@phdthesis {426,
	title = {Interference Alignment in MIMO Networks: Feasibility and Transceiver Design},
	year = {2014},
	school = {University of Cantabria},
	url = {http://hdl.handle.net/10902/5900},
	author = {Gonz{\'a}lez, {\'O}scar}
}
@article {407,
	title = {A Quadratically Convergent Method for Interference Alignment in MIMO Interference Channels},
	journal = {IEEE Signal Processing Letters},
	volume = {21},
	year = {2014},
	month = {November},
	pages = {1423-1427},
	keywords = {alternating minimization, Gauss-Newton, interference alignment, interference channel, steepest descent},
	doi = {10.1109/LSP.2014.2338132},
	author = {Gonz{\'a}lez, {\'O}scar and Lameiro, Christian and Santamar{\'\i}a, Ignacio}
}
@article {335,
	title = {On the Number of Interference Alignment Solutions for the K-User MIMO Channel with Constant Coefficients},
	journal = {IEEE Transaction on Information Theory},
	volume = {61},
	year = {2015},
	month = {November},
	pages = {6028-6048},
	abstract = {In this paper, we study the number of different interference alignment (IA) solutions that exists for the K-user multiple-input multiple-output (MIMO) interference channels with constant coefficients, when the alignment is performed via beamforming and without symbol extensions. When counting the number of IA solutions for a given problem, the most interesting case happens when the number of equations and variables of the polynomial system of equations are the same and the system is feasible. In this situation, the number of IA solutions is finite and, as we show in this paper, is given by an integral formula that can be numerically approximated using Monte Carlo integration methods. More precisely, the number of solutions is the scaled average over a subset of the solution variety (formed by all triplets of channels, precoders and decoders satisfying the IA polynomial equations) of the determinant of a certain Hermitian matrix related to the geometry of the problem. Interestingly, while the value of this determinant at an arbitrary point can be used to check the feasibility of the IA problem, the average of the determinant (properly scaled) gives us the number of solutions. Our results can be applied to arbitrary interference MIMO networks, with any number of users, antennas and streams per user.},
	doi = {10.1109/TIT.2015.2482493},
	author = {Gonz{\'a}lez, {\'O}scar and Beltr{\'a}n, Carlos and Santamar{\'\i}a, Ignacio}
}
@article {482,
	title = {Homotopy Continuation for Spatial Interference Alignment in Arbitrary MIMO X Networks},
	journal = {IEEE Transactions on Signal Processing},
	volume = {65},
	year = {2017},
	month = {April},
	pages = {1752-1764},
	issn = {1053-587X},
	doi = {10.1109/TSP.2016.2637310},
	author = {Fanjul, Jacobo and Gonz{\'a}lez, {\'O}scar and Santamar{\'\i}a, Ignacio and Beltr{\'a}n, Carlos}
}
@article {Trans_Inst_Meas_2011,
	title = {Frequency-Domain Methodology for Measuring {MIMO} Channels Using a Generic Test Bed},
	journal = {IEEE Transactions on Instrumentation and Measurement},
	volume = {60},
	number = {3},
	year = {2011},
	month = {March},
	pages = {827{\textendash}838},
	abstract = {A multiple-input multiple-output (MIMO) frequency-domain channel measurement methodology is presented. This methodology can be implemented in any transmit/receive hardware consisting of radio frequency modules and baseband digital processing units. It involves the transmission and reception of frequency and phase-optimized complex exponentials through antenna arrays, followed by an offline frequency estimation, which makes additional synchronization circuitry unnecessary. To test the feasibility of this method, a series of measurements is presented, employing a 4{\texttimes}4 dual-band (2.4/5 GHz) MIMO test bed.},
	author = {Guti{\'e}rrez, Jes{\'u}s and Gonz{\'a}lez, {\'O}scar and P{\'e}rez, Jes{\'u}s and Ram{\'\i}rez, David and Vielva, Luis and Ib{\'a}{\~n}ez, Jes{\'u}s and Santamar{\'\i}a, Ignacio}
}
@article {336,
	title = {A Feasibility Test for Linear Interference Alignment in MIMO Channels with Constant Coefficients},
	journal = {IEEE Transactions on Information Theory.},
	volume = {60},
	year = {2014},
	month = {March},
	pages = {1840-1856},
