Optimized Tone Reservation for Opportunistic OFDM Communications and Sensing

We consider the problem of peak-to-average power ratio (PAPR) reduction in orthogonal frequency division multiplexing (OFDM) systems via optimized sparsification of tone reservation (TR). In particular, we propose a novel TR optimization method in which the minimum number of effectively used peak-reserved tones (PRTs) required to satisfy a prescribed PAPR level is found, leaving the remaining PRTs free to be opportunistically utilized by other functionalities, such as joint communication and sensing (JCAS), index modulation (IM), cognitive radio (CR) and others. The proposed method relies on an l0 norm regularization approach to penalize the number of PRTs, leading to a problem convexized via fractional programming (FP), whose solution is shown to ensure that the prescribed PAPR is achieved with high probability with a smaller number of PRTs than state of the art (SotA) methods. The contribution can be seen as a mechanism to enable the opportunistic integration of adjacent functionalities into existing OFDM-based systems.

Discrete Aware Matrix Completion via Convexized $\ell_0$-Norm Approximation

We consider a novel algorithm, for the completion of partially observed low-rank matrices in a structured setting where each entry can be chosen from a finite discrete alphabet set, such as in common recommender systems. The proposed low-rank matrix completion (MC) method is an improved variation of state-of-the-art (SotA) discrete aware matrix completion method which we previously proposed, in which discreteness is enforced by an $\ell_0$-norm regularizer, not by replaced with the $\ell_1$-norm, but instead approximated by a continuous and differentiable function normalized via fractional programming (FP) under a proximal gradient (PG) framework. Simulation results demonstrate the superior performance of the new method compared to the SotA techniques as well as the earlier $\ell_1$-norm-based discrete-aware matrix completion approach.