The optimal (feedback-free) fusion rule for binary hypothesis testing consists of (binary) Likelihood Radio Quantizers (LRQs) at the peripheral sensors and a LRQ at the fusion, when the observations are statistically independent from sensor to sensor. Feedback introduces correlation between local and global decisions that complicates the optimal fusion design. In this paper we consider the optimal fusion design in the presence of non-hierarchical feedback. Optimal fusion design requires the explicit knowledge of the underlying statistics. The design of feedback-free fusion is considered under reduced statistical knowledge using projection. The constrained optimal linear centralized and distributed fusion rules are derived. Fusion design with projection only requires knowledge of the first two moments of the data and is applicable in cases of limited statistical information about the operational statistics.