A Rate-Splitting Approach to Fading Channels with Imperfect Channel-State Information

As shown by M\'edard, the capacity of fading channels with imperfect channel-state information (CSI) can be lower-bounded by assuming a Gaussian channel input $X$ with power $P$ and by upper-bounding the conditional entropy $h(X|Y,\hat{H})$ by the entropy of a Gaussian random variable with variance equal to the linear minimum mean-square error in estimating $X$ from $(Y,\hat{H})$. We demonstrate that, using a rate-splitting approach, this lower bound can be sharpened: by expressing the Gaussian input $X$ as the sum of two independent Gaussian variables $X_1$ and $X_2$ and by applying M\'edard's lower bound first to bound the mutual information between $X_1$ and $Y$ while treating $X_2$ as noise, and by applying it a second time to the mutual information between $X_2$ and $Y$ while assuming $X_1$ to be known, we obtain a capacity lower bound that is strictly larger than M\'edard's lower bound. We then generalize this approach to an arbitrary number $L$ of layers, where $X$ is expressed as the sum of $L$ independent Gaussian random variables of respective variances $P_{\ell}$, $\ell = 1,\dotsc,L$ summing up to $P$. Among all such rate-splitting bounds, we determine the supremum over power allocations $P_\ell$ and total number of layers $L$. This supremum is achieved for $L\to\infty$ and gives rise to an analytically expressible capacity lower bound. For Gaussian fading, this novel bound is shown to converge to the Gaussian-input mutual information as the signal-to-noise ratio (SNR) grows, provided that the variance of the channel estimation error $H-\hat{H}$ tends to zero as the SNR tends to infinity.Comment: 28 pages, 8 figures, submitted to IEEE Transactions on Information Theory. Revised according to first round of review

Analysis of massive MIMO performance in an indoor picocell with high number of users

This paper presents an analysis of the massive multiple input and multiple output (MIMO) channel in an indoor picocell with a high number of active user terminals and a base station consisting of a virtual array with up to one hundred elements. The analysis is based on the results of a measurement campaign carried out in the 3.2 to 4 GHz band in a scenario of reduced size and with a symmetrical geometry, in which users are also placed in an orderly manner. The channel meets the condition of favorable propagation depending on several factors, one of the most important being the spatial distribution of users. Results concerning the inverse condition number as well as the channel sum capacity are included. Another factor that determines the performance of massive MIMO systems when operated in an orthogonal frequency division multiplexing (OFDM) framework is the frequency selectivity of the channel that limits the size of the coherence block (ChB). Focusing on the most significant results achieved, it can be concluded that the channel reaches a capacity of 89% with respect to an i.i.d. Rayleigh channel. Concerning the cumulative distribution function (CDF) of the sum capacity, it can also be observed that the tails are not very pronounced, which indicates that a homogeneous service can be given to all users. Regarding the number of samples that make up the ChB, although it is high in all cases (of the order of tens of thousands), it strongly depends on the degree of correlation used to calculate the coherence bandwidth.This work was supported in part by the Spanish Ministerio de Economía, Industria y Competitividad, under Grant TEC2017-86779-C2-1-R, in part by the European economic community (EEC) through Fondo Europeo de Desarrollo Regional (FEDER) funds, and in part by the Spanish Ministerio de Ciencia e Innovación under Grant UCAN08-4E-010

