Signals, Systems, and Computers},
	year = {2014},
	month = {November},
	address = {Pacific Grove, USA},
	author = {Ram{\'\i}rez, David and Schreier, Peter J. and V{\'\i}a, Javier and Santamar{\'\i}a, Ignacio and Louis L. Scharf}
}
@conference {572,
	title = {Rate Region of the K-user MIMO Interference Channel with Imperfect Transmitters},
	booktitle = {European Signal Processing Conference (EUSIPCO 2020)},
	year = {2020},
	month = {August},
	pages = {1638-1642},
	address = {Amsterdamd, The Netherlands},
	abstract = {This paper studies the rate region of a multiple-input, multiple-output (MIMO) system with imperfect transmitters when interference is treated as noise at the receiver side. We consider a K-user MIMO interference channel (IC) in which the transmitters suffer from an additive hardware distortion (HWD) modeled as spatially uncorrelated Gaussian noise with covariance matrix proportional to the transmit covariance matrix. We employ the difference of convex programming (DCP) technique to solve the rate-region optimization problem and obtain its stationary points. Our proposed HWD-aware algorithm outperforms the HWD-unaware design that disregards HWD. Our results show that the performance of the K-user MIMO IC is highly affected by HWD, especially in high signal-to-noise-ratio scenarios.},
	author = {Mohammad Soleymani and Santamar{\'\i}a, Ignacio and Maham, Behrouz and Schreier, Peter J.}
}
@conference {348,
	title = {Power-CCA: Maximizing the Correlation Coefficient between the Power of Projections},
	booktitle = {IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP 2013)},
	year = {2013},
	month = {May},
	address = {Vancouver, Canada},
	doi = {10.1109/ICASSP.2013.6638864},
	author = {Ram{\'\i}rez, David and Schreier, Peter J. and V{\'\i}a, Javier and Nikulin, Vadim V.}
}
@conference {512,
	title = {Performance analysis of maximally improper signaling for multiple-antenna systems},
	booktitle = {IEEE Wireless Communications and Networking Conference (WCNC)},
	year = {2018},
	month = {April},
	address = {Barcelona, Spain},
	author = {Lameiro, Christian and Santamar{\'\i}a, Ignacio and Schreier, Peter J.}
}
@conference {461,
	title = {Maximally Improper Interference in Underlay Cognitive Radio Networks},
	booktitle = {IEEE International Conference on Acoustics, Speech and Signal Processing},
	year = {2016},
	month = {March},
	address = {Shanghai, China},
	author = {Lameiro, Christian and Santamar{\'\i}a, Ignacio and Utschick, Wolfgang and Schreier, Peter J.}
}
@conference {516,
	title = {Improper Signaling for OFDM Underlay Cognitive Radio Systems},
	booktitle = {IEEE Statistical Signal Processing Workshop (SSP)},
	year = {2018},
	month = {June},
	address = {Freiburg, Germany},
	abstract = {Improper signaling, where real and imaginary parts of the transmit
signal are correlated and/or have unequal power, has received a lot
of attention lately because it has been shown to increase achievable
rates in many interference-limited communication systems. In this paper, we study whether improper signaling can also benefit an orthogonal frequency-division multiplexing (OFDM) underlay cognitive radio (UCR) system. We assume that the primary user (PU) transmits proper signals, while the secondary user (SU) is allowed to employ improper signaling. We consider two different rate constraints for the rate of the PU: i) the total rate of the PU, and ii) the rate of the PU in each subband. We propose an algorithm to implement improper signaling for each constraint. In both cases, we show that the benefits of improper signaling are relatively small and decrease rapidly with increasing number of subbands. This rather negative result shows that the use of improper signaling in interference scenarios needs to be justified on a case-by-case basis.},
	author = {Mohammad Soleymani and Lameiro, Christian and Schreier, Peter J. and Santamar{\'\i}a, Ignacio}
}
@conference {539,
	title = {Improper Gaussian Signaling for the Two-user Broadcast Channel Treating Interference as Noise},
	booktitle = {IEEE Int. Conference on Acoustics, Speech, and Signal Processing (ICASSP)},
	year = {2019},
	month = {May},
	address = {Brighton, UK},
	abstract = {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 {\textquotedblleft}TIN{\textquotedblright} at every receiver. For this scenario, we derive a closed-formcharacterization of the rate region boundary with IGS. ThePareto-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.},
