Frequency hopping does not increase anti-jamming resilience of wireless channels

TL;DR

This paper demonstrates that frequency hopping does not improve anti-jamming resilience in wireless channels from an information-theoretic perspective, but it does increase the channel capacity when sender power exceeds jammer power.

Contribution

It provides a rigorous analysis showing frequency hopping does not enhance anti-jamming resilience, contrasting with its capacity-increasing effect under certain power conditions.

Findings

Capacity equals CR capacity if sender power exceeds jammer power

Frequency hopping does not improve resilience against jamming

Bounds on the CR capacity are established

Abstract

The effectiveness of frequency hopping for anti-jamming protection of wireless channels is analyzed from an information-theoretic perspective. The sender can input its symbols into one of several frequency subbands at a time. Each subband channel is modeled as an additive noise channel. No common randomness between sender and receiver is assumed. It is shown that capacity is positive, and then equals the common randomness assisted (CR) capacity, if and only if the sender power strictly exceeds the jammer power. Thus compared to transmission over any fixed frequency subband, frequency hopping is not more resilient towards jamming, but it does increase the capacity. Upper and lower bounds on the CR capacity are provided.