Yu. S. Radchenko, R. V. Titov
While using indoor ultra-wide band signals one needs to cope with their multipath propagation. A typical object from which the signal scatters often has a cluster structure.
A mathematical model of the field received by the antenna array is a conditional Gaussian process. At small values of signal angle of arrival (AOA) fluctuations caused by cluster structure of the scatterer it is possible to obtain a rather simple equation for the signal correlation matrix. The elements of this matrix are proportional to the characteristic function of AOA fluctuations. The signal model considered in this case has some special features i.e. time and space processing can be separated and the signal is stochastic in the space domain. Moreover, in the extreme case the received signal can degenerate into one plain wave.
The signal space processing algorithm is synthesized. This algorithm estimates two parameters i.e. signal AOA and signal angle spread. Because of a priori limitations of estimated parameters the algorithm has some special features i.e. delta components of the probability densities of the estimates appear at the boundaries of a priori range. Their appearance is confirmed by statistical simulation. In addition, approximations of the probability densities of the estimates are suggested.
Estimations offsets are also obtained during simulation. For AOA the offset is rather small and changes slowly as the AOA changes. For angle spread it is vice versa. First offsets derivatives are considered in the Cramer-Rao bound calculation. When Cramer-Rao bounds were compared with standard deviations of the estimates obtained during simulation it appeared that they do not match. The standard deviation of AOA is much higher than its bound, while the standard deviation of the angle spread estimate crosses its bound. It shows that it is necessary to consider the behavior of these AOA and angle spread estimates at their a priori range boundaries as well as the possibility of signal degeneration.