A Lower Bound To The Expected Discovery Time In One-Way Random Neighbor Discovery

TL;DR

This paper establishes a fundamental lower bound on the expected time for one-way neighbor discovery in multi-antenna systems, based on probabilistic transmission strategies and success rates.

Contribution

It introduces a theoretical lower bound on discovery time considering variable directional transmission probabilities in multi-antenna systems.

Findings

Lower bound is the reciprocal of average success probabilities.

The bound applies to one-way neighbor discovery schemes.

Provides a theoretical benchmark for evaluating discovery algorithms.

Abstract

We provide a lower bound on the expected discovery time of one-way neighbor discovery in multi antenna system. We assume that the scheme allows to use different directional transmission probabilities, which result in different probability of successful discovery between nodes. The proof shows that the lower bound to the expected discovery time, that node $i$ takes to discover its neighbors, is given by the reciprocal of the average probabilities of successful discovery.