	abstract = {In this paper, we consider the feasibility of linear interference alignment (IA) for multiple-input-multiple-output (MIMO) channels with constant coefficients for any number of users, antennas, and streams per user, and propose a polynomial-time test for this problem. Combining algebraic geometry techniques with differential topology ones, we first prove a result that generalizes those previously published on this topic. In particular, we consider the input set (complex projective space of MIMO interference channels), the output set (precoder and decoder Grassmannians), and the solution set (channels, decoders, and precoders satisfying the IA polynomial equations), not only as algebraic sets, but also as smooth compact manifolds. Using this mathematical framework, we prove that the linear alignment problem is feasible when the algebraic dimension of the solution variety is larger than or equal to the dimension of the input space and the linear mapping between the tangent spaces of both smooth manifolds given by the first projection is generically surjective. If that mapping is not surjective, then the solution variety projects into the input space in a singular way and the projection is a zero-measure set. This result naturally yields a simple feasibility test, which amounts to checking the rank of a matrix. We also provide an exact arithmetic version of the test, which proves that testing the feasibility of IA for generic MIMO channels belongs to the bounded-error probabilistic polynomial complexity class.},
	keywords = {algebraic geometry, differential topology, interference alignment, MIMO interference channel, polynomial equations},
	issn = {0018-9448},
	doi = {10.1109/TIT.2014.2301440},
	author = {Gonz{\'a}lez, {\'O}scar and Beltr{\'a}n, Carlos and Santamar{\'\i}a, Ignacio}
}
@article {439,
	title = {Experimental Evaluation of Interference Alignment for Broadband WLAN Systems},
	journal = {EURASIP Journal on Wireless Communications and Networking},
	year = {2015},
	month = {June},
	abstract = {In this paper, we present an experimental study on the performance of spatial interference alignment (IA) in indoor wireless local area network scenarios that use orthogonal frequency division multiplexing (OFDM) according to the physical-layer specifications of the IEEE 802.11a standard. Experiments have been carried out using a wireless network testbed capable of implementing a 3-user MIMO interference channel. We have implemented IA decoding schemes that can be designed according to distinct criteria (e.g., zero-forcing or MaxSINR). The measurement methodology has been validated considering practical issues like the number of OFDM training symbols used for channel estimation or feedback time. In case of asynchronous users, a time-domain IA decoding filter is also compared to its frequency-domain counterpart. We also evaluated the performance of IA from bit error ratio measurement-based results in comparison to different time-division multiple access transmission schemes. The comparison includes single- and multiple-antenna systems transmitting over the dominant mode of the MIMO channel. Our results indicate that spatial IA is suitable for practical indoor scenarios in which wireless channels often exhibit relatively large coherence times.},
	doi = {10.1186/s13638-015-0409-z},
	author = {Lameiro, Christian and Gonz{\'a}lez, {\'O}scar and Garc{\'\i}a-Naya, J. A. and Santamar{\'\i}a, Ignacio and Castedo, Luis}
}
@conference {281,
	title = {Pre- and Post-FFT Interference Leakage Minimization for MIMO OFDM Networks},
	booktitle = {The Ninth International Symposium on Wireless Communication Systems (ISWCS 2012)},
	year = {2012},
	month = {August},
	address = {Paris, France},
	author = {Lameiro, Christian and Gonz{\'a}lez, {\'O}scar and V{\'\i}a, Javier and Santamar{\'\i}a, Ignacio and Heath Jr., Robert W.}
}
@conference {394,
	title = {Physical Layer Authentication based on Channel Response Tracking using Gaussian Processes},
	booktitle = {2014 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)},
	year = {2014},
	month = {May},
	pages = {2429--2433},
	abstract = {Physical-layer authentication techniques exploit the unique properties of the wireless medium to enhance traditional higher-level authentication procedures. We propose to reduce the higher-level authentication overhead by using a state-of-the-art multi-target tracking technique based on Gaussian processes. The proposed technique has the additional advantage that it is capable of automatically learning the dynamics of the trusted user{\textquoteright}s channel response and the time-frequency fingerprint of intruders. Numerical simulations show very low intrusion rates, and an experimental validation using a wireless test bed with programmable radios demonstrates the technique{\textquoteright}s effectiveness.},
