From AMS Glossary
In radar, the power spectrum of the complex signal, expressed as a function of Doppler frequency or Doppler velocity. Denoted by S(v), it may be thought of as the reflectivity- weighted radial velocity distribution of the scatterers in a distributed target.
That is, S(v) dv denotes the received power in the velocity interval dv. With this definition, S(v) is normalized such that
is the mean received power as defined by the radar equation.