On the Distribution of a Two-Dimensional Random Walk With Restricted Angles
Abstract
In this paper, we derive the distribution of a twodimensional (complex) random walk in which the angle of each step is restricted to a subset of the circle. This setting appears in various domains, such as in over-the-air computation in signal processing. In particular, we derive the exact joint and marginal distributions for two steps, numerical solutions for a general number of steps, and approximations for a large number of steps. Furthermore, we provide an exact characterization of the support for an arbitrary number of steps. The results in this work provide a reference for future work involving such problems.
Fields of Study & Subjects
Diffusion and Search Dynamics
Wireless Communication Security Techniques
Point processes and geometric inequalities
Publication details
- Journal / source
- IEEE Transactions on Signal Processing
- Volume
- 74
- Pages
- 2316–2330
- Publication date
- 1 January 2026
- Language
- EN