A Generalised Multi-Receiver Radio Network and Its Decomposition into Independent Transmitter-Receiver Pairs: Simple Feasibility Condition and Power Levels in Closed Form

We consider a generalised multi-receiver radio network under a quality-of-service (QoS) constraint that involves generalised carrier-to-interference ratios. This model includes as special cases many well-known schemes, such as those discussed by Yates (JSAC, 13(7): 1341-1348, 1995). A simple feasibility condition for the QoS targets, and a power-vector that yields those targets are given in closed form for the case in which additive noise is negligible and the key functions are homogeneous of degree one. The condition has the simple form, k_i <= q_i, where "i" identifies a terminal, "k_i" its desired QoS level, and "q_i" its quality of service when all power levels equal unity. If the feasibility condition is satisfied, the power levels P_i = k_i / q_i yield or exceed the desired levels of quality. The generalised multi-receiver network can be conservatively represented by an equivalent set of independent transmitter-receiver pairs, with q_i equal to the channel gain of the pair that represents "i". Macro-diversity and multiple-connection reception are some of the specific models discussed as examples.