Polyphase And Spectrally-Constrained Sequence Research Based On Simulated Annealing

Simulated annealing algorithm(SA)is an adaptive heuristic optimization algorithm for combinatorial optimization problems.The key feature of simulated annealing is that it can accept the solution of worsening objective function value with certain probability,so as to escape local optima.The algorithm has strong global optimization ability,so it has been widely used in various fields.With the rapid development of wireless communication,sequence design,as an important part of wireless communication system design,plays an increasingly important role.Polyphase sequences with good correlation characteristics are an integral part of many active sensing and communication systems,which are widely used in multiple access communication,channel estimation,synchronization,etc.At the same time,as the spectrum becomes increasingly congested and fragmented,traditional sequences are not applicable in spectrally-constrained systems,so the spectrally-constrained system needs a more "intelligent" sequence design method.From the perspective of sequence numerical optimization,the SA algorithm is used to study the polyphase sequence and spectrally-constrained sequence in this paper.The main research contents and achievements of this paper are as follows:(1)According to the definition of the aperiodic auto-correlation function(AACF)of a sequence,a formula based on the fast Fourier transform is derived to represent the integrated sidelobe level(ISL)of the AACF of a single sequence.(2)According to the global optimization capability of SA algorithm,the relation between SA and the optimal phase search of the sequence is established,and a polyphase sequence search algorithm based on SA is proposed.Numerical results indicate that it is feasible and effective to use SA algorithm to search for polyphase sequence with good correlation,especially when the sequence length is long.(3)In view of the numerical optimization algorithm for obtaining low AACF and low Peak-to-Average Power Ratio(PAPR)spectrally-constrained sequence proposed by Hu and Liu in 2014,a spectrally-constrained sequence search algorithm based on SA is proposed to further optimize the numerical optimization results of the algorithm proposed by Hu and Liu.Numerical experimental results show that the sequence obtained by the algorithm proposed in this paper not only satisfy the spectrum constraints,but also have lower AACF and lower PAPR compared with the sequence obtained by the algorithm proposed by Hu and Liu.