The capacity of downlink fading channels with variable rate and power

We obtain the Shannon capacity region of the down-link (broadcast) channel in fading and additive white Gaussian noise (AWGN) for time-division, frequency-division, and code-division. For all of these techniques, the maximum capacity is achieved when the transmitter varies the data rate sent to each user as their channels vary. This optimal scheme requires channel estimates at the transmitter; dynamic allocation of timeslots, bandwidth, or codes; and variable-rate and power transmission. For both AWGN and fading channels, nonorthogonal code-division with successive decoding has the largest capacity region, while time-division, frequency-division, and orthogonal code-division have the same smaller region. However, when all users have the same average received power, the capacity region for all these techniques is the same. In addition, the optimal nonorthogonal code is a multiresolution code which does not increase the signal bandwidth. Spread-spectrum code-division with successive interference cancellation has a similar rate region as this optimal technique, however, the region is reduced due to bandwidth expansion. We also examine the capacity region of nonorthogonal code-division without interference cancellation and of orthogonal code-division when multipath corrupts the code orthogonality. Our results can be used to bound the spectral efficiency of the downlink channel using time-division, frequency-division, and code-division, both with and without multiuser detection.