After placement of the HAFs, each HAF allocates its radio blocks to every active user connected to it in every periodic time interval, T . If the radio resource demand is greater than the available radio blocksR, the F-GW performs OPC to tune transmit
powers of HAFs. The objective of OPC model is to maximize the sum of transmission powers of all HAFs so that resource demand at each HAF from its connected users can be satisfied. It chooses HIZone users (SG and NSG) who will be served by the MBS when the transmission powers of the HAFs, to whom they are connected currently, are reduced from Pmax. In such a case, the selected HIZone users must be ensured at
least a SIN RP C
T h from the MBS in order to be served by it.
OPC Formulation: F is used to denote the set of all HAFs in the building and M is the set of MBSs. All the sub-regions in the HIZone and indoor form the sets H and I, respectively. Di and Dh are the demand of ith IU E and hth HIZone user,
respectively, inT time interval. PM denotes the transmission power of the MBS. We
use the following variables to determine the connectivity of each sub-region to an HAF and to determine whether a sub-region is occupied.
• Indoor HAF connectivity variable x = {xif|xif = {0, 1}; i ∈ I; f ∈ F }, i.e.,
xif = 1 if indoor sub-region i is connected to HAF f , 0 otherwise.
• HIZone HAF connectivity variable y = {yhf|yhf = {0, 1}; h ∈ H; f ∈ F }, i.e.,
yhf = 1 if HIZone sub-region h is connected to HAF f , 0 otherwise.
• HIZone Macro connectivity variable z = {zh|zh = {0, 1}; h ∈ H}, i.e., zh = 1 if
HIZone sub-regionh is connected to a HAF f , 0 if connected to M .
• Indoor sub-region occupancy opi = {qi|qi = {0, 1}; i ∈ I}, i.e., qi = 1 if indoor
sub-region i is occupied by a user, 0 otherwise.
• HIZone sub-region occupancy oph = {qh|qh = {0, 1}; h ∈ H}, i.e., qh = 1 if
HIZone sub-regionh is occupied by a user, 0 otherwise.
To ensure that every HAF can serve the users connected to it with minimum number of radio resources, the OPC maximizes the total transmission power of all the HAFs, that is,
maxX
f ∈F
Pf (7.8)
To ensure that every indoor sub-region, i, is connected to exactly one HAF and that any HIZone sub-region,h, if not connected to the MBS is associated with only a single
HAF, Equation (7.8) is subject to the connectivity constraints (7.9) and (7.10). X f ∈F xif = 1 ∀i ∈ I (7.9) X f ∈F yhf = zh ∀h ∈ H (7.10)
We use the SINR constraint given in Equation (7.11) to make sure that all the indoor sub-regions, which are connected to HAF, f , get at least SIN RP C
T h which is
equal to λi for indoor sub-regions.
Inf ∗ (1 − xif) +gifPf No+ X f0∈F \f gif0Pf0 + X m∈M gimPm ≥ λi ∀i ∈ I, f ∈ F (7.11)
In order to ensure SIN RP C
T h, λh, to HIZone sub-regions from their respective
HAFs, constraint given in Equation (7.12) is used. Inf ∗ (1 − yhf) +ghfPf No+ X f0∈F \f ghf0Pf0 + X m∈M ghmPm ≥ λh ∀h ∈ H, f ∈ F (7.12)
where, ghf and ghm are the gains from HAF, f , and MBS, m, to the HIZone sub-
region h, respectively. For a HAF f , Equation (7.12) uses Inf to filter the