## 4 Proposed Scheme  
In this section, the CoMP scheme using the SPC in base station is introduced for the HetNet system. In the CoMP scheme proposed in this paper, all base stations in the cells transmit signals by applying the constructive and destructive SPC adaptively according to the location of the mobile. There are three cases according to the location of the mobile. In case 1, location of the mobile is the center of the pico cell 1. In case 2, location of the mobile is between the pico cells 1 and 2. Finally, in case 3, the mobile is located among the three pico cells. Figures 4-6 show cases 1, 2 and 3 respectively. Figure 4: The case 1 of the proposed scenario. Figure 3: Destructive 1-bit and 2-bit feedback SPC. Case 1: Figure 4 shows case 1, in which the mobile is located in the center of the pico cell. In this case, the base station transmits the signal to the mobile through the conventional communications system. The base station transmits the signal to the mobile by using the single input single output (SISO) OFDM technique. The mobile receives one signal transmitted from the base station, as follows,  
\[Y_{Case\,1}=H_{SB,1}S_{1}+N. \tag{8}\]  
The \(H_{SB,1}\) is the channel coefficient between the base station of the pico cell 1 and the mobile, \(S_{1}\) is the transmitted OFDM symbol, and \(N\) is the AWGN. Case 2: Figure 5 shows case 2, in which that the mobile is located between the pico cells 1 2. When the mobile is located between the the two cells, it receives a signal which is distorted by the interference signal transmitted from the base station of the pico cell 2. The received signal is as follows,  
\[Y_{IC,1}=\underbrace{H_{SB,1}S_{1}}_{a1}+\underbrace{H_{SB,2}S_{2}}_{b1}+N. \tag{9}\]  
Figure 5: Case 2 in the proposed scenario. Figure 6: Case 3 in the proposed scenario. \(S_{2}\) is the signal transmitted from the base station of pico cell 2. \(H_{SB,2}\) is the channel coefficient between the base station of the pico cell 2 and the mobile. \(a1\) refers to the desired signal. Because \(b1\) is not a desired signal, it is regarded as noise by the mobile. The Equation (9) describes a received signal when the mobile is located within the intersection of two pico cells. When the number of the pico cells is increased, the received signal is as follows,  
\[Y_{ICI,1}=\underbrace{H_{SB,1}S_{1}}_{a1}+\underbrace{\left[\sum_{i=1}^{N}H_{ SB,i}\right]\cdot S_{2}}_{b1}+N. \tag{10}\]  
In Equation (10), \(i\) means the index of the pico cell and \(N\) denotes the number of the pico cells. In case 2, the proposed CoMP scheme forms the virtual MISO system in cooperation with the base station of the macro cell for improving diversity gain of the mobile and interference mitigation. One of the base station antennas of the macro cell transmits the signal using the constructive 2-bit feedback SPC scheme, in order to improve the diversity gain of the mobile by raising the SNR of the desired signal. Additionally, the other antenna transmits the signal with the destructive 2-bit feedback SPC scheme in order to mitigate the effects of interference by reducing the SNR of the interference signal. After the constructive and destructive SPC scheme are applied, the received signal is as follows,  
\[Y_{Case2} =H_{SB,1}S_{1}+H_{LB,1}\cdot C_{2}^{s}S_{1}+H_{SB,2}S_{2}+H_{LB,2 }\cdot C_{2}^{d}S_{2}+N \tag{11}\] \[=\underbrace{\big{(}H_{SB,1}+H_{LB,1}\cdot C_{2}^{s}\big{)}S_{1}} _{a2}+\underbrace{\big{(}H_{SB,2}+H_{LB,2}\cdot C_{2}^{d}\big{)}}_{b2}\big{)}S_ {2}+N.\]  
In this case, the pre-coding vectors of \(C_{2}^{s}\) and \(C_{2}^{d}\) facilitate that the channel coefficient is either constructively and destructively superimposed, respectively. \(a2\) can be larger than \(a1\) and \(b2\) can be smaller than \(b1\). Therefore, the SNR of the desired signal is increased, and the SNR of the interference signal is reduced. As such, the diversity gain of the mobile is improved and interference is mitigated.