Recently, there has been a proliferation of wireless communication technologies in unlicensed bands for the Internet of Things. A key question is whether these networks can coexist given that they have different power levels, symbol periods, and access protocols. The main challenge is to characterize the impact of mutual interference arising from distinct unco-ordinated networks. It is known that when interferers form a homogeneous Poisson point process and transmit only on a single subband, the interference is often well-modeled by the heavy-tailed α-stable distribution. In this paper, we focus on the scenario where interferers transmit on multiple subbands. Under a policy where each interferer independently accesses each band with probability p, we provide an exact characterization of the interference random vector. Exploiting this characterization, we derive optimal linear combining weights and an analytical approximation for the bit error rate (BER), accurate for large transmit power. A key observation is that the expression for the BER admits an interpretation in terms of an array gain and a fractional diversity gain.