We usually consider multi-carrier (interchangeably multi-channel) communications.
By using the multi-carrier system, instead of one-broadband system, we can obtain many advantages, for example, able to send multiple data streams simultaneously, robust against frequency-selective fading effects, etc.
Whenever I do simulations of subcarrier and power allocation in multi-user, multi-carrier communication system, e.g., OFDM, I can see that the sum rate is constant regardless of the number of subcarriers.
Intuitively, as the number of subcarriers increases, the network throughput seems to be increased as well. However, it didn't.
Also, in this paper IEEE JSAC paper, the authors showed that the average sum rate is constant regardless of the number of subcarriers, as follows:
I want to know why this result occurs theoretically.