Large-scale cloud radio access network (LS-CRAN) is a highly promising next-generation cellular network architecture whereby lots of base stations (BSs) equipped with a massive antenna array are connected to a cloud-computing based central processor unit via digital front/backhaul links. This paper studies an asymptotic behavior of downlink (DL) performance of a LS-CRAN with three practical constraints: 1) limited transmit power, 2) limited front/backhaul capacity, and 3) limited pilot resource. As an asymptotic performance measure, the scaling exponent of the signal-to-interference-plus-noise-ratio (SINR) is derived for interference-free (IF), maximum-ratio transmission (MRT), and zero-forcing (ZF) operations. Our asymptotic analysis reveals four fundamental operating regimes and the performances of both MRT and ZF operations are fundamentally limited by the UL transmit power for estimating user's channel state information, not the DL transmit power. We obtain the conditions that MRT or ZF operation becomes interference-free, i.e., order-optimal with three practical constraints. Specifically, as higher UL transmit power is provided, more users can be associated and the data rate per user can be increased simultaneously while keeping the order-optimality as long as the total front/backhaul overhead is $Ω(N^{η_{\rm{bs}}+η_{\rm{ant}}+η_{\rm{user}}+\frac{2}αρ^{\rm{ul}}})$ and $Ω(N^{η_{\rm{user}}-η_{\rm{bs}}})$ pilot resources are available. It is also shown that how the target quality-of-service (QoS) in terms of SINR and the number of users satisfying the target QoS can simultaneously grow as the network size increases and the way how the network size increases under the practical constraints, which can provide meaningful insights for future cellular systems.