Covert wireless communications are unprecedentedly vital for security and privacy of individuals, government, and military bodies. Besides encryption, hiding signal transmission deeply under noise background highly proliferates the covertness in the physical layer. A deep signal hiding leads to a low interception probability at the interceptor but a poor data recovery at the receiver. To ensure both high covertness and high-fidelity recovery, massive and dense optical comb channels are utilized for deep denoising through the analog spectrum convolution. Using an external modulation-based optical frequency comb (OFC) and a single detection branch, the available optical comb channels can sustainably scale up by breaking or greatly mitigating physical bottlenecks on immense hardware and spectrum requirements. Thus, a striking signal-to-noise ratio (SNR) rise can be achieved for deep denoising. Combination of 1024 comb channels (the first parallel comb channel number beyond 1000) and the analog spectrum convolution enable a record SNR enhancement of 29 dB for a microwave signal with a 10.24 GHz bandwidth and a 10 Mbit/s data rate, which is deeply hidden below the in-band noises by 18 dB or even 30 dB in both the frequency and time domains. This method opens a new avenue for covert communications.