Multiuser Constrained Water-Pouring for Continuous-Time Overloaded Gaussian Multiple-Access Channels

In this paper, signature waveforms and signal powers are jointly optimized for multiuser communications over strictly bandlimited, continuous-time, overloaded channels corrupted by additive white Gaussian noise (AWGN). The total signal power is minimized subject to general asymmetric signal-to-interference-plus-noise ratio (SINR) constraints at the output of linear minimum mean-squared error (LMMSE) receivers. Using vectorized Fourier transform (VFT) technique, the optimal solutions as well as a necessary and sufficient condition for the existence of a feasible solution are derived in the frequency domain. It turns out that every optimal solution performs the same as the optimal frequency-division multiple-access (FDMA) system. A geometric procedure called multiuser constrained water-pouring is developed to construct every possible optimal solution, of which profiles of signal power and equivalent bandwidth are, respectively, the same as those of signal power and physical bandwidth of the optimal FDMA system. It is shown that orthogonal signature waveforms are assigned to oversized users and continuous-time equivalents of generalized Welch bound equality (CTE-GWBE) sequences are assigned to non-oversized users.