Load in CDMA Cellular Systems and its Relation to the Perron Root

It is well known that the feasibility of the power allocation problem in CDMA systems is directly linked to the Perron root of a channel gain matrix. In this paper, we show how the concept of load, as used in the CDMA network planning community, is linked to the Perron root and propose to use the Perron root as a load estimate. Specifically, we propose a practical iterative method to estimate the Perron root and revise various other approaches. All methods are analysed with respect to their suitability for analytical use in early-stage network planning. In addition, we extend the use of these methods from primitive matrices to cover the general case of non-negative channel gain matrices and illustrate the use of the irreducible normal form to provide tighter bounds than direct application under certain circumstances. In contrast to the use of traditional load equations, the proposed methods do not require the solution of the power allocation problem. Numerical examples show that particularly the proposed iterative solution provides very good results at low complexity.