  This paper investigates the capacity and capacity per unit cost of Gaussian
multiple access-channel (GMAC) with peak power constraints. We first devise an
approach based on Blahut-Arimoto Algorithm to numerically optimize the sum rate
and quantify the corresponding input distributions. The results reveal that in
the case with identical peak power constraints, the user with higher SNR is to
have a symmetric antipodal input distribution for all values of noise variance.
Next, we analytically derive and characterize an achievable rate region for the
capacity in cases with small peak power constraints, which coincides with the
capacity in a certain scenario. The capacity per unit cost is of interest in
low power regimes and is a target performance measure in energy efficient
communications. In this work, we derive the capacity per unit cost of additive
white Gaussian channel and GMAC with peak power constraints. The results in
case of GMAC demonstrate that the capacity per unit cost is obtained using
antipodal signaling for both users and is independent of users rate ratio. We
characterize the optimized transmission strategies obtained for capacity and
capacity per unit cost with peak-power constraint in detail and specifically in
contrast to the settings with average-power constraints.
