I get the “output power spectral density” form dw1000 datasheet is -39dBm/MHz，I found out there were other units “dBm/500MHz” ,What are the two differences about “dBm/MHz” and “dBm/500MHz”,Is there any conversion relationship (mathematical formula)between them?
dBm/MHz is power in a 1MHz band while dBm/500MHz is over a 500MHz band.
So if the power is uniform over the band there will be a factor of 500 (or 27dB) difference between them.
The 500MHz bandwidth measurement is because that is (for most channels) the total power over the full signal bandwidth.
The regulatory limit is -41dBm/MHz but allows you to measure over a 50 MHz bandwidth. This is what you want to do, the wider bandwidth effectively averages out any narrow spikes, since the limit is based on the peak measured not the average this allows a higher transmit power to be used.