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Abstract:
This 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 probThis 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.[+][-]