Determining a subset of base stations in a wireless network

1 . A method of determining a subset of base stations (BSs) in a wireless network, the method comprising:

forming a minimization problem, wherein the minimization problem represents a problem of determining a subset of BSs in the wireless network to which one or more user equipments (UEs) in the wireless network can connect, so as to maximize a measure of efficiency of the wireless network, wherein the minimization problem comprises a quadratic unconstrained binary optimization (QUBO) problem;

wherein forming the QUBO problem comprises:

defining a binary integer linear programming (BILP) problem, wherein the BILP problem comprises a problem of determining a subset of BSs in the wireless network to which UEs in the wireless network can connect so as to maximize a measure of efficiency of the wireless network;

wherein a first plurality of binary variables of the BILP problem correspond to whether or not each UE in the wireless network is allocated to a respective one of the base stations in the wireless network;

wherein a second plurality of binary variables of the BILP problem

correspond to whether or not each BS is in the subset of BSs; expressing the BILP problem as a QUBO problem;

executing the minimization problem using a quantum computing device to determine the subset of BSs; and

activating and/or deactivating BSs in the wireless network in accordance with the determined subset of BSs.

2 . The method of claim 1 , wherein the minimization problem further represents a problem of determining an allocation of a respective one of the determined subset of BSs for each of the one or more UEs.

3 . The method of claim 2 , wherein executing the minimization problem using a quantum computing device further determines the allocation of a respective one of the determined subset of BSs for each of the one or more UEs.

4 . The method of claim 3 , further comprising, for each of the one or more UEs, initiating the UE to connect to a respective one of the determined subset of BSs to which the UE has been allocated.

5 . The method of claim 1 , wherein executing the minimization problem using a quantum computing device further determines, based on the determined subset of BSs, that one or more BSs in the wireless network are to be activated or deactivated.

6 . The method of claim 1 , wherein the measure of efficiency of the wireless network represents a data rate of the one or more UEs in the wireless network over an energy consumption of the subset of BSs to which the one or more UEs can connect.

7 . The method of claim 6 , wherein the objective function comprises:

a first component that represents the data rate of the one or more UEs in the wireless network; and

a second component that represents the energy consumption of the BSs in thewireless network.

8 . The method of claim 1 , wherein each BS in the wireless network is associated with a micro cell of the wireless network that has a coverage area at least partially within a coverage area of a macro cell of the wireless network.

9 . The method of claim 1 , wherein the BILP problem further comprises a problem of determining an allocation of a respective one of the determined subset of BSs for each of the one or more UEs.

10 . The method of claim 1 , wherein the BILP problem comprises a problem of determining a subset of BSs in the wireless network to which UEs in the wireless network can connect so as to maximize a value of an objective function of the BILP problem, and wherein the value of the objective function indicates the measure of efficiency of the wireless network.

11 . The method of claim 10 , wherein the objective function includes one or more constraints including:

a first constraint whereby each of the one or more UEs may be allocated to a maximum of one BS in the wireless network; and/or

a second constraint whereby a number of UEs allocated to a BS may be limited by an available throughput of the respective BS.

12 . The method of claim 10 , wherein expressing the BILP problem as the QUBO problem comprises:

determining a Lagrangian multiplier based on coefficients of the objective function;

negating one or more components of the objective function, so as to form a modified objective function that represents a minimization form of the objective function;

transforming one or more constraints of the modified objective function into a general matrix equation form Ax=b, where A is a matrix containing coefficients of binary variables in a column vector x, and b is a column vector containing constants in a system of linear equations, to form a quadratic penalty function (Ax-b) 2 ;

combining the modified objective function, the quadratic penalty function, and the Lagrangian multiplier into a single quadratic expression equivalent to the form xrQx; and

determining a matrix Q from the quadratic expression,

wherein the binary variables represent logical qubits in a problem graph for the quantum computing device.

13 . The method of claim 12 , wherein transforming the one or more constraints of the modified objective function initially comprises transforming linear inequality constraints of the modified objective function into linear equality constraints by addition of binary representations of a slack variable to each linear inequality constant.

14 . The method of claim 12 , wherein combining the modified objective function, the quadratic penalty function, and the Lagrangian multiplier comprises scaling the quadratic penalty function by the Lagrangian multiplier.

15 . The method of claim 1 , wherein for each of the BSs in the wireless network that do not form part of the determined subset of BSs, the method further comprises initiating the BS to deactivate.

16 . The method of claim 1 , wherein for each of the BSs in the wireless network that form part of the determined subset of BSs, the method further comprises initiating the BS to activate.

17 . The method of claim 1 , wherein executing the QUBO problem on the quantum computing device comprises performing a quantum annealing process.

18 . An apparatus for determining a subset of base stations (BSs) in a wireless network, the apparatus comprising:

processing circuitry; and

a memory comprising instructions executable by the processing circuitry such that the apparatus is operable to:

form a minimization problem, wherein the minimization problem represents a problem of determining a subset of BSs in the wireless network to which one or more user equipments (UEs) in the wireless network can connect, so as to maximize a measure of efficiency of the wireless network, wherein the minimization problem comprises a quadratic unconstrained binary optimization (QUBO) problem;

wherein forming the QUBO problem comprises:

defining a binary integer linear programming (BILP) problem, wherein the BILP problem comprises a problem of determining a subset of BSs in the wireless network to which UEs in the wireless network can connect so as to maximize a measure of efficiency of the wireless network;

wherein a first plurality of binary variables of the BILP problem correspond to whether or not each UE in the wireless network is allocated to a respective one of the base stations in the wireless network;

wherein a second plurality of binary variables of the BILP problem correspond to whether or not each BS is in the subset of BSs;

expressing the BILP problem as a QUBO problem;

execute the QUBO problem using a quantum computing device to determine the subset of BSs; and

activate and/or deactivate BSs in the wireless network in accordance with the determined subset of BSs.