On The effect of self-interference in Gaussian two-way channels with erased outputs

It is well-known that the so-called Shannon Achievable Region (SAR) in a collocated two-user Gaussian Two-Way Channel (GTWC) does not depend on the self-interference that is due to the leakage of the signal transmitted by each user at its own receiver. This is simply because each user can completely remove its self-interference. In this paper, we study a class of GTWCs where each user is unable to cancel the self interference due to random erasures at its receiver. The mixture of the intended signal for each user and its self-interference is erased independently from transmission slot to transmission slot. It is assumed that both users adopt PAM constellations for transmission purposes. Due to the fact that both users are unaware of the erasure pattern, the noise plus interference at each user is mixed Gaussian. To analyze this setup, a sequence of upper and lower bounds are developed on the differential entropy of a general mixed Gaussian random variable where it is shown that the upper and lower bounds meet as the sequence index increases. Utilizing such bounds, it is shown that the achievable rate for each user is monotonically increasing in terms of the level of self-interference and eventually saturates as self-interference grows to infinity. This saturation effect is justified analytically by showing that as self-interference increases, each user is enabled to extract the erasure pattern at its receiver. Treating the erasure pattern as side information, both users are able to cancel self-interference and decode the useful information at higher transmission rates.