From Multi-Keyholes to Measure of Correlation and Power Imbalance in MIMO Channels: Outage Capacity Analysis

An information-theoretic analysis of a multi-keyhole channel, which includes a number of statistically independent keyholes with possibly different correlation matrices, is given. When the number of keyholes or/and the number of Tx/Rx antennas is large, there is an equivalent Rayleigh-fading channel such that the outage capacities of both channels are asymptotically equal. In the case of a large number of antennas and for a broad class of fading distributions, the instantaneous capacity is shown to be asymptotically Gaussian in distribution, and compact, closed-form expressions for the mean and variance are given. Motivated by the asymptotic analysis, a simple, full-ordering scalar measure of spatial correlation and power imbalance in MIMO channels is introduced, which quantifies the negative impact of these two factors on the outage capacity in a simple and well-tractable way. It does not require the eigenvalue decomposition, and has the full-ordering property. The size-asymptotic results are used to prove Telatar's conjecture for semi-correlated multi-keyhole and Rayleigh channels. Since the keyhole channel model approximates well the relay channel in the amplify-and-forward mode in certain scenarios, these results also apply to the latterComment: accepted by IEEE IT Trans., 201

On Outage Probability and Diversity-Multiplexing Tradeoff in MIMO Relay Channels

Fading MIMO relay channels are studied analytically, when the source and destination are equipped with multiple antennas and the relays have a single one. Compact closed-form expressions are obtained for the outage probability under i.i.d. and correlated Rayleigh-fading links. Low-outage approximations are derived, which reveal a number of insights, including the impact of correlation, of the number of antennas, of relay noise and of relaying protocol. The effect of correlation is shown to be negligible, unless the channel becomes almost fully correlated. The SNR loss of relay fading channels compared to the AWGN channel is quantified. The SNR-asymptotic diversity-multiplexing tradeoff (DMT) is obtained for a broad class of fading distributions, including, as special cases, Rayleigh, Rice, Nakagami, Weibull, which may be non-identical, spatially correlated and/or non-zero mean. The DMT is shown to depend not on a particular fading distribution, but rather on its polynomial behavior near zero, and is the same for the simple "amplify-and-forward" protocol and more complicated "decode-and-forward" one with capacity achieving codes, i.e. the full processing capability at the relay does not help to improve the DMT. There is however a significant difference between the SNR-asymptotic DMT and the finite-SNR outage performance: while the former is not improved by using an extra antenna on either side, the latter can be significantly improved and, in particular, an extra antenna can be traded-off for a full processing capability at the relay. The results are extended to the multi-relay channels with selection relaying and typical outage events are identified.Comment: accepted by IEEE Trans. on Comm., 201

Diversity-Multiplexing Tradeoff in the Low-SNR Regime

An extension of the popular diversity-multiplexing tradeoff framework to the low-SNR (or wideband) regime is proposed. The concept of diversity gain is shown to be redundant in this regime since the outage probability is SNR-independent and depends on the multiplexing gain and the channel power gain statistics only. The outage probability under the DMT framework is obtained in an explicit, closed form for a broad class of channels. The low and high-SNR regime boundaries are explicitly determined for the scalar Rayleigh-fading channel, indicating a significant limitation of the SNR-asymptotic DMT when the multiplexing gain is small.Comment: accepted by IEEE Comm. Letter

Diversity-Multiplexing Tradeoff via Asymptotic Analysis of Large MIMO Systems

Diversity-multiplexing tradeoff (DMT) presents a compact framework to compare various MIMO systems and channels in terms of the two main advantages they provide (i.e. high data rate and/or low error rate). This tradeoff was characterized asymptotically (SNR-> infinity) for i.i.d. Rayleigh fading channel by Zheng and Tse [1]. The asymptotic DMT overestimates the finite-SNR one [2]. In this paper, using the recent results on the asymptotic (in the number of antennas) outage capacity distribution, we derive and analyze the finite-SNR DMT for a broad class of channels (not necessarily Rayleigh fading). Based on this, we give the convergence conditions for the asymptotic DMT to be approached by the finite-SNR one. The multiplexing gain definition is shown to affect critically the convergence point: when the multiplexing gain is defined via the mean (ergodic) capacity, the convergence takes place at realistic SNR values. Furthermore, in this case the diversity gain can also be used to estimate the outage probability with reasonable accuracy. The multiplexing gain definition via the high-SNR asymptote of the mean capacity (as in [1]) results in very slow convergence for moderate to large systems (as 1/ln(SNR)^2) and, hence, the asymptotic DMT cannot be used at realistic SNR values. For this definition, the high-SNR threshold increases exponentially in the number of antennas and in the multiplexing gain. For correlated keyhole channel, the diversity gain is shown to decrease with correlation and power imbalance of the channel. While the SNR-asymptotic DMT of Zheng and Tse does not capture this effect, the size-asymptotic DMT does.Comment: To appear in 2007 IEEE International Symposium on Information Theory (ISIT 2007), Nice, June 200

Философия предпринимательства: от навязывания нравственных идеалов к исполнению норм

In the paper I analyze the expectations of Russian society towards the business community. My hypothesis is that the society tends to impose moral ideals of charity as an obligatory form of action. And one could only encourage moral ideals and shouldn’t demand them. Following the moral ideals unlike moral rules are not supposed to be obligatory. In the paper I also critically reconstruct possible arguments justifying external society pressure on the businessmen. I outline two main arguments. First one ‘the criminal argument’ is based on the idea that the source of businessman’s wealth is wicked and therefore a businessman owes the society more than others. The second argument ‘the argument of new normativity’ is based on the premises that, even if the business is ethically flawless, additional moral rules for businessmen are created by the institutional fact of doing business, The scrutiny of the arguments for additional moral requirements for businessmen leads me to the conclusion that suggestive power of those arguments is grounded in the fact of reflecting society’s desires, and not in some sort of rational foundations. В статье анализируются ожидания российского общества относительно предпринимательского класса. Высказывается гипотеза о том, что благотворительная деятельность навязывается предпринимателям в качестве обязательной. Хотя благотворительность — это нравственный идеал, а нравственные идеалы в отличие от норм не должны быть обязательными для исполнения для всех членов общества. Также в статье критически реконструируются возможные аргументы, оправдывающие такое внешние давление общества на предпринимательский класс. Выделяются два основных аргумента. Первый аргумент, «криминальный аргумент», исходит из того, что богатство «дельца» имеет «нечистое» происхождение и потому он должен обществу больше других. Второй аргумент, «аргумент новой нормативности», исходит из того, что новые моральные нормы для предпринимателей порождаются самим институциональным фактом их занятости даже при условии этической безупречности такого рода занятий. Разбор потенциальных аргументов в пользу дополнительных нравственных требований к предпринимателям приводит автора к выводу о том, что суггестивная сила этих аргументов кроется скорее в том, что они отражают желания членов общества, нежели в том, что за ними стоят рациональные доводы