Effect of threshold quantization in opportunistic splitting algorithm

This paper discusses algorithms to find the optimal threshold and also investigates the impact of threshold quantization on the scheduling outage performance of the opportunistic splitting scheduling algorithm. Since this algorithm aims at finding the user with the highest channel quality within the minimal number of mini-slots by adjusting the threshold every mini-slot, optimizing the threshold is of paramount importance. Hence, in this paper we first discuss how to compute the optimal threshold along with two tight approximations for the optimal threshold. Closed-form expressions are provided for those approximations for simple calculations. Then, we consider linear quantization of the threshold to take the limited number of bits for signaling messages in practical systems into consideration. Due to the limited granularity for the quantized threshold value, an irreducible scheduling outage floor is observed. The numerical results show that the two approximations offer lower scheduling outage probability floors compared to the conventional algorithm when the threshold is quantized.