  We characterize the ergodic spectral efficiency of a non-cooperative and a
cooperative type of K-tier heterogeneous networks with limited feedback. In the
non-cooperative case, a multi-antenna base station (BS) serves a single-antenna
user using maximum-ratio transmission based on limited feedback. In the
cooperative case, a BS coordination set is formed by using dynamic clustering
across the tiers, wherein the intra-cluster interference is mitigated by using
multi-cell zero-forcing also based on limited feedback. Modeling the network
based on stochastic geometry, we derive analytical expressions for the ergodic
spectral efficiency as a function of the system parameters. Leveraging the
obtained expressions, we formulate feedback partition problems and obtain
solutions to improve the ergodic spectral efficiency. Simulations show the
spectral efficiency improvement by using the obtained feedback partitions. Our
major findings are as follows: 1) In the non-cooperative case, the feedback is
only useful in a particular tier if the mean interference is small enough. 2)
In the cooperative case, allocating more feedback to stronger intra-cluster BSs
is efficient. 3) In both cases, the obtained solutions do not change depending
on instantaneous signal-to-interference ratio.
