FSO Physical-Layer Security
Power that the receiver and an off-axis eavesdropper collect from a Gaussian beam, their SNRs and the wiretap secrecy capacity for a free-space optical link.
Bob's received power
0.808 dBm
beam radius 0.197 m at Bob
Eve's received power
-18.1 dBm
beam radius 0.197 m at Eve
Bob / Eve power ratio
18.9 dB
optical power
SNR Bob / Eve
65.6 / 27.9 dB
(P / (NEP·√B))²
Secrecy capacity
12.5 Gb/s
12.5 bit/s/Hz × B
Beam divergence
0.395 mrad
full angle 2λ/(πw₀)
Eve's power and the secrecy capacity vs her offset from the beam axis
Each receiver collects the part of the Gaussian beam (radius w(z) = w₀√(1 + (z/z_R)²)) that falls on its aperture, computed exactly, so no receiver gets more than the transmitted power even in the near field. Eve is assumed not to block Bob's beam.
Secrecy capacity of the Gaussian wiretap channel: C_s = B[log₂(1 + SNR_B) − log₂(1 + SNR_E)]⁺ (Leung-Yan-Cheong and Hellman, 1978), with SNR = (P/(NEP·√B))² for receivers limited by the same amplifier noise. This is an illustration of why a narrow beam is hard to tap; an intensity-modulated link is not a Gaussian channel, and the figure is not a security guarantee.
Model and references
Illustrative. A simplified model that shows trends and orders of magnitude. Don't use its numbers for design. About the tiers
Exact Gaussian-beam capture (vacuum, no turbulence; Eve sits before Bob, off his path); SNR (P/(NEP·√B))² with Bob's NEP for Eve too; Gaussian wiretap capacity applied to an IM/DD link. Not a security guarantee.
- Leung-Yan-Cheong S. K., Hellman M. E. (1978). The Gaussian wire-tap channel. IEEE Trans. Inf. Theory 24(4), 451–456. Secrecy capacity C_B − C_E. doi:10.1109/TIT.1978.1055917