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We show that iterative power control by measuring intercell interference can converge faster than by measuring total receiver power. This interesting result is obtained by reducing the dimension of quality of service (QoS) constraint equations from the number of mobile stations (MSs) to the number of base stations (BSs) in the system. By observing the intercell interference and total received power, we first derive the microscopic descriptions, namely, the QoS constraint equations expressed in terms of number of MSs. Then the microscopic descriptions are transformed as macroscopic descriptions, which are the QoS constraint equations expressed in terms of number of BSs. Theoretic and simulation results show that the pair of description matrices for microscopic and macroscopic descriptions share the same spectral radius, which is the convergence rate or contracting rate indicator of related power-control iterations. Comparison of the macroscopic description matrices based on total received power and intercell interference shows that the former has the larger spectral radius, which justifies our main conclusion. We also show that the convergence rate indicator decreases with the increase of number of MSs and their QoS requirements, typically the required Eb/N0. The asynchronous algorithms are also investigated and are proved to have faster convergence speed than the synchronous ones. Numerical simulations are conducted to verify the theoretic results and to examine the performance of the proposed algorithms.