## 2015 |

Bravo-Santos, Ángel M; Djuric, Petar M Detectors for Cooperative Mesh Networks with Decode-and-Forward Relays Journal Article IEEE Transactions on Signal Processing, 63 (1), pp. 5–17, 2015, ISSN: 1053-587X. Abstract | Links | BibTeX | Tags: Cooperative systems, Detectors, Mesh networks, Modulation, Relays, spread spectrum communication, Wireless communication @article{Bravo-Santos2014b, title = {Detectors for Cooperative Mesh Networks with Decode-and-Forward Relays}, author = {Ángel M Bravo-Santos and Petar M Djuric}, url = {http://ieeexplore.ieee.org/xpl/articleDetails.jsp?arnumber=6928514}, doi = {10.1109/TSP.2014.2364016}, issn = {1053-587X}, year = {2015}, date = {2015-01-01}, journal = {IEEE Transactions on Signal Processing}, volume = {63}, number = {1}, pages = {5--17}, publisher = {IEEE}, abstract = {We consider mesh networks composed of groups of relaying nodes which operate in decode-andforward mode. Each node from a group relays information to all the nodes in the next group. We study these networks in two setups, one where the nodes have complete state information about the channels through which they receive the signals, and another when they only have the statistics of the channels. We derive recursive expressions for the probabilities of errors of the nodes and present several implementations of detectors used in these networks. We compare the mesh networks with multi-hop networks formed by a set of parallel sections of multiple relaying nodes. We demonstrate with numerous simulations that there are significant improvements in performance of mesh over multi-hop networks in various scenarios.}, keywords = {Cooperative systems, Detectors, Mesh networks, Modulation, Relays, spread spectrum communication, Wireless communication}, pubstate = {published}, tppubtype = {article} } We consider mesh networks composed of groups of relaying nodes which operate in decode-andforward mode. Each node from a group relays information to all the nodes in the next group. We study these networks in two setups, one where the nodes have complete state information about the channels through which they receive the signals, and another when they only have the statistics of the channels. We derive recursive expressions for the probabilities of errors of the nodes and present several implementations of detectors used in these networks. We compare the mesh networks with multi-hop networks formed by a set of parallel sections of multiple relaying nodes. We demonstrate with numerous simulations that there are significant improvements in performance of mesh over multi-hop networks in various scenarios. |

Bravo-Santos, Ángel M; Djuric, Petar M Detectors for Cooperative Mesh Networks with Decode-and-Forward Relays Journal Article IEEE Transactions on Signal Processing, 63 (1), pp. 5–17, 2015, ISSN: 1053-587X. Abstract | Links | BibTeX | Tags: Cooperative systems, Detectors, Journal, Mesh networks, Modulation, Relays, spread spectrum communication, Wireless communication @article{Bravo-Santos2014bb, title = {Detectors for Cooperative Mesh Networks with Decode-and-Forward Relays}, author = {Ángel M Bravo-Santos and Petar M Djuric}, url = {http://ieeexplore.ieee.org/articleDetails.jsp?arnumber=6928514}, doi = {10.1109/TSP.2014.2364016}, issn = {1053-587X}, year = {2015}, date = {2015-01-01}, journal = {IEEE Transactions on Signal Processing}, volume = {63}, number = {1}, pages = {5--17}, publisher = {IEEE}, abstract = {We consider mesh networks composed of groups of relaying nodes which operate in decode-andforward mode. Each node from a group relays information to all the nodes in the next group. We study these networks in two setups, one where the nodes have complete state information about the channels through which they receive the signals, and another when they only have the statistics of the channels. We derive recursive expressions for the probabilities of errors of the nodes and present several implementations of detectors used in these networks. We compare the mesh networks with multi-hop networks formed by a set of parallel sections of multiple relaying nodes. We demonstrate with numerous simulations that there are significant improvements in performance of mesh over multi-hop networks in various scenarios.}, keywords = {Cooperative systems, Detectors, Journal, Mesh networks, Modulation, Relays, spread spectrum communication, Wireless communication}, pubstate = {published}, tppubtype = {article} } We consider mesh networks composed of groups of relaying nodes which operate in decode-andforward mode. Each node from a group relays information to all the nodes in the next group. We study these networks in two setups, one where the nodes have complete state information about the channels through which they receive the signals, and another when they only have the statistics of the channels. We derive recursive expressions for the probabilities of errors of the nodes and present several implementations of detectors used in these networks. We compare the mesh networks with multi-hop networks formed by a set of parallel sections of multiple relaying nodes. We demonstrate with numerous simulations that there are significant improvements in performance of mesh over multi-hop networks in various scenarios. |

