# Nonlinearity Correction of FMCW SAR

The continuous transmit and receive signals during the entire PRI of FMCW SAR induces the problem that the phase linearity cannot be maintained. The nonlinearity of the transmitted signal will severely affect the performance of the range compression, and furthermore deteriorate the image resolution.

The nonlinearity correction is the prior issue in FMCW SAR signal processing, since the range compression is the foundation of the following signal processing. Both hardware and software solutions have been proposed to solve this problem. Hardware approaches are proposed to eliminate nonlinearity in signal generating stage, such as using pre-distortion techniques to compensate for nonlinearity in VCOs response characteristics, using a tuning voltage converter to correct varactor tuning curves, direct digital synthesizer [10-12], and other compensation circuits.

However, these techniques are either expensive or increasing the complexity of the system. Moreover, the performances of hardware approaches suffer from external conditions. Software approaches can be implemented without restrictions of hardware methods. Jiang et al. [13] suggested an adaptive sampling method to correct nonlinearity in FMCW radar. Kulpa et al. [14] presented a nonlinearity estimation algorithm with curve fitting. Nevertheless, both algorithms are based on specific approximated nonlinearity models, which limit their generalities in practical FMCW SAR applications. Meta et al. [15] proposed a transmitted nonlinearity estimation algorithm regarding the nonlinearity in beat signal as the derivative of transmitted nonlinearity. By performing integral operation on beat signal with known propagation delay, the transmitted nonlinearity can be estimated. However, this algorithm is inherently biased since the derivative approximation is used, and its performance degrades rapidly as time delay increases.

In this section, the nonlinearity problem is analyzed by signal modeling, and the existing method is introduced, and its limitations are discussed. Moreover, the proposed algorithm based on homomorphic deconvolution and the correction strategy are presented, and simulation results are shown to demonstrate the validity of the proposed algorithm.