## 3 Simulation Environment and RMWBI System
### RMWBI System and Visualization in the Simulation Environment  
For the detection of breast tumors, the source signal of the transmission is Gaussian waves and the backscattered signal from the target is received and recorded. The recorded signals are preprocessed to remove artifacts from system components such as skin and tissues as well as antenna coupling signals [77]. Other signals that are greater than the amplitude of the tumor response are then suppressed and filtered. Thus, a low-amplitude tumor response is obtained. We developed an RMWBI system on CST MWS with a Vivaldi antenna. The antenna is used to transmit the signal and collect the reflected signal. The proposed Vivaldi antenna is rotated in twelve different positions around the created tumorous heterogeneous breast phantom. The measurement taken from the tumor-free heterogeneous phantom was used for the calibration process. This is the subtraction method stage in which the signals scattered from healthy breast tissues are subtracted from the total number of signal scattered from the tumorous breast and recorded on the receiving antenna. The most dominant part here is the signals emitted from the skin. The signal reflected from the tumor is large compared to its amplitude. It is very difficult to find a tumor response without removing the dominant parts because it will result in heavy noise in the tumor response due to the dominant signals. The subtraction method is expressed in Equation (4):  
\[S^{TY}=S^{T}-S^{H} \tag{4}\]  
In Equation (4), \(S^{T}\) represents the signal in each channel, \(S^{H}\) represents the signal scattered from the tumor-free breast, and \(S^{TY}\) represents the tumor response signal obtained as a result of filtering. An image enhancement method using Gaussian band-pass filtering is proposed for this imaging system. The proposed method is typically used to eliminate short  
Figure 7: Positioning of Vivaldi antennas around the heterogeneous breast phantom. pulse signal averaging artifact effects [96]. The Hilbert transform was used to integrate a modulated Gaussian pulse of the incident wave into a radar-based microwave imaging system. A peak is formed at the center of the integrated signal, and the maximum peaks of this tumor point are collected at a focal point, and the location of the tumor is displayed. In order to obtain a smooth image from the Gaussian signal, which is the tumor response, the envelope of the signal is taken with the Hilbert transform. This transformation is expressed in Equation (5):  
\[H[s(t)]=\frac{1}{\Pi}\int_{-\infty}^{+\infty}\frac{s(\Gamma)}{s(t-\Gamma)} \mathrm{d}\Gamma \tag{5}\]  
\[S_{A}(t)=s(t)+jh[s(t)] \tag{6}\]  
\[S_{A}(t)=A(t)\mathrm{e}^{i\omega(t)} \tag{7}\]  
Here, \(S_{A}(t)\) is the analytical signal, \(s(t)\) is the filtered real signal, \(H[s(t)]\) is the complex composition, and Equation (7) shows the time envelope. The DMAS focusing method was used for tumor detection using the UWB microwave imaging technique. In DMAS, using the finite difference method, signals reflected from the target are shifted in the time domain, doubled, and summed to create a focal spot. The difference multiplication operation was performed according to DAS. The DMAS focusing algorithm is shown in Equation (8):  
\[I(\Gamma_{0})=\int_{0}^{T}\left[\sum_{m=1}^{M-1}\sum_{j=m+1}^{M}x_{m}(r_{m}(r_{ 0})).x_{j}(r_{j}(r_{0}))\right]^{2}\mathrm{d}t \tag{8}\]  
Here, for each pixel, \(\tau_{m}\) represents the delay time, \(x_{m}\) represents the tumor response, and the energy of the pixel energy at distance \(\Gamma\) is expressed as \(I(\Gamma_{0})\). \(I(\Gamma)\) is the energy of pixels at location \(\Gamma(x\), \(y\), \(z)\). Here, \(v\) is the wave velocity, \(\Delta t\) is the time steps, and \(\mathrm{d}_{i}\) is the distance between the pixel and the antenna.