Covert Communications When the Warden Does Not Know the Background Noise Power

If the warden Willie attempting to detect the transmission knows the statistics of his receiver noise, Alice can transmit no more than
$\mathcal{O}(\sqrt{n})$
covert bits reliably to Bob in
$n$
channel uses of an AWGN channel. However, if Willie does not know his noise statistics exactly, Alice can covertly transmit
$\mathcal{O}(n)$
bits. In this letter, Willie lacks knowledge of his channel statistics but observes
$T(n)$
length-
$n$
codeword slots, where some number may be used by Alice to attempt covert transmission. We show that Willie can often limit Alice to the same performance scaling as when he knows his channel statistics.