This paper proposed a miniature neural interface system. A single chip neural recording SoC was fabricated in 40nm CMOS process with an area of 3 mm*3 mm. It integrated a 16 channel analog front end (AFE), and a low power constant envelope polar transmitter. The general form of continuous phase modulation was used as the modulation scheme. Algorithms for receiver including frequency offset calibration, frame synchronization, and symbol demodulation were proposed and implemented on a software-defined radio platform. Simulation results show that a bit error rate of 10^-4 is achieved at the signal to noise ratio of 19 dB at high data rate mode of 971.4 kbps. A graphic user interface is designed for channel decoding and real-time display. Experimental results showed that the input referred noise of the AFE is 2.87 uVrms, and the energy efficiency of the transmitter is 2.8nJ/bit. The proposed chip consumes 5.47 mW power in total in its maximum workload. The neural signal can be correctly decoded at least at a RSSI (Received Signal Strength Indicator) of -95 dBm, and a working distance of 8 m. In-vivo tests on rat have been conducted, showing a good usability of the proposed system.