Using Fractional Programming for Zero-Norm Approximation
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This paper proposes the use of fractional programming (FP) to solve problems involving the zero-norm. FP is used to transform a non-convex ratio to a convex problem that can be solved iteratively, and guaranteed to converge to the global optimum under some constraints on the numerator and denominator. Recently the FP approach was extended to sums of ratios with proven convergence to a stationary point. In this paper, we reformulate the zero-norm as a ratio satisfying the FP conditions and transform the problem into iterative convex optimization. To assess the proposed tool, we investigate the power minimization problem under signal-to-interference-plus-noise ratio (SINR) constraints, when constraints on the transmitted and circuit power are accounted for. Specifically, the consumed circuit power depends on the number of active antennas, which can be modeled using zero-norm. Numerical simulations illustrate the validity of our proposed approach, demonstrating that significant performance gains over the state of the art can be obtained.
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