  We consider a D2D wireless network where $n$ users are densely deployed in a
squared planar region and communicate with each other without the help of a
wired infrastructure. For this network, we examine the 3-phase hierarchical
cooperation (HC) scheme and the 2-phase improved HC scheme based on the concept
of {\em network multiple access}. Exploiting recent results on the optimality
of treating interference as noise in Gaussian interference channels, we
optimize the achievable average per-link rate and not just its scaling law. In
addition, we provide further improvements on both the previously proposed
hierarchical cooperation schemes by a more efficient use of TDMA and spatial
reuse. Thanks to our explicit achievable rate expressions, we can compare HC
scheme with multihop routing (MR), where the latter can be regarded as the
current practice of D2D wireless networks. Our results show that the improved
and optimized HC schemes yield very significant rate gains over MR in realistic
conditions of channel propagation exponents, signal to noise ratio, and number
of users. This sheds light on the long-standing question about the real
advantage of HC scheme over MR beyond the well-known scaling laws analysis. In
contrast, we also show that our rate optimization is non-trivial, since when HC
is applied with off-the-shelf choice of the system parameters, no significant
rate gain with respect to MR is achieved. We also show that for large pathloss
exponent the sum rate is a nearly linear function of the number of users $n$ in
the range of networks of practical size. This also sheds light on a
long-standing dispute on the effective achievability of linear sum rate scaling
with HC. Finally, we notice that the achievable sum rate for large $\alpha$ is
much larger than for small $\alpha$. This suggests that HC scheme may be a very
effective approach for networks operating at mm-waves.
