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.

中文翻译：

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克罗内克结构恒模星座的一级检测器

为了实现与短数据块的可靠通信，我们为 Kronecker 结构的恒模信号提出了一种新颖的解码策略，该策略提供了低误码率 (BER)，尤其是在低每比特能量与噪声功率谱密度比方面 $(E_b/N_o)$. 编码器利用以下事实：任何百万美元-PSK 星座可以分解为低阶或等阶 PSK 星座集的 Kronecker 乘积。首先推导出两类方案的构造。对于这种 Kronecker 结构的方案，提出了一种概念上简单的解码算法，称为 Kronecker-RoD（秩一检测器）。解码器基于“张量化”接收数据块的秩一近似，具有内置的噪声抑制能力和比最先进的检测器更小的实现复杂性。与具有硬和软 Viterbi 解码的卷积码相比，Kronecker-RoD 在相同频谱效率下的 BER 性能优于后者。