Capacity limits of bursty interference channels

Mención Internacional en el título de doctorThis dissertation studies the effects of interference burstiness in the transmission of data in wireless networks. In particular, we investigate the effects of this phenomenon on the largest data rate at which one can communicate with a vanishing small probability of error, i.e., on channel capacity. Specifically, we study the capacity of two different channel models as described in the next sections. Linear deterministic bursty interference channel. First, we consider a two-user linear deterministic bursty interference channel (IC), where the presence or absence of interference is modeled by a block- independent and identically distributed (IID) Bernoulli process that stays constant for a duration of T consecutive symbols (this is sometimes referred to as a coherence block) and then changes independently to a new interference state. We assume that the channel coefficients of the communication and interference links remain constant during the whole message transmission. For this channel, we consider both its quasi-static setup where the interference state remains constant during the whole transmission of the codeword (which corresponds to the case whether the blocklength N is smaller than T) and its ergodic setup where a codeword spans several coherence blocks. For the quasi-static setup, we follow the seminal works by Khude, Prabhakaran and Viswanath and study the largest sum rate of a coding strategy that provides reliable communication at a basic (or worstcase) rate R and allows an increased (opportunistic) rate ΔR in absence of interference. For the ergodic scenario, we study the largest achievable sum rate as commonly considered in the multi-user information theory literature. We study how (noncausal) knowledge of the interference state, referred to as channel state information (CSI), affects the sum capacity. Specifically, for both scenarios, we derive converse and achievability bounds on the sum capacity for (i) local CSI at the receiverside only; (ii) when each transmitter and receiver has local CSI, and (iii) global CSI at all nodes, assuming both that interference states are independent of each other and that they are fully correlated. Our bounds allow us to identify regions and conditions where interference burstiness is beneficial and in which scenarios global CSI improves upon local CSI. Specifically, we show the following: • Exploiting burstiness: For the quasi-static scenario we have shown that in presence of local CSI, burstiness is only beneficial if the interference region is very weak or weak. In contrast, for global CSI, burstiness is beneficial for all interference regions, except the very strong interference region, where the sum capacity corresponds to that of two parallel channels without interference. For the ergodic scenario, we have shown that, under global CSI, burstiness is beneficial for all interference regions and all possible values of p. For local CSI at the receiver-side only, burstiness is beneficial for all values of p and for very weak and weak interference regions. However, for moderate and strong interference regions, burstiness is only of clear benefit if the interference is present at most half of the time. • Exploiting CSI: For the quasi-static scenario, local CSI at the transmitter is not beneficial. This is in stark contrast to the ergodic scenario, where local CSI at the transmitter-side is beneficial. Intuitively, in the ergodic scenario the input distributions depend on the realizations of the interference states. Hence, adapting the input distributions to these realizations increases the sum capacity. In contrast, in the quasi-static case, the worst-case scenario (presence of interference) and the best-case scenario (absence of interference) are treated separately. Hence, there is no difference to the case of having local CSI only at the receiver side. Featuring global CSI at all nodes yields an increased sum rate for both the quasi-static and the ergodic scenarios. The joint treatment of the quasi-static and the ergodic scenarios allows us to thoroughly compare the sum capacities of these two scenarios. While the converse bounds for the quasi-static scenario and local CSI at the receiver-side appeared before in the literature, we present a novel proof based on an information density approach and the Verd´u-Han lemma. This approach does not only allow for rigorous yet clear proofs, it also enables more refined analyses of the probabilities of error that worst-case and opportunistic messages can be decoded correctly. For the converse bounds in the ergodic scenario, we use Fano’s inequality as the standard approach to derive converse bounds in the multi-user information theory literature. Bursty noncoherent wireless networks. The linear deterministic model can be viewed as a rough approximation of a fading channel, which has additive and multiplicative noise. The multiplicative noise is referred to as fading. As we have seen in the previous section, the linear deterministic model provides a rough understanding of the effects of interference burstiness on the capacity of the two-user IC. Now, we extend our analysis to a wireless network with a very large number of users and we do not approximate the fading channel by a linear deterministic model. That is, we consider a memoryless flat-fading channel with an infinite number of interferers. We incorporate interference burstiness by an IID Bernoulli process that stays constant during the whole transmission of the codeword. The channel capacity of wireless networks is often studied under the assumption that the communicating nodes have perfect knowledge of the fading coefficients in the network. However, it is prima-facie unclear whether this perfect knowledge of the channel coefficients can actually be obtained in practical systems. For this reason, we study in this dissertation the channel capacity of a noncoherent model where the nodes do not have perfect knowledge of the fading coefficients. More precisely, we assume that the nodes know only the statistics of the channel coefficients but not their realizations. We further assume that the interference state (modeling interference burstiness) is known non-causally at the receiver-side only. To the best of our knowledge, one of the few works that studies the capacity of noncoherent wireless networks (without considering interference burstiness) is by Lozano, Heath, and Andrews. Inter alia, Lozano et al. show that in the absence of perfect knowledge of the channel coefficients, if the channel inputs are given by the square-root of the transmit power times a power-independent random variable, and if interference is always present (hence, it is non-bursty), then the achievable information rate is bounded in the signal-to-noise ratio (SNR). However, the considered inputs do not necessarily achieve capacity, so one may argue that the information rate is bounded in the SNR because of the suboptimal input distribution. Therefore, in our analysis, we allow the input distribution to change arbitrarily with the SNR. We analyze the asymptotic behavior of the channel capacity in the limit as the SNR tends to infinity. We assume that all nodes (transmitting and interfering) use the same codebook. This implies that each node is transmitting at the same rate, while at the same time it keeps the analysis tractable. We demonstrate that if the nodes do not cooperate and if the variances of the path gains decay exponentially or slower, then the achievable information rate remains bounded in the SNR, even if the input distribution is allowed to change arbitrarily with the transmit power, irrespective of the interference burstiness. Specifically, for this channel, we show the following: • The channel capacity is bounded in the SNR. This suggests that noncoherent wireless networks are extremely power inefficient at high SNR. • Our bound further shows that interference burstiness does not change the behavior of channel capacity. While our upper bound on the channel capacity grows as the channel becomes more bursty, it remains bounded in the SNR. Thus, interference burstiness cannot be exploited to mitigate the power inefficiency at high SNR. Possible strategies that could mitigate the power inefficiency of noncoherent wireless networks and that have not been explored in this thesis are cooperation between users and improved channel estimation strategies. Indeed, coherent wireless networks, in which users have perfect knowledge of the fading coefficients, have a capacity that grows to infinity with the SNR. Furthermore, for such networks, the most efficient transmission strategies, such as interference alignment, rely on cooperation. Our results suggest that these two strategies may be essential to obtain an unbounded capacity in the SNR.Programa Oficial de Doctorado en Multimedia y Comunicaciones por la Universidad Carlos III de Madrid y la Universidad Rey Juan CarlosPresidente: Ignacio Santamaría Caballero.- Secretario: David Ramírez García, David.- Vocal: Paul de Kerre

