Table 1 Notation summary.

Total number of FBS

Total number of clients

Hardware noise and environmental noise

Time frame

Maximum backhaul link capacity

Constant parameter for the SINR threshold of MBS

Constant parameter for the SINR threshold of the FBS

Constant parameter for the maximum transmission power of clients

Constant parameter for the maximum transmission power of MBS

Constant parameter for the maximum transmission power of FBS

Weight parameter for the weighted sum approach

Transmission power vector of clients

Transmission power vector of BS

Measured power of client at client using channel

Measured power of BS at BS

Uplink achievable throughput from client to BS using frequency

Downlink achievable throughput from BS to client using frequency

Transmission gain matrix between network elements. Note that index 0 represents

the MBS, indices 1 to represent FBSs, and indices to represent clients

Coverage scheme variable for set of public users associated with MBS

Coverage scheme constant for set of private users associated with an FBS

Coverage scheme variable for set of public users associated with FBS

Uplink channel assignment variable for client using frequency

Downlink channel assignment variable for BS using frequency

Uplink throughput objective function

Distributed uplink throughput objective function at each client

Downlink throughput objective function

Distributed downlink throughput for the MBS

Distributed downlink throughput at each FBS

Uplink compensation objective function

Downlink compensation objective function

Distributed compensation objective function at each client

Distributed downlink compensation objective function at each BS

Weighted sum problem for uplink model

Distributed uplink weighted sum problem

Weighted sum problem for downlink model

Distributed downlink weighted sum problem at the MBS

Distributed downlink weighted sum problem at each FBS

Distributed achievable throughput from client to BS using frequency at each client

Downlink achievable throughput from BS to client using frequency at each BS