[{"department":[{"_id":"263"}],"user_id":"43497","_id":"40838","publication":"IEEE Trans. Instrum. Meas.","type":"journal_article","status":"public","abstract":[{"text":"A multiple-input multiple-output (MIMO) frequency-domain channel measurement methodology is pre- sented. 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 unnecesary. To test the feasibility of this method, a series of measurements is presented, employing a $4 \\times 4$ dual-band (2.4/5 GHz) MIMO test bed.","lang":"eng"}],"volume":60,"author":[{"first_name":"J.","last_name":"Gutiérrez","full_name":"Gutiérrez, J."},{"first_name":"J.","full_name":"Pérez, J.","last_name":"Pérez"},{"first_name":"D.","full_name":"Ramírez, D.","last_name":"Ramírez"},{"last_name":"Vielva","full_name":"Vielva, L.","first_name":"L."},{"first_name":"J.","full_name":"Ibáñez, J.","last_name":"Ibáñez"},{"full_name":"Santamaría, I.","last_name":"Santamaría","first_name":"I."}],"date_created":"2023-01-30T11:52:00Z","date_updated":"2023-01-30T11:56:48Z","doi":"10.1109/TIM.2010.2082432","title":"Frequency-Domain Methodology for Measuring MIMO Channels Using a Generic Test Bed","issue":"3","page":"827–838","intvolume":"        60","citation":{"apa":"Gutiérrez, J., Pérez, J., Ramírez, D., Vielva, L., Ibáñez, J., &#38; Santamaría, I. (2011). Frequency-Domain Methodology for Measuring MIMO Channels Using a Generic Test Bed. <i>IEEE Trans. Instrum. Meas.</i>, <i>60</i>(3), 827–838. <a href=\"https://doi.org/10.1109/TIM.2010.2082432\">https://doi.org/10.1109/TIM.2010.2082432</a>","short":"J. Gutiérrez, J. Pérez, D. Ramírez, L. Vielva, J. Ibáñez, I. Santamaría, IEEE Trans. Instrum. Meas. 60 (2011) 827–838.","mla":"Gutiérrez, J., et al. “Frequency-Domain Methodology for Measuring MIMO Channels Using a Generic Test Bed.” <i>IEEE Trans. Instrum. Meas.</i>, vol. 60, no. 3, 2011, pp. 827–838, doi:<a href=\"https://doi.org/10.1109/TIM.2010.2082432\">10.1109/TIM.2010.2082432</a>.","bibtex":"@article{Gutiérrez_Pérez_Ramírez_Vielva_Ibáñez_Santamaría_2011, title={Frequency-Domain Methodology for Measuring MIMO Channels Using a Generic Test Bed}, volume={60}, DOI={<a href=\"https://doi.org/10.1109/TIM.2010.2082432\">10.1109/TIM.2010.2082432</a>}, number={3}, journal={IEEE Trans. Instrum. Meas.}, author={Gutiérrez, J. and Pérez, J. and Ramírez, D. and Vielva, L. and Ibáñez, J. and Santamaría, I.}, year={2011}, pages={827–838} }","ama":"Gutiérrez J, Pérez J, Ramírez D, Vielva L, Ibáñez J, Santamaría I. Frequency-Domain Methodology for Measuring MIMO Channels Using a Generic Test Bed. <i>IEEE Trans Instrum Meas</i>. 2011;60(3):827–838. doi:<a href=\"https://doi.org/10.1109/TIM.2010.2082432\">10.1109/TIM.2010.2082432</a>","chicago":"Gutiérrez, J., J. Pérez, D. Ramírez, L. Vielva, J. Ibáñez, and I. Santamaría. “Frequency-Domain Methodology for Measuring MIMO Channels Using a Generic Test Bed.” <i>IEEE Trans. Instrum. Meas.</i> 60, no. 3 (2011): 827–838. <a href=\"https://doi.org/10.1109/TIM.2010.2082432\">https://doi.org/10.1109/TIM.2010.2082432</a>.","ieee":"J. Gutiérrez, J. Pérez, D. Ramírez, L. Vielva, J. Ibáñez, and I. Santamaría, “Frequency-Domain Methodology for Measuring MIMO Channels Using a Generic Test Bed,” <i>IEEE Trans. Instrum. Meas.</i>, vol. 60, no. 3, pp. 827–838, 2011, doi: <a href=\"https://doi.org/10.1109/TIM.2010.2082432\">10.1109/TIM.2010.2082432</a>."},"year":"2011"},{"department":[{"_id":"263"}],"user_id":"43497","_id":"40839","status":"public","abstract":[{"lang":"eng","text":"Hardware platforms and testbeds are an essential tool to evaluate, in realistic scenarios, the performance of wireless communications systems. In this work we present a multiuser Multiple-Input Multiple-Output (MIMO) testbed made up of 6 nodes, each one with 4 antennas, which allows us to evaluate Interference Alignment (IA) techniques in indoor scenarios. We specifically study the performance of IA for the 3-user interference channel in the 5 GHz band. Our analysis identifies the main practical issues that potentially degrade the IA performance such as channel estimation errors or collinearity between the desired signal and interference subspaces."}],"publication":"Proc. Int. ITG Work. on Smart Antennas","type":"conference","doi":"10.1109/WSA.2011.5741921","title":"Experimental Validation of Interference Alignment Techniques using a Multiuser MIMO Testbed","author":[{"first_name":"D.","full_name":"Ramírez, D.","last_name":"Ramírez"},{"first_name":"I.","last_name":"Santamaría","full_name":"Santamaría, I."},{"last_name":"García-Naya","full_name":"García-Naya, J. A.","first_name":"J. A."},{"full_name":"Castedo, L.","last_name":"Castedo","first_name":"L."}],"date_created":"2023-01-30T11:52:00Z","date_updated":"2023-01-30T11:56:46Z","citation":{"ama":"Ramírez D, Santamaría I, García-Naya JA, Castedo L. Experimental Validation of Interference Alignment Techniques using a Multiuser MIMO Testbed. In: <i>Proc. Int. ITG Work. on Smart Antennas</i>. ; 2011. doi:<a href=\"https://doi.org/10.1109/WSA.2011.5741921\">10.1109/WSA.2011.5741921</a>","ieee":"D. Ramírez, I. Santamaría, J. A. García-Naya, and L. Castedo, “Experimental Validation of Interference Alignment Techniques using a Multiuser MIMO Testbed,” 2011, doi: <a href=\"https://doi.org/10.1109/WSA.2011.5741921\">10.1109/WSA.2011.5741921</a>.","chicago":"Ramírez, D., I. Santamaría, J. A. García-Naya, and L. Castedo. “Experimental Validation of Interference Alignment Techniques Using a Multiuser MIMO Testbed.” In <i>Proc. Int. ITG Work. on Smart Antennas</i>. Aachen, Germany, 2011. <a href=\"https://doi.org/10.1109/WSA.2011.5741921\">https://doi.org/10.1109/WSA.2011.5741921</a>.","apa":"Ramírez, D., Santamaría, I., García-Naya, J. A., &#38; Castedo, L. (2011). Experimental Validation of Interference Alignment Techniques using a Multiuser MIMO Testbed. <i>Proc. Int. ITG Work. on Smart Antennas</i>. <a href=\"https://doi.org/10.1109/WSA.2011.5741921\">https://doi.org/10.1109/WSA.2011.5741921</a>","short":"D. Ramírez, I. Santamaría, J.A. García-Naya, L. Castedo, in: Proc. Int. ITG Work. on Smart Antennas, Aachen, Germany, 2011.","mla":"Ramírez, D., et al. “Experimental Validation of Interference Alignment Techniques Using a Multiuser MIMO Testbed.” <i>Proc. Int. ITG Work. on Smart Antennas</i>, 2011, doi:<a href=\"https://doi.org/10.1109/WSA.2011.5741921\">10.1109/WSA.2011.5741921</a>.","bibtex":"@inproceedings{Ramírez_Santamaría_García-Naya_Castedo_2011, place={Aachen, Germany}, title={Experimental Validation of Interference Alignment Techniques using a Multiuser MIMO Testbed}, DOI={<a href=\"https://doi.org/10.1109/WSA.2011.5741921\">10.1109/WSA.2011.5741921</a>}, booktitle={Proc. Int. ITG Work. on Smart Antennas}, author={Ramírez, D. and Santamaría, I. and García-Naya, J. A. and Castedo, L.}, year={2011} }"},"place":"Aachen, Germany","year":"2011"},{"user_id":"43497","department":[{"_id":"263"}],"_id":"40826","status":"public","type":"journal_article","publication":"J.\\ Time Ser.\\ Anal.","doi":"10.1111/j.1467-9892.2010.00682.x","title":"Locally stationary harmonizable complex improper stochastic processes","author":[{"first_name":"Patrik","last_name":"Wahlberg","full_name":"Wahlberg, Patrik"},{"last_name":"Schreier","full_name":"Schreier, Peter J.","first_name":"Peter J."}],"date_created":"2023-01-30T11:51:58Z","volume":32,"publisher":"Blackwell Publishing Ltd","date_updated":"2023-01-30T11:57:47Z","citation":{"ieee":"P. Wahlberg and P. J. Schreier, “Locally stationary harmonizable complex improper stochastic processes,” <i>J.\\ Time Ser.\\ Anal.</i>, vol. 32, no. 1, pp. 33–46, 2011, doi: <a href=\"https://doi.org/10.1111/j.1467-9892.2010.00682.x\">10.1111/j.1467-9892.2010.00682.x</a>.","chicago":"Wahlberg, Patrik, and Peter J. Schreier. “Locally Stationary Harmonizable Complex Improper Stochastic Processes.” <i>J.\\ Time Ser.\\ Anal.</i> 32, no. 1 (2011): 33–46. <a href=\"https://doi.org/10.1111/j.1467-9892.2010.00682.x\">https://doi.org/10.1111/j.1467-9892.2010.00682.x</a>.","ama":"Wahlberg P, Schreier PJ. Locally stationary harmonizable complex improper stochastic processes. <i>J\\ Time Ser\\ Anal</i>. 