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:

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I want to know why this result occurs theoretically.

  • \$\begingroup\$ Instead of one horse you have a thousand chickens pulling your cart. \$\endgroup\$
    – user16324
    Jul 30, 2021 at 13:05

1 Answer 1


If you increase the number of subcarriers then each one must be of narrower bandwidth to avoid spectral overlap and so it will be able to carry less data.

Reducing the bandwidth for each carrier would reduce the noise power but assuming the total transmit power over all carriers remains constant the SNR will remain constant so the data rate will be proportional to the spectral width of each carrier.

Although there is no data rate improvement by having more carriers it provides more flexibility for optimizing the total capacity where noise or other impairments are not constant across the band.

  • \$\begingroup\$ Ideally, I (also in the above referred paper) considered that the total bandwidth is B and each carrier’s bandwidth is B/K when the number of subcarriers is K. Then, Shannon capacity is exploited, i.e., data rate is (B/K)log(1+(h_k*p_k)/(N0*B/K) for subcarrier k, where h_k and p_k is channel power gain and power allocation on subcarrier k, respectively, and N0 is noise spectral density. More specifically, in an OFDM case, one user with highest channel gain is selected for each subcarrier, and power allocation is performed by water-filling scheme. \$\endgroup\$
    – Danny_Kim
    Jul 29, 2021 at 23:25
  • \$\begingroup\$ So, that agrees with what Kevin wrote, @danny_kim \$\endgroup\$
    – mmmm
    Jul 29, 2021 at 23:29

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