## 2014 |

Alvarado, Alex; Brannstrom, Fredrik; Agrell, Erik; Koch, Tobias High-SNR Asymptotics of Mutual Information for Discrete Constellations With Applications to BICM Journal Article IEEE Transactions on Information Theory, 60 (2), pp. 1061–1076, 2014, ISSN: 0018-9448. Abstract | Links | BibTeX | Tags: additive white Gaussian noise channel, Anti-Gray code, bit-interleaved coded modulation, discrete constellations, Entropy, Gray code, high-SNR asymptotics, IP networks, Labeling, minimum-mean square error, Modulation, Mutual information, Signal to noise ratio, Vectors @article{Alvarado2014, title = {High-SNR Asymptotics of Mutual Information for Discrete Constellations With Applications to BICM}, author = {Alex Alvarado and Fredrik Brannstrom and Erik Agrell and Tobias Koch}, url = {http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=6671479 http://www.tsc.uc3m.es/~koch/files/IEEE_TIT_60%282%29.pdf}, issn = {0018-9448}, year = {2014}, date = {2014-01-01}, journal = {IEEE Transactions on Information Theory}, volume = {60}, number = {2}, pages = {1061--1076}, abstract = {Asymptotic expressions of the mutual information between any discrete input and the corresponding output of the scalar additive white Gaussian noise channel are presented in the limit as the signal-to-noise ratio (SNR) tends to infinity. Asymptotic expressions of the symbol-error probability (SEP) and the minimum mean-square error (MMSE) achieved by estimating the channel input given the channel output are also developed. It is shown that for any input distribution, the conditional entropy of the channel input given the output, MMSE, and SEP have an asymptotic behavior proportional to the Gaussian Q-function. The argument of the Q-function depends only on the minimum Euclidean distance (MED) of the constellation and the SNR, and the proportionality constants are functions of the MED and the probabilities of the pairs of constellation points at MED. The developed expressions are then generalized to study the high-SNR behavior of the generalized mutual information (GMI) for bit-interleaved coded modulation (BICM). By means of these asymptotic expressions, the long-standing conjecture that Gray codes are the binary labelings that maximize the BICM-GMI at high SNR is proven. It is further shown that for any equally spaced constellation whose size is a power of two, there always exists an anti-Gray code giving the lowest BICM-GMI at high SNR.}, keywords = {additive white Gaussian noise channel, Anti-Gray code, bit-interleaved coded modulation, discrete constellations, Entropy, Gray code, high-SNR asymptotics, IP networks, Labeling, minimum-mean square error, Modulation, Mutual information, Signal to noise ratio, Vectors}, pubstate = {published}, tppubtype = {article} } Asymptotic expressions of the mutual information between any discrete input and the corresponding output of the scalar additive white Gaussian noise channel are presented in the limit as the signal-to-noise ratio (SNR) tends to infinity. Asymptotic expressions of the symbol-error probability (SEP) and the minimum mean-square error (MMSE) achieved by estimating the channel input given the channel output are also developed. It is shown that for any input distribution, the conditional entropy of the channel input given the output, MMSE, and SEP have an asymptotic behavior proportional to the Gaussian Q-function. The argument of the Q-function depends only on the minimum Euclidean distance (MED) of the constellation and the SNR, and the proportionality constants are functions of the MED and the probabilities of the pairs of constellation points at MED. The developed expressions are then generalized to study the high-SNR behavior of the generalized mutual information (GMI) for bit-interleaved coded modulation (BICM). By means of these asymptotic expressions, the long-standing conjecture that Gray codes are the binary labelings that maximize the BICM-GMI at high SNR is proven. It is further shown that for any equally spaced constellation whose size is a power of two, there always exists an anti-Gray code giving the lowest BICM-GMI at high SNR. |

