  Instead of achievable rate in the conventional association, we utilize the
effective rate to design two association schemes for load balancing in
heterogeneous cellular networks (HCNs), which are both formulated as such
problems with maximizing the sum of effective rates. In these two schemes, the
one just considers user association, but the other introduces power control to
mitigate interference and reduce energy consumption while performing user
association. Since the effective rate is closely related to the load of some BS
and the achievable rate of some user, it can be used as a key factor of
association schemes for load balancing in HCNs. To solve the association
problem without power control, we design a one-layer iterative algorithm, which
converts the sum-of-ratio form of original optimization problem into a
parameterized polynomial form. By combining this algorithm with power control
algorithm, we propose a two-layer iterative algorithm for the association
problem with power control. Specially, the outer layer performs user
association using the algorithm of problem without power control, and the inner
layer updates the transmit power of each BS using a power update function
(PUF). At last, we give some convergence and complexity analyses for the
proposed algorithms. As shown in simulation results, the proposed schemes have
superior performance than the conventional association, and the scheme with
joint user association and power control achieves a higher load balancing gain
and energy efficiency than conventional scheme and other offloading scheme.
