Optimizing Weighted-Sum Energy Efficiency in Downlink and Uplink NOMA Systems

In this paper, weighted sum energy efficiency (WSEE) in uplink and downlink of a multi-user non-orthogonal multiple access (NOMA) system is considered. we adopt a more realistic power consumption model where signal processing power is modeled as a linear function of transmit power. Rather than the well-known network-centric global energy efficiency (GEE) metric, which is a pseudo-concave (PC) function, the weighted sum energy efficiency metric is considered, which is not PC in general. To find the optimum user power allocation Dinkelbach-like algorithm is adopted, by which each individual fractional EE function is converted to a parametric function where under some conditions on the weights falls into a class of convex optimization problems and it is solved in the dual domain. The dual variables are updated using a sub-gradient and cutting plane-based algorithm, which here ellipsoid method is used. Since the optimum solution restricts user weights, a low complexity suboptimum algorithm that does not consider any condition on user's weights is proposed. The problem is non-convex in general; hence, epigraph form followed by successive convex approximation (SCA) is used to deal with that problem. Results demonstrate that with the user-oriented metric, one can provide different priorities to users, and by choosing proper weights entail fairness among users.