Rephased CLuP

TL;DR

This paper introduces the rephasing phenomenon in CLuP, a powerful algorithm for large-scale MIMO detection, showing it maintains ML performance even in challenging low alpha regimes through theoretical analysis and numerical validation.

Contribution

It reveals the rephasing phenomenon in CLuP, enhancing its robustness for large-scale MIMO detection in low alpha regimes, supported by theoretical insights and numerical experiments.

Findings

Rephasing enables CLuP to maintain ML performance in low alpha regimes.

CLuP can handle problems with thousands of unknowns efficiently.

Numerical results align well with theoretical predictions.

Abstract

In \cite{Stojnicclupint19,Stojnicclupcmpl19,Stojnicclupplt19} we introduced CLuP, a \bl{\textbf{Random Duality Theory (RDT)}} based algorithmic mechanism that can be used for solving hard optimization problems. Due to their introductory nature, \cite{Stojnicclupint19,Stojnicclupcmpl19,Stojnicclupplt19} discuss the most fundamental CLuP concepts. On the other hand, in our companion paper \cite{Stojniccluplargesc20} we started the story of going into a bit deeper details that relate to many of other remarkable CLuP properties with some of them reaching well beyond the basic fundamentals. Namely, \cite{Stojniccluplargesc20} discusses how a somewhat silent RDT feature (its algorithmic power) can be utilized to ensure that CLuP can be run on very large problem instances as well. In particular, applying CLuP to the famous MIMO ML detection problem we showed in \cite{Stojniccluplargesc20} that its a large scale variant, $\text{CLuP}^{r_0}$, can handle with ease problems with \textbf{\emph{several thousands}} of unknowns with theoretically minimal complexity per iteration (only a single matrix-vector multiplication suffices). In this paper we revisit MIMO ML detection and discuss another remarkable phenomenon that emerges within the CLuP structure, namely the so-called \bl{\textbf{\emph{rephasing}}}. As MIMO ML enters the so-called low $\alpha$ regime (fat system matrix with ratio of the number of rows and columns, $\alpha$, going well below $1$) it becomes increasingly difficult even for the basic standard CLuP to handle it. However, the discovery of the rephasing ensures that CLuP remains on track and preserves its ability to achieve the ML performance. To demonstrate the power of the rephasing we also conducted quite a few numerical experiments, compared the results we obtained through them to the theoretical predictions, and observed an excellent agreement.