Sequence design can find diverse applications in areas, including active sensing, communications, and medical imaging. In recent years, computational methods have been devised to synthesize arbitrary waveforms under various practical constraints, including the constant modulus constrains and spectrum containment restrictions. Indeed, as the hardware cost of arbitrary waveform generators decreases, arbitrary waveforms become widely popular in diverse systems, such as cognitive active sensing systems. However, for massive commercial markets, the active sensing systems, such as the automotive radar systems, must be rather inexpensive. Therefore, highly diverse binary sequences with arbitrary lengths are primary candidates for these systems due to the low-cost hardware advantages of generating these sequences. In this chapter, we will review well-known binary sequences and their properties. We will also discuss recent advances of binary sequence designs and their applications.

This chapter is framed in the mentioned context with the goal of providing a comprehensive study on the design of unimodular (in particular binary) sequences possessing good aperiodic autocorrelation properties for radar systems. To this end, a new technically sound procedure aimed at designing continuous/discrete phase sequences with good aperiodic autocorrelation function (in terms of PSL and ISL) is introduced in this chapter. Specifically, resorting to the Pareto framework, the weighted sum of PSL and ISL is considered as an objective function to optimize under the phase -only constraint on the probing waveform. Hence, an iterative procedure based on the coordinate descent (CD) method is introduced to deal with the resulting non -deterministic polynomial -time hardness (NP -hard) optimization problem. Each iteration of the devised method requires the solution of a nonconvex min -max problem. It is handled either through a novel bisection or a fast Fourier transform (FFT)-based method, respectively, for the continuous and the discrete phase constraint. Several numerical examples will illustrate the performance enhancement (especially in the highly important binary case) of the devised algorithm.

In this chapter, the problem of joint transmit code and receive filter design has been considered to optimize the achieved SINR of extended targets in the presence of signal -dependent interference. Due to uncertainties about the TIR, a worst case optimization framework has been proposed over two different T1R uncertainty sets. The former contains T1R's samples corresponding to some TAAs, whereas the latter is equivalent to bounding the actual T1R within a spherical set. Additionally, a PAR constraint has been imposed on the transmitted waveform so as to ensure its practical implementation. The obtained non -convex optimization problem has been divided into two sequential relaxed SDP problems. Their corresponding solutions have then been exploited to synthesize the code -filter pair via randomization methods.

A multiple input multiple output (MIMO) radar transmits several probing waveforms simultaneously from its transmit antennas. It can improve the interference rejection capability and parameter identifiability as well as provide fl exibility for transmit beam pattern design . In addition, a cognitive approach for radar systems, which capitalizes on the information obtained from the surrounding environment or the prior knowledge stored in the platform, was proposed . The significance of MIMO radar and the cognitive approach has recently motivated active research into the waveform design. A well -designed waveform can allow for more accurate detection and estimation.

In this chapter, the authors cope with the joint optimization of fast-time LAF and waveform spectrum. A novel objective function with a weighting factor to trade-off the WISL with respect to range-Doppler sidelobes and the spectral stopband energy is proposed. The energy and PAR constraints are forced on the designed signal, which further generalize the problem we developed. To handle the resulting non-convex quadratic problem, a new iterative sequential quadratic optimization (ISQO) algorithm is proposed [30]. In each iteration, it transforms the optimization problem into a tractable quadratic subproblem that is further converted to a linear optimization problem with a closed-form solution by resorting to the first-order Taylor expansion. The proposed algorithm has polynomial time complexity that is linear with the number of iterations and polynomial with the size of the designed waveform and the number of the considered range-Doppler bins. The simulation results highlight the superiority of the proposed algorithm contrast to AISO algorithm in terms of the objective value, computational time, and the capability of prohibiting the sidelobes of a strong return and narrowband spectral interferences from masking weak targets. The experimental results show that the hardware limitation influences the level suppressed in both energy spectral density (ESD) and WISL and confirms the effectiveness of spectral coexistence in prohibiting the sidelobes suppressed in the LAF rising.