Multiuser signaling in the symbol-synchronous AWGN channel

Multiuser signal set design for the energy-constrained linear real-additive symbol-synchronous additive white Gaussian noise channel is investigated in this correspondence. An argument is presented showing the suboptimality of binary alphabets which, in turn, uncovers a rule for the formation of multiuser signal sets. This simple rule leads to a theorem stating the dimensionality at which additional users can be added to a multiuser system without decreasing the minimum Euclidean distance. Specific vector sets with the desired property are then constructed as examples and some generalizations are discussed. The theorem may also be used as a platform for the design of more efficient multiuser codes incorporating redundant signal sets. Two such codes are presented. In particular, a code combining four-dimensional unit-energy signals with a rate-2/3 convolutional code obtains a summed rate of 1.75 bits/dimension in the two-user adder channel with received minimum Euclidean distance of 2