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We study the asymptotic performance of two multi-hop overlaid ad-hoc networksthat utilize the same temporal, spectral, and spatial resources based on randomaccess schemes. The primary network consists of Poisson distributed legacyusers with density \lambda^{(p)} and the secondary network consists of Poissondistributed cognitive radio users with density \lambda^{(s)} =(\lambda^{(p)})^{\beta} (\beta>0, \beta \neq 1) that utilize the spectrumopportunistically. Both networks are decentralized and employ ALOHA mediumaccess protocols where the secondary nodes are additionally equipped withrange-limited perfect spectrum sensors to monitor and protect primarytransmissions. We study the problem in two distinct regimes, namely \beta>1 and0<\beta<1. We show that in both cases, the two networks can achieve theircorresponding stand-alone throughput scaling even without secondary spectrumsensing (i.e., the sensing range set to zero); this implies the need for a morecomprehensive performance metric than just throughput scaling to evaluate theinfluence of the overlaid interactions. We thus introduce a new criterion,termed the asymptotic multiplexing gain, which captures the effect ofinter-network interferences with different spectrum sensing setups. With thismetric, we clearly demonstrate that spectrum sensing can substantially improveprimary network performance when \beta>1. On the contrary, spectrum sensingturns out to be unnecessary when \beta<1 and setting the secondary network'sALOHA parameter appropriately can substantially improve primary networkperformance.

Large Overlaid Cognitive Radio Networks: From Throughput Scaling to Asymptotic Multiplexing Gain