Capacity limits of bursty interference channels

Abstract

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