  We investigate Gaussian widely linear precoding known as improper Gaussian
signaling for the cellular uplink with inter-cell interference, known as
interference multiple access channel (IMAC). This transmission scheme provides
extra degrees of freedom by treating the real and imaginary components of the
complex Gaussian signal differently. Since current standards mainly utilize
linear beamforming for waveform generation, we highlight the benefits of widely
linear beamforming over multiple temporal dimensions (symbol extension in time)
in the IMAC. This scheme achieves significantly higher information rates
compared to conventional proper Gaussian signaling at the expense of extra
complexity at the transmission phase. We study the sum-power minimization
problem under rate constraints. This problem is a difference of concave
functions (DC) program, hence, a non-convex problem. By numerical simulations,
we observe the benefits of improper Gaussian signaling alongside symbol
extension in power consumption for both single-antenna and multi-antenna base
stations. Interestingly, we observe that at strong interference scenarios, the
efficiency of improper Gaussian signaling outperforms conventional proper
Gaussian signaling at low rate demands. Moreover, in such scenarios the
sum-power required for achieving particular rate demands is significantly
reduced.