2011;32(1):33–46. doi:<a href=\"https://doi.org/10.1111/j.1467-9892.2010.00682.x\">10.1111/j.1467-9892.2010.00682.x</a>","mla":"Wahlberg, Patrik, and Peter J. Schreier. “Locally Stationary Harmonizable Complex Improper Stochastic Processes.” <i>J.\\ Time Ser.\\ Anal.</i>, vol. 32, no. 1, Blackwell Publishing Ltd, 2011, pp. 33–46, doi:<a href=\"https://doi.org/10.1111/j.1467-9892.2010.00682.x\">10.1111/j.1467-9892.2010.00682.x</a>.","bibtex":"@article{Wahlberg_Schreier_2011, title={Locally stationary harmonizable complex improper stochastic processes}, volume={32}, DOI={<a href=\"https://doi.org/10.1111/j.1467-9892.2010.00682.x\">10.1111/j.1467-9892.2010.00682.x</a>}, number={1}, journal={J.\\ Time Ser.\\ Anal.}, publisher={Blackwell Publishing Ltd}, author={Wahlberg, Patrik and Schreier, Peter J.}, year={2011}, pages={33–46} }","short":"P. Wahlberg, P.J. Schreier, J.\\ Time Ser.\\ Anal. 32 (2011) 33–46.","apa":"Wahlberg, P., &#38; Schreier, P. J. (2011). Locally stationary harmonizable complex improper stochastic processes. <i>J.\\ Time Ser.\\ Anal.</i>, <i>32</i>(1), 33–46. <a href=\"https://doi.org/10.1111/j.1467-9892.2010.00682.x\">https://doi.org/10.1111/j.1467-9892.2010.00682.x</a>"},"page":"33–46","intvolume":"        32","year":"2011","issue":"1"},{"type":"journal_article","publication":"{IEEE} {T}rans.\\ {S}ignal\\ {P}rocess.","status":"public","user_id":"43497","department":[{"_id":"263"}],"_id":"40827","issue":"11","citation":{"ama":"Adali T, Schreier PJ, Scharf LL. Complex-Valued Signal Processing: The Proper Way to Deal With Impropriety. <i>{IEEE} {T}rans\\ {S}ignal\\ {P}rocess</i>. 2011;59(11):5101–5125. doi:<a href=\"https://doi.org/10.1109/TSP.2011.2162954\">10.1109/TSP.2011.2162954</a>","chicago":"Adali, Tülay, Peter J. Schreier, and Louis L. Scharf. “Complex-Valued Signal Processing: The Proper Way to Deal With Impropriety.” <i>{IEEE} {T}rans.\\ {S}ignal\\ {P}rocess.</i> 59, no. 11 (2011): 5101–5125. <a href=\"https://doi.org/10.1109/TSP.2011.2162954\">https://doi.org/10.1109/TSP.2011.2162954</a>.","ieee":"T. Adali, P. J. Schreier, and L. L. Scharf, “Complex-Valued Signal Processing: The Proper Way to Deal With Impropriety,” <i>{IEEE} {T}rans.\\ {S}ignal\\ {P}rocess.</i>, vol. 59, no. 11, pp. 5101–5125, 2011, doi: <a href=\"https://doi.org/10.1109/TSP.2011.2162954\">10.1109/TSP.2011.2162954</a>.","short":"T. Adali, P.J. Schreier, L.L. Scharf, {IEEE} {T}rans.\\ {S}ignal\\ {P}rocess. 59 (2011) 5101–5125.","mla":"Adali, Tülay, et al. “Complex-Valued Signal Processing: The Proper Way to Deal With Impropriety.” <i>{IEEE} {T}rans.\\ {S}ignal\\ {P}rocess.</i>, vol. 59, no. 11, 2011, pp. 5101–5125, doi:<a href=\"https://doi.org/10.1109/TSP.2011.2162954\">10.1109/TSP.2011.2162954</a>.","bibtex":"@article{Adali_Schreier_Scharf_2011, title={Complex-Valued Signal Processing: The Proper Way to Deal With Impropriety}, volume={59}, DOI={<a href=\"https://doi.org/10.1109/TSP.2011.2162954\">10.1109/TSP.2011.2162954</a>}, number={11}, journal={{IEEE} {T}rans.\\ {S}ignal\\ {P}rocess.}, author={Adali, Tülay and Schreier, Peter J. and Scharf, Louis L.}, year={2011}, pages={5101–5125} }","apa":"Adali, T., Schreier, P. J., &#38; Scharf, L. L. (2011). Complex-Valued Signal Processing: The Proper Way to Deal With Impropriety. <i>{IEEE} {T}rans.\\ {S}ignal\\ {P}rocess.</i>, <i>59</i>(11), 5101–5125. <a href=\"https://doi.org/10.1109/TSP.2011.2162954\">https://doi.org/10.1109/TSP.2011.2162954</a>"},"intvolume":"        59","page":"5101–5125","year":"2011","date_created":"2023-01-30T11:51:58Z","author":[{"last_name":"Adali","full_name":"Adali, Tülay","first_name":"Tülay"},{"first_name":"Peter J.","last_name":"Schreier","full_name":"Schreier, Peter J."},{"full_name":"Scharf, Louis L.","last_name":"Scharf","first_name":"Louis L."}],"volume":59,"date_updated":"2023-01-30T11:57:45Z","doi":"10.1109/TSP.2011.2162954","title":"Complex-Valued Signal Processing: The Proper Way to Deal With Impropriety"},{"type":"journal_article","publication":"Numer. Algorithms","status":"public","user_id":"43497","department":[{"_id":"263"}],"_id":"40825","issue":"4","citation":{"mla":"Rüffer, B. S., and Fabian R. Wirth. “Stability Verification for Monotone Systems Using Homotopy Algorithms.” <i>Numer. Algorithms</i>, vol. 58, no. 4, 2011, pp. 529–543, doi:<a href=\"https://doi.org/10.1007/s11075-011-9468-3\">10.1007/s11075-011-9468-3</a>.","short":"B.S. Rüffer, F.R. Wirth, Numer. Algorithms 58 (2011) 529–543.","bibtex":"@article{Rüffer_Wirth_2011, title={Stability verification for monotone systems using homotopy algorithms}, volume={58}, DOI={<a href=\"https://doi.org/10.1007/s11075-011-9468-3\">10.1007/s11075-011-9468-3</a>}, number={4}, journal={Numer. Algorithms}, author={Rüffer, B. S. and Wirth, Fabian R.}, year={2011}, pages={529–543} }","apa":"Rüffer, B. S., &#38; Wirth, F. R. (2011). Stability verification for monotone systems using homotopy algorithms. <i>Numer. Algorithms</i>, <i>58</i>(4), 529–543. <a href=\"https://doi.org/10.1007/s11075-011-9468-3\">https://doi.org/10.1007/s11075-011-9468-3</a>","ieee":"B. S. Rüffer and F. R. Wirth, “Stability verification for monotone systems using homotopy algorithms,” <i>Numer. Algorithms</i>, vol. 58, no. 4, pp. 529–543, 2011, doi: <a href=\"https://doi.org/10.1007/s11075-011-9468-3\">10.1007/s11075-011-9468-3</a>.","chicago":"Rüffer, B. S., and Fabian R. Wirth. “Stability Verification for Monotone Systems Using Homotopy Algorithms.” <i>Numer. Algorithms</i> 58, no. 4 (2011): 529–543. <a href=\"https://doi.org/10.1007/s11075-011-9468-3\">https://doi.org/10.1007/s11075-011-9468-3</a>.","ama":"Rüffer BS, Wirth FR. Stability verification for monotone systems using homotopy algorithms. <i>Numer Algorithms</i>. 2011;58(4):529–543. doi:<a href=\"https://doi.org/10.1007/s11075-011-9468-3\">10.1007/s11075-011-9468-3</a>"},"page":"529–543","intvolume":"        58","year":"2011","author":[{"last_name":"Rüffer","full_name":"Rüffer, B. S.","first_name":"B. S."},{"full_name":"Wirth, Fabian R.","last_name":"Wirth","first_name":"Fabian R."}],"date_created":"2023-01-30T11:51:58Z","volume":58,"date_updated":"2023-01-30T11:57:43Z","doi":"10.1007/s11075-011-9468-3","title":"Stability verification for monotone systems using homotopy algorithms"},{"user_id":"43497","department":[{"_id":"263"}],"_id":"40829","type":"conference","publication":"Int. Work. COST Action IC0902","status":"public","author":[{"first_name":"G.","full_name":"Vazquez-Vilar, G.","last_name":"Vazquez-Vilar"},{"first_name":"D.","full_name":"Romero, D.","last_name":"Romero"},{"first_name":"R.","full_name":"López-Valcarce, R.","last_name":"López-Valcarce"},{"first_name":"D.","last_name":"Ramírez","full_name":"Ramírez, D."},{"first_name":"J.","last_name":"Vía","full_name":"Vía, J."},{"first_name":"I.","full_name":"Santamaría, I.","last_name":"Santamaría"},{"full_name":"Sala, J.","last_name":"Sala","first_name":"J."}],"date_created":"2023-01-30T11:51:58Z","date_updated":"2023-01-30T11:57:41Z","title":"Recent advances in multiantenna spectrum sensing: complexity, noise uncertainty, and signal rank issues","citation":{"mla":"Vazquez-Vilar, G., et al. “Recent Advances in Multiantenna Spectrum Sensing: Complexity, Noise Uncertainty, and Signal Rank Issues.” <i>Int. Work. COST Action IC0902</i>, 2011.","short":"G. Vazquez-Vilar, D. Romero, R. López-Valcarce, D. Ramírez, J. Vía, I. Santamaría, J. Sala, in: Int. Work. COST Action IC0902, Barcelona, Spain, 2011.","bibtex":"@inproceedings{Vazquez-Vilar_Romero_López-Valcarce_Ramírez_Vía_Santamaría_Sala_2011, place={Barcelona, Spain}, title={Recent advances in multiantenna spectrum sensing: complexity, noise uncertainty, and signal rank issues}, booktitle={Int. Work. COST Action IC0902}, author={Vazquez-Vilar, G. and Romero, D. and López-Valcarce, R. and Ramírez, D. and Vía, J. and Santamaría, I. and Sala, J.}, year={2011} }","apa":"Vazquez-Vilar, G., Romero, D., López-Valcarce, R., Ramírez, D., Vía, J., Santamaría, I., &#38; Sala, J. (2011). Recent advances in multiantenna spectrum sensing: complexity, noise uncertainty, and signal rank issues. <i>Int. Work. COST Action IC0902</i>.","chicago":"Vazquez-Vilar, G., D. Romero, R. López-Valcarce, D. Ramírez, J. Vía, I. Santamaría, and J. Sala. “Recent Advances in Multiantenna Spectrum Sensing: Complexity, Noise Uncertainty, and Signal Rank Issues.” In <i>Int. Work. COST Action IC0902</i>. Barcelona, Spain, 2011.","ieee":"G. Vazquez-Vilar <i>et al.