	author = {Lameiro, Christian and Santamar{\'\i}a, Ignacio and Schreier, Peter J.}
}
@conference {311,
	title = {GLRT For Testing Separability Of A Complex-Valued Mixture Based On The Strong Uncorrelating Transform},
	booktitle = {2012 IEEE International Workshop on Machine Learning for Signal Processing},
	year = {2012},
	month = {September},
	address = {Santander, Spain},
	abstract = {The Strong Uncorrelating Transform (SUT) allows blind separation of a mixture of complex independent sources if and only if all sources have distinct circularity coefficients. In practice, the circularity coefficients need to be estimated from observed data. We propose a generalized likelihood ratio test (GLRT) for separability of a complex mixture using the SUT, based on estimated circularity coefficients. For distinct circularity coefficients (separable case), the maximum likelihood (ML) estimates, required for the GLRT, are straightforward. However, for circularity coefficients with multiplicity larger than one  (non-separable case), the ML estimates are much more difficult to find. Numerical simulations show the good performance of the proposed detector.},
	author = {Ram{\'\i}rez, David and Schreier, Peter J. and V{\'\i}a, Javier and Santamar{\'\i}a, Ignacio}
}
@conference {554,
	title = {Energy-Efficient Improper Signaling for K-user Interference Channels},
	booktitle = {European Signal Processing Conference (EUSIPCO)},
	year = {2019},
	month = {September},
	abstract = {This paper investigates the energy efficiency (EE) of improper Gaussian signaling (IGS) in a K-user interference channel (IC). IGS allows unequal variances and/or correlation between the real and imaginary parts, and it has recently been shown to be advantageous in various interference-limited scenarios. In this paper, we propose an energy-efficient IGS design for the K-user IC, which is based on a separate optimization of the powers and complementary variances of the users. We compare the EE region achieved by the proposed scheme with that achieved by conventional proper signaling and show that IGS can significantly improve the EE region.},
	author = {Mohammad Soleymani and Lameiro, Christian and Santamar{\'\i}a, Ignacio and Schreier, Peter J.}
}
@conference {541,
	title = {Energy-Efficient Design for Underlay Cognitive Radio using Improper Signaling},
	booktitle = {IEEE Int. Conference on Acoustics, Speech, and Signal Processing (ICASSP)},
	year = {2019},
	month = {May},
	address = {Brighton, UK},
	abstract = {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 theoptimality 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.},
	author = {Mohammad Soleymani and Lameiro, Christian and Schreier, Peter J. and Santamar{\'\i}a, Ignacio}
}
@conference {556,
	title = {Benefits of Improper Signaling for Overlay Cognitive Radio},
	booktitle = {IEEE Global Communication Conference (GLOBECOM)},
	year = {2019},
	month = {December},
	address = {Waikoloa, HI, USA},
	abstract = {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.},
	author = {Lameiro, Christian and Santamar{\'\i}a, Ignacio and Schreier, Peter J.}
}
@conference {433,
	title = {An asymptotic LMPI test for cyclostationarity detection with application to cognitive radio},
	booktitle = {IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)},
	year = {2015},
	month = {April},
	address = {Brisbane, Australia},
	author = {Ram{\'\i}rez, David and Schreier, Peter J. and V{\'\i}a, Javier and Santamar{\'\i}a, Ignacio and Louis L. Scharf}
}
@conference {388,
	title = {An asymptotic GLRT for the detection of cyclostationary signals},
	booktitle = {International Conference on Acoustics, Speech, and Signal Processing (ICASSP)},
	year = {2014},
	month = {May},
	address = {Florence, Italy},
	author = {Ram{\'\i}rez, David and Louis L. Scharf and V{\'\i}a, Javier and Santamar{\'\i}a, Ignacio and Schreier, Peter J.}
}
@conference {430,
	title = {Analysis of maximally improper signalling schemes for underlay cognitive radio},
	booktitle = {IEEE International Conference on Communications (ICC)},
	year = {2015},
	month = {June},
	address = {London, UK},
	author = {Lameiro, Christian and Santamar{\'\i}a, Ignacio and Schreier, Peter J.}
}
