On optimal load setting of load-coupled cells in heterogeneous LTE networks

In multi-cell long term evolution (LTE) networks, the load levels that represent the cells´ resource consumption are coupled due to mutual interference. The coupling relation forms a non-linear system, in which one cell´s load governs the interference seen by the other cells. For heterogeneous networks with shared resource, load coupling takes place within the macro cell and small cell layers, as well as across the two layers. We investigate the problem of setting cell load levels for maximizing the overall system utility, where the utility is an increasing and concave function in served traffic. The paper presents the following contributions. First, we provide and prove the problem´s NP-hardness. Second, for the sub-problem of resource allocation for given cell load, we present optimality conditions and tractability, along with detailing the computation for logarithmic utility functions. Third, for the non-convex problem of optimal load selection, we provide necessary optimality conditions to guide load adjustment in seeking utility improvement. Repeatedly applying load adjustment leads to a search algorithm for load optimization. Fourth, we illustrate cell load optimization for a representative LTE heterogeneous network scenario, and highlight the impact of utility function and the range of small cells on optimal load and user throughput.