Structured Compute-and-Forward with phase precoding scheme: Beyond integers

In this work, we focus on the K-user Gaussian Symmetric Complex-valued Interference Channels (GS-CIC). The Compute-and-Forward (CoF) protocol in wireless networks have been employed for Gaussian Symmetric Real-valued Interference Channels (GS-RIC) to achieve approximately the capacity of such channels and making Interference Alignment (IA) by solving a system of linear equations at destinations. We aim to adapt this protocol to GS-CIC. At high Signal-to-Noise Ratio (SNR), this protocol shows a fading behavior of the achievable sum-rate for strong and very strong interference regimes. In complex field this random-like behavior is related to the phase of complex cross channel coefficients. To avoid this fading-like behavior, we consider ℤ[i]-lattice codes and we propose a phase precoding scheme for CoF protocol with partial feedback. In this method the phase of channel coefficients will then be fed back to the transmitters in order to choose the best precoder factors to control this random behavior. We further simulate the achievable sum-rate given by this scheme and showing significant gain improvement can be obtained in terms of limiting the random behavior of achievable sum-rate.