  Phase Modulation on the Hypersphere (PMH) is a power efficient modulation
scheme for the \textit{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 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.
