  This paper proposes a cellular network exploiting millimeter-wave (mmWave)
and ultra-densified base stations (BSs) to achieve the far-reaching 5G aim in
downlink average rate. The mmWave overlaid network however incurs a pitfall
that its ample data rate is only applicable for downlink transmissions due to
the implementation difficulty at mobile users, leading to an immense difference
between uplink and downlink rates. We therefore turn our attention not only to
maximize downlink rate but also to ensure the minimum uplink rate. With this
end, we firstly derive the mmWave overlaid ultra-dense cellular network
spectral efficiencies for both uplink and downlink cases in closed forms by
using stochastic geometry via a lower bound approximation. In a practical
scenario, such tractable results of the proposed network reveal that incumbent
micro-wave ($\mu$Wave) cellular resource should be mostly dedicated to uplink
transmissions in order to correspond with the mmWave downlink rate improvement.
Furthermore, increasing uplink rate via $\mu$Wave BS densification cannot
solely cope with the mmWave downlink/uplink rate asymmetry, and thus requires
additional $\mu$Wave spectrum in 5G cellular networks.
