## 2 System Model
### GA-Based MIMO Detection  
For MIMO detection based on the GA, several terms between the GA algorithm and MIMO system need to be matched. An individual represent the candidate transmitted signal vectors and the _gene_ means the element of the constellation alphabet \(\mathbf{\hat{S}}\). Since we consider a real-valued MIMO system, the dimension of an individual is \(2N_{t}\) and the population forms a \(2N_{t}\times P\) matrix, where \(P\) denote a population size. Choosing a suitable initial population is an important factor in GA convergence [29]. Some initialization procedures (e.g., using ZF or MMSE solutions) can accelerate GA convergence [29; 30].  
Figure 3: Flowchart of the basic GA process.  
Figure 2: Generation process of a new population through the genetic operations.  
Therefore, we use a randomly generated set of individuals, including the MMSE solution, as an initial population for MIMO detection.  
The fitness function should evaluate each individual and provide each individual's assessment information. In MIMO detection, the measure of goodness for each individual can be determined by the distance from the transmitted signal vector. Thus, the reciprocal of Euclidean distance (4) is appropriate as a fitness function, as follows  
\[Fit=\frac{1}{d(\mathbf{\bar{x}})}=\frac{1}{\|\mathbf{\bar{y}}-\mathbf{\bar{H} \mathbf{x}}\|^{2}}. \tag{5}\]  
A higher value of fitness function indicates a fitter candidate solution.  
In order to gradually improve the candidate solutions in the population, the parents for the next generation should be selected based on their fitness value. Here, we use the roulette wheel selection method in which the probability of selection for genetic operations is determined by the fitness of the parent individual. Unfortunately, there are no rules for determining GA parameters such as population size, maximum number of generations, _selection_ probability, _crossover_ probability, and _mutation_ probability. Therefore, it is necessary to select an appropriate value according to the number of transmission antennas \(N_{t}\) and the modulation order \(M\) to be used. Based on the conversion of GA to MIMO detection, GA can be used as a detection method for MIMO systems through the procedure described in Figure 3.  
In order to find the optimal solution using search-based techniques, it is important to perform efficient searches that explore as much as possible in areas where the fitness is expected to be good. However, in the basic GA, premature convergence reduces the diversity of the population and leads to the problem of the repeated exploration of already searched space. Moreover, the genetic operations of the basic GA are randomly selected according to each operation's rate, and the operation of each genetic operation is also performed using the randomness. Because of these high randomnesses, we can not control the searching direction of GA, which means that it is hard to perform an intensive search in a high fitness area. These repeated search and randomness weakens the search ability of the GA, which degrades its BER performance and increases the computational complexity of GA-based MIMO detection.