High Resolution Estimation of AoA, AoD and TdoA from MIMO Channel Sounding Measurements with Virtual Antenna Arrays: Maximum-Likelihood vs. Unitary Tensor-ESPRIT

Estimating the parameters of a geometric propagation model from MIMO channel sounding measurements will be considered, which requires the solution of an inverse problem. Thus, a model of the measured data is derived, which incorporates a model of the measurement system as well as the parameters of interest. Based on the data model a maximum-likelihood estimator will be derived to infer the model parameters. Because virtual antenna arrays are considerer, formed by step-wise rotating directive antennas at transmitter and receiver side, the MIMO measurements are conducted in the beam-space. Hence, the data model can be described by a multidimensional convolution of the measurement system and the propagation channel. Based on the convolutional modelling, the parameter estimation problem is transformed into a harmonic retrieval problem, which can be solved by an Unitary Tensor-ESPRIT algorithm. The maximum-likelihood and ESPRIT estimator are compared by Monte-Carlo simulations according to their root-mean-square estimation error.

Deviations from unitary symmetry for resonant states

1. The symmetry breaking interactions The fact that the meson or baryon states observed to have a particular spin-parity value appear grouped into unitary patterns of charge multiplets has made it apparent that the strong nuclear interactions satisfy SU 3 symmetry . At the same time, the large mass differences which exist between the charge multiplets constituting a given unitary multiplet show clearly that there also exist moderately strong interactions which do not have this symmetry, although they satisfy the SU 2 symmetry of charge independence and the gauge symmetry of hypercharge conservation. The simplest hypothesis possible for these symmetry breaking interactions is that they have the following unitary tensor form: L m . s . = λ T 3 3 .