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Although the massive MIMO enabled heterogeneous networks (HetNets) can intensify the spectral efficiency benefits, the proper user association and resource allocation are both crucial to achieve desirable performance since the power consumption of base station (BS) scales with the large number of antennas. This paper aims to investigate joint design of user association and power allocation with loads constraint and transmit power constraint for the massive MIMO HetNets by considering proportional fairness about the spectral efficiency under imperfect channel state information. First, we derive a closed-form lower bound on the ergodic spectral efficiency with linear zero-forcing beamforming, based on which, a mixed-integer nonlinear programming problem is formulated. It is difficult to efficiently obtain an exact solution since it is non-convex and combinational. To solve this NP-hard problem, an effective algorithm with guaranteed convergence is proposed, where the original problem is decomposed into the corresponding subproblems, which can be solved by low complexity approaches, respectively. Numerical results show that how the number of antennas and the number of BSs affect the spectral efficiency, and our proposed algorithm outperforms other algorithms in terms of the spectral efficiency and load balancing.

Joint Design of User Association and Power Allocation With Proportional Fairness in Massive MIMO HetNets