This paper proposes an optical gateway that converts pulse amplitude modulation (PAM) format to phase shift keying (PSK) modulation format, enabling flexible intensity-to-phase mapping without relying on optical-electrical-optical data conversion at heterogenous network connections. A proof-of-principle experiment shows that optically converted PSK signals from regular PAM signals will induce non-uniform irregular phase noise distortion. The proposed optical gateway is designed to provide an optimized phase distance for PSK signals such that an achievable information rate is maximized by a deep learning-based decision on the receiver side. The phase distance-tuned PSK signals offer performance improvement of about 4 dB gain at a target generalized mutual information by making use of a digital neural network recovery.