Phase Modulation on the Hypersphere (PMH) is a power efficient modulation scheme for the load-modulated multiple-input multiple-output (MIMO) transmitters with central power amplifiers (CPA). However, it is difficult to obtain the precise channel state information (CSI), and the traditional optimal maximum likelihood (ML) detection scheme incurs high complexity which increases exponentially with the number of transmitting antennas and the number of bits carried per antenna in the PMH modulation. To detect the PMH signals without knowing the prior CSI, we first propose a signal detection scheme, termed as the hypersphere clustering scheme based on the expectation maximization (EM) algorithm with maximum likelihood detection (HEM-ML). By leveraging machine learning, the proposed detection scheme can accurately obtain information of the channel from a few of the received symbols with little resource cost and achieve comparable detection results as that of the optimal ML detector. To further reduce the computational complexity in the ML detection in HEM-ML, we also propose the second signal detection scheme, termed as the hypersphere clustering scheme based on the EM algorithm with KD-tree detection (HEM-KD). The CSI obtained from the EM algorithm is used to build a spatial KD-tree receiver codebook and the signal detection problem can be transformed into a nearest neighbor search (NNS) problem. The detection complexity of HEM-KD is significantly reduced without any detection performance loss as compared to HEM-ML. Extensive simulation results verify the effectiveness of our proposed detection schemes.

中文翻译：

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负载调制 MIMO 系统中基于机器学习的 PMH 信号信号检测

Hypersphere 上的相位调制 (PMH) 是一种功率高效的调制方案，适用于 带有中央功率放大器 (CPA) 的负载调制多输入多输出 (MIMO) 发射机。然而，很难获得精确的信道状态信息（CSI），传统的最优最大似然（ML）检测方案的复杂度很高，随着发射天线的数量和PMH中每根天线承载的比特数呈指数增长调制。为了在不知道先验 CSI 的情况下检测 PMH 信号，我们首先提出了一种信号检测方案，称为基于最大似然检测（HEM-ML）的期望最大化（EM）算法的超球面聚类方案。通过利用机器学习，所提出的检测方案可以以很少的资源成本从少数接收符号中准确地获取信道信息，并获得与最佳ML检测器相当的检测结果。为了进一步降低 HEM-ML 中 ML 检测的计算复杂度，我们还提出了第二种信号检测方案，称为基于 EM 算法和 KD 树检测（HEM-KD）的超球面聚类方案。从 EM 算法获得的 CSI 用于构建空间 KD 树接收器码本，信号检测问题可以转化为最近邻搜索 (NNS) 问题。与 HEM-ML 相比，HEM-KD 的检测复杂度显着降低，而没有任何检测性能损失。大量的仿真结果验证了我们提出的检测方案的有效性。