## 2012 |

Salamanca, Luis; Murillo-Fuentes, Juan Jose; Perez-Cruz, Fernando Bayesian Equalization for LDPC Channel Decoding Journal Article IEEE Transactions on Signal Processing, 60 (5), pp. 2672–2676, 2012, ISSN: 1053-587X. Abstract | Links | BibTeX | Tags: Approximation methods, Bayes methods, Bayesian equalization, Bayesian estimation problem, Bayesian inference, Bayesian methods, BCJR (Bahl–Cocke–Jelinek–Raviv) algorithm, BCJR algorithm, Channel Coding, channel decoding, channel equalization, channel equalization problem, Channel estimation, channel state information, CSI, Decoding, equalisers, Equalizers, expectation propagation, expectation propagation algorithm, fading channels, graphical model representation, intersymbol interference, Kullback-Leibler divergence, LDPC, LDPC coding, low-density parity-check decoder, Modulation, parity check codes, symbol posterior estimates, Training @article{Salamanca2012b, title = {Bayesian Equalization for LDPC Channel Decoding}, author = {Luis Salamanca and Juan Jose Murillo-Fuentes and Fernando Perez-Cruz}, url = {http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=6129544}, issn = {1053-587X}, year = {2012}, date = {2012-01-01}, journal = {IEEE Transactions on Signal Processing}, volume = {60}, number = {5}, pages = {2672--2676}, abstract = {We describe the channel equalization problem, and its prior estimate of the channel state information (CSI), as a joint Bayesian estimation problem to improve each symbol posterior estimates at the input of the channel decoder. Our approach takes into consideration not only the uncertainty due to the noise in the channel, but also the uncertainty in the CSI estimate. However, this solution cannot be computed in linear time, because it depends on all the transmitted symbols. Hence, we also put forward an approximation for each symbol's posterior, using the expectation propagation algorithm, which is optimal from the Kullback-Leibler divergence viewpoint and yields an equalization with a complexity identical to the BCJR algorithm. We also use a graphical model representation of the full posterior, in which the proposed approximation can be readily understood. The proposed posterior estimates are more accurate than those computed using the ML estimate for the CSI. In order to illustrate this point, we measure the error rate at the output of a low-density parity-check decoder, which needs the exact posterior for each symbol to detect the incoming word and it is sensitive to a mismatch in those posterior estimates. For example, for QPSK modulation and a channel with three taps, we can expect gains over 0.5 dB with same computational complexity as the ML receiver.}, keywords = {Approximation methods, Bayes methods, Bayesian equalization, Bayesian estimation problem, Bayesian inference, Bayesian methods, BCJR (Bahl–Cocke–Jelinek–Raviv) algorithm, BCJR algorithm, Channel Coding, channel decoding, channel equalization, channel equalization problem, Channel estimation, channel state information, CSI, Decoding, equalisers, Equalizers, expectation propagation, expectation propagation algorithm, fading channels, graphical model representation, intersymbol interference, Kullback-Leibler divergence, LDPC, LDPC coding, low-density parity-check decoder, Modulation, parity check codes, symbol posterior estimates, Training}, pubstate = {published}, tppubtype = {article} } We describe the channel equalization problem, and its prior estimate of the channel state information (CSI), as a joint Bayesian estimation problem to improve each symbol posterior estimates at the input of the channel decoder. Our approach takes into consideration not only the uncertainty due to the noise in the channel, but also the uncertainty in the CSI estimate. However, this solution cannot be computed in linear time, because it depends on all the transmitted symbols. Hence, we also put forward an approximation for each symbol's posterior, using the expectation propagation algorithm, which is optimal from the Kullback-Leibler divergence viewpoint and yields an equalization with a complexity identical to the BCJR algorithm. We also use a graphical model representation of the full posterior, in which the proposed approximation can be readily understood. The proposed posterior estimates are more accurate than those computed using the ML estimate for the CSI. In order to illustrate this point, we measure the error rate at the output of a low-density parity-check decoder, which needs the exact posterior for each symbol to detect the incoming word and it is sensitive to a mismatch in those posterior estimates. For example, for QPSK modulation and a channel with three taps, we can expect gains over 0.5 dB with same computational complexity as the ML receiver. |