</i>, “Recent advances in multiantenna spectrum sensing: complexity, noise uncertainty, and signal rank issues,” 2011.","ama":"Vazquez-Vilar G, Romero D, López-Valcarce R, et al. Recent advances in multiantenna spectrum sensing: complexity, noise uncertainty, and signal rank issues. In: <i>Int. Work. COST Action IC0902</i>. ; 2011."},"place":"Barcelona, Spain","year":"2011"},{"status":"public","type":"conference","publication":"Proc. IEEE American Contr. Conf.","user_id":"43497","department":[{"_id":"263"}],"_id":"40824","citation":{"bibtex":"@inproceedings{Ito_Jiang_Dashkovskiy_Rüffer_2011, title={A Small-Gain Theorem and Construction of Sum-Type Lyapunov Functions for Networks of iISS Systems}, booktitle={Proc. IEEE American Contr. Conf.}, author={Ito, Hiroshi and Jiang, Zhong-Ping and Dashkovskiy, Sergey N. and Rüffer, Björn S.}, year={2011}, pages={1971–1977} }","mla":"Ito, Hiroshi, et al. “A Small-Gain Theorem and Construction of Sum-Type Lyapunov Functions for Networks of IISS Systems.” <i>Proc. IEEE American Contr. Conf.</i>, 2011, pp. 1971–1977.","short":"H. Ito, Z.-P. Jiang, S.N. Dashkovskiy, B.S. Rüffer, in: Proc. IEEE American Contr. Conf., 2011, pp. 1971–1977.","apa":"Ito, H., Jiang, Z.-P., Dashkovskiy, S. N., &#38; Rüffer, B. S. (2011). A Small-Gain Theorem and Construction of Sum-Type Lyapunov Functions for Networks of iISS Systems. <i>Proc. IEEE American Contr. Conf.</i>, 1971–1977.","ama":"Ito H, Jiang Z-P, Dashkovskiy SN, Rüffer BS. A Small-Gain Theorem and Construction of Sum-Type Lyapunov Functions for Networks of iISS Systems. In: <i>Proc. IEEE American Contr. Conf.</i> ; 2011:1971–1977.","ieee":"H. Ito, Z.-P. Jiang, S. N. Dashkovskiy, and B. S. Rüffer, “A Small-Gain Theorem and Construction of Sum-Type Lyapunov Functions for Networks of iISS Systems,” in <i>Proc. IEEE American Contr. Conf.</i>, 2011, pp. 1971–1977.","chicago":"Ito, Hiroshi, Zhong-Ping Jiang, Sergey N. Dashkovskiy, and Björn S. Rüffer. “A Small-Gain Theorem and Construction of Sum-Type Lyapunov Functions for Networks of IISS Systems.” In <i>Proc. IEEE American Contr. Conf.</i>, 1971–1977, 2011."},"page":"1971–1977","year":"2011","title":"A Small-Gain Theorem and Construction of Sum-Type Lyapunov Functions for Networks of iISS Systems","date_created":"2023-01-30T11:51:58Z","author":[{"last_name":"Ito","full_name":"Ito, Hiroshi","first_name":"Hiroshi"},{"first_name":"Zhong-Ping","last_name":"Jiang","full_name":"Jiang, Zhong-Ping"},{"first_name":"Sergey N.","full_name":"Dashkovskiy, Sergey N.","last_name":"Dashkovskiy"},{"full_name":"Rüffer, Björn S.","last_name":"Rüffer","first_name":"Björn S."}],"date_updated":"2023-01-30T11:57:38Z"},{"abstract":[{"text":"This work addresses the problem of deciding whether a set of realizations of a vector-valued time series with unknown temporal correlation are spatially correlated or not. For wide sense stationary (WSS) Gaussian processes, this is a problem of deciding between two different power spectral density matrices, one of them diagonal. Specifically, we show that for arbitrary Gaussian processes (not necessarily WSS) the generalized likelihood ratio test (GLRT) is given by the quotient between the determinant of the sample space-time covariance matrix and the determinant of its block-diagonal version. Furthermore, for WSS processes, we present an asymptotic frequency-domain approximation of the GLRT which is given by a function of the Hadamard ratio (quotient between the determinant of a matrix and the product of the elements of the main diagonal) of the estimated power spectral density matrix. The Hadamard ratio is known to be the GLRT detector for vector-valued random variables and, therefore, what this paper shows is how frequency-dependent Hadamard ratios must be merged into a single test statistic when the vector-valued random variable is replaced by a vector-valued time series with temporal correlation. For bivariate time series, the derived frequency domain detector can be rewritten as a function of the well-known magnitude squared coherence (MSC) spectrum, which suggests a straightforward extension of the MSC spectrum to the general case of multivariate time series. Finally, the performance of the proposed method is illustrated by means of simulations.","lang":"eng"}],"status":"public","publication":"{IEEE} {T}rans.\\ {S}ignal\\ {P}rocess.","type":"journal_article","_id":"40843","department":[{"_id":"263"}],"user_id":"43497","year":"2010","intvolume":"        58","page":"5006–5015","citation":{"apa":"Ramírez, D., Vía, J., Santamaría, I., &#38; Scharf, L. L. (2010). Detection of Spatially Correlated Gaussian Time Series. <i>{IEEE} {T}rans.\\ {S}ignal\\ {P}rocess.</i>, <i>58</i>(10), 5006–5015. <a href=\"https://doi.org/10.1109/TSP.2010.2053360\">https://doi.org/10.1109/TSP.2010.2053360</a>","short":"D. Ramírez, J. Vía, I. Santamaría, L.L. Scharf, {IEEE} {T}rans.\\ {S}ignal\\ {P}rocess. 58 (2010) 5006–5015.","mla":"Ramírez, D., et al. “Detection of Spatially Correlated Gaussian Time Series.” <i>{IEEE} {T}rans.\\ {S}ignal\\ {P}rocess.</i>, vol. 58, no. 10, 2010, pp. 5006–5015, doi:<a href=\"https://doi.org/10.1109/TSP.2010.2053360\">10.1109/TSP.2010.2053360</a>.","bibtex":"@article{Ramírez_Vía_Santamaría_Scharf_2010, title={Detection of Spatially Correlated Gaussian Time Series}, volume={58}, DOI={<a href=\"https://doi.org/10.1109/TSP.2010.2053360\">10.1109/TSP.2010.2053360</a>}, number={10}, journal={{IEEE} {T}rans.\\ {S}ignal\\ {P}rocess.}, author={Ramírez, D. and Vía, J. and Santamaría, I. and Scharf, L. L.}, year={2010}, pages={5006–5015} }","ama":"Ramírez D, Vía J, Santamaría I, Scharf LL. Detection of Spatially Correlated Gaussian Time Series. <i>{IEEE} {T}rans\\ {S}ignal\\ {P}rocess</i>. 2010;58(10):5006–5015. doi:<a href=\"https://doi.org/10.1109/TSP.2010.2053360\">10.1109/TSP.2010.2053360</a>","ieee":"D. Ramírez, J. Vía, I. Santamaría, and L. L. Scharf, “Detection of Spatially Correlated Gaussian Time Series,” <i>{IEEE} {T}rans.\\ {S}ignal\\ {P}rocess.</i>, vol. 58, no. 10, pp. 5006–5015, 2010, doi: <a href=\"https://doi.org/10.1109/TSP.2010.2053360\">10.1109/TSP.2010.2053360</a>.","chicago":"Ramírez, D., J. Vía, I. Santamaría, and L. L. Scharf. “Detection of Spatially Correlated Gaussian Time Series.” <i>{IEEE} {T}rans.\\ {S}ignal\\ {P}rocess.</i> 58, no. 10 (2010): 5006–5015. <a href=\"https://doi.org/10.1109/TSP.2010.2053360\">https://doi.org/10.1109/TSP.2010.2053360</a>."},"issue":"10","title":"Detection of Spatially Correlated Gaussian Time Series","doi":"10.1109/TSP.2010.2053360","date_updated":"2023-01-30T11:56:44Z","volume":58,"author":[{"last_name":"Ramírez","full_name":"Ramírez, D.","first_name":"D."},{"full_name":"Vía, J.","last_name":"Vía","first_name":"J."},{"full_name":"Santamaría, I.","last_name":"Santamaría","first_name":"I."},{"first_name":"L. L.","full_name":"Scharf, L. L.","last_name":"Scharf"}],"date_created":"2023-01-30T11:52:00Z"},{"date_updated":"2023-01-30T11:56:41Z","author":[{"first_name":"D.","last_name":"Ramírez","full_name":"Ramírez, D."},{"first_name":"J.","full_name":"Vía, J.","last_name":"Vía"},{"last_name":"Santamaría","full_name":"Santamaría, I.","first_name":"I."}],"date_created":"2023-01-30T11:52:00Z","title":"Multiantenna spectrum sensing: The case of wideband rank-one primary signals","doi":"10.1109/SAM.2010.5606502","year":"2010","place":"Israel","citation":{"apa":"Ramírez, D., Vía, J., &#38; Santamaría, I. (2010). Multiantenna spectrum sensing: The case of wideband rank-one primary signals. <i>Proc.\\ IEEE Sensor Array and Multichannel Signal Process. Work.</i> <a href=\"https://doi.org/10.1109/SAM.2010.5606502\">https://doi.org/10.1109/SAM.2010.5606502</a>","mla":"Ramírez, D., et al. “Multiantenna Spectrum Sensing: The Case of Wideband Rank-One Primary Signals.” <i>Proc.\\ IEEE Sensor Array and Multichannel Signal Process. Work.