  In this paper, the ergodic sum-rate of a fading cognitive multiple access
channel (C-MAC) is studied, where a secondary network (SN) with multiple
secondary users (SUs) transmitting to a secondary base station (SBS) shares the
spectrum band with a primary user (PU). An interference power constraint (IPC)
is imposed on the SN to protect the PU. Under such a constraint and the
individual transmit power constraint (TPC) imposed on each SU, we investigate
the power allocation strategies to maximize the ergodic sum-rate of a fading
C-MAC without successive interference cancellation (SIC). In particular, this
paper considers two types of constraints: (1) average TPC and average IPC, (2)
peak TPC and peak IPC. For the first case, it is proved that the optimal power
allocation is dynamic time-division multiple-access (D-TDMA), which is exactly
the same as the optimal power allocation to maximize the ergodic sum-rate of
the fading C-MAC with SIC under the same constraints. For the second case, it
is proved that the optimal solution must be at the extreme points of the
feasible region. It is shown that D-TDMA is optimal with high probability when
the number of SUs is large. Besides, we show that, when the SUs can be sorted
in a certain order, an algorithm with linear complexity can be used to find the
optimal power allocation.
