# (a) Inconstant velocity error of the platform

In an ideal SAR system, the platform is assumed to be moving with a constant velocity, and the signal is transmitted with PRF. The signal is transmitted and received with a constant PRF, and the azimuth signal is uniformly sampled. However, if the PRF remains constant, and the platform velocity is changing, the azimuth signal sampling is no longer uniform, and the azimuth resolution will be deteriorated. The geometry of azimuth non-uniform sampling is illustrated in Fig. 6.3.

In a signal processing point of view, according to Eq. 2.2.6, the Doppler modulation rate of a stationary target can be expressed as

If is V_{a} no longer constant, *f _{dr}* will be a changing value. Thus, using a constant

*f*as a matched filter will lead to the azimuth defocus.

_{dr}There are two ways to solve this problem: re-sampling algorithm [2] and phase compensation algorithm. Both algorithms use the velocity data recorded by the INS to compensate the motion error. However, these two algorithms are high dependent to the accuracy of the INS data, and the signal processing complexity is increased.

The most practical way to solve this problem in an airborne SAR system is to change the time-constant PRF into space-constant PRF [3]. By altering the value of PRF according to the velocity of the platform, the PRF-to-velocity ratio K_{v} remains constant. According to Eq. 2.2.5, the azimuth phase of a target in SAR can be expressed as

where azimuth time *t _{a} = — —f*:

^{:}if. Substitute this equation into Eq. 6.2.5, it is

noted that the Doppler modulation rate is constant with a constant K_{v}.