Análisis experimental de un canal massive MIMO en una picocelda de interior

[EN] This paper presents an analysis of the massive MIMO channel in an indoor picocell. The analysis is based on the results of a measurement campaign carried out in the 3.2 to 4 GHz band in a scenario of reduced size and with a symmetrical geometry. It is well known that the performance of massive MIMO systems depends largely on the fact that the radio channel meets the condition of favorable propagation. In order to evaluate the performance of the resulting massive MIMO channel, results concerning the sum capacity are included. A second factor that determines the performance of massive MIMO systems when it is operated in a TDD-OFDM framework is the frequency selectivity of the channel that limits the size of the coherence block. In this sense, results of the coherence bandwidths achieved are also presented and analyzed.Este trabajo ha sido financiado por los proyectos del Plan Estatal de Investigación Científica y Técnica y de Innovación TEC2017-86779-C2-1-R y TEC2017-86779-C2-2-R.Torres, RP.; Pérez, JR.; Basterrechea, J.; Valle, L.; Domingo, M.; Rubio Arjona, L.; Rodrigo Peñarrocha, VM.... (2020). Análisis experimental de un canal massive MIMO en una picocelda de interior. Universidad de Málaga. 1-4. http://hdl.handle.net/10251/178585S1

Eficiencia espectral y capacidad en un canal MIMO masivo con alta densidad de usuarios

[EN] This paper presents an analysis of the massive MIMO channel in an indoor picocell with a high number of active user terminals. The analysis is based on the results of a measurement campaign carried out in the 3.2 to 4 GHz band in a scenario of reduced size, in which users (up to 20) are placed in an orderly manner. In order to evaluate the performance of the resulting massive MIMO channel, results concerning both the sum capacity as well as the spectral efficiency are included. Furthermore and concerning the channel spectral efficiency, an analysis showing the spread and differences between the individual contributions of each active user is reported and discussed.Este trabajo ha sido financiado por los proyectos del Plan Estatal de Investigación Científica y Técnica y de Innovación TEC2017-86779-C2-1-R y TEC2017-86779-C2-2-R.Alejandro Rodríguez Aparicio; Jesús R. Pérez; Luis Valle; Torres Jiménez, RP.; Rubio Arjona, L.; Rodrigo Peñarrocha, VM.; Reig, J. (2021). Eficiencia espectral y capacidad en un canal MIMO masivo con alta densidad de usuarios. Íñigo Cuiñas Gómez. 1-4. http://hdl.handle.net/10251/1910821

The Degrees-of-Freedom of Multi-way Device-to-Device Communications is Limited by 2

A 3-user device-to-device (D2D) communications scenario is studied where each user wants to send and receive a message from each other user. This scenario resembles a 3-way communication channel. The capacity of this channel is unknown in general. In this paper, a sum-capacity upper bound that characterizes the degrees-of-freedom of the channel is derived by using genie-aided arguments. It is further shown that the derived upper bound is achievable within a gap of 2 bits, thus leading to an approximate sum-capacity characterization for the 3-way channel. As a by-product, interesting analogies between multi-way communications and multi-way relay communications are concluded.Comment: 5 pages, ISIT 201