Grace Villacrés Estrada, a PhD student in the Signal Processing Group of the University Carlos III de Madrid is defending her doctoral thesis titled “Capacity Limits of Bursty Interference Channels” on April, 11th

- Title: “Capacity Limits of Bursty Interference Channels”
- Advisor: Tobias Koch.
- Event Date: Thursday, April 11, 2019, at 11:00 am.
- Location: Salón de Grados, Padre Soler Building, Leganés Campus. Universidad Carlos III de Madrid.

**Abstract**

In modern wireless networks, interference constitutes a key limiting factor for the efficient use of the spectrum and to achieve higher data rates. Consequently, this phenomenon is extensively studied in the information theory literature. Most of the studies consider that interference is inherent to the network and that it is always present. However, physical phenomena like shadowing can make the presence of interference intermittent or bursty. Interference can also be bursty due to the bursty nature of data traffic, distributed medium access control mechanisms, and decentralized networking protocols. For this reason, there has been an increasing interest in understanding and exploring the effects of burstiness of interference on the transmission of data. In this thesis, we avoid the pessimistic assumption that interference is always present by studying the effect of burstiness on the capacity of channels with state. Specifically, we study two different channel models as described below.

In the first part, we consider a two-user linear deterministic bursty interference channel, where the presence/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 and then changes independently to a new state. We consider both a 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 an ergodic setup where a codeword spans several coherence blocks. For the quasi-static setup, we study the largest sum rate of a coding strategy that provides reliable communication at a basic (or worst-case) rate and allows an increased (opportunistic) rate when there is no interference. For the ergodic setup, we study the largest achievable sum rate as commonly considered in the multi-user information theory literature. We study how (non-causal) knowledge of the interference state, referred to as channel-state information (CSI), affects the sum capacity.

In the second part, we study the effects of interference burstiness on capacity of large wireless networks. Specifically, we consider a memoryless flat-fading channel with an infinite number of interferers. We incorporate 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. However, it is prima facie unclear whether this perfect knowledge 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. 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, 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 assume that all nodes (transmitting and interfering) use the same codebook. 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. A capacity that is bounded in the SNR suggests that noncoherent wireless networks are extremely power inefficient. Our result further show that interference burstiness does not change the behavior of channel capacity. While our upper bound on 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.