2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/133871This paper deals with throughput scaling laws for random ad-hoc wireless networks in a rich scattering environment. We develop schemes to optimize the ratio, $ρ(n)$ of achievable network sum capacity to the sum of the point-to-point capacities of source-destinations pairs operating in isolation. For fixed SNR networks, i.e., where the worst case SNR over the source-destination pairs is fixed independent of $n$, we show that collaborative strategies yield a scaling law of $ρ(n) = {\cal O}(\frac{1}{n^{1/3}})$ in contrast to multi-hop strategies which yield a scaling law of $ρ(n) = {\cal O}(\frac{1}{\sqrt{n}})$. While, networks where worst case SNR goes to zero, do not preclude the possibility of collaboration, multi-hop strategies achieve optimal throughput. The plausible reason is that the gains due to collaboration cannot offset the effect of vanishing receive SNR. This suggests that for fixed SNR networks, a network designer should look for network protocols that exploit collaboration. The fact that most current networks operate in a fixed SNR interference limited environment provides further motivation for considering this regime.26 pages single column, submitted to Transactions on Information TheoryInformation Theorytext