# Millimetre-Wave Backhaul for 5G Networks: Challenges and Solutions
## 5 Framework Design for 5G Mm-Wave Backhaul
### Transmission Path Selection
Since multi-stream multiplexing is available in mm-wave backhauling, an SBS may route data streams through multiple separate relays to the destination. However, to avoid a device becoming extremely congested, the number of wireless data streams from one device should better be restricted by the number of RF chains available at the device, shown in Constraint (2c), where \(f(N_{RF})\) is a function of the number of available RF chains. For example, the number of streams may be restricted to be no more than twice the number of RF chains if there are not many requested flows in the system, where \(f(N_{RF})=2N_{RF}\). However, if the link between \(b_{i}\) and \(b_{j}\) is connected by fibre, it is excluded from Constraint (2c). * Flow constraint: For each flow, the outgoing data from the source and the incoming data to the destination must be larger than zero (Constraint (2d)). Meanwhile, there should be no incoming data to the source or outgoing data from the destination for every flow (Constraint (2e)). If full duplex is adopted, a relay may receive and transfer data simultaneously. For an SBS that is neither the source nor the destination of a specific flow, the incoming amount of data to the SBS and the outgoing amount of data from the SBS should be equal, which is depicted in Constraint (2f). Constraint (2g) shows that for any two SBSs, the total amount of data transmitted between them is limited by the corresponding link capacity. The above optimization problem is a mixed integer linear programming (MILP) problem, which could be solved by toolboxes, such as YALMIP [23]. Combining new physical layer techniques into path selection, the top part of Figure 3(a) shows an example of the routing result for three required flows, namely, \(b_{5}\to b_{2}\), \(b_{1}\to b_{3}\) and \(b_{3}\to b_{4}\), in a five-SBS backhaul system using the above method. The matrix \(\mathbf{C}\) stores the channel capacity (in units of Gbps) between each pair of devices. For a specific layout of SBSs, matrix \(\mathbf{C}\) could be obtained from rate estimation through channel measurement. The setting of \(\mathbf{C}\) for the example is shown in Figure 3(a). The row index and column index refer to the SBS indices of the transmitter and the receiver, respectively. For example, the element in the first row and the second column of \(\mathbf{C}\) shows that the capacity of the backhaul link from \(b_{1}\) to \(b_{2}\) is 8.7 Gbps. We assume that \(b_{3}\) and \(b_{4}\) are totally blocked, while there is an alternative link between \(b_{4}\) and \(b_{5}\) with higher loss. The wired link between \(b_{1}\) and \(b_{4}\) holds larger capacity. We assume that the available RFchains at each SBS in this example are three, and \(f(N_{RF})=N_{RF}=3\) due to the quite limited number of requested flows. It could be observed that the original Flow 2 and Flow 3 are separated into multiple new flows due to the availability of multi-stream beamforming. The number of incoming/outgoing flows at each SBS is restricted by \(N_{RF}\), except that the number of flows sending from \(b_{1}\) exceeds three, which is because the wired link from \(b_{1}\) to \(b_{4}\) is excluded from Constraint (2c). With the optimization goal of maximizing overall capacity, the rate for each new flow is re-allocated according to the full duplex constraint, _i.e._, the total incoming flow rate and the outgoing rate at each SBS (neither source nor destination) are the same, as well as the capacity constraint, _i.e._, the total rate of each link is lower than the link capacity. Compared to the conventional routing of Dijkstra/Floyd-Warshall shown in the bottom part of Figure 4a, the proposed routing scheme can fully exploit the potentials of mm-wave channels, leading to an improved backhaul performance.