Polar Quantisation of Uniformly Distributed Signals on the Hypersphere for OMA

The Outphasing MIMO Architecture (OMA) is a novel energy and cost-efficient Multiple Input Multiple Output (MIMO) transmitter architecture consisting of a Power Oscillator (PO) and an analogue network. The latter is composed of a binary tree of tunable power splitters with phase shifters at the leaves to which the antennas are connected. Due to the constant output power of the PO, transmit signals generated by OMA lie on a hypersphere. This work derives criteria for optimal Llyod- Max quantisation of power splitters and phase shifters in OMA. The objective is to minimise the Mean Squared Error (MSE) between a uniformly distributed signal on the hypersphere and its quantised version. The optimum resolutions for the individual quantisers are calculated for various numbers of antennas and the achievable MSE is plotted over the number of necessary bits per signal dimension. A comparison with the Shannon lower bound yields a gap of approximately 3.5 dB and a slightly smaller slope of −5.9 dB per bit per dimension for the derived quantisers. For a given resolution of some selected quantisers, lower bounds on the minimum achievable MSE are derived.