(Continuous) Phase Modulation on the Hypersphere

Abstract

We introduce phase modulation on the hypersphere (PMH) for load-modulated multiple-input multiple-output (MIMO) transmitters with a single central power amplifier. In PMH, the peak to average ratio of the sum power before pulse shaping is 1; thus, the central power amplifier of load-modulated MIMO transmitters does not require any back-off. We derive the capacity of PMH on an additive white Gaussian noise channel and show that the input signal should be uniformly distributed on a hypersphere. The mutual information of uniformly distributed PMH input is derived in an uplink multiple-access independent identically distributed Gaussian MIMO channel using the replica method from statistical physics. Furthermore, discrete PMH is introduced using spherical codes and also generalizing minimum shift keying from the complex unit circle to the hypersphere. We investigate different pulse shaping methods for PMH including a novel spherical filtering. Using spherical pulse shaping, the signal stays on the hypersphere. Various filters are investigated, and a tradeoff between spectral shape and peak-to-average-sum-power ratio (PASPR) is found. For as few as four antennas, good spectral properties (similar to root-raised cosine pulses) can be achieved at very low PASPR. Both former and latter further improve with increasing the number of antennas.