This paper presents closed-form expressions for the ergodic channel capacity of SIMO (single-input and multiple output) wireless systems operating in a Nakagami-m fading channel. As the performance of SIMO channel is closely related to the diversity combining techniques, we present closed-form expressions for the capacity of maximal ratio combining (MRC), equal gain combining (EGC), selection combining (SC), and switch and stay (SSC) diversity systems operating in Nakagami-m fading channels. Also, the ergodic capacity of a SIMO system in a Nakagami-m fading channel without any diversity technique is derived. The latter scenario is further investigated for a large amount of receive antennas. Finally, numerical results are presented for illustration.