Rank-One Detector for Kronecker-Structured Constant Modulus Constellations

• Published in: IEEE signal processing letters 2020, Vol.27, p.1420-1424
• Main Authors: E-Asim, Fazal, de Almeida, Andre L. F., Haardt, Martin, Cavalcante, Charles C., Nossek, Josef A.
• Format: Article
• Language: English
• Subjects: Algorithms; Binary phase shift keying; Coders; Codes; Constellations; Decoding; Density ratio; Detectors; Encoding; Fading channels; Gaussian approximation; Kronecker coding; LS- Kronecker factorization; Power spectral density; rank-one approximation; Tensile stress; Viterbi decoding
• ISSN: 1070-9908; 1558-2361
• DOI: 10.1109/LSP.2020.3010133

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_o). 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.