Binary phase noise waveform is difficult to detect due to its thrum nail ambiguity function, has high transmission efficiency due to its constant magnitude, and is simple for implementation. Because of these advantages, binary phase noise waveform is widely used in noise radar. Many techniques have been developed to design binary phase noise waveform including Bernoulli trial, logistic mapping function, neural network optimization, genetic algorithm, kicked rotor chaos, polyphase perturbing, and particle swarm optimization techniques. In this paper, we first discuss the characteristics that good binary phase noise waveform needs to have. Then we introduce Kolmogorov-Smirnov (KS) two sample test in nonparametric statistics and derive balanced random walk. From balanced random walk theory, we propose balanced random based approach for noise waveform design and demonstrate that the noise waveforms generated by balanced random walk approach have zero direct components. We implement the proposed approach for noise waveform design and show that the proposed method is over 10% better on maximum sidelobes, 30% better on sidelobe energy than Bernoulli trial noise waveform design and selection.
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