Optimal Non-regenerative Relay Processing with Improper Signals

Improper signals - complex signals that have (i) different power in the real and imaginary parts and/or (ii) correlation between the real and imaginary parts - have inevitable applications in wireless communications including modulations such as BPSK, ASK and GMSK. Taking into consideration the impropriety of the source signal, we represent the signals using realvalued representation and propose a novel closed-form relay and receive filter design which minimize the mean squared error (MSE). The proposed relay strategy and receive filter design draw parallels with widely-linear processing applied conventionally at the receivers and achieve a smaller MSE than a conventional layer-1 relay with minimum MSE receive filter in the complex domain.