## 2012 |

## Inproceedings |

O'Mahony, Niamh; Perez-Cruz, Fernando A novel Sequential Bayesian Approach to GPS Acquisition (Inproceeding) 2012 3rd International Workshop on Cognitive Information Processing (CIP), pp. 1–6, IEEE, Baiona, 2012, ISBN: 978-1-4673-1878-5. (Abstract | Links | BibTeX | Tags: Bayes methods, coarse synchronization, Correlators, data acquisition, Delay, Doppler effect, Global Positioning System, GPS acquisition, GPS signal parameters, learning (artificial intelligence), online learning algorithm, Receivers, Satellites, sequential Bayesian approach, signal acquisition, signal detection, Synchronization) @inproceedings{O'Mahony2012, title = {A novel Sequential Bayesian Approach to GPS Acquisition}, author = {O'Mahony, Niamh and Perez-Cruz, Fernando}, url = {http://ieeexplore.ieee.org/articleDetails.jsp?arnumber=6232921}, isbn = {978-1-4673-1878-5}, year = {2012}, date = {2012-01-01}, booktitle = {2012 3rd International Workshop on Cognitive Information Processing (CIP)}, pages = {1--6}, publisher = {IEEE}, address = {Baiona}, abstract = {In this work, a novel online learning algorithm is presented for the synchronization of Global Positioning System (GPS) signal parameters at the acquisition, or coarse synchronization, stage. The algorithm is based on a Bayesian approach, which has, to date, not been exploited for the acquisition problem. Simulated results are presented to illustrate the algorithm performance, in terms of accuracy and acquisition time, along with results from the acquisition of signals from live GPS satellites using both the new algorithm and a state-of-the-art approach for comparison.}, keywords = {Bayes methods, coarse synchronization, Correlators, data acquisition, Delay, Doppler effect, Global Positioning System, GPS acquisition, GPS signal parameters, learning (artificial intelligence), online learning algorithm, Receivers, Satellites, sequential Bayesian approach, signal acquisition, signal detection, Synchronization}, pubstate = {published}, tppubtype = {inproceedings} } In this work, a novel online learning algorithm is presented for the synchronization of Global Positioning System (GPS) signal parameters at the acquisition, or coarse synchronization, stage. The algorithm is based on a Bayesian approach, which has, to date, not been exploited for the acquisition problem. Simulated results are presented to illustrate the algorithm performance, in terms of accuracy and acquisition time, along with results from the acquisition of signals from live GPS satellites using both the new algorithm and a state-of-the-art approach for comparison. |

## 2010 |

## Journal Articles |

Koch, Tobias; Lapidoth, Amos On Multipath Fading Channels at High SNR (Journal Article) IEEE Transactions on Information Theory, 56 (12), pp. 5945–5957, 2010, ISSN: 0018-9448. (Abstract | Links | BibTeX | Tags: approximation theory, capacity pre-loglog, capacity to loglog, channel capacity, channels with memory, Delay, Fading, fading channels, frequency-selective fading, high signal-to-noise ratio, high SNR, Limiting, multipath, multipath channels, noncoherent, noncoherent multipath fading channel, Receivers, Signal to noise ratio, signal-to-noise ratio, Transmitters) @article{Koch2010b, title = {On Multipath Fading Channels at High SNR}, author = {Koch, Tobias and Lapidoth, Amos}, url = {http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=5625630}, issn = {0018-9448}, year = {2010}, date = {2010-01-01}, journal = {IEEE Transactions on Information Theory}, volume = {56}, number = {12}, pages = {5945--5957}, abstract = {A noncoherent multipath fading channel is considered, where neither the transmitter nor the receiver is cognizant of the realization of the path gains, but both are cognizant of their statistics. It is shown that if the delay spread is large in the sense that the variances of the path gains decay exponentially or slower, then capacity is bounded in the signal-to-noise ratio (SNR). For such channels, capacity does not tend to infinity as the SNR tends to infinity. In contrast, if the variances of the path gains decay faster than exponentially, then capacity is unbounded in the SNR. It is further demonstrated that if the number of paths is finite, then at high SNR capacity grows double-logarithmically with the SNR, and the capacity pre-loglog-defined as the limiting ratio of capacity to loglog(SNR) as the SNR tends to infinity-is 1 irrespective of the number of paths. The results demonstrate that at high SNR multipath fading channels with an infinite number of paths cannot be approximated by multipath fading channels with only a finite number of paths. The number of paths that are needed to approximate a multipath fading channel typically depends on the SNR and may grow to infinity as the SNR tends to infinity.}, keywords = {approximation theory, capacity pre-loglog, capacity to loglog, channel capacity, channels with memory, Delay, Fading, fading channels, frequency-selective fading, high signal-to-noise ratio, high SNR, Limiting, multipath, multipath channels, noncoherent, noncoherent multipath fading channel, Receivers, Signal to noise ratio, signal-to-noise ratio, Transmitters}, pubstate = {published}, tppubtype = {article} } A noncoherent multipath fading channel is considered, where neither the transmitter nor the receiver is cognizant of the realization of the path gains, but both are cognizant of their statistics. It is shown that if the delay spread is large in the sense that the variances of the path gains decay exponentially or slower, then capacity is bounded in the signal-to-noise ratio (SNR). For such channels, capacity does not tend to infinity as the SNR tends to infinity. In contrast, if the variances of the path gains decay faster than exponentially, then capacity is unbounded in the SNR. It is further demonstrated that if the number of paths is finite, then at high SNR capacity grows double-logarithmically with the SNR, and the capacity pre-loglog-defined as the limiting ratio of capacity to loglog(SNR) as the SNR tends to infinity-is 1 irrespective of the number of paths. The results demonstrate that at high SNR multipath fading channels with an infinite number of paths cannot be approximated by multipath fading channels with only a finite number of paths. The number of paths that are needed to approximate a multipath fading channel typically depends on the SNR and may grow to infinity as the SNR tends to infinity. |

