The physical mechanism and output properties of the plasma relativistic microwave noise amplifier (PRNA) are studied numerically by using the all electromagnetic particle-in-cell (PIC) code. Firstly, the dispersion relation between the operating mode and the slow space charge wave of relativistic electron beam without coupling is simulated and analyzed. Simulation results show that both the plasma density n _pand radial thickness Δ r _paffect the dispersion characteristics markedly and their increasing can lead the frequency at the beam-wave resonant point to be enhanced. The beam voltage and current also affect the resonant frequency, but the effect is relatively slight. Secondly, variation of the linear growth rate and the bandwidth are then evaluated by using the linear theory. Calculations show that the PRNA has the virtue of wideband output. Its bandwidth can reach a GHz level. By adjusting the plasma parameters n _pand Δ r _p, the relativistic electron beam voltage and current, the operating frequency can be tuned over a wide frequency range. Therefore the PRNA also has virtue of fine frequency tunability. Based on the above calculation results, the whole PIC simulations of the PRNA are then carried out to verify the virtues of wideband microwave output and frequency tunability. The basic features of the field distributions of the operating in the evolution process and out coupling process are given. The bunching process and the energy release process of relativistic electron beam are also plotted. Simulations show that with a plasma density of 1.4×10 ¹⁹/m ³, beam voltage and current of 500 kV and 2 kA and applied magnetic field of 2.0 T, 200 MW output microwave with efficiency about 20% can be obtained. The frequency ranges from about 7.0 to 9.0 GHz, the band width reaches 2 GHz. And the output mode is the TEM mode of the coaxial waveguide. Both n _pand Δ r _paffect the dispersion relations markedly and the output frequency increases clearly with n _pand Δ r _pincreasing. The influence of beam voltage and current on the output frequency are both relatively small and the gap distance between the plasma and electron beam has little effect on the output frequency. The research results will provide useful reference for further designing the PRNA.