A balanced precoding scheme for the two-user SISO X channel with optimal DoF and a small power offset

In this paper we propose a structured low-latency interference alignment scheme for the two-user single-input single-output (SISO) time-invariant X channel. The scheme is based on asymmetric (non-circular) complex signals generated by linear precoders and linear zero-forcing receivers. In addition to achieving the optimal (sum) degrees of freedom (DoF) of 4/3, the precoders are balanced in the sense that for pairs of symbols the signal-to-noise ratio at the input to the decoder is the same. Furthermore, the sum rate is shown to have a small power offset-in one simple scenario that offset is at least 6 dB smaller than the offset of an existing scheme. The principles that underlie this scheme are extended to a time-varying channel with delayed feedback in which either asymmetric symmetric signalling is used.