</i>, 2010, doi:<a href=\"https://doi.org/10.1109/SAM.2010.5606502\">10.1109/SAM.2010.5606502</a>.","short":"D. Ramírez, J. Vía, I. Santamaría, in: Proc.\\ IEEE Sensor Array and Multichannel Signal Process. Work., Israel, 2010.","bibtex":"@inproceedings{Ramírez_Vía_Santamaría_2010, place={Israel}, title={Multiantenna spectrum sensing: The case of wideband rank-one primary signals}, DOI={<a href=\"https://doi.org/10.1109/SAM.2010.5606502\">10.1109/SAM.2010.5606502</a>}, booktitle={Proc.\\ IEEE Sensor Array and Multichannel Signal Process. Work.}, author={Ramírez, D. and Vía, J. and Santamaría, I.}, year={2010} }","ieee":"D. Ramírez, J. Vía, and I. Santamaría, “Multiantenna spectrum sensing: The case of wideband rank-one primary signals,” 2010, doi: <a href=\"https://doi.org/10.1109/SAM.2010.5606502\">10.1109/SAM.2010.5606502</a>.","chicago":"Ramírez, D., J. Vía, and I. Santamaría. “Multiantenna Spectrum Sensing: The Case of Wideband Rank-One Primary Signals.” In <i>Proc.\\ IEEE Sensor Array and Multichannel Signal Process. Work.</i> Israel, 2010. <a href=\"https://doi.org/10.1109/SAM.2010.5606502\">https://doi.org/10.1109/SAM.2010.5606502</a>.","ama":"Ramírez D, Vía J, Santamaría I. Multiantenna spectrum sensing: The case of wideband rank-one primary signals. In: <i>Proc.\\ IEEE Sensor Array and Multichannel Signal Process. Work.</i> ; 2010. doi:<a href=\"https://doi.org/10.1109/SAM.2010.5606502\">10.1109/SAM.2010.5606502</a>"},"_id":"40842","user_id":"43497","department":[{"_id":"263"}],"type":"conference","publication":"Proc.\\ IEEE Sensor Array and Multichannel Signal Process. Work.","abstract":[{"text":"One of the key problems in cognitive radio (CR) is the detection of primary activity in order to determine which parts of the spectrum are available for opportunistic access. In this work, we present a new multiantenna detector which fully exploits the spatial and temporal structure of the signals. In particular, we derive the generalized likelihood ratio test (GLRT) for the problem of detecting a wideband rank-one signal under spatially uncorrelated noise with equal or different power spectral densities. In order to simplify the maximum likelihood (ML) estimation of the unknown parameters, we use the asymptotic likelihood in the frequency domain. Interestingly, for noises with different distributions and under a low SNR approximation, the GLRT is obtained as a function of the largest eigenvalue of the spectral coherence matrix. Finally, the performance of the proposed detectors is evaluated by means of numerical simulations, showing important advantages over previously proposed approaches.","lang":"eng"}],"status":"public"},{"type":"conference","publication":"Proc.\\ IEEE Int.\\ Conf.\\ Acoustics, Speech and Signal Process.","abstract":[{"text":"In this paper the two main definitions of quaternion properness (or second order circularity) are reviewed, showing their connection with the structure of the optimal quaternion linear processing. Specifically, we present a rigorous generalization of the most common multivariate statistical analysis techniques to the case of quaternion vectors, and show that the different kinds of quaternion improperness require different kinds of widely linear processing. In general, the optimal linear processing is \\emph{full-widely linear}, which requires the joint processing of the quaternion vector and its involutions over three pure unit quaternions. However, in the case of jointly $\\mathbbQ$-proper and $\\mathbbC^{\\eta}$-proper vectors, the optimal processing reduces, respectively, to the \\emphconventional and \\emph{semi-widely linear processing}, with the latter only requiring to operate on the quaternion vector and its involution over the pure unit quaternion $\\eta$. Finally, a simulation example poses some interesting questions for future research.","lang":"eng"}],"status":"public","_id":"40849","user_id":"43497","department":[{"_id":"263"}],"place":"Dallas, USA","year":"2010","citation":{"chicago":"Vía, J., D. Ramírez, I. Santamaría, and L. Vielva. “Widely and Semi-Widely Linear Processing of Quaternion Vectors.” In <i>Proc.\\ IEEE Int.\\ Conf.\\ Acoustics, Speech and Signal Process.</i> Dallas, USA, 2010. <a href=\"https://doi.org/10.1109/ICASSP.2010.5495787\">https://doi.org/10.1109/ICASSP.2010.5495787</a>.","ieee":"J. Vía, D. Ramírez, I. Santamaría, and L. Vielva, “Widely and semi-widely linear processing of quaternion vectors,” 2010, doi: <a href=\"https://doi.org/10.1109/ICASSP.2010.5495787\">10.1109/ICASSP.2010.5495787</a>.","ama":"Vía J, Ramírez D, Santamaría I, Vielva L. Widely and semi-widely linear processing of quaternion vectors. In: <i>Proc.\\ IEEE Int.\\ Conf.\\ Acoustics, Speech and Signal Process.</i> ; 2010. doi:<a href=\"https://doi.org/10.1109/ICASSP.2010.5495787\">10.1109/ICASSP.2010.5495787</a>","apa":"Vía, J., Ramírez, D., Santamaría, I., &#38; Vielva, L. (2010). Widely and semi-widely linear processing of quaternion vectors. <i>Proc.\\ IEEE Int.\\ Conf.\\ Acoustics, Speech and Signal Process.</i> <a href=\"https://doi.org/10.1109/ICASSP.2010.5495787\">https://doi.org/10.1109/ICASSP.2010.5495787</a>","mla":"Vía, J., et al. “Widely and Semi-Widely Linear Processing of Quaternion Vectors.” <i>Proc.\\ IEEE Int.\\ Conf.\\ Acoustics, Speech and Signal Process.</i>, 2010, doi:<a href=\"https://doi.org/10.1109/ICASSP.2010.5495787\">10.1109/ICASSP.2010.5495787</a>.","bibtex":"@inproceedings{Vía_Ramírez_Santamaría_Vielva_2010, place={Dallas, USA}, title={Widely and semi-widely linear processing of quaternion vectors}, DOI={<a href=\"https://doi.org/10.1109/ICASSP.2010.5495787\">10.1109/ICASSP.2010.5495787</a>}, booktitle={Proc.\\ IEEE Int.\\ Conf.\\ Acoustics, Speech and Signal Process.}, author={Vía, J. and Ramírez, D. and Santamaría, I. and Vielva, L.}, year={2010} }","short":"J. Vía, D. Ramírez, I. Santamaría, L. Vielva, in: Proc.\\ IEEE Int.\\ Conf.\\ Acoustics, Speech and Signal Process., Dallas, USA, 2010."},"date_updated":"2023-01-30T11:56:53Z","date_created":"2023-01-30T11:52:01Z","author":[{"full_name":"Vía, J.","last_name":"Vía","first_name":"J."},{"last_name":"Ramírez","full_name":"Ramírez, D.","first_name":"D."},{"last_name":"Santamaría","full_name":"Santamaría, I.","first_name":"I."},{"first_name":"L.","last_name":"Vielva","full_name":"Vielva, L."}],"title":"Widely and semi-widely linear processing of quaternion vectors","doi":"10.1109/ICASSP.2010.5495787"},{"year":"2010","page":"330","citation":{"ama":"Schreier PJ, Scharf LL. <i>Statistical Signal Processing of Complex-Valued Data: The Theory of Improper and Noncircular Signals</i>. Cambridge University Press; 2010.","chicago":"Schreier, Peter J., and Louis L. Scharf. <i>Statistical Signal Processing of Complex-Valued Data: The Theory of Improper and Noncircular Signals</i>. Cambridge University Press, 2010.","ieee":"P. J. Schreier and L. L. Scharf, <i>Statistical Signal Processing of Complex-Valued Data: The Theory of Improper and Noncircular Signals</i>. Cambridge University Press, 2010.","apa":"Schreier, P. J., &#38; Scharf, L. L. (2010). <i>Statistical Signal Processing of Complex-Valued Data: The Theory of Improper and Noncircular Signals</i>. Cambridge University Press.","mla":"Schreier, Peter J., and Louis L. Scharf. <i>Statistical Signal Processing of Complex-Valued Data: The Theory of Improper and Noncircular Signals</i>. Cambridge University Press, 2010.","short":"P.J. Schreier, L.L. Scharf, Statistical Signal Processing of Complex-Valued Data: The Theory of Improper and Noncircular Signals, Cambridge University Press, 2010.","bibtex":"@book{Schreier_Scharf_2010, title={Statistical Signal Processing of Complex-Valued Data: The Theory of Improper and Noncircular Signals}, publisher={Cambridge University Press}, author={Schreier, Peter J. and Scharf, Louis L.}, year={2010} }"},"publisher":"Cambridge University Press","date_updated":"2023-01-30T11:56:39Z","author":[{"first_name":"Peter J.","full_name":"Schreier, Peter J.","last_name":"Schreier"},{"last_name":"Scharf","full_name":"Scharf, Louis L.","first_name":"Louis L."