## 2 Methods
### Time Delay  
Generally, antennas with very high return loss are ideal for detecting weak reflected signals. In the signals received by the antenna, the energy of the skin-reflected signal is about 90 dB higher than that of the tumor signal. The use of antenna arrays in a system often results in antenna-coupling effects [25; 26]. In this study, these antenna couplings and skin-reflected signals are referred to as pre-artifacts. In this paper, a distance compensation-based dual adaptive artifact removal (DCAF) algorithm was used to remove pre-artifacts. In the DCAF algorithm, the reflection coefficients received by the antenna are first converted to the time domain using discrete inverse Fourier transform [27]. The attenuation effect due to electromagnetic wave propagation is then compensated for, and the temporal entropy threshold of the grouped signals is adaptively selected. Finally, the signals are fed into an adaptive filter with variable filter parameters to reduce the artifacts prior to imaging [28]. After removing the artifacts, the signal received by antenna \(\overset{\rightarrow}{q}_{j}\) transmitting \(\overset{\rightarrow}{q}_{j}\) after pre-artifact removal is set to \(s_{i,j}(n)\), where \(i\) and \(j\) are the antenna index and \(n\) denotes the time series. The position of the antenna is given by \(\overset{\rightarrow}{q}_{0},...,\overset{\rightarrow}{q}_{i},...,\overset{ \rightarrow}{q}_{N-1}\), where \(N\) indicates the number of antennas. The block diagram of the MICF-DMAS algorithm can be seen in Figure 2. The processed tumor signals are inversely delayed and focused to each focal point of the breast. The time for propagation of the scattered signal through the breast is obtained by calculating the path from the transmitting antenna to the scattering point and to the receiving antenna [14]. The time delay \(\gamma_{i,j,e}\) from the transmitting antenna \(\overset{\rightarrow}{q}_{i}\) to the focal point \(\overset{\rightarrow}{m}_{e}\) in the imaging region to the receiving antenna \(\overset{\rightarrow}{q}_{j}\) is [29]  
\[\gamma_{i,j,e}=\frac{(||\overset{\rightarrow}{q}_{i}-\overset{\rightarrow} {m}_{e}||+||\overset{\rightarrow}{q}_{j}-\overset{\rightarrow}{m}_{e}||)}{v}, \tag{1}\]  
where \(||\overset{\rightarrow}{q}_{i}+\overset{\rightarrow}{m}_{e}||\)represents the propagation distance of the signal from the transmitting antenna to the focal point \(\overset{\rightarrow}{m}_{e}\), where \(||\overset{\rightarrow}{q}_{j}-\overset{\rightarrow}{m}_{e}||\) represents the propagation distance of the signal from the receiving antenna to the focal point \(\overset{\rightarrow}{m}_{e}\), and where e denotes the index of the focal point in the imaging region; \(v=c/\sqrt{\varepsilon}\) is the speed of propagation of an electromagnetic wave in a breast, and \(\varepsilon\) is the dielectric constant of normal breast tissue. The signal after the time delay is denoted as  
\[s_{i,j,e}(n)=s_{i,j}(n+\gamma_{i,j,e}). \tag{2}\]  
If the presence of multiple reflections and the additional propagation delay caused by the denser organization inside the phantom are not taken into account [30], the signals have the same phase at focal points where scatterers are present, with the best focusing quality between the signals. The signals at locations other than the focal points where scatterers are present have poorer focusing quality [29].