On the convergence of linear power control for cellular radio systems

So far most of the linear power control algorithms, such as the algorithm suggested by Foschini and Miljanic (1993), have been of first-order. That is, the algorithms have utilized only measurements of current power and carrier-to-interference plus noise power ratio (CIR) for computing the power update. Recently, two second-order algorithms utilizing both current and previous powers and CIR values have been suggested by the authors (see IEEE Journal on Selected Areas in Communication, vol. SAC-18, p.447-57, 2000 and Proc. IEEE ISSSTA 2000, September 2000). The gain of using higher order dynamics is faster convergence. Another reason for using higher order algorithms is to take the CIR estimation dynamics into account. For example, it has been suggested that the received interference power should first be filtered with the first-order infinite impulse response (IIR) filter before the CIR estimate is calculated. In this paper, we suggest a general linear distributed power control (GLDPC) algorithm, which contains many of the earlier algorithms as a special case and the ability to incorporate CIR estimator dynamics. The convergence of GLDPC is shown to depend on the Schur stability of a certain polynomial, which in turn can be investigated by the Nyquist criterion.