}],"date_created":"2023-01-30T11:52:00Z","title":"Statistical Signal Processing of Complex-Valued Data: The Theory of Improper and Noncircular Signals","type":"book","abstract":[{"text":"Complex-valued random signals are embedded in the very fabric of science and engineering, yet the usual assumptions made about their statistical behavior are often a poor representation of the underlying physics. This book deals with improper and noncircular complex signals, which do not conform to classical assumptions, and it demonstrates how correct treatment of these signals can have significant payoffs. The book begins with detailed coverage of the fundamental theory and presents a variety of tools and algorithms for dealing with improper and noncircular signals. It provides a comprehensive account of the main applications, covering detection, estimation, and signal analysis of stationary, nonstationary, and cyclostationary processes. Providing a systematic development from the origin of complex signals to their probabilistic description makes the theory accessible to newcomers. This book is ideal for graduate students and researchers working with complex data in a range of research areas from communications to oceanography.","lang":"eng"}],"status":"public","_id":"40840","department":[{"_id":"263"}],"user_id":"43497"},{"issue":"3","page":"147–155","intvolume":"         3","citation":{"ama":"Tong J, Ping L. Performance analysis of superposition coded modulation. <i>Physical Comm</i>. 2010;3(3):147–155. doi:<a href=\"https://doi.org/10.1016/j.phycom.2009.08.008\">10.1016/j.phycom.2009.08.008</a>","chicago":"Tong, Jun, and Li Ping. “Performance Analysis of Superposition Coded Modulation.” <i>Physical Comm.</i> 3, no. 3 (2010): 147–155. <a href=\"https://doi.org/10.1016/j.phycom.2009.08.008\">https://doi.org/10.1016/j.phycom.2009.08.008</a>.","ieee":"J. Tong and L. Ping, “Performance analysis of superposition coded modulation,” <i>Physical Comm.</i>, vol. 3, no. 3, pp. 147–155, 2010, doi: <a href=\"https://doi.org/10.1016/j.phycom.2009.08.008\">10.1016/j.phycom.2009.08.008</a>.","mla":"Tong, Jun, and Li Ping. “Performance Analysis of Superposition Coded Modulation.” <i>Physical Comm.</i>, vol. 3, no. 3, 2010, pp. 147–155, doi:<a href=\"https://doi.org/10.1016/j.phycom.2009.08.008\">10.1016/j.phycom.2009.08.008</a>.","short":"J. Tong, L. Ping, Physical Comm. 3 (2010) 147–155.","bibtex":"@article{Tong_Ping_2010, title={Performance analysis of superposition coded modulation}, volume={3}, DOI={<a href=\"https://doi.org/10.1016/j.phycom.2009.08.008\">10.1016/j.phycom.2009.08.008</a>}, number={3}, journal={Physical Comm.}, author={Tong, Jun and Ping, Li}, year={2010}, pages={147–155} }","apa":"Tong, J., &#38; Ping, L. (2010). Performance analysis of superposition coded modulation. <i>Physical Comm.</i>, <i>3</i>(3), 147–155. <a href=\"https://doi.org/10.1016/j.phycom.2009.08.008\">https://doi.org/10.1016/j.phycom.2009.08.008</a>"},"year":"2010","volume":3,"author":[{"first_name":"Jun","full_name":"Tong, Jun","last_name":"Tong"},{"full_name":"Ping, Li","last_name":"Ping","first_name":"Li"}],"date_created":"2023-01-30T11:52:00Z","date_updated":"2023-01-30T11:56:37Z","doi":"10.1016/j.phycom.2009.08.008","title":"Performance analysis of superposition coded modulation","publication":"Physical Comm.","type":"journal_article","status":"public","abstract":[{"text":"This paper presents a comprehensive analysis of superposition coded modulation (SCM). Two types of SCM schemes, i.e., the single-code SCM (SC-SCM) and multi-code SCM (MC-SCM), are analyzed. The basic features of SCM are described, followed by the information-theoretic analysis. Different encoding/decoding strategies are compared from the capacity point of view. A semi-analytical evolution technique is proposed to track the convergence behavior of iterative decoding. Analytical error-rate analysis is then conducted to predict the asymptotic performance. Numerous examples demonstrate that the analysis tools discussed in this paper can provide reasonably accurate performance prediction for SCM schemes.","lang":"eng"}],"department":[{"_id":"263"}],"user_id":"43497","_id":"40841"},{"date_updated":"2023-01-30T11:56:50Z","volume":90,"author":[{"first_name":"Patrik","last_name":"Wahlberg","full_name":"Wahlberg, Patrik"},{"full_name":"Schreier, Peter J.","last_name":"Schreier","first_name":"Peter J."}],"date_created":"2023-01-30T11:52:01Z","title":"On Wiener filtering of certain locally stationary stochastic processes","doi":"10.1016/j.sigpro.2009.09.013","issue":"3","year":"2010","intvolume":"        90","page":"885–890","citation":{"chicago":"Wahlberg, Patrik, and Peter J. Schreier. “On Wiener Filtering of Certain Locally Stationary Stochastic Processes.” <i>Signal Process.</i> 90, no. 3 (2010): 885–890. <a href=\"https://doi.org/10.1016/j.sigpro.2009.09.013\">https://doi.org/10.1016/j.sigpro.2009.09.013</a>.","ieee":"P. Wahlberg and P. J. Schreier, “On Wiener filtering of certain locally stationary stochastic processes,” <i>Signal Process.</i>, vol. 90, no. 3, pp. 885–890, 2010, doi: <a href=\"https://doi.org/10.1016/j.sigpro.2009.09.013\">10.1016/j.sigpro.2009.09.013</a>.","ama":"Wahlberg P, Schreier PJ. On Wiener filtering of certain locally stationary stochastic processes. <i>Signal Process</i>. 2010;90(3):885–890. doi:<a href=\"https://doi.org/10.1016/j.sigpro.2009.09.013\">10.1016/j.sigpro.2009.09.013</a>","mla":"Wahlberg, Patrik, and Peter J. Schreier. “On Wiener Filtering of Certain Locally Stationary Stochastic Processes.” <i>Signal Process.</i>, vol. 90, no. 3, 2010, pp. 885–890, doi:<a href=\"https://doi.org/10.1016/j.sigpro.2009.09.013\">10.1016/j.sigpro.2009.09.013</a>.","short":"P. Wahlberg, P.J. Schreier, Signal Process. 90 (2010) 885–890.","bibtex":"@article{Wahlberg_Schreier_2010, title={On Wiener filtering of certain locally stationary stochastic processes}, volume={90}, DOI={<a href=\"https://doi.org/10.1016/j.sigpro.2009.09.013\">10.1016/j.sigpro.2009.09.013</a>}, number={3}, journal={Signal Process.}, author={Wahlberg, Patrik and Schreier, Peter J.}, year={2010}, pages={885–890} }","apa":"Wahlberg, P., &#38; Schreier, P. J. (2010). On Wiener filtering of certain locally stationary stochastic processes. <i>Signal Process.</i>, <i>90</i>(3), 885–890. <a href=\"https://doi.org/10.1016/j.sigpro.2009.09.013\">https://doi.org/10.1016/j.sigpro.2009.09.013</a>"},"_id":"40850","department":[{"_id":"263"}],"user_id":"43497","publication":"Signal Process.","type":"journal_article","abstract":[{"text":"We study linear minimum mean squared error filters for continuous-time second-order stochastic processes that are locally stationary in Silverman’s sense. We show that the optimal filter is rarely locally stationary even when the covariance functions have Gaussian shape. Using Mehler’s formula we derive series expansions of the filter kernel for locally stationary covariances that are determined by Gaussians.","lang":"eng"}],"status":"public"},{"citation":{"short":"D. Ramírez, J. Vía, I. Santamaría, R. López-Valcarce, L.L. Scharf, in: Proc.\\ IEEE Int.\\ Conf.\\ Acoustics, Speech and Signal Process., Dallas, USA, 2010.","bibtex":"@inproceedings{Ramírez_Vía_Santamaría_López-Valcarce_Scharf_2010, place={Dallas, USA}, title={Multiantenna Spectrum Sensing: Detection of Spatial Correlation Among Time-Series With Unknown Spectra}, DOI={<a href=\"https://doi.org/10.1109/ICASSP.2010.5496151\">10.1109/ICASSP.2010.5496151</a>}, booktitle={Proc.\\ IEEE Int.\\ Conf.\\ Acoustics, Speech and Signal Process.}, author={Ramírez, D. and Vía, J. and Santamaría, I. and López-Valcarce, R. and Scharf, L. L.}, year={2010} }","mla":"Ramírez, D., et al. “Multiantenna Spectrum Sensing: Detection of Spatial Correlation Among Time-Series With Unknown Spectra.” <i>Proc.\\ IEEE Int.\\ Conf.\\ Acoustics, Speech and Signal Process.</i>, 2010, doi:<a href=\"https://doi.org/10.1109/ICASSP.2010.5496151\">10.1109/ICASSP.2010.5496151</a>.","apa":"Ramírez, D., Vía, J., Santamaría, I., López-Valcarce, R., &#38; Scharf, L. L. (2010). Multiantenna Spectrum Sensing: Detection of Spatial Correlation Among Time-Series With Unknown Spectra. <i>Proc.\\ IEEE Int.\\ Conf.