Interference has been a fundamental performance bottleneck in wireless communication.
Conventional interference control schemes, which are mainly based on channel
orthogonalization, are non-capacity achieving in general. To improve the performance of
wireless networks, cooperative interference control schemes are proposed. In particular,
interference alignment (IA), a recently developed interference control scheme, achieves
optimal capacity scaling in a wide range of wireless networks. The key idea of IA is
to reduce the effect of aggregated interference by aligning interference from different
transmitters into a lower dimensional subspace at each receiver. However, to achieve the
optimal capacity scaling, classical IA schemes require infinite dimension of signal space,
which i...[
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Interference has been a fundamental performance bottleneck in wireless communication.
Conventional interference control schemes, which are mainly based on channel
orthogonalization, are non-capacity achieving in general. To improve the performance of
wireless networks, cooperative interference control schemes are proposed. In particular,
interference alignment (IA), a recently developed interference control scheme, achieves
optimal capacity scaling in a wide range of wireless networks. The key idea of IA is
to reduce the effect of aggregated interference by aligning interference from different
transmitters into a lower dimensional subspace at each receiver. However, to achieve the
optimal capacity scaling, classical IA schemes require infinite dimension of signal space,
which is difficult to implement in practice. To overcome this problem, researchers have
proposed IA designs with signal space dimension limited by the number of antennas.
However, despite the numerous works dedicated to IA, when the signal space has finite
dimension, two fundamental questions remain open in general: 1) Under what network
topology is IA feasible? 2) In a feasible network, how can we find an IA solution? The
feasibility analysis of IA is difficult as the IA constraints are sets of non-linear equations,
for which no systematic tool exists to characterize the feasible region. Finding solutions of
IA is challenging due to the non-convex nature of the interference minimization problem.
In this thesis, by adopting tools from algebraic geometry, we establish a framework
which shows the (almost surely) equivalence of the feasibility of IA problem, the algebraic
independence of IA constraints, and the linear independence of the first order terms of IA
constraints. This framework enables us to propose and prove a necessary and sufficient
condition for IA to be feasible in MIMO interference networks with general topology.
Based on this condition, we generate several insights into the relation between network
topology and IA feasibility.
In addition, by exploiting the connection between algebraic independence and full
rankness of Jacobian matrix, we prove that when IA is feasible, in the corresponding
interference minimization problem, there is no performance gap between local and global
optimums. This fact enables us to find IA solutions by adopting existing local search
algorithms. Combining the results on IA feasibility analysis and algorithm design, we
have established a unified algebraic framework that consolidates the theoretical basis of
IA.
Further, we extend IA to networks with partial connectivity. Classical IA algorithms
are designed for networks with fully connected interference graphs. We envision that in
interference networks, partial connectivity can potentially allow IA algorithms to cancel
interference more efficiently. We develop a new IA algorithm that dynamically adapts
to partial connectivity parameters and hence achieves better performance than classical
IA algorithms.
Finally, we extend IA to cellular networks. Classical IA algorithms, designed for
interference networks, exploit the fact that the channel state of direct links and cross
(i.e. interfering) links are statistically independent. However, in cellular networks, there
is overlap between the direct and cross links. With this overlap, classical IA algorithms
will cancel part of the desired signals when canceling interference. To overcome this
challenge, we decompose the IA problem for cellular networks into equivalent intra- and
inter-cell interference cancellation problems and develop an IA algorithm for MIMO
cellular networks.
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