Robust Sparse Reconstruction of mmWave Channel Estimates via Fractional Programming

Abstract

We reinterpret the millimeter-wave (mmWave) channel estimation problem from the perspective of fractional programming (FP). A novel sparse recovery formulation of the associated l 0 norm optimization is then proposed as an equivalent convex program. To this end, a tight parametric approximation of the l 0 -norm is used together with the quadratic transform (QT) to reformulate the sparse optimization problem associated with the mmWave channel estimation. This original reinterpretation of the mmWave channel state information (CSI) recovery leads to a new iterative robust reconstruction algorithm. The proposed art exhibits denoising sparsity enhancement and estimation performance improvement over the State-of-the-Art (SotA) basis pursuit methods in both medium and low signal-to noise-ratio (SNR) regimes, as shown via simulations. As a bonus, the performance of our estimation scheme is found to scale well with increasing antenna array sizes, common to mmWave systems.