No abstract

No abstract

In this study, the principle of minimum spectral energy leakage is applied, and the mathematical model is also established by the general function through adding different constraints. To allow the target baseband signal to have a high-quality time-domain representation, it is assumed that the baseband signal is an even function. The time-domain waveform has symmetry about the y-axis, and the objective function is obtained by Fourier series approximation. The frequency-domain characteristics of the baseband signals are obtained by adding the energy limitation condition and the boundary restriction condition. Limit a point at the appropriate position of the main lobe of the normalized energy spectral density function, and at the same time, limit the appropriate point at the first side lobe. The changes of the points modified the whole characteristic of the frequency-domain. To more conveniently compare the characteristics of the signal under different constraints, according to the symmetry of the frequency-domain of the signal, the normalized energy spectrum main lobe energy ratio is defined as a parameter, and thereby the spectral performance of the signal is discriminated by the size of this parameter. Through comparative analysis, the signal with the frequency-domain restriction conditions added has a larger normalized energy spectrum main lobe energy ratio. With increasing roll-off factor n, the energy ratio of the main energy spectrum of the normalized spectrum increases accordingly, i.e., the energy leakage is effectively suppressed. The baseband signal can be considered more suitable as a modern wireless communication system and can be obtained by adding a suitable restriction condition and establishing a model with a general function.

In this paper, the optimal mathematical generic function model is established using the minimum out-of-band energy radiation criterion. Firstly, the energy limit conditions, boundary constraints, and peak-to-average ratio constraints are applied to the generic function model; thus, the analytical solutions are obtained under different parameters. Secondly, a single symbol signal energy constraint condition and boundary constraint condition are added to the generic function model; thus, the numerical solution of the different parameters is obtained. In the process of solving the analytical solution, the partial solution process is simplified to solve the analytical solution, and there are also digital truncation problems. In addition, the corresponding order of the Lagrange differential equation increases by a multiple of 2 when the parameter n increases, which makes the solution extremely complicated or even impossible to solve. The numerical solution is in line with the current development trend of digital communication, and there is no need to simplify the solution process in the process of solving the numerical solution. When the parameter n and the Fourier series m take different values, the obtained symbol signals can also meet the needs of different communication occasions. The relevant data of the above research process were solved by a MATLAB software simulation, which proves the correctness of the method and the superiority of the numerical method.

No abstract