## 5 Our Proposed Novel Resource Allocation Scheme
### Proposed Algorithm  
Through the discussions presented in Sections 5.1-5.4 we convert the intractable problem described by Equations (10)-(14) into the tractable suboptimal problem as below:  
\[\text{P2}:\underset{\beta,\boldsymbol{r},\boldsymbol{\Phi}}{\max}\sum \limits_{i=1}^{N}\sum\limits_{j=1}^{N}\sum\limits_{k=1}^{K}x_{i,j,k}f_{i,j,k} \tag{30}\]  
\[s.t.\sum\limits_{j=1}^{N}\sum\limits_{k=1}^{K}x_{i,j,k}=1,\;\forall i \tag{31}\]  
\[\sum\limits_{i=1}^{N}\sum\limits_{k=1}^{K}x_{i,j,k}=1,\;\forall j \tag{32}\]  
\[\sum\limits_{i=1}^{N}\sum\limits_{j=1}^{N}x_{i,j,k}\leqslant 1,\;\forall k \tag{33}\]  
\[\boldsymbol{r}^{T}1\leqslant C_{BH} \tag{34}\]  
\[\alpha\left(i\right)=k \tag{35}\]  
\[\beta\left(i\right)=j \tag{36}\]  
In conclusion, for fixed \(\boldsymbol{x}\) and \(\boldsymbol{r}\), optimal \(\boldsymbol{\Phi}^{*}\) can be explicitly expressed by \(\boldsymbol{r}\); for fixed \(\boldsymbol{x}\) and \(\boldsymbol{\Phi}\), optimal \(\boldsymbol{r}^{*}\) is obtained by solving a convex problem; for fixed \(\boldsymbol{\Phi}\) and \(\boldsymbol{r}\), \(\boldsymbol{x}\) is decomposed into two variables \(\alpha\) and \(\beta\), where the former guarantees worse case optimality and the latter is linear relaxed without any optimality loss [31; 32; 33]. Therefore, we have developed an alternative optimization algorithm (Algorithm 1) by solving the convex problem and linear programming alternately. According to [16], this algorithm converges to the optimal solution of problem P2 defined by Equations (30)-(36). We summarize it in the following [17; 18]:```
1. Mapping users in cell A onto K subcarriers using \(\alpha\)
2. Initialize \(\beta^{(0)}\) and \(\mathbf{r}^{(0)}\) randomly, let \(t=~{}0\). 3. Repeat:
4. \(t=t+~{}1\)
5. Get \(\mathbf{r}^{(t)}\) by convex optimization;
6. Compute \(\mathbf{\Phi}^{(t)}=diag(\eta_{1}^{(t)},\eta_{2}^{(t)},...,\eta_{K}^{(t)})\); using (18)
7. Compute \(f_{i,j,k}^{(t)}(\beta^{(t-1)},\mathbf{r}^{(t)})\) using (24)
8. Get \(\beta^{(t)}\) by linear programming. 9. Compute objective function \(f^{(t)}\) given \(\mathbf{r}^{(t)}\), \(\mathbf{\Phi}^{(t)}\), \(\beta^{(t)}\)
10. Until \(F^{(t)}\) converges
```

**Algorithm 1**The Proposed Novel Resource Allocation Algorithm

In our proposed algorithm, there are three steps:

The first step is the optimization of compression noise, where the complexity is \(o(N\times K)\) The second step is resource allocation, where the complexity is: \(o(length(\overline{x}))\) The last step is user pairing and subcarrier mapping, the complexity is: \(o(N!\times K)\) So the complexity of our method is: \(length(\overline{x})\times o(N\times K)\times o(N!\times K)\)

## 6 Simulation and Analysis

In this part, we propose the simulation and analysis. In Section 6.1, a theoretical analysis has been given for a two base station scenario, link level transmission has been adopted in this part, then theoretical analysis of our proposed method is analyzed [34; 35; 36]. To make our method credible and practicable, we propose a system level simulation to support the system level performance of our method in Section 6.2. The system level simulation platform supports the multi-users, multi-base stations scenario, which could reflect the performance of our proposed algorithm in a real scenario. References for our simulation platform can be found in [37; 38]. ### Theoretical Analysis

First of all, we evaluate the performance of our algorithm on the MATLAB platform. The distance between two BSs is 500 m. The radius of each cell is 300 m, which is illustrated in Figure 2. In the uplink scenario, users are transmitting signals to both of the base stations and signals are also interference to an adjacent base station. Two base stations are connected using the backhaul link. User pairing is proposed in coordinated demodulation of the received signal and the resource allocation in backhaul link is proposed to make full use of the system.