Cruz-Roldan, Fernando; Dominguez-Jimenez, María Elena; Vidal, Gabriela Sansigre; Amo-Lopez, Pedro; Blanco-Velasco, Manuel; Bravo-Santos, Ángel M On the Use of Discrete Cosine Transforms for Multicarrier Communications Journal Article IEEE Transactions on Signal Processing, 60 (11), pp. 6085–6090, 2012, ISSN: 1053-587X. Abstract | Links | BibTeX | Tags: broadband networks, carrier frequency offset, Carrier-frequency offset (CFO), CFO, channel equalization, computer simulations, Convolution, Data communication, data symbol, DCT, DFT, discrete cosine transform (DCT), discrete cosine transform domain, Discrete cosine transforms, discrete Fourier transforms, discrete multitone modulation (DMT), discrete trigonometric domain, element-by-element multiplication, equalisers, equivalent channel impulse response, linear convolution, mobile broadband wireless communication, mobile radio, Modulation, multicarrier communications, multicarrier data transmission, multicarrier modulation (MCM), multicarrier transceiver, OFDM, orthogonal frequency-division multiplexing (OFDM), Receivers, Redundancy, subcarrier equalizers, symmetric convolution-multiplication property, symmetric redundancy, time-domain analysis, transient response, transmission channel @article{Cruz-Roldan2012, title = {On the Use of Discrete Cosine Transforms for Multicarrier Communications}, author = {Fernando Cruz-Roldan and María Elena Dominguez-Jimenez and Gabriela Sansigre Vidal and Pedro Amo-Lopez and Manuel Blanco-Velasco and Ángel M Bravo-Santos}, url = {http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=6252068}, issn = {1053-587X}, year = {2012}, date = {2012-01-01}, journal = {IEEE Transactions on Signal Processing}, volume = {60}, number = {11}, pages = {6085--6090}, abstract = {In this correspondence, the conditions to use any kind of discrete cosine transform (DCT) for multicarrier data transmission are derived. The symmetric convolution-multiplication property of each DCT implies that when symmetric convolution is performed in the time domain, an element-by-element multiplication is performed in the corresponding discrete trigonometric domain. Therefore, appending symmetric redundancy (as prefix and suffix) into each data symbol to be transmitted, and also enforcing symmetry for the equivalent channel impulse response, the linear convolution performed in the transmission channel becomes a symmetric convolution in those samples of interest. Furthermore, the channel equalization can be carried out by means of a bank of scalars in the corresponding discrete cosine transform domain. The expressions for obtaining the value of each scalar corresponding to these one-tap per subcarrier equalizers are presented. This study is completed with several computer simulations in mobile broadband wireless communication scenarios, considering the presence of carrier frequency offset (CFO). The obtained results indicate that the proposed systems outperform the standardized ones based on the DFT.}, keywords = {broadband networks, carrier frequency offset, Carrier-frequency offset (CFO), CFO, channel equalization, computer simulations, Convolution, Data communication, data symbol, DCT, DFT, discrete cosine transform (DCT), discrete cosine transform domain, Discrete cosine transforms, discrete Fourier transforms, discrete multitone modulation (DMT), discrete trigonometric domain, element-by-element multiplication, equalisers, equivalent channel impulse response, linear convolution, mobile broadband wireless communication, mobile radio, Modulation, multicarrier communications, multicarrier data transmission, multicarrier modulation (MCM), multicarrier transceiver, OFDM, orthogonal frequency-division multiplexing (OFDM), Receivers, Redundancy, subcarrier equalizers, symmetric convolution-multiplication property, symmetric redundancy, time-domain analysis, transient response, transmission channel}, pubstate = {published}, tppubtype = {article} } In this correspondence, the conditions to use any kind of discrete cosine transform (DCT) for multicarrier data transmission are derived. The symmetric convolution-multiplication property of each DCT implies that when symmetric convolution is performed in the time domain, an element-by-element multiplication is performed in the corresponding discrete trigonometric domain. Therefore, appending symmetric redundancy (as prefix and suffix) into each data symbol to be transmitted, and also enforcing symmetry for the equivalent channel impulse response, the linear convolution performed in the transmission channel becomes a symmetric convolution in those samples of interest. Furthermore, the channel equalization can be carried out by means of a bank of scalars in the corresponding discrete cosine transform domain. The expressions for obtaining the value of each scalar corresponding to these one-tap per subcarrier equalizers are presented. This study is completed with several computer simulations in mobile broadband wireless communication scenarios, considering the presence of carrier frequency offset (CFO). The obtained results indicate that the proposed systems outperform the standardized ones based on the DFT. |