## 2008 |

## Inproceedings |

Koch, Tobias; Lapidoth, Amos On Multipath Fading Channels at High SNR (Inproceeding) 2008 IEEE International Symposium on Information Theory, pp. 1572–1576, IEEE, Toronto, 2008, ISBN: 978-1-4244-2256-2. (Abstract | Links | BibTeX | Tags: channel capacity, Delay, discrete time systems, discrete-time channels, Entropy, Fading, fading channels, Frequency, Mathematical model, multipath channels, multipath fading channels, noncoherent channel model, Random variables, Signal to noise ratio, signal-to-noise ratios, SNR, statistics, Transmitters) @inproceedings{Koch2008, title = {On Multipath Fading Channels at High SNR}, author = {Koch, Tobias and Lapidoth, Amos}, url = {http://ieeexplore.ieee.org/articleDetails.jsp?arnumber=4595252}, isbn = {978-1-4244-2256-2}, year = {2008}, date = {2008-01-01}, booktitle = {2008 IEEE International Symposium on Information Theory}, pages = {1572--1576}, publisher = {IEEE}, address = {Toronto}, abstract = {This paper studies the capacity of discrete-time multipath fading channels. It is assumed that the number of paths is finite, i.e., that the channel output is influenced by the present and by the L previous channel inputs. A noncoherent channel model is considered where neither transmitter nor receiver are cognizant of the fading's realization, but both are aware of its statistic. The focus is on capacity at high signal-to-noise ratios (SNR). In particular, the capacity pre-loglog-defined as the limiting ratio of the capacity to loglog(SNR) as SNR tends to infinity-is studied. It is shown that, irrespective of the number of paths L, the capacity pre-loglog is 1.}, keywords = {channel capacity, Delay, discrete time systems, discrete-time channels, Entropy, Fading, fading channels, Frequency, Mathematical model, multipath channels, multipath fading channels, noncoherent channel model, Random variables, Signal to noise ratio, signal-to-noise ratios, SNR, statistics, Transmitters}, pubstate = {published}, tppubtype = {inproceedings} } This paper studies the capacity of discrete-time multipath fading channels. It is assumed that the number of paths is finite, i.e., that the channel output is influenced by the present and by the L previous channel inputs. A noncoherent channel model is considered where neither transmitter nor receiver are cognizant of the fading's realization, but both are aware of its statistic. The focus is on capacity at high signal-to-noise ratios (SNR). In particular, the capacity pre-loglog-defined as the limiting ratio of the capacity to loglog(SNR) as SNR tends to infinity-is studied. It is shown that, irrespective of the number of paths L, the capacity pre-loglog is 1. |