\\ Acoustics, Speech and Signal Process.</i> <a href=\"https://doi.org/10.1109/ICASSP.2010.5496151\">https://doi.org/10.1109/ICASSP.2010.5496151</a>","ama":"Ramírez D, Vía J, Santamaría I, López-Valcarce R, Scharf LL. Multiantenna Spectrum Sensing: Detection of Spatial Correlation Among Time-Series With Unknown Spectra. In: <i>Proc.\\ IEEE Int.\\ Conf.\\ Acoustics, Speech and Signal Process.</i> ; 2010. doi:<a href=\"https://doi.org/10.1109/ICASSP.2010.5496151\">10.1109/ICASSP.2010.5496151</a>","ieee":"D. Ramírez, J. Vía, I. Santamaría, R. López-Valcarce, and L. L. Scharf, “Multiantenna Spectrum Sensing: Detection of Spatial Correlation Among Time-Series With Unknown Spectra,” 2010, doi: <a href=\"https://doi.org/10.1109/ICASSP.2010.5496151\">10.1109/ICASSP.2010.5496151</a>.","chicago":"Ramírez, D., J. Vía, I. Santamaría, R. López-Valcarce, and L. L. Scharf. “Multiantenna Spectrum Sensing: Detection of Spatial Correlation Among Time-Series With Unknown Spectra.” In <i>Proc.\\ IEEE Int.\\ Conf.\\ Acoustics, Speech and Signal Process.</i> Dallas, USA, 2010. <a href=\"https://doi.org/10.1109/ICASSP.2010.5496151\">https://doi.org/10.1109/ICASSP.2010.5496151</a>."},"year":"2010","place":"Dallas, USA","doi":"10.1109/ICASSP.2010.5496151","title":"Multiantenna Spectrum Sensing: Detection of Spatial Correlation Among Time-Series With Unknown Spectra","author":[{"last_name":"Ramírez","full_name":"Ramírez, D.","first_name":"D."},{"full_name":"Vía, J.","last_name":"Vía","first_name":"J."},{"full_name":"Santamaría, I.","last_name":"Santamaría","first_name":"I."},{"full_name":"López-Valcarce, R.","last_name":"López-Valcarce","first_name":"R."},{"first_name":"L. L.","full_name":"Scharf, L. L.","last_name":"Scharf"}],"date_created":"2023-01-30T11:52:01Z","date_updated":"2023-01-30T11:55:28Z","status":"public","abstract":[{"lang":"eng","text":"One of the key problems in cognitive radio (CR) is the detection of primary activity in order to determine which parts of the spectrum are available for opportunistic access. This detection task is challenging, since the wireless environment often results in very low SNR conditions. Moreover, calibration errors and imperfect analog components at the CR spectral monitor result in uncertainties in the noise spectrum, making the problem more difficult. In this work, we present a new multiantenna detector which is based on the fact that the observation noise processes are spatially uncorrelated, whereas any primary signal present should result inspatial correlation. In particular, we derive the generalized likelihood ratio test (GLRT) for this problem, which is given by the quotient between the determinant of the sample covariance matrix and the determinant of its block-diagonal version. For stationary processes the GLRT tends asymptotically to the integral of the logarithm of the Hadamard ratio of the estimated power spectral density matrix. Additionally, we present an approximation of the frequency domain detector in the low SNR regime, which results in computational savings. The performance of the proposed detectors is evaluated by means of numerical simulations, showing important advantages over existing detectors."}],"type":"conference","publication":"Proc.\\ IEEE Int.\\ Conf.\\ Acoustics, Speech and Signal Process.","user_id":"43497","department":[{"_id":"263"}],"_id":"40848"},{"status":"public","abstract":[{"text":"In this paper, the second-order circularity of quater- nion random vectors is analyzed. Unlike the case of complex vectors, there exist three different kinds of quaternion properness, which are based on the vanishing of three different complemen- tary covariance matrices. The different kinds of properness have direct implications on the Cayley–Dickson representation of the quaternion vector, and also on several well-known multivariate statistical analysis methods. In particular, the quaternion exten- sions of the partial least squares (PLS), multiple linear regression (MLR) and canonical correlation analysis (CCA) techniques are analyzed, showing that, in general, the optimal linear processing is \\emph{full-widely linear}. However, in the case of jointly $\\mathbbQ$-proper or $\\mathbbC^{\\eta}$-proper vectors, the optimal processing reduces, respectively, to the \\emphconventional or \\emph{semi-widely linear} processing. Finally, a measure for the degree of improperness of a quaternion random vector is proposed, which is based on the Kullback–Leibler diver- gence between two zero-mean Gaussian distributions, one of them with the actual augmented covariance matrix, and the other with its closest proper version. This measure quantifies the entropy loss due to the improperness of the quaternion vector, and it admits an intuitive geometrical interpretation based on Kullback–Leibler projections onto sets of proper augmented covariance matrices.","lang":"eng"}],"publication":"IEEE Trans.\\ Inform.\\ Theory","type":"journal_article","department":[{"_id":"263"}],"user_id":"43497","_id":"40847","page":"3502–3515","intvolume":"        56","citation":{"ama":"Vía J, Ramírez D, Santamaría I. Properness and Widely Linear Processing of Quaternion Random Vectors. <i>IEEE Trans\\ Inform\\ Theory</i>. 2010;56(7):3502–3515. doi:<a href=\"https://doi.org/10.1109/TIT.2010.2048440\">10.1109/TIT.2010.2048440</a>","chicago":"Vía, J., D. Ramírez, and I. Santamaría. “Properness and Widely Linear Processing of Quaternion Random Vectors.” <i>IEEE Trans.\\ Inform.\\ Theory</i> 56, no. 7 (2010): 3502–3515. <a href=\"https://doi.org/10.1109/TIT.2010.2048440\">https://doi.org/10.1109/TIT.2010.2048440</a>.","ieee":"J. Vía, D. Ramírez, and I. Santamaría, “Properness and Widely Linear Processing of Quaternion Random Vectors,” <i>IEEE Trans.\\ Inform.\\ Theory</i>, vol. 56, no. 7, pp. 3502–3515, 2010, doi: <a href=\"https://doi.org/10.1109/TIT.2010.2048440\">10.1109/TIT.2010.2048440</a>.","bibtex":"@article{Vía_Ramírez_Santamaría_2010, title={Properness and Widely Linear Processing of Quaternion Random Vectors}, volume={56}, DOI={<a href=\"https://doi.org/10.1109/TIT.2010.2048440\">10.1109/TIT.2010.2048440</a>}, number={7}, journal={IEEE Trans.\\ Inform.\\ Theory}, author={Vía, J. and Ramírez, D. and Santamaría, I.}, year={2010}, pages={3502–3515} }","short":"J. Vía, D. Ramírez, I. Santamaría, IEEE Trans.\\ Inform.\\ Theory 56 (2010) 3502–3515.","mla":"Vía, J., et al. “Properness and Widely Linear Processing of Quaternion Random Vectors.” <i>IEEE Trans.\\ Inform.\\ Theory</i>, vol. 56, no. 7, 2010, pp. 3502–3515, doi:<a href=\"https://doi.org/10.1109/TIT.2010.2048440\">10.1109/TIT.2010.2048440</a>.","apa":"Vía, J., Ramírez, D., &#38; Santamaría, I. (2010). Properness and Widely Linear Processing of Quaternion Random Vectors. <i>IEEE Trans.\\ Inform.\\ Theory</i>, <i>56</i>(7), 3502–3515. <a href=\"https://doi.org/10.1109/TIT.2010.2048440\">https://doi.org/10.1109/TIT.2010.2048440</a>"},"year":"2010","issue":"7","doi":"10.1109/TIT.2010.2048440","title":"Properness and Widely Linear Processing of Quaternion Random Vectors","volume":56,"author":[{"first_name":"J.","last_name":"Vía","full_name":"Vía, J."},{"first_name":"D.","last_name":"Ramírez","full_name":"Ramírez, D."},{"first_name":"I.","last_name":"Santamaría","full_name":"Santamaría, I."}],"date_created":"2023-01-30T11:52:01Z","date_updated":"2023-01-30T11:55:25Z"},{"status":"public","abstract":[{"lang":"eng","text":"This paper deals with the clipping method used in orthogonal frequency-division multiplexing (OFDM) systems to reduce the peak-to-average power ratio (PAPR). An iterative soft compensation method is proposed to mitigate the clipping distortion, which can outperform conventional treatments. The impact of signaling schemes on the residual clipping noise power is studied via the symbol variance analysis. It is found that superposition coded modulation (SCM) can minimize the residual clipping noise power among all possible signaling schemes. This indicates that SCM-based OFDM systems are more robust to clipping effect than other alternatives when soft compensation is applied. It is also shown that a multi-code SCM scheme can further reduce the clipping effect and its overall performance can be quickly evaluated using a semi-analytical evolution method. Numerical examples are provided to verify the analysis."