	keywords = {gaussian processes, multi-target tracking, physical-layer authentication, wireless communications},
	isbn = {978-1-4799-2892-7},
	author = {Van Vaerenbergh, Steven and Gonz{\'a}lez, {\'O}scar and V{\'\i}a, Javier and Santamar{\'\i}a, Ignacio}
}
@conference {MONAMI_2010,
	title = {Maximum Sum-Rate Interference Alignment Schemes for the 3-user Deterministic {MIMO} Channel},
	booktitle = {2nd International ICST Conference on Mobile Networks and Management (MONAMI 2010)},
	year = {2010},
	month = {September},
	address = {Santander, Spain},
	author = {Gonz{\'a}lez, {\'O}scar and Santamar{\'\i}a, Ignacio}
}
@conference {Globecom_2010,
	title = {Maximum sum-rate interference alignment algorithms for MIMO channels},
	booktitle = {IEEE Global Communications Conference (GLOBECOM 2010)},
	year = {2010},
	month = {December},
	address = {Miami, FL, USA},
	author = {Santamar{\'\i}a, Ignacio and Gonz{\'a}lez, {\'O}scar and Heath Jr., Robert W. and Peters, S. W.}
}
@conference {Icassp12_IA_pub,
	title = {Interference Leakage Minimization for Convolutive {MIMO} Interference Channels},
	booktitle = {IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP 2012)},
	year = {2012},
	month = {March},
	address = {Kyoto, Japan},
	author = {Gonz{\'a}lez, {\'O}scar and Lameiro, Christian and V{\'\i}a, Javier and Santamar{\'\i}a, Ignacio and Heath Jr., Robert W.}
}
@conference {ICASSP_2011_IA_HC,
	title = {Interference Alignment in Single-Beam {MIMO} Networks via Homotopy Continuation},
	booktitle = {IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP 2011)},
	year = {2011},
	month = {May},
	address = {Prague, Czech Republic},
	abstract = {In this paper we consider the application of a homotopy-continuation based method for finding interference alignment (IA) solutions for the deterministic K-user multiple-input multiple-output (MIMO) channel, when all users wish to send one stream of data. Homotopy continuation is based on the idea of deforming a start system, whose solution can easily be found, to reach the target system that we want to solve. For the IA problem we show that a good initial system is obtained by considering a rank-one approximation of the original MIMO interference channels. Specifically, as long as the original system is feasible, a rank-one approximation of the MIMO channels allow us to find a closed-form interference-free solution. The proposed algorithm is shown to have a lower complexity than previous methods with comparable sum-rate performance. Furthermore, it is also shown that the trivial system (rank-one MIMO channels) and target system (full-rank MIMO channels) have exactly the same number of solutions. Exploiting this equivalence, an efficient method to enumerate all the IA solutions that exist in a single-beam MIMO network is proposed.},
	author = {Gonz{\'a}lez, {\'O}scar and Santamar{\'\i}a, Ignacio}
}
@conference {349,
	title = {An Interference Alignment Algorithm for Structured Channels},
	booktitle = {IEEE 14th Workshop on Signal Processing Advances in Wireless Communications (SPAWC 2013)},
	year = {2013},
	month = {June},
	address = {Darmstadt, Germany},
	author = {Lameiro, Christian and Gonz{\'a}lez, {\'O}scar and Santamar{\'\i}a, Ignacio}
}
@conference {399,
	title = {Homotopy Continuation for Vector Space Interference Alignment in MIMO X Networks},
	booktitle = {2014 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)},
	year = {2014},
	month = {May},
	pages = {6232--6236},
	author = {Gonz{\'a}lez, {\'O}scar and Fanjul, Jacobo and Santamar{\'\i}a, Ignacio}
}
@conference {278,
	title = {A general test to check the feasibility of linear interference alignment},
	booktitle = {IEEE International Symposium on Information Theory (ISIT 2012), Cambridge, MA, USA},
	year = {2012},
	month = {July, 2012},
	keywords = {feasibility, IA},
	author = {Gonz{\'a}lez, {\'O}scar and Santamar{\'\i}a, Ignacio and Beltr{\'a}n, Carlos}
}
@conference {359,
	title = {Finding the Number of Feasible Solutions for Linear Interference Alignment Problems},
	booktitle = {2013 IEEE International Symposium on Information Theory},
	year = {2013},
	month = {July},
	pages = {384--388},
	address = {Istanbul, Turkey},
