Joint transmitter and receiver optimization for continuous-time overloaded Gaussian multiple-access channels

Under general asymmetric signal-to-interference-plus-noise ratio (SINR) constraints at the output of linear minimum mean-squared error (LMMSE) receivers, the joint transmitter and receiver optimization is performed to achieve the minimum total signal power for overloaded multiuser communications in additive white Gaussian noise (AWGN). Unlike previous works that find the optimal signature sequences, the signal powers, and despreading sequences, the problem is solved to find strictly band-limited, continuous-time signature waveforms, signal powers, and receive waveforms. A necessary and sufficient condition for user admissibility is derived, and the optimal solutions are obtained in the frequency domain through vectorized Fourier transform (VFT) technique. A geometric procedure called multi-user constrained water-pouring is proposed to construct optimal solutions. It turns out that the optimal FDMA system is among the optimal multiple-access schemes given the optimality criterion.