Code for Angle of Arrival and Time of Arrival in Geometric Single-Reflection Elliptical Model for Micro-Cells

In micro-cell wireless communication scenarios, the geometric single-reflection elliptical model is a commonly used multipath channel modeling approach. This model assumes that signals travel from the transmitter, undergo a single reflection, and then arrive at the receiver, with the propagation path satisfying elliptical geometric properties—meaning the reflection point lies on an ellipse with the transmitter and receiver as its foci. Core Implementation Logic: Environment Modeling: First, the coordinate positions of the transmitter (Tx) and receiver (Rx) need to be determined, as these serve as the foci of the ellipse. Based on the distribution of reflecting objects (such as building walls), calculate ellipse parameters (like major axis and eccentricity) to determine possible reflection point trajectories. In code implementation, this typically involves creating coordinate system objects and defining geometric constraints using vector mathematics. Reflection Point Calculation: Using elliptical geometric properties combined with the physical principle that the angle of incidence equals the angle of reflection, derive mathematical expressions for reflection point coordinates. This usually requires solving nonlinear equations, which can be approached using numerical methods like Newton-Raphson iteration for optimal solution approximation. The implementation would involve creating functions that handle matrix operations and convergence criteria for iterative solvers. Angle of Arrival and Time of Arrival Computation: Angle of Arrival/Departure (AoA/AoD): Calculate the signal arrival or departure angles based on the connection direction between the reflection point and Rx/Tx (typically referenced to horizontal or vertical planes). Code implementation would use trigonometric functions (arctan2 for robust angle calculation) and coordinate transformation methods. Time of Arrival (ToA): Calculate signal propagation delay by dividing the path length (transmitter → reflection point → receiver) by the speed of light. This requires efficient distance calculation algorithms and proper unit conversions in the code. Extended Considerations: Practical applications need to account for the impact of reflecting material properties (such as reflection coefficients) on signal strength. This can be implemented through material property databases and signal attenuation functions. If multiple reflection paths exist, clustering algorithms like K-means should be incorporated to distinguish primary reflectors and prevent model over-complexity. The code would need pattern recognition modules and clustering parameter optimization. The model can be further extended to three-dimensional space by introducing elevation angle parameters to improve positioning accuracy, requiring 3D coordinate system implementations and additional angular calculations. Through these implementation steps, this model can effectively simulate multipath characteristics of signals in micro-cells, providing theoretical foundations for channel estimation and positioning algorithms. The complete code structure would typically include main simulation functions, geometric calculation modules, numerical solver components, and result visualization capabilities.