A microwave photonic (MWP) radar system with improved signal-to-noise ratio (SNR) performance is proposed and experimentally demonstrated. By improving the SNR of echoes through properly designed radar waveforms and resonant amplification in the optical domain, the proposed radar system can detect and image weak targets that were previously hidden in noise. Echoes with a common low-level SNR obtain high optical gain and the in-band noise is suppressed during resonant amplification. The designed radar waveforms, based on random Fourier coefficients, reduce the effect of optical nonlinearity while providing reconfigurable waveform performance parameters for different scenarios. A series of experiments are developed to verify the feasibility of the SNR improvement of the proposed system. Experimental results show a maximum SNR improvement of 3.6 dB with an optical gain of 28.6 dB for the proposed waveforms over a wide input SNR range. From a comparison with linear frequency modulated signals in microwave imaging of rotating targets, significant quality enhancement is observed. The results confirm the ability of the proposed system to improve SNR performance of MWP radars and its great application potential in SNR-sensitive scenarios.