The non-randomized optimal hard decision fusion under Neyman-Pearson criterion is known to be an NP-hard classical 0-1 Knapsack problem with exponential complexity. In this paper, we show analytically that though the low-complexity non-randomized single-threshold likelihood ratio based test (non-rand-st LRT) is sub-optimal, its performance approaches the upper-bound obtained by randomized LRT (rand LRT) with the increase in the number of participating sensors (N). This alleviates the need for employing the exponentially complex non-randomized optimal solution for large N. Receiver operating characteristics are plotted to verify the performance of the non-rand-st LRT with reference to the upper-bound obtained by rand LRT for different scenarios. © 2018 IEEE.