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In this paper, we show that the adaptive projected subgradient method (APSM) is bounded perturbation resilient. To illustrate a potential application of this result, we propose a set-theoretic framework for MIMO detection, and we devise algorithms based on a superiorized APSM. Various low-complexity MIMO detection algorithms achieve excellent performance on i.i.d. Gaussian channels, but they typically incur high performance loss if realistic channel models (e.g., correlated channels) are considered. Compared to existing low-complexity iterative detectors such as individually optimal large-MIMO approximate message passing (IO-LAMA), the proposed algorithms can achieve considerably lower symbol error ratios over correlated channels. At the same time, the proposed methods do not require matrix inverses, and their complexity is similar to IO-LAMA.
Set-theoretic estimation is at the heart of a large variety of signal processing techniques. It works by expressing any available information about the sought solution in the form of constraint sets, and by finding a feasible point, i.e., a point that is consistent with each of these constraints . In many cases, this point can be computed with very simple algorithms based on projection methods. A famous example is the widely used projections onto convex sets (POCS) algorithm , , , which finds a point in the intersection of a finite family of closed convex sets by computing projections onto each of the sets in a cyclic manner. The appeal of projection methods like POCS lies in their simple structure and their potential to tackle very large problems , .
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