# A Communication Framework for Image Transmission through LPWAN Technology
## 4 Analysis Results  
The following results from the various stages of the proposal framework are presented. Thus, stage I demonstrated image processing in which the sparsity was evaluated using wavelet, Kronecker, and Discrete Cosine (DC) transforms. This seeks to establish a common foundation for improving information reduction. Figure 2 depicts the integration of stages I and II, where it is possible to observe the PSNR values versus sparsity percentage and conclude that when the sparsification percentage is increased, the wavelet transform achieves the best PSNR results. The coefficients of the DCT, wavelet, and Kronecker transforms are shown in Figure 3a-c. It is possible to see that wavelet has a minor data deviation, indicating an improvement in Stage II of compressive sensing. Figure 2: PSNR values vs sparcity percentage. All algorithms (IHT, OMP, GPSR, and Twist) were used in the reconstruction process. The sparse vector signals and the sample matrix were used as inputs, and the outputs were a PSNR-based relationship between the rebuilt signal and the original signal, as well as the number of rebuilt samples (M). Figure 4 shows that the Twist algorithm achieves the highest reconstruction index in terms of M.  
LoRa symbols were created using encoded data. As previously stated, preamble and synchronization chirp symbols are generated; in our case, 10 preamble symbols (up-chirps) and 2 synchronizations (down-chirps) were modulated before the start of the data  
Figure 4: Reconstruction algorithms evaluation. Figure 3: Coefficients distribution. symbols to create the total LoRa frame to be transmitted on SDR platforms. It is important to remember that any chirp symbol (preamble, synchronization, or data) has the same symbol time, which is proportional to the value of SF. Figure 5 depicts LoRa symbols for an up-chirp, a down-chirp, and a data symbol created and transmitted on the SDR platform. Figure 6 illustrates the spectrogram of the transmitted LoRa frame signal, which contains symbols for 10 preamble up-chirps, 2 synchronization down-chirps, and coded data chirps. At the receiver of stage III, the operating frequency and the master click rate were configured on the SDR. The received chirps are presented in Figure 7 and the received spectrogram is presented in Figure 8. In stage IV, after the LoRa demodulation process, it is necessary to sweep from the beginning of the received vector until its end. Here, it  
Figure 5: (**a**) up-chirp, (**b**) down-chirp, and (**c**) coded LoRa signal with \(SF=8\) and \(BW=500\) kHz. Figure 6: Transmission spectogram. is considered the first symbols (10 of preamble and 2 of synchronization). These twelve symbols are necessary to retrieve the data in the received symbols. Figure 9 shows a complete received LoRa frame signal in time, where preamble synchronization and data are shown. Signal peaks allow to find the preamble and the synchronization chirp symbols, after two synchronization symbols (\(2T\)), it is possible to find the beginning of the data. Figure 8: Reception spectrogram. Figure 7: (a) up-chirp, (b) down-chirp, and (c) received coded LoRa signals. To decode the image information and find the original values (wavelet transform representation), a program was created that converts the received data (LoRa symbols) into their base representation again. Decoding the received data is required to restore the image. As a result, a vector of similar length must be integrated among the many packets received. This vector contains information on wavelet transform output values, positions, and negative value positions. After using the reconstruction procedure to rebuild the vector using their features, the original vector of information is recovered using wavelet inverse transform. Finally, the initial size of matrix \(nxn\) must be adjusted, and the image must be screened. The framework's final section illustrates the differences between the original and rebuilt images.