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

: Boche, H.; Stanczak, Slawomir


Matthews, M.B. ; Naval Postgraduate School, Monterey/Calif.:
Thirty-Seventh Asilomar Conference on Signals, Systems & Computers 2003. Conference record. Vol.1 : November 9 - 12, 2003, Pacific Grove, California
Piscataway, NJ: IEEE, 2003
ISBN: 0-7803-8104-1
Asilomar Conference on Signals, Systems and Computers <37, 2003, Pacific Grove/Calif.>
Conference Paper
Fraunhofer HHI ()

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.