	abstract = {In this paper, we study how many different solutions exist for a feasible interference alignment (IA) problem. We focus on linear IA schemes without symbol extensions for the K-user multiple-input multiple-output (MIMO) interference channel. When the IA problem is feasible and the number of variables matches the number of equations in the polynomial system, the number of solutions is known to be finite. Unfortunately, the exact number of solutions is only known for a few particular cases, mainly single-beam MIMO networks. In this paper, we prove that the number of IA solutions is given by an integral formula that can be numerically approximated using Monte Carlo integration methods. More precisely, the number of solutions is the scaled average over a subset of the solution variety (formed by all triplets of channels, precoders and decoders satisfying the IA polynomial equations) of the determinant of certain Hermitian matrix related to the geometry of the problem. Our results can be applied to arbitrary interference MIMO networks, with any number of users, antennas and streams per user.},
	isbn = {978-1-4799-0446-4},
	author = {Gonz{\'a}lez, {\'O}scar and Santamar{\'\i}a, Ignacio and Beltr{\'a}n, Carlos}
}
@conference {WSA_2011,
	title = {Experimental Validation of Interference Alignment Techniques using a Multiuser {MIMO} Testbed},
	booktitle = {International ITG Workshop on Smart Antennas (WSA 2011)},
	year = {2011},
	month = {February},
	address = {Aachen, Germany},
	author = {Gonz{\'a}lez, {\'O}scar and Ram{\'\i}rez, David and Santamar{\'\i}a, Ignacio and Garc{\'\i}a-Naya, J. A. and Castedo, Luis}
}
@conference {Eusipco2011_IA,
	title = {Experimental Evaluation of Interference Alignment Under Imperfect Channel State Information},
	booktitle = {19th European Signal Processing Conference (EUSIPCO 2011)},
	year = {2011},
	month = {August},
	address = {Barcelona, Spain},
	author = {Garc{\'\i}a-Naya, J. A. and Castedo, Luis and Gonz{\'a}lez, {\'O}scar and Ram{\'\i}rez, David and Santamar{\'\i}a, Ignacio}
}
@conference {FutureNetworkMobileSummit_2010,
	title = {Experimental evaluation of an {RF-MIMO} transceiver for 802.11a {WLAN}},
	booktitle = {Future Network and MobileSummit 2010},
	year = {2010},
	month = {June},
	address = {Florence, Italy},
	author = {Gonz{\'a}lez, {\'O}scar and Guti{\'e}rrez, Jes{\'u}s and Ib{\'a}{\~n}ez, Jes{\'u}s and Vielva, Luis and Eickhoff, R.}
}
@conference {354,
	title = {Computing the Degrees of Freedom for Arbitrary MIMO Interference Channels},
	booktitle = {IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP 2013)},
	year = {2013},
	month = {May},
	address = {Vancouver, Canada},
	abstract = {In this paper we provide an efficient procedure to compute the total number of degrees of freedom (DoF), achievable by linear beamforming, of the K-user multiple-input multiple-output (MIMO) interference channel with an arbitrary number of Tx-Rx antennas at each link. Firstly, we derive an analytical outer bound that generalizes the results that exist for the symmetric K-user M x N interference channel. Secondly, we obtain a tighter bound by solving a convex optimization problem that includes as constraints the DoF characterizations for point-to-point MIMO links and for 2-user interference channels. The solution to this convex problem admits an interesting waterfilling interpretation. Finally, exploiting this outer bound and using a recently proposed feasibility test, we show that it is possible to obtain the DoF for any interference channel in an efficient way. Some simulations results are included to illustrate the tightness of the derived bounds, as well as to study the DoF achievable for the 4-user channel when we distribute the total number of antennas among users and between transmitters and receivers in different ways.},
	keywords = {convex optimization, degrees of freedom, interference alignment, multiple-input multiple-output},
	isbn = {978-1-4799-0356-6},
	author = {Gonz{\'a}lez, {\'O}scar and Lameiro, Christian and V{\'\i}a, Javier and Beltr{\'a}n, Carlos and Santamar{\'\i}a, Ignacio}
}
@conference {ICASSP2010_MIMOPlatform,
	title = {Building a Web Platform for Learning Advanced Digital Communications using a {MIMO} Testbed},
	booktitle = {IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP 2010)},
	year = {2010},
	month = {March},
	address = {Dallas, USA},
	author = {Vielva, Luis and V{\'\i}a, Javier and Guti{\'e}rrez, Jes{\'u}s and Gonz{\'a}lez, {\'O}scar and Ib{\'a}{\~n}ez, Jes{\'u}s and Santamar{\'\i}a, Ignacio}
}
