## 4 Enabling Technologies for FSO Communication
### Asynchronous Transmission Scheme  
Unlike the FSO system that uses synchronous transmission, asynchronous scheme allows the source node to transmit different data to each relay node in an uncoordinated manner. In this transmission method, \(X_{0}\
eq X_{1}\
eq\ldots\
eq X_{M}\). To recover the data and attain diversity gain from the different links transmitting various data, an electronic signal combiner and a squared signal combination method can be employed at the Rx. This method involves squaring the received signals before combining them. During this process, the \(j\)-th combined and squared signal (for \(j=1,\ldots,H\)) can be mathematically expressed as  
\[Z_{j}=\left[\sum_{i=0}^{M}w_{ji}(Y_{i}+N_{i})\right]^{2}, \tag{52}\]  
where the electrical signal \(Y_{i}\) is anticipated to be bipolar with fewer amplitudes after applying the square operator. The coefficient \(w_{j,i}\) functions as a relay selection indicator, taking the value of 1 if the relay node \(R_{i}\) is chosen to produce \(Z_{j}\), and 0 otherwise.  
The data on each link can be recovered by jointly processing the signals before and after the square operation, allowing for improved data recovery and reduced redundancy. In this context, the complexity of relay selection can be simplified by employing the pairwise combination method, where each link is supported by another link in pairs for signal combination. The corresponding coefficient matrix can then be denoted as [284]  
\[w=\left[\begin{array}{cccc}w_{00}&\cdots&w_{0M}\\ \vdots&\ldots&\vdots\\ w_{M0}&\cdots&w_{MM}\end{array}\right]=\left[\begin{array}{cccccc}1&1&0&0& \cdots&0\\ 0&0&1&1&0&\vdots\\ \vdots&\ddots&\ddots&\ddots&\ddots&0\\ 0&0&\cdots&0&1&1\end{array}\right]. \tag{53}\]  
Additionally, a Least Mean Squares algorithm can be used to eliminate the product term of signal and noise from \(Z_{j}\). The resulting signal, \(Y_{ac1}^{j}\), is given by  
\[Y_{ac1}^{j}=\left(\sum_{i=0}^{M}w_{j,i}\cdot Y_{i}\right)^{2}+\left(\sum_{i=0 }^{M}w_{j,i}\cdot N_{i}\right)^{2} \tag{54}\]  
The square operator improves the SNR of the received signal without increasing its amplitudes. However, it does not allow for the direct determination of the bipolar amplitude (i.e., whether the amplitude is positive or negative) from the squared signal \(Y_{ac1}^{j}\). It is essential to recognize that the combined signal prior to squaring retains the bipolarity, which aids in determining the amplitude. Therefore, the merged signal before the square operator can be defined as  
\[Y_{ac2}^{j}=\sum_{i=0}^{M}w_{j,i}\cdot(Y_{i}+N_{i}). \tag{55}\]  
In principle, by jointly sampling the signals \(Y_{ac1}^{j}\) and \(Y_{ac2}^{j}\), the transmitted data can be recovered with a lower BER.  
Both synchronous and asynchronous transmission schemes have their advantages and challenges. Synchronous transmission ensures coordinated signal arrival, which simplifies signal processing at the destination node. However, it requires precise timing synchronization, which can be challenging in practical implementations. On the other hand, asynchronous transmission offers more flexibility and reduces link redundancy by allowing independent data transmission on different links. The squared signal combination method in asynchronous transmission provides diversity gain, enhancing data recovery. Consequently, the choice between synchronous and asynchronous transmission schemes in cooperative FSO systems is contingent upon the specific requirements and limitations of the application. Asynchronous transmission, with its reduced redundancy and flexibility, presents a promising approach for enhancing the performance and reliability of FSO communication systems.