## 4 Case Study A: LED Array MIMO Multiplexing
### Experimentation  
Due to the underlying hardware issues, a new methodology had to be taken to show that the system, specifically the model, is capable of working even with the hardware issues. To showcase this, the following steps were taken:  
* Step 1: Find the number of characters, which will be called the chunk size for the remainder of the study, that can be successfully transmitted without any type of error (Camera or LED). As mentioned earlier, for shorter transmission the hardware inconsistencies are not prevalent;
* Step 2: Transmit a 1000 word file in a single transmission. This was the original/ideal target for the empirical study to transmit with as few errors as possible;
* Step 3: Evaluate the 1000 word file transmission by dividing it into chunks established from Step 1 and evaluate each chunk;
* Step 4: Transmit the 1000 word file in several videos in which each video sends one chunk of data where the chunk size is defined by the the steps used in Step 1;
* Step 5: Analyze the results. The reason why the chunk size is established is to showcase the effectiveness of the model as independently as possible, rather than with the entire system. Similarly the reason why a single transmission of a 1000 word file is compared versus a fragmented transmission of a 1000 word file is, again, to showcase the models performance but, more importantly, to illustrate how the hardware issues can cause serious problem for this communication system. To achieve Step 1, several videos of varying character length were transmitted at each distance. After computing the results, 100 character transmissions were found to be the best chunk size. One hundred character transmissions were roughly 17 packets; 18 packets if the starting and ending markers are included. The results showed that across five trials at each distance from 1 m to 7 m, there are no hardware issues nor model misclassifications except for when the distance is at 7 m. This is when a few model misclassifications start to appear. Out of the nearly 6200 frames collected across the five trials at a distance of 7 m, there were only 16 model misclassifications. this illustrates another point which is that as the LED moves farther and farther away, the model is susceptible to more misclassifications for multiple reasons, some of which include the resolution of the image becoming too degraded. Steps 2 and 3 was performed by transmitting the 1000 word file at each distance twice. Then, every 17 packets, which is roughly equal to 100 characters which equals 1 chunk, were analyzed for byte errors only for the data and not for the packet metadata. In the 1000 word file, there were about 50 chunks or about 850 packets worth of data. After demodulating the transmission, the 50 chunks were checked for the total number of packets with any number of errors, and the Cumulative Average Packet Error Rate was also calculated. The reason why the cumulative average was used was because, as will be discussed later, the hardware issues would pop up randomly during the transmission and distort the transmission. Thus, to obtain an intuitive idea of the success of the entire transmission, the cumulative average was utilized. The formula for the Cumulative Average Packet ErrorRate is given in Equation (1). Then, the average of both the number of packet errors and Cumulative Average Packet Error Rate between the two trials was calculated. \[PER(chunk\ number\ N)=\frac{\#\ of\ packets\ in\ error\ for\ N\ chunks}{total\ number\ of\ packets\ in\ N\ chunks} \tag{1}\]  
For Step 4, instead of transmitting a single 1000 word file in 1 video, the 1000 word file was sliced such that approximately 100 characters were transmitted in each video. This resulted in having to transmit 50 videos to obtain the entire 1000 word file.