The wideband slope region of BPSK and QPSK for broadcast channels in the low-power regime

We consider a multi-user scenario, where the users are operating at a low SNR level. The low SNR level entails that the energy per bit of each user is close to the minimum that allows for reliable transmission. In existing work of the last years, the wideband slope was introduced, which describes the behavior of capacity as SNR tends to zero and which thus is an adequate quality criterion for channels with low SNR. It has already been shown that in single-user channels, QPSK achieves the optimum slope reached by Gaussian alphabets, while BPSK only achieves half the slope. In this paper, we extend this result to two-user broadcast channels and show that the users achieve the optimum slope region if they use QPSK. As in the single-user case, each user's slope attainable with QPSK is halved when using BPSK instead. Furthermore, we show that the suboptimality of the TDMA slope region, which was already shown for multi-user channels with Gaussian inputs, persists.