}],"type":"journal_article","publication":"IEEE Trans.\\ Comm.","user_id":"43497","department":[{"_id":"263"}],"_id":"40844","citation":{"chicago":"Tong, Jun, Li Ping, Zhonghao Zhang, and Vijay K. Bhargava. “Iterative Soft Compensation for OFDM Systems with Clipping and Superposition Coded Modulation.” <i>IEEE Trans.\\ Comm.</i> 58, no. 10 (2010): 2861–2870. <a href=\"https://doi.org/10.1109/TCOMM.2010.083110.09296\">https://doi.org/10.1109/TCOMM.2010.083110.09296</a>.","ieee":"J. Tong, L. Ping, Z. Zhang, and V. K. Bhargava, “Iterative soft compensation for OFDM systems with clipping and superposition coded modulation,” <i>IEEE Trans.\\ Comm.</i>, vol. 58, no. 10, pp. 2861–2870, 2010, doi: <a href=\"https://doi.org/10.1109/TCOMM.2010.083110.09296\">10.1109/TCOMM.2010.083110.09296</a>.","ama":"Tong J, Ping L, Zhang Z, Bhargava VK. Iterative soft compensation for OFDM systems with clipping and superposition coded modulation. <i>IEEE Trans\\ Comm</i>. 2010;58(10):2861–2870. doi:<a href=\"https://doi.org/10.1109/TCOMM.2010.083110.09296\">10.1109/TCOMM.2010.083110.09296</a>","bibtex":"@article{Tong_Ping_Zhang_Bhargava_2010, title={Iterative soft compensation for OFDM systems with clipping and superposition coded modulation}, volume={58}, DOI={<a href=\"https://doi.org/10.1109/TCOMM.2010.083110.09296\">10.1109/TCOMM.2010.083110.09296</a>}, number={10}, journal={IEEE Trans.\\ Comm.}, author={Tong, Jun and Ping, Li and Zhang, Zhonghao and Bhargava, Vijay K.}, year={2010}, pages={2861–2870} }","short":"J. Tong, L. Ping, Z. Zhang, V.K. Bhargava, IEEE Trans.\\ Comm. 58 (2010) 2861–2870.","mla":"Tong, Jun, et al. “Iterative Soft Compensation for OFDM Systems with Clipping and Superposition Coded Modulation.” <i>IEEE Trans.\\ Comm.</i>, vol. 58, no. 10, 2010, pp. 2861–2870, doi:<a href=\"https://doi.org/10.1109/TCOMM.2010.083110.09296\">10.1109/TCOMM.2010.083110.09296</a>.","apa":"Tong, J., Ping, L., Zhang, Z., &#38; Bhargava, V. K. (2010). Iterative soft compensation for OFDM systems with clipping and superposition coded modulation. <i>IEEE Trans.\\ Comm.</i>, <i>58</i>(10), 2861–2870. <a href=\"https://doi.org/10.1109/TCOMM.2010.083110.09296\">https://doi.org/10.1109/TCOMM.2010.083110.09296</a>"},"intvolume":"        58","page":"2861–2870","year":"2010","issue":"10","doi":"10.1109/TCOMM.2010.083110.09296","title":"Iterative soft compensation for OFDM systems with clipping and superposition coded modulation","author":[{"full_name":"Tong, Jun","last_name":"Tong","first_name":"Jun"},{"full_name":"Ping, Li","last_name":"Ping","first_name":"Li"},{"full_name":"Zhang, Zhonghao","last_name":"Zhang","first_name":"Zhonghao"},{"first_name":"Vijay K.","last_name":"Bhargava","full_name":"Bhargava, Vijay K."}],"date_created":"2023-01-30T11:52:01Z","volume":58,"date_updated":"2023-01-30T11:57:00Z"},{"_id":"40845","user_id":"43497","department":[{"_id":"263"}],"abstract":[{"text":"It has been recently proved that the two main kinds of quaternion improperness require two different kinds of widely linear process- ing. In this work, we show that these definitions satisfy some im- portant properties, which include the invariance to quaternion lin- ear transformations and right Clifford translations, as well as some clear connections with the case of proper complex vectors. More- over, we introduce a new kind of quaternion properness, which clearly relates the two previous definitions, and propose three mea- sures for the degree of improperness of a quaternion vector. The proposed measures are based on the Kullback-Leibler divergence between two zero-mean quaternion Gaussian distributions, one of them with the actual augmented covariance matrix, and the other with its closest proper version. These measures allow us to quan- tify the entropy loss due to the improperness of the quaternion vec- tor, and they admit an intuitive geometrical interpretation based on Kullback-Leibler projections onto sets of proper augmented co- variance matrices.","lang":"eng"}],"status":"public","type":"conference","publication":"Proc.\\ IEEE Int.\\ Work. Machine Learning for Signal Process.","title":"Improperness Measures for Quaternion Random Vectors","doi":"10.1109/MLSP.2010.5589225","date_updated":"2023-01-30T11:56:58Z","author":[{"full_name":"Vía, J.","last_name":"Vía","first_name":"J."},{"last_name":"Ramírez","full_name":"Ramírez, D.","first_name":"D."},{"first_name":"I.","full_name":"Santamaría, I.","last_name":"Santamaría"},{"last_name":"Vielva","full_name":"Vielva, L.","first_name":"L."}],"date_created":"2023-01-30T11:52:01Z","place":"Finland","year":"2010","citation":{"ieee":"J. Vía, D. Ramírez, I. Santamaría, and L. Vielva, “Improperness Measures for Quaternion Random Vectors,” 2010, doi: <a href=\"https://doi.org/10.1109/MLSP.2010.5589225\">10.1109/MLSP.2010.5589225</a>.","chicago":"Vía, J., D. Ramírez, I. Santamaría, and L. Vielva. “Improperness Measures for Quaternion Random Vectors.” In <i>Proc.\\ IEEE Int.\\ Work. Machine Learning for Signal Process.</i> Finland, 2010. <a href=\"https://doi.org/10.1109/MLSP.2010.5589225\">https://doi.org/10.1109/MLSP.2010.5589225</a>.","ama":"Vía J, Ramírez D, Santamaría I, Vielva L. Improperness Measures for Quaternion Random Vectors. In: <i>Proc.\\ IEEE Int.\\ Work. Machine Learning for Signal Process.</i> ; 2010. doi:<a href=\"https://doi.org/10.1109/MLSP.2010.5589225\">10.1109/MLSP.2010.5589225</a>","apa":"Vía, J., Ramírez, D., Santamaría, I., &#38; Vielva, L. (2010). Improperness Measures for Quaternion Random Vectors. <i>Proc.\\ IEEE Int.\\ Work. Machine Learning for Signal Process.</i> <a href=\"https://doi.org/10.1109/MLSP.2010.5589225\">https://doi.org/10.1109/MLSP.2010.5589225</a>","mla":"Vía, J., et al. “Improperness Measures for Quaternion Random Vectors.” <i>Proc.\\ IEEE Int.\\ Work. Machine Learning for Signal Process.</i>, 2010, doi:<a href=\"https://doi.org/10.1109/MLSP.2010.5589225\">10.1109/MLSP.2010.5589225</a>.","bibtex":"@inproceedings{Vía_Ramírez_Santamaría_Vielva_2010, place={Finland}, title={Improperness Measures for Quaternion Random Vectors}, DOI={<a href=\"https://doi.org/10.1109/MLSP.2010.5589225\">10.1109/MLSP.2010.5589225</a>}, booktitle={Proc.\\ IEEE Int.\\ Work. Machine Learning for Signal Process.}, author={Vía, J. and Ramírez, D. and Santamaría, I. and Vielva, L.}, year={2010} }","short":"J. Vía, D. Ramírez, I. Santamaría, L. Vielva, in: Proc.\\ IEEE Int.\\ Work. Machine Learning for Signal Process., Finland, 2010."}},{"place":"Beijing, China","year":"2010","citation":{"mla":"Santamaría, Ignacio, et al. “Capacity Region of the Multiantenna Gaussian Broadcast Channel with Analog TX-RX Beamforming.” <i>Proc. Int. ICST Conf. Comm. and Networking in China</i>, 2010.","short":"I. Santamaría, J. Vía, A. Nazábal, C. Lameiro, in: Proc. Int. ICST Conf. Comm. and Networking in China, Beijing, China, 2010.","bibtex":"@inproceedings{Santamaría_Vía_Nazábal_Lameiro_2010, place={Beijing, China}, title={Capacity region of the multiantenna Gaussian broadcast channel with analog TX-RX beamforming}, booktitle={Proc. Int. ICST Conf. Comm. and Networking in China}, author={Santamaría, Ignacio and Vía, Javier and Nazábal, Alfredo and Lameiro, Christian}, year={2010} }","apa":"Santamaría, I., Vía, J., Nazábal, A., &#38; Lameiro, C. (2010). Capacity region of the multiantenna Gaussian broadcast channel with analog TX-RX beamforming. <i>Proc. Int. ICST Conf. Comm. and Networking in China</i>.","ama":"Santamaría I, Vía J, Nazábal A, Lameiro C. Capacity region of the multiantenna Gaussian broadcast channel with analog TX-RX beamforming. In: <i>Proc. Int. ICST Conf. Comm. and Networking in China</i>. ; 2010.","ieee":"I. Santamaría, J. Vía, A. Nazábal, and C. Lameiro, “Capacity region of the multiantenna Gaussian broadcast channel with analog TX-RX beamforming,” 2010.","chicago":"Santamaría, Ignacio, Javier Vía, Alfredo Nazábal, and Christian Lameiro. “Capacity Region of the Multiantenna Gaussian Broadcast Channel with Analog TX-RX Beamforming.” In <i>Proc. Int. ICST Conf. Comm. and Networking in China</i>. Beijing, China, 2010."