  This paper studies the information-theoretic limits of a secondary or
cognitive radio (CR) network under spectrum sharing with an existing primary
radio network. In particular, the fading cognitive multiple-access channel
(C-MAC) is first studied, where multiple secondary users transmit to the
secondary base station (BS) under both individual transmit-power constraints
and a set of interference-power constraints each applied at one of the primary
receivers. This paper considers the long-term (LT) or the short-term (ST)
transmit-power constraint over the fading states at each secondary transmitter,
combined with the LT or ST interference-power constraint at each primary
receiver. In each case, the optimal power allocation scheme is derived for the
secondary users to achieve the ergodic sum capacity of the fading C-MAC, as
well as the conditions for the optimality of the dynamic
time-division-multiple-access (D-TDMA) scheme in the secondary network. The
fading cognitive broadcast channel (C-BC) that models the downlink transmission
in the secondary network is then studied under the LT/ST transmit-power
constraint at the secondary BS jointly with the LT/ST interference-power
constraint at each of the primary receivers. It is shown that D-TDMA is indeed
optimal for achieving the ergodic sum capacity of the fading C-BC for all
combinations of transmit-power and interference-power constraints.
