The aim of 5G wireless networks to provide Mbps and Gbps data rates to end users is expected to be fulfilled by the advanced technologies such as multi-input multi-output (MIMO), carrier aggregation (CA), inter/intra-cell communication, and adaptive modulation and coding techniques, which would be all realized in the Long Term Evolution-Advanced (LTE-A) heterogeneous network constituted by macrocells (MCs) and small cells (SCs) adopting these 5G advanced techniques. Given the potential of significantly increasing the network performance, the resource allocation (RA) problem involved becomes harder than ever especially when MIMO and CA are included in the RA problem involving multiple types of resources to be concurrently determined for the global optimization. Facing this challenge, we develop a framework to jointly optimize energy efficiency (EE), spectrum efficiency (SE), and queue length for downlink transmissions with an overall and comprehensive consideration of dynamically allocating resource blocks (RBs), component carriers (CCs), modulation and coding schemes (MCSs), and deciding user association (UA) with a power control (PC) mechanism on discrete power levels (PLs) in the heterogeneous LTE-based MIMO wireless networks. Specially, for the complex joint RA, UA, and PC problem, we conduct a mixed integer programming model to accommodate the stochastic optimization problem involved with the drift-plus-penalty (DPP) approach for Lyapunov opportunistic optimization. In particular, although it involves a nondeterministic polynomial time (NP) problem, we can still show a reduced problem to be solved easily through linear relaxation when its coefficient matrix is totally unimodular (TUM), and to be solved efficiently as well even when the TUM property is not guaranteed. Based on the reduction, we further develop a distributed or semi-distributed algorithm operated on two levels to approach the optimal results with lower complexity if the UA requirement can be relaxed. Finally, apart from exhibiting its performance on the weighting parameters, the numerical experiments also show our approach to make a good tradeoff among SE, EE, and queue length, and outperform the greedy-based state-of-the-art algorithms.
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