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.

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To solve the problem that the low capacity in hot-spots and coverage holes of conventional cellular networks, the base stations (BSs) having lower transmit power are deployed to form heterogeneous cellular networks (HetNets). However, because of these introduced disparate power BSs, the user distributions among them looked fairly unbalanced if an appropriate user association scheme hasn't been provided. For effectively tackling this problem, we jointly consider the load of each BS and user's achievable rate instead of only utilizing the latter when designing an association algorithm, and formulate it as a network-wide weighted utility maximization problem. Note that, the load mentioned above relates to the amount of required subbands decided by actual rate requirements, i.e., QoS, but the number of associated users, thus it can reflect user's actual load level. As for the proposed problem, we give a maximum probability (max-probability) algorithm by relaxing variables as well as a low-complexity distributed algorithm with a near-optimal solution that provides a theoretical performance guarantee.Experimental results show that, compared with the association strategy advocated by Ye, our strategy has a speeder convergence rate, a lower call blocking probability and a higher load balancing level.

In heterogeneous cellular networks (HCNs), the user association is a challenging topic since some different base stations coexist. Moreover, because of the asymmetric uplink and downlink in HCNs, a joint uplink and the downlink association algorithm should be designed to improve the system performance. For the practical implementation, the authors need to ensure that the algorithm is highly effective. Thus, they try to design an association strategy that jointly maximises downlink sum rate and minimises uplink sum power, and formulate it as a sum-utility maximisation problem. To solve this problem, they design a centralised association algorithm via a gradient descent method, and develop a distributed association algorithm via dual decomposition. Simulation results show that, compared with the signal strength-based association, range expansion association and the method proposed by Ye, their scheme has some significant advantages in the mass.

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