RMS bandwidth constrained signature waveforms that maximize the total capacity of PAM-synchronous CDMA channels

Optimum time-limited signal sets of equal and unequal energies are obtained under root mean square (RMS) bandwidth constraints. The total capacity and the total asymptotic efficiency of the PAM synchronous Gaussian CDMA (PSG-CDMA) channel are considered as the optimality criteria. The latter measure is monotonic with the determinant of the correlation matrix, R, and the former is monotonic with det(I+σ ^-2R), where σ² represents the noise level. Average as well as maximum RMS bandwidth constraints are considered in the equal-energy case, and the energy-weighted RMS bandwidth constraint is considered for unequal energy signals. For the equal-energy problem, signal sets are found that simultaneously optimize the total asymptotic efficiency under both average and maximum RMS bandwidth constraints. For the total capacity measure, such simultaneously optimal signal sets are also obtained, albeit under the restriction that the number of signals n be a Hadamard matrix dimension. When the Hadamard dimension is in particular a power of two, we obtain optimum signal sets that are shown to yield equal optimum multiuser detector asymptotic efficiencies for all users of an uncoded PSG-CDMA channel. Unequal energy signal sets are also found under an energy-weighted RMS bandwidth constraint for both optimality criteria