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This paper investigates the performance limits of cognitive-uplink fixed satellite service (FSS) and terrestrial fixed service (FS) operating in the range 27.5-29.5 GHz for Ka-band. In light of standard recommendations from the International Telecommunications Union and a rain-fading channel model, we analyze the interference level at the FS receiver by considering statistical properties of the channel, propagation losses, and antenna patterns. By employing the interference constraint criterion at the FS, an analytical expression for the capacity of the cognitive-uplink FSS is derived, which is useful in understanding the limits in performance and the potential application of the considered coexistence scenario. Simulations are carried out to verify the theoretical derivations and highlight the impact of key parameters on the performance limits.