Log-concavity of SIR and characterization of feasible SIR region for CDMA channels

We consider a power-controlled CDMA channel where each user is required to satisfy a certain quality-of-service (QoS) requirement. It is assumed that there is a one-to-one relationship between a QoS parameter of interest and the signal-to-interference ratio (SIR) at the output of a linear receiver. The set of all feasible QoS requirements is called the feasibility region. The paper shows under what conditions the feasibility region is a convex set. Furthermore, we prove that the SIR is a log-concave function of powers when the powers are expressed in logarithmic scale. These properties open the door to a widely developed theory for characterizing strategies to optimally allocate scarce resources in wireless communication networks.