Moving Target Indicator (MTI) and Pulse Doppler Radars,

The clutter power spectrum can be written as the sum of fixed (stationary) and random (due to frequency spreading) components, as

where is the PRI (i.e., , is the PRF), is the clutter power or clutter mean square value, and is the clutter spectral spreading parameter as defined in Eq. (10.1). As clearly indicated by Eq. (10.2), the clutter PSD is periodic with period equal to . Furthermore, the clutter PSD extends about each multiple integer of the PRF. It must be noted that this spread is relatively small and thus the relation is always true. This is illustrated in Fig. 10.1. The mean square value can be calculated from

Let denote the central portion of Eq. (10.2) (i.e., ); then is be expressed by

f 0= f f

Sc f  Pc

Tf 2 ------------------- f k T– 2

2f2 ------------------------–  

  exp

= T 1 fr fr Pcf

fr

f fr«

Pc T Sc f  fd fr-2

= Sc0 f  k 0= Pc

Pc T Sc0 f  fd –

=

where is a Gaussian shape function given by

and .