  Radio spectrum is a high-demand finite resource. To meet growing demands of
data throughput for forthcoming and deployed wireless networks, new wireless
technologies must operate in shared spectrum over unlicensed bands (coexist).
As an example application, we consider a model of Long-Term Evolution (LTE)
License-Assisted Access (LAA) with incumbent IEEE 802.11 wireless-fidelity
(Wi-Fi) systems in a coexistence scenario. This scenario considers multiple LAA
and Wi-Fi links sharing an unlicensed band; however, a multitude of other
scenarios could be applicable to our general approach. We aim to improve
coexistence by maximizing the key performance indicators (KPIs) of two networks
simultaneously via dimension reduction and multi-criteria optimization. These
KPIs are network throughputs as a function of medium access control (MAC)
protocols and physical layer parameters. We perform an exploratory analysis of
coexistence behavior by approximating active subspaces to identify
low-dimensional structure in the optimization criteria, i.e., few linear
combinations of parameters for simultaneously maximizing LAA and Wi-Fi
throughputs. We take advantage of an aggregate low-dimensional subspace
parametrized by approximate active subspaces of both throughputs to regularize
a multi-criteria optimization. Additionally, a choice of two-dimensional
subspace enables visualizations augmenting interpretability and explainability
of the results. The visualizations and approximations suggest a predominantly
convex set of KPIs over active coordinates leading to a regularized manifold of
approximately Pareto optimal solutions. Subsequent geodesics lead to continuous
traces through parameter space constituting non-dominated solutions in contrast
to random grid search.
