Ergodic Sum-Rate Maximization for Fading Cognitive Multiple Access Channels without Successive Interference Cancellation

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.