An alternative to decoding interference or treating interference as Gaussian noise

This paper addresses the following question regarding Gaussian networks: Is there an alternative to decoding interference or treating interference as Gaussian noise? By answering this question we aim to establish a benchmark for practical systems where multiuser decoding is not a common practice. To state our result, we study a decentralized network of one Primary User (PU) and one Secondary User (SU) modeled by a two-user Gaussian interference channel. The primary transmitter is constellation-based, i.e., PU is equipped with a modulator and its code-book is constructed over a modulation signal set. SU utilizes random Gaussian codewords with controlled transmission power that guarantees a certain level of Interference-to-Noise Ratio (INR) at the primary receiver. Both users are unaware of each other´s code-book, however, SU is smart in the sense that it is aware of the constellation set of PU. While interference at the primary receiver is modeled as additive Gaussian noise, the secondary receiver can utilize the structure of PU´s modulator as side information to decode its message without decoding the message of PU. The instantaneous realizations of symbols in a codeword transmitted by PU are unknown to both ends of SU´s direct link, however, the sample space of such symbols is available to SU. This makes the interference plus noise at the secondary receiver be a mixed Gaussian process. Invoking entropy power inequality and an upper bound on the differential entropy of a mixed Gaussian vector, we develop an achievable rate for SU that is robust to the structure of PU´s modulation signal set and only depends on its constellation size and the dimension of the euclidean space that the constellation points lie in. Moreover, we obtain an achievable rate for PU using Fano´s inequality in conjunction with a Gallager-type upper bound on the probability of error in decoding constellation points at the primary receiver. The developed achievable rates for PU and SU enable- - us to show that the sum rate can be improved compared to a scenario where both users employ Gaussian codewords and treat each other as Gaussian noise.