Rank-one Detector for Kronecker-Structured Constant Modulus Constellations

TL;DR

This paper introduces a novel low-complexity decoding algorithm called Kronecker-RoD for Kronecker-structured constant modulus signals, significantly improving BER performance in low SNR conditions compared to traditional methods.

Contribution

It proposes a new decoding algorithm based on rank-one approximation for Kronecker-structured signals, enhancing performance and reducing complexity.

Findings

Kronecker-RoD outperforms Viterbi decoding in BER at same spectral efficiency.

The decoder has built-in noise rejection and lower implementation complexity.

The approach is effective for short data blocks in low SNR regimes.

Abstract

To achieve a reliable communication with short data blocks, we propose a novel decoding strategy for Kronecker-structured constant modulus signals that provides low bit error ratios (BERs) especially in the low energy per bit to noise power spectral density ratio $(E_b/N_0)$. The encoder exploits the fact that any M-PSK constellation can be factorized as Kronecker products of lower or equal order PSK constellation sets. A construction of two types of schemes is first derived. For such Kronecker-structured schemes, a conceptually simple decoding algorithm is proposed, referred to as Kronecker-RoD (rank-one detector). The decoder is based on a rank-one approximation of the "tensorized" received data block, has a built-in noise rejection capability and a smaller implementation complexity than state-of-the-art detectors. Compared with convolutional codes with hard and soft Viterbi decoding, Kronecker-RoD outperforms the latter in BER performance at same spectral efficiency.