  The paper investigates the weighted sum-rate maximization (WSRM) problem with
latent interfering sources outside the known network, whose power allocation
policy is hidden from and uncontrollable to optimization. The paper extends the
famous alternate optimization algorithm weighted minimum mean square error
(WMMSE) [1] under a causal inference framework to tackle with WSRM.
Specifically, with the possibility of power policy shifting in the hidden
network, computing an iterating direction based only on the observed
interference inherently implies that counterfactual is ignored in decision
making. A method called synthetic control (SC) is used to estimate the
counterfactual. For any link in the known network, SC constructs a convex
combination of the interference on other links and uses it as an estimate for
the counterfactual. Power iteration in the proposed SC-WMMSE is performed
taking into account both the observed interference and its counterfactual.
SC-WMMSE requires no more information than the original WMMSE in the
optimization stage. To our best knowledge, this is the first paper explores the
potential of SC in assisting mathematical optimization in addressing classic
wireless optimization problems. Numerical results suggest the superiority of
the SC-WMMSE over the original in both convergence and objective.
