## 3 Methodology
### Signal Acquisition with Genetic Control  
**Step 1. ** Doppler frequency and code delay encoding  
The first step in employing GC to conduct signal acquisition is to convert the locally generated Doppler frequency and code delay to string by way of a binary encoding method [27]. The respective upper bound of Doppler frequency and code delay (\(u_{maxup}\) and \(v_{maxup}\)) is converted to string and the length is expressed as \(\mathrm{m}\) and \(\mathrm{n}\), respectively. \[ \begin{array}{l}u_{maxup}\xrightarrow{\mathrm{encoding}}\mathrm{S}_{\mathrm{f}} :\mathrm{a}_{\mathrm{m}}\mathrm{a}_{\mathrm{m}-1}..\mathrm{a}_{\mathrm{1}}.. \mathrm{a}_{\mathrm{1}}..\mathrm{a}_{\mathrm{2}}\mathrm{a}_{\mathrm{1}}\\ v_{maxup}\xrightarrow{\mathrm{encoding}}\mathrm{S}_{\mathrm{g}}:\mathrm{b}_{ \mathrm{n}}\mathrm{b}_{\mathrm{n}-1}...\mathrm{b}_{\mathrm{k}}...\mathrm{b}_{ \mathrm{2}}\mathrm{b}_{\mathrm{1}}\end{array} \quad\mathrm{a}_{\mathrm{k}}, \mathrm{b}_{\mathrm{1}}\in\{0,1\} \tag{6}\]  
where \(\mathrm{S}_{\mathrm{f}}\) and \(\mathrm{S}_{\mathrm{g}}\) are the Doppler frequency and code delay individuals, respectively. \(\mathrm{m}\) and \(\mathrm{n}\) are the maximum bit number of Doppler frequency and code delay individuals. Each bit in the individual is termed as genetic gene. **Step 2. ** Fitness function determination  
After the parameters are encoded, it is necessary to define fitness function to evaluate the quality of each individual. To put it simply, fitness function is the performance index which determines the quality of the individual, retains the superior gene and removes the inferior gene in order to gradually upgrade the overall performance index through evolution by generation. During the signal acquisition process, the signal detection margin serves as fitness function, which is defined by  
\[Q_{z}=10\cdot\log_{10}\{\frac{E[y(u_{z},v_{z})]}{E[w_{z}]}\},\quad z=1,2,3,...,Z \tag{7}\]  
where \(w_{k}=w_{\iota k}+j\,w_{\varrho k}\) is the noise term as depicted in Equation 3. \(E[\cdot]\) is the expectation value and \(Z\) is the initial population size depicted in step 3. The output \(y(u_{z},v_{z})\) can be obtained through correlation of coherent integration and non-coherent integration. The goal of GC is to find the optimal \(u_{z}\) and \(v_{z}\) parameters in order to maximize \(Q_{z}\) value. **Step 3. ** Initial population size selection  
In Step 1 the search parameters have been encoded as one pair, which are one set of solution in the signal acquisition result. Before utilizing GC, \(Z\) sets of parameters must be produced randomly, which represents initial population indicated by  
\[\mathrm{U}=\left\{(u_{1},v_{1}),(u_{2},v_{2}),...,(u_{z},v_{i}),...,(u_{Z-1},v _{Z-1}),(u_{Z},v_{Z})\right\} \tag{8}\]  
The evolution of initial populations is adopted to obtain an optimal solution. The number of initial populations depends on the complexity of the search problem. The solution derived from the adoption of initial population may be poor in performance. However, through the evolution process, the subsequent generation outperforms the previous one and finally achieves the optimal value. **Step 4. ** Selection and reproduction  
Similar to the cell division of organisms, the probability of reproduction is based on the rule of survival of the fittest. Selection is the process that prefers individuals with high fitness over low-fitness ones. Thus, the probability of choosing certain individuals is in proportion to its fitness. Suppose the fitness value of \(i\)-th individual \((u_{i},v_{i})\) is \(Q_{i}\), the probability of reproduction is represented by  
\[\Delta_{i}=Q_{i}/\sum_{i=1}^{Z}Q_{i} \tag{9}\]  
The most prevalent natural selection method of reproduction is a roulette wheel game, the slot division of which is proportional to the fitness value of the individual. The high-fitness ones stand a higher chance of being selected in roulette game. **Step 5. ** Crossover  
Biologically, crossover is the exchange of genes between the chromosomes of two parents.