  The merit of evolutionary algorithms (EA) to solve convex optimization
problems is widely acknowledged. In this paper, a genetic algorithm (GA)
optimization based waveform design framework is used to improve the features of
radar pulses relying on the orthogonal frequency division multiplexing (OFDM)
structure. Our optimization techniques focus on finding optimal phase code
sequences for the OFDM signal. Several optimality criteria are used since we
consider two different radar processing solutions which call either for single
or multiple-objective optimizations. When minimization of the so-called
peak-to-mean envelope power ratio (PMEPR) single-objective is tackled, we
compare our findings with existing methods and emphasize on the merit of our
approach. In the scope of the two-objective optimization, we first address
PMEPR and peak-to-sidelobe level ratio (PSLR) and show that our approach based
on the non-dominated sorting genetic algorithm-II (NSGA-II) provides design
solutions with noticeable improvements as opposed to random sets of phase
codes. We then look at another case of interest where the objective functions
are two measures of the sidelobe level, namely PSLR and the integrated-sidelobe
level ratio (ISLR) and propose to modify the NSGA-II to include a constrain on
the PMEPR instead. In the last part, we illustrate via a case study how our
encoding solution makes it possible to minimize the single objective PMEPR
while enabling a target detection enhancement strategy, when the SNR metric
would be chosen for the detection framework.
