AFDM Chirp-Permutation-Index Modulation with Quantum-Accelerated Codebook Design

TL;DR

This paper introduces AFDM chirp-permutation-index modulation (CPIM), a novel scheme that enhances data encoding in doubly-dispersive channels by permuting chirp sequences, and leverages quantum algorithms for optimized codebook design and detection.

Contribution

It proposes a new AFDM-based index modulation scheme and applies quantum Grover search to optimize codebook design and detection complexity.

Findings

Demonstrates improved performance over classical AFDM

Develops a quantum-based approach for codebook optimization

Validates the scheme through simulation results

Abstract

We describe a novel index modulation (IM) scheme exploiting a unique feature of the recently proposed affine frequency division multiplexing (AFDM) in doubly-dispersive (DD) channels. Dubbed AFDM chirp-permutation-index modulation (CPIM), the proposed method encodes additional information via the permutation of the discrete affine Fourier Transform (DAFT) chirp sequence, without any sacrifice of the various beneficial properties of the AFDM waveform in DD channels. The effectiveness of the proposed method is validated via simulation results leveraging a novel reduced-complexity minimum mean-squared-error (MMSE)-based maximum-likelihood (ML) detector, highlighting the gains over the classical AFDM. As part of the work two interesting problems related to optimizing AFDM-CPIM are identified: the optimal codebook design problem, over a discrete solution space of dimension $\binom{N!}{K}$, where $N$ is the number of subcarriers and $K$ is the number of codewords; and the ML detection problem whose solution space is of dimension $KM^N$, where $M$ is the constellation size. In order to alleviate the computational complexity of these problems and enable large-scale variations of AFDM-CPIM, the two problems are reformulated as a higher-order binary optimization problem and mapped to the well-known quantum Grover adaptive search (GAS) algorithm for their solution.