# Multi-User Detection Based on Improved Cheetah Optimization Algorithm
## 2 Methods
### Differential Evolution Algorithm  
DE, as an optimization algorithm driven by population intelligence, is distinguished by its robustness, adaptability, and capacity for global search. It emulates the natural process of individual genetic variation, crossover, and selection. DE is not only able to adapt to the problems of nonlinearity, high dimensionality, and multi-peak ability but also does not need the gradient information of the problem, which, taken together, makes it an  
Figure 2: CO Strategy Map.  
evolutionary algorithm that can effectively cope with the problem of multi-user detection in a complex environment.  
The basic idea of the DE algorithm is to update the individuals in the population by random mutation, crossover, and selection operations. Specifically, the DE algorithm includes the following steps:  
1. Initialize the population Setting up a \(d\)-dimensional space with \(M\) individuals, then the initialized population can be represented as \[E_{x}(0)=E_{x,1}(0),E_{x,2}(0),\ldots,E_{x,d}(0)\quad x=1,2,\ldots,M\] (12) The \(i\)th individual in the \(j\)th dimension is initialized as \[E_{x,y}(0)=L_{y}+rand(0,1)(U_{y}-L_{y})\quad x=1,2,\ldots,M\quad y=1,2,3,\ldots,d\] (13) Here, \(U_{y}\) represents the upper range and \(L_{y}\) represents the lower range in the \(j\)-dimensional space.
2. Mutation DE mainly operates on individuals for mutation by differential strategy; in a certain iteration, three individuals are randomly selected and mutated as follows \[H_{x}(e)=E_{p1}(e)+F\times(E_{p2}(e)-E_{p3}(e))\] (14) Here, \(E_{p1}(e)\), \(E_{p2}(e)\), and \(E_{p3}(e)\) are the randomly selected individuals for \(e\) iterations, respectively, \(F\) is the scaling factor of the variance, and the convergence of the local extreme points is inversely proportional to \(F\).
3. Crossover Setting a certain fixed crossover probability, according to which the new mutant individuals undergo crossover with the original individuals, this operation significantly enriches the population's diversity. Mathematically represented as \[V_{x,y}=\left\{\begin{array}{l}h_{x,y}(e),rang(0,1)\leq cr\\ E_{x,y}(e),else\end{array}\right.\] (15) where \(cr\) is the crossover probability. In this scenario, \(E_{x,y}(e)\) represents the original individual in the population, while \(h_{x,y}(e)\) represents the individual undergoing the crossover operation.
4. Selection All individuals of the current generation corresponding to the crossover individuals and individuals of the original population are judged by their fitness value, and eugenic selection of well-adapted individuals as the next generation, in which all individuals \(E_{x}(e+1)\) are not inferior \(E_{x}(e)\). The mathematical representation of this part is \[E_{x}(e+1)=\left\{\begin{array}{l}V_{x}(e),F(V_{x}(e))<F(E_{x}(e))\\ E_{x}(e),else\end{array}\right.\] (16) where \(E_{x,y}(e)\) represents the original individual in the population, \(V_{x}(e)\) is the crossover individual, \(E_{x}(e+1)\) is the next generation individual, and \(F(V_{x}(e))\) and \(F(E_{x}(e))\) are the fitness values of the crossover and original population individuals, respectively.