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In the last decade, the nonstationary properties of channel models have attracted more and more attention for many scenarios, that is, vehicle-to-vehicle (V2V), mobile-to-mobile (M2M), and high-speed train (HST). However, little research has been done on the real-physical channel model. In this paper, we propose a generalized three-dimensional (3D) nonstationary channel model, in which the scatterers are assumed to be distributed around the transmitter (Tx) and receiver (Rx) on a two-sphere model. By employing the von Mises-Fisher distribution, the mean values of the azimuth angle of departure (AAoD) and elevation angle of departure (EAoD) and the azimuth angle of arrival (AAoA) and elevation angle of arrival (EAoA) are tracked by time-variant (TV) Brownian Markov (BM) motion paths, which ensure the nonstationarity of the proposed channel model. Moreover, the TV autocorrelation function (ACF) and Doppler power spectrum density (DPSD) of the proposed nonstationary channel model are calculated by using signal processing tools, for example, fast Fourier transform (FFT) and short-time Fourier transform (STFT). In addition, the simulation results show that the TV scatterer distribution results in a nonstationary nonisotropic channel model, and the proposed model can be employed to simulate the 3D nonstationary channel model.

We examine the relationship between covariant and canonical (Ashtekar/Rovelli/Smolin) loop variables in the context of BF type topological field theories in 2+1 and 3+1 dimensions, with respective gauge groups SO(2,1) and SO(3,1). The latter model can be considered as the simplest topological gravity theory in 3+1 dimensions. We carry out the canonical quantization of this model in both the connection and loop representations, for the two spatial topologies T 3 and S 2 × S 1 .

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