},"date_updated":"2023-01-30T11:56:55Z","author":[{"full_name":"Santamaría, Ignacio","last_name":"Santamaría","first_name":"Ignacio"},{"last_name":"Vía","full_name":"Vía, Javier","first_name":"Javier"},{"first_name":"Alfredo","full_name":"Nazábal, Alfredo","last_name":"Nazábal"},{"last_name":"Lameiro","full_name":"Lameiro, Christian","first_name":"Christian"}],"date_created":"2023-01-30T11:52:01Z","title":"Capacity region of the multiantenna Gaussian broadcast channel with analog TX-RX beamforming","publication":"Proc. Int. ICST Conf. Comm. and Networking in China","type":"conference","abstract":[{"text":"In this paper we characterize the capacity boundary of the two-user multiple-input multiple-output (MIMO) broadcast channel (BC) when the multiantenna terminals use analog beamforming at both sides of the link. Basically, the problem reduces to finding the optimal transmit direction and the optimal power allocation between users to operate at any point on the boundary. We show that both optimization problems can be solved in closed form. First, exploiting the fact that any Pareto optimal pair of rates must also be Pareto optimal of a convex region defined by the channel energies, the optimal transmit direction is shown to be the principal eigenvector of a matrix. Second, the optimal power allocation is obtained by exploiting again the Pareto optimality of the sought pair of rates. Although this paper focuses on the BC, the obtained results also serve to characterize the dual multiple-access channel (MAC). Moreover, this explicit characterization of the boundary can be extended to a $K$-user system for $K>2$. Numerical examples are provided to illustrate the results of the paper, and to show the enlargement of the capacity region achieved by analog beamforming in comparison to a single-input single-output (SISO) BC.","lang":"eng"}],"status":"public","_id":"40846","department":[{"_id":"263"}],"user_id":"43497"},{"doi":"10.1109/ICASSP.2009.4960395","title":"On ICA of improper and noncircular sources","author":[{"first_name":"Peter J.","last_name":"Schreier","full_name":"Schreier, Peter J."},{"first_name":"Tülay","full_name":"Adali, Tülay","last_name":"Adali"},{"first_name":"Louis L.","full_name":"Scharf, Louis L.","last_name":"Scharf"}],"date_created":"2023-01-30T11:52:02Z","date_updated":"2023-01-30T11:55:45Z","citation":{"short":"P.J. Schreier, T. Adali, L.L. Scharf, in: Proc.\\ IEEE Int.\\ Conf.\\ Acoustics, Speech and Signal Process., 2009, pp. 3561–3564.","bibtex":"@inproceedings{Schreier_Adali_Scharf_2009, title={On ICA of improper and noncircular sources}, DOI={<a href=\"https://doi.org/10.1109/ICASSP.2009.4960395\">10.1109/ICASSP.2009.4960395</a>}, booktitle={Proc.\\ IEEE Int.\\ Conf.\\ Acoustics, Speech and Signal Process.}, author={Schreier, Peter J. and Adali, Tülay and Scharf, Louis L.}, year={2009}, pages={3561–3564} }","mla":"Schreier, Peter J., et al. “On ICA of Improper and Noncircular Sources.” <i>Proc.\\ IEEE Int.\\ Conf.\\ Acoustics, Speech and Signal Process.</i>, 2009, pp. 3561–3564, doi:<a href=\"https://doi.org/10.1109/ICASSP.2009.4960395\">10.1109/ICASSP.2009.4960395</a>.","apa":"Schreier, P. J., Adali, T., &#38; Scharf, L. L. (2009). On ICA of improper and noncircular sources. <i>Proc.\\ IEEE Int.\\ Conf.\\ Acoustics, Speech and Signal Process.</i>, 3561–3564. <a href=\"https://doi.org/10.1109/ICASSP.2009.4960395\">https://doi.org/10.1109/ICASSP.2009.4960395</a>","ama":"Schreier PJ, Adali T, Scharf LL. On ICA of improper and noncircular sources. In: <i>Proc.\\ IEEE Int.\\ Conf.\\ Acoustics, Speech and Signal Process.</i> ; 2009:3561–3564. doi:<a href=\"https://doi.org/10.1109/ICASSP.2009.4960395\">10.1109/ICASSP.2009.4960395</a>","chicago":"Schreier, Peter J., Tülay Adali, and Louis L. Scharf. “On ICA of Improper and Noncircular Sources.” In <i>Proc.\\ IEEE Int.\\ Conf.\\ Acoustics, Speech and Signal Process.</i>, 3561–3564, 2009. <a href=\"https://doi.org/10.1109/ICASSP.2009.4960395\">https://doi.org/10.1109/ICASSP.2009.4960395</a>.","ieee":"P. J. Schreier, T. Adali, and L. L. Scharf, “On ICA of improper and noncircular sources,” in <i>Proc.\\ IEEE Int.\\ Conf.\\ Acoustics, Speech and Signal Process.</i>, 2009, pp. 3561–3564, doi: <a href=\"https://doi.org/10.1109/ICASSP.2009.4960395\">10.1109/ICASSP.2009.4960395</a>."},"page":"3561–3564","year":"2009","user_id":"43497","department":[{"_id":"263"}],"_id":"40857","status":"public","abstract":[{"text":"We provide a review of independent component analysis (ICA) for complex-valued improper and noncircular random sources. An improper random signal is correlated with its complex conjugate, and a noncircular random signal has a rotationally variant probability distribution. We present methods for ICA using second-order statistics, and higher-order statistics. For ICA based on second-order statistics, we emphasize the key role played by the circularity coefficients, which are the canonical correlations between the source and the complex conjugate. For ICA based on higher-order statistics, we show how to extend algorithms for real-valued ICA to the complex domain using Wirtinger calculus.","lang":"eng"}],"type":"conference","publication":"Proc.\\ IEEE Int.\\ Conf.\\ Acoustics, Speech and Signal Process."},{"citation":{"ama":"Wahlberg P, Schreier PJ. Gabor discretization of the Weyl product for modulation spaces and filtering of nonstationary stochastic processes. <i>Appl\\ Comput\\ Harmon\\ Anal</i>. 2009;26(1):97–120. doi:<a href=\"https://doi.org/10.1016/j.acha.2008.02.005\">10.1016/j.acha.2008.02.005</a>","chicago":"Wahlberg, Patrik, and Peter J. Schreier. “Gabor Discretization of the Weyl Product for Modulation Spaces and Filtering of Nonstationary Stochastic Processes.” <i>Appl.\\ Comput.\\ Harmon.\\ Anal.</i> 26, no. 1 (2009): 97–120. <a href=\"https://doi.org/10.1016/j.acha.2008.02.005\">https://doi.org/10.1016/j.acha.2008.02.005</a>.","ieee":"P. Wahlberg and P. J. Schreier, “Gabor discretization of the Weyl product for modulation spaces and filtering of nonstationary stochastic processes,” <i>Appl.\\ Comput.\\ Harmon.\\ Anal.</i>, vol. 26, no. 1, pp. 97–120, 2009, doi: <a href=\"https://doi.org/10.1016/j.acha.2008.02.005\">10.1016/j.acha.2008.02.005</a>.","apa":"Wahlberg, P., &#38; Schreier, P. J. (2009). Gabor discretization of the Weyl product for modulation spaces and filtering of nonstationary stochastic processes. <i>Appl.\\ Comput.\\ Harmon.\\ Anal.</i>, <i>26</i>(1), 97–120. <a href=\"https://doi.org/10.1016/j.acha.2008.02.005\">https://doi.org/10.1016/j.acha.2008.02.005</a>","short":"P. Wahlberg, P.J. Schreier, Appl.\\ Comput.\\ Harmon.\\ Anal. 26 (2009) 97–120.","bibtex":"@article{Wahlberg_Schreier_2009, title={Gabor discretization of the Weyl product for modulation spaces and filtering of nonstationary stochastic processes}, volume={26}, DOI={<a href=\"https://doi.org/10.1016/j.acha.2008.02.005\">10.1016/j.acha.2008.02.005</a>}, number={1}, journal={Appl.\\ Comput.\\ Harmon.\\ Anal.}, author={Wahlberg, Patrik and Schreier, Peter J.}, year={2009}, pages={97–120} }","mla":"Wahlberg, Patrik, and Peter J. Schreier. “Gabor Discretization of the Weyl Product for Modulation Spaces and Filtering of Nonstationary Stochastic Processes.” <i>Appl.\\ Comput.\\ Harmon.\\ Anal.</i>, vol. 26, no. 1, 2009, pp. 97–120, doi:<a href=\"https://doi.org/10.1016/j.acha.2008.02.005\">10.1016/j.acha.2008.02.005</a>."},"page":"97–120","intvolume":"        26","year":"2009","issue":"1","doi":"10.1016/j.acha.2008.02.005","title":"Gabor discretization of the Weyl product for modulation spaces and filtering of nonstationary stochastic processes","author":[{"full_name":"Wahlberg, Patrik","last_name":"Wahlberg","first_name":"Patrik"},{"full_name":"Schreier, Peter J.","last_name":"Schreier","first_name":"Peter J."}],"date_created":"2023-01-30T11:52:02Z","volume":26,"date_updated":"2023-01-30T11:55:43Z","status":"public","type":"journal_article","publication":"Appl.\\ Comput.\\ Harmon.\\ Anal.","user_id":"43497","department":[{"_id":"263"}],"_id":"40851"}]