## 2010 |

## Journal Articles |

Koch, Tobias; Lapidoth, Amos Gaussian Fading Is the Worst Fading (Journal Article) IEEE Transactions on Information Theory, 56 (3), pp. 1158–1165, 2010, ISSN: 0018-9448. (Abstract | Links | BibTeX | Tags: Additive noise, channel capacity, channels with memory, Distribution functions, ergodic fading processes, Fading, fading channels, flat fading, flat-fading channel capacity, Gaussian channels, Gaussian fading, Gaussian processes, H infinity control, high signal-to-noise ratio (SNR), Information technology, information theory, multiple-input single-output fading channels, multiplexing gain, noncoherent, noncoherent channel capacity, peak-power limited channel capacity, Signal to noise ratio, signal-to-noise ratio, single-antenna channel capacity, spectral distribution function, time-selective, Transmitters) @article{Koch2010a, title = {Gaussian Fading Is the Worst Fading}, author = {Koch, Tobias and Lapidoth, Amos}, url = {http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=5429105}, issn = {0018-9448}, year = {2010}, date = {2010-01-01}, journal = {IEEE Transactions on Information Theory}, volume = {56}, number = {3}, pages = {1158--1165}, abstract = {The capacity of peak-power limited, single-antenna, noncoherent, flat-fading channels with memory is considered. The emphasis is on the capacity pre-log, i.e., on the limiting ratio of channel capacity to the logarithm of the signal-to-noise ratio (SNR), as the SNR tends to infinity. It is shown that, among all stationary and ergodic fading processes of a given spectral distribution function and whose law has no mass point at zero, the Gaussian process gives rise to the smallest pre-log. The assumption that the law of the fading process has no mass point at zero is essential in the sense that there exist stationary and ergodic fading processes whose law has a mass point at zero and that give rise to a smaller pre-log than the Gaussian process of equal spectral distribution function. An extension of these results to multiple-input single-output (MISO) fading channels with memory is also presented.}, keywords = {Additive noise, channel capacity, channels with memory, Distribution functions, ergodic fading processes, Fading, fading channels, flat fading, flat-fading channel capacity, Gaussian channels, Gaussian fading, Gaussian processes, H infinity control, high signal-to-noise ratio (SNR), Information technology, information theory, multiple-input single-output fading channels, multiplexing gain, noncoherent, noncoherent channel capacity, peak-power limited channel capacity, Signal to noise ratio, signal-to-noise ratio, single-antenna channel capacity, spectral distribution function, time-selective, Transmitters}, pubstate = {published}, tppubtype = {article} } The capacity of peak-power limited, single-antenna, noncoherent, flat-fading channels with memory is considered. The emphasis is on the capacity pre-log, i.e., on the limiting ratio of channel capacity to the logarithm of the signal-to-noise ratio (SNR), as the SNR tends to infinity. It is shown that, among all stationary and ergodic fading processes of a given spectral distribution function and whose law has no mass point at zero, the Gaussian process gives rise to the smallest pre-log. The assumption that the law of the fading process has no mass point at zero is essential in the sense that there exist stationary and ergodic fading processes whose law has a mass point at zero and that give rise to a smaller pre-log than the Gaussian process of equal spectral distribution function. An extension of these results to multiple-input single-output (MISO) fading channels with memory is also presented. |

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. |

## 2009 |

## Journal Articles |

Koch, Tobias; Lapidoth, Amos; Sotiriadis, Paul Channels That Heat Up (Journal Article) IEEE Transactions on Information Theory, 55 (8), pp. 3594–3612, 2009, ISSN: 0018-9448. (Abstract | Links | BibTeX | Tags: additive noise channel, Capacity per unit cost, channel capacity, channels with memory, cooling, electronic circuits, heat dissipation, heat sinks, high signal-to-noise ratio, high signal-to-noise ratio (SNR), intrinsic thermal noise, low transmit power, network analysis, noise variance, on-chip communication, thermal noise) @article{Koch2009, title = {Channels That Heat Up}, author = {Koch, Tobias and Lapidoth, Amos and Sotiriadis, Paul P.}, url = {http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=5165190}, issn = {0018-9448}, year = {2009}, date = {2009-01-01}, journal = {IEEE Transactions on Information Theory}, volume = {55}, number = {8}, pages = {3594--3612}, abstract = {This paper considers an additive noise channel where the time-A; noise variance is a weighted sum of the squared magnitudes of the previous channel inputs plus a constant. This channel model accounts for the dependence of the intrinsic thermal noise on the data due to the heat dissipation associated with the transmission of data in electronic circuits: the data determine the transmitted signal, which in turn heats up the circuit and thus influences the power of the thermal noise. The capacity of this channel (both with and without feedback) is studied at low transmit powers and at high transmit powers. At low transmit powers, the slope of the capacity-versus-power curve at zero is computed and it is shown that the heating-up effect is beneficial. At high transmit powers, conditions are determined under which the capacity is bounded, i.e., under which the capacity does not grow to infinity as the allowed average power tends to infinity.}, keywords = {additive noise channel, Capacity per unit cost, channel capacity, channels with memory, cooling, electronic circuits, heat dissipation, heat sinks, high signal-to-noise ratio, high signal-to-noise ratio (SNR), intrinsic thermal noise, low transmit power, network analysis, noise variance, on-chip communication, thermal noise}, pubstate = {published}, tppubtype = {article} } This paper considers an additive noise channel where the time-A; noise variance is a weighted sum of the squared magnitudes of the previous channel inputs plus a constant. This channel model accounts for the dependence of the intrinsic thermal noise on the data due to the heat dissipation associated with the transmission of data in electronic circuits: the data determine the transmitted signal, which in turn heats up the circuit and thus influences the power of the thermal noise. The capacity of this channel (both with and without feedback) is studied at low transmit powers and at high transmit powers. At low transmit powers, the slope of the capacity-versus-power curve at zero is computed and it is shown that the heating-up effect is beneficial. At high transmit powers, conditions are determined under which the capacity is bounded, i.e., under which the capacity does not grow to infinity as the allowed average power tends to infinity. |