Design of Binary Coded Pulse Trains with Good Autocorrelation Properties for Radar Communications

Finite length of sequences that are modulated both in phase and amplitude and have an ideal autocorrelation function (ACF) consisting of merely a pulse have many applications in control and communication systems. They are widely applied in control and communication systems, such as in pulse compression systems for radar and deep-space ranging problems [1-5]. In radar design, the important part is to choose a waveform, which is suitable to be transmitted because the waveform controls resolution in clutter performance. In addition, it can solve a general signal problem particularly related to the digital processing. Energy ratio (ER), total side lobe energy (SLE), and peak sidelobe level (PSL) are three properties of such sequences interest. This paper presents a method using the Complementation, Cyclic Shift and Bit Addition for synthesizing and optimizing a binary sequence implemented to improve the sequences of a similar quality with the Barker sequence, particularly for lengths greater than 13. All of these methods are guided by the specific parameter with good characteristics in ACF (ER, SLE, and PSL) [6,7,8]. Such sequences can then be effectively used to improve the range and Doppler resolution of radars.

Wieferich pairs and Barker sequences, II

We show that if a Barker sequence of length $n>13$ exists, then either n $=$ 3 979 201 339 721 749 133 016 171 583 224 100, or $n > 4\cdot 10^{33}$. This improves the lower bound on the length of a long Barker sequence by a factor of nearly $2000$. We also obtain eighteen additional integers $n<10^{50}$ that cannot be ruled out as the length of a Barker sequence, and find more than 237 000 additional candidates $n<10^{100}$. These results are obtained by completing extensive searches for Wieferich prime pairs and using them, together with a number of arithmetic restrictions on $n$, to construct qualifying integers below a given bound. We also report on some updated computations regarding open cases of the circulant Hadamard matrix problem.