On sum capacity of continuous-time overloaded CDMA systems

In this paper, the optimal design problem of overloaded code-division multiple-access (CDMA) systems is examined. Unlike previous results for chip or symbol synchronous systems, a continuous-time, band-limited, additive white Gaussian noise channel is considered for the multiple-access communications. First, non-information theoretic results are summarized, where the total transmit power is minimized, subject to lower bounds on the signal-to-interference-plus-noise ratio at the output of the linear minimum mean-squared error receivers. Second, the sum capacity is derived and shown to be the same as that of the optimal frequency-division multiple-access system, where each user's bandwidth is upper-bounded by the cycle frequency of the corresponding CDMA system. As the non-information theoretic results, the geometric procedure called multi-user constrained water-pouring leads to the optimal system that maximizes the sum rate. It is shown that orthogonal waveforms are assigned to oversized users and continuous-time equivalents of generalized Welch bound equality sequences are assigned to non-oversized users. A method to construct an optimal codebook is also proposed to be used in a CDMA signal modulator in each transmitter.