Pulse compression techniques are widely used in modern radar systems to enhance range resolution and detection capability. As signal design is one of the basic factors of an efficient radar system, the problem of designing a radar signal with good characteristics using pulse compression is addressed in this paper. A linear frequency modulated (LFM) waveform has been widely used for conventional radars. However, it has a higher sidelobe level which makes the detection of weak targets very difficult in presence of strong targets returns and as a result the problem of masking occurs. In order to get suppressed sidelobes of radar matched filter output as well as preserve the main lobe resolution and level to overcome the problem of masking, nonlinear frequency modulated (NLFM) signals are used in modern radars. In this paper, we will introduce two different approaches to design an optimized NLFM signal which is characterized by optimized sidelobe level (SLL). The first is the exponential piecewise linear function (EPWL) which is the modification of piecewise linear (PWL) functions relying on an exponential predistortioning function. The second is the odd-term polynomial approximation (OTPA) in which the generation of NLFM signal depends only on odd-powered terms of the polynomial function. Furthermore, the simulation results of autocorrelation functions (ACF) of the proposed signals show its superiority over the traditional LFM signals and significantly enhancement compared to the recent background work. The Doppler sensitivity of the designed signals has been evaluated, revealing that the first approach offers Doppler tolerance and is suitable for surveillance radar systems, while the second approach with a lower sidelobe level is used in applications such as Synthetic Aperture Radar (SAR). Finally, the ambiguity function of the designed signals has been measured to illustrate the effect of the Doppler effect relative to different velocities.