The theoretical bandwidth advantage of CDMA over FDMA in a Gaussian MAC

We develop an expression for the minimum extra bandwidth needed for a frequency-division multiple-access (FDMA) system to out perform its code-division (CDMA) counterpart uniformly (that is, for all rate n-tuples) in a Gaussian multiple-access channel (MAC). For equal-power sources, the behavior of this factor is as an iterated logarithm of the number of users; hence it increases slowly yet is unbounded. Asymmetric power cases are also studied and it is shown that the equal power scenario provides the least bandwidth expansion factor assuming constant constraint on total power.