Upper bound and approximation of random access throughput over chase combining HARQ

Massive MTC (mMTC) scenarios featuring a tremendous number of devices challenge the conventional multiple access protocols, which are mostly based on classic ALOHA algorithms known for their instability at higher loads. While numerous modifications of ALOHA adopt the unrealistic assumption on the fixed number of contending uses, we in this paper study a model where a random number of users activate within the slot. In particular, we explore a modification of ALOHA augmented with the Chase combining HARQ (HARQ-CC) and derive an approximation for and a simple upper bound on the system throughput. While the former perfectly matches the corresponding simulation results for the SNR of up to 10dB, the latter constitutes an increasingly tight limit as the SNR grows. Based on both analytical considerations, the resulting system throughput may be significantly improved with the optimal choice of the transmission probability and code spectral efficiency.