Periodicity is one of the main cues for pitch-related speech perception but is poorly encoded in cochlear implants (CIs). Most efforts towards CI periodicity enhancement involve explicit fundamental frequency (F0) detection, which requires additional computational loads and may not be reliable in real settings. Here we propose a new strategy, namely F0inTFS, which encodes F0 information without explicit F0 detection. Our idea is inspired by the fact that temporal fine structures (TFS) at the low-frequency channels inherently contain strong F0-related periodicity cues. In F0inTFS, the TFS of the lowest-frequency channel is integrated into the temporal envelopes at all higher-frequency channels using a specifically designed algorithm. F0inTFS can be lightly implemented in the FFT-based framework of one clinically used strategy, i.e., the Advanced Combination Encoder (ACE) strategy. The benefits of F0inTFS are supported by a lexical tone perception experiment in simulated CI users.