Fast algorithm for designing unimodular sequence and related mismatched filter with flexible correlation properties

Unimodular (i.e. constant modulus) sequences with good correlation properties are useful in many areas like communication and radar/sonar. However, several algorithms for designing unimodular sequences with the minimisation of correlation sidelobes, which usually cost a lot of calculation time and hardware resources, are not suitable for real-time applications. Here, a fast algorithm, the inversion of the shaped output with a mismatched filter (ISO-MMF), is proposed to suppress correlation sidelobes to the designed level over specified regions. The closed-form solution is presented to give a fast implementation without thousands of iterations. Several experiments are also conducted to illustrate the effectiveness and efficiency of the proposed method. The theoretical evaluation and experiments show that the proposed ISO-MMF significantly improves the effectiveness of minimising correlation sidelobes and yields better results than existing methods.