This paper presents a Medium Access Control (MAC) protocol solution designed to properly handle collisions when in the presence of a multi-packet detection receiver for Single-Carrier (SC) modulations with Frequency-Domain Equalization (FDE). It is considered an iterative frequency-domain receiver that jointly performs equalization, multi-packet separation and channel decoding operations, for up to Q_{max} mobile terminals transmitting in one slot. In this work, it is proposed and evaluated a p-persistent Network Diversity Multiple Access (NDMA) random MAC protocol designed to cope with a total number of mobile terminals J, for a maximum decoding capability of Q_{max} simultaneous packets. An accurate analytical model is presented to optimize two different scenarios: in the first one, a saturated network is considered and it is determined the packet transmission probability that maximizes the uplink throughput; the second represents a non-saturated network and the goal is to compute the optimal transmission probability associated to each mobile terminal that minimizes the packet transmission delay. In the end, analytical results obtained through physical and MAC layer simulations are discussed.