Waveform design has been subject of interest from the past years till today in different scientific departments. In the past years, it was a believe that transmitting of a signal with high time-bandwidth product, will provide a better system performance. Accordingly, different waveforms with this characteristic have been proposed and are highly in attention. However, the time illustrated that there are many different criteria to design a ``good" waveform. In radar systems, auto-correlation function usually is a tool to analyze the goodness of a designed waveform. The merit of the auto-correlation function of a waveform is in line with small out-of-phase correlation values. Indeed the sequences with low Peak Sidelobe Level (PSL) and small Integrated Sidelobe Level (ISL) are desirable. Considering the researches of waveform design with small sidelobes form the past years till now, illustrates that there is a gap for PSL minimization in Single Input Single Output (SISO) radar systems. In the other word, in the previous works, direct minimization of the PSL metic for designing of sequences from the small alphabets is not considered in the literature. In this dissertation the problem of waveform design is considered as a weighted function of PSL and ISL for SISO radar systems. Then, with insight of the Coordinate Descent (CD) approach, an iterative method for designing sequences with small auto-correlation sidelobes is proposed considering the constraints of constant amplitude and continuous/discrete phases. To tackle the Np-hard non-convex design problem for the case of continuous phase sequences, the solution of a min-max optimization problem is obtained via the bisection algorithm in each iteration of the proposed algorithm. Besides, for discrete phase design problem, a fast search method based on Fast Fourier Transform (FFT) is proposed in this thesis. Minimization of p-norm auto-correlation sidelobes to provide sequences with small PSL, is another achievement of the in hand dissertation in the field of SISO radar systems. In this case, instead of direct minimization of the PSL, we minimize the p-norm of the auto-correlation sidelobes of sequences setting p very large values. It is worth noting that setting p equal to infinity for the p-norm of auto-correlation sidelobes leads to the problem of PSL minimization while by setting = 2 we take into the account the ISL minimization problem. In the field of Multi Input Multi Output (MIMO) radar systems, we have designed set of binary sequences with small auto- and cross-correlation sidelobes. In this case, again a weighted function of PSL and ISL is considered in this dissertation. Then, by using a two-step CD approach, the problem in hand is resorted to a problem for designing a vector in the first step and designing a scalar in the second step. In each iteration of the second step, a fast approach based on FFT is proposed to tackle the design problem. With the aim of the proposed approach, a set of good binary sequences appropriate for MIMO radar systems is obtained in this dissertation. In the other hand, the problem of waveform design to improve the detection performance with known Doppler and in presence of clutter is considered in this paper. In this regard, using the Majorization-Minimization (MM) algorithm, a method is proposed to improve the detection performance of radar systems.