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In wireless cellular networks that are interference-limited, a variety of power control problems can be formulated as nonlinear optimization with a system-wide objective, e.g., maximizing total system throughput under many QoS constraints from individual users. Previous work have been done in the high SIR regime by turning these problems with nonlinear objectives and constraints into convex optimization problems. However, in the medium to low SIR regime, these problems cannot be transformed into tractable convex optimization problems.
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