## 2 System Model
### IRC Receiver to Suppress ICI in Small-Cells  
This part of the paper presents the system model for the IRC receiver in small-cells, continued with the former WHT-NOMA. The block diagram for the WHT with joint NOMA and IRC is given in Figure 4. As mentioned in Section 1, that IRC receiver needs to know the interference signals and the desired signal, i.e., the correct covariance matrix estimation that includes the information of interfering signals, and the channel matrix estimation of the serving cell, respectively. Thus, to achieve accurate estimates of these matrices using IRC, efficient estimation schemes are required [6]. In the current high-end wireless networks, the serving cells' channel matrix estimation is possible using the downlink reference signals (RSs). The covariance matrix can be estimated using the RS-based scheme proposed in the 3 GPP release R1-111562 [35]. This scheme extracts the serving cell's portion, and the noise and interference portion from the covariance matrices. The former portion, i.e., attaining covariance matrix of the serving cell, can be achieved via the phases and channel amplitudes of the serving cell, which can be estimated by the RS of the serving cell. On the contrary, the latter part, i.e., the covariance matrix estimation that includes only the noise and interference, can be achieved by the subtraction of replica symbols of the serving cell, based on the estimated channel matrix and the known RS sequence, from the received RS signals. As IRC is particularly used for the interference suppression, the estimation accuracy of the latter is more important than the former. In this work, for simplicity, the ideal IRC scenario is used where the composite signal information of the interferers is known at the IRC performing receiver. To present the system model for IRC, the model used is the same as for the NOMA in small-cells, but for a better understanding, it is presented here from the perspective of multiple antenna receivers, as IRC can suppress the ICI if the number of receiver antennas is higher than the desired data streams [6]. The IRC model developed in this work is based on the work performed in [6]. Considering that \(N_{Rx}\) is the number of receiver antenna branches and the total number of cells, including the macro and small-cells, is given by \(N_{Cell}\), then the received signal is given as:  
\[y=\sum_{q=1}^{N_{Cell}}H_{q}W_{q}s_{q}^{H}\sqrt{P_{q}}+n, \tag{32}\]  
where, \(H_{q}\) is the complex channel matrix between the \(q\)th small-cell and UE, \(s_{q}^{H}\) is the WHT-based signal information of the \(q\)th cell, \(P_{q}\) is the transmission power of the \(q\)th small-cell, \(W_{q}\) is the precoding weight matrix of the \(q\)th small-cell, and \(n\) is the \(N_{Rx}\)-dimensional noise. Considering that the \(b\)th SBS is serving a high-gain UE-\(m\) from the total \(k\) NOMA-paired UEs, the recovered WHT signal after successful removal of the ICI using IRC at the UE-\(m\), i.e., \(s_{bm}^{H}\), is detected using the \((N_{stream}\times N_{Rx})\) receiver weight matrix \(W_{Rx,bm}\), where \(N_{stream}\) is the total number of streams received at the UE. The desired signal is given as:  
\[s_{bm}^{H}=W_{Rx,bm}y. \tag{33}\]  
The IRC receiver weight matrix, which contains the covariance matrix with interference information and the estimated channel matrix, is given as:  
\[W_{IRC}=W_{Rx,bm}=\sqrt{P_{bm}}G_{bm}R_{yy}^{-1}\, \tag{34}\]  
\[G_{bm}=H_{bm}W_{bm}\, \tag{35}\]  
where, \(G_{bm}\), \(P_{bm}\), and \(R_{yy}\) denote the composite channel of the \(b\)th small-cell, the transmission power of the serving \(b\)th SBS, and the covariance matrix, respectively. Using \(W_{IRC}\) in (34) instead of \(W_{Rx,bm}\) in (33) gives us the desired signal by supressing the interference information.