This paper analyzes the throughput of an unlicensed wireless network where messages decoded in outage may be retransmitted. We assume that some wireless devices such as sensors are the unlicensed users, which communicate in the licensed uplink channel. In this case, the licensed users that interfere with the unlicensed transmissions devices are mobile devices whose spatial distribution are assumed to follow a Poisson point process with respect to a reference unlicensed link. We investigate how the number of allowed retransmissions and the spectrum efficiency jointly affect the throughput in [bits/s/Hz] of a reference unlicensed link for different licensed network densities, constrained by a given required error rate. The optimal throughput is derived for this case as a function of the network density. We also prove that the optimal constrained throughput can always reach the unconstrained optimal value. Our numerical results corroborate those of the analytical findings, also illustrating how the number of allowed retransmissions that leads to the optimal throughput changes with the error rate requirements.