Suboptimality of TDMA in the low power regime

We consider multiaccess, broadcast and interference channels with additive Gaussian noise. Although the set of rate pairs achievable by time-division multiple-access (TDMA) is not equal to the capacity region, the TDMA achievable region converges to the capacity region as the power decreases. Furthermore, TDMA achieves the optimum minimum energy per bit. Despite those features, this paper shows that the growth of TDMA-achievable rates with the energy per bit is suboptimal in the low-power regime except in special cases: multiaccess channels where the users' energy per bit are identical and broadcast channels where the receivers have identical signal-to-noise ratios. For the additive Gaussian noise interference channel, we identify a small region of interference parameters outside of which TDMA is also shown to be suboptimal. The effect of fading (known to the receiver) on the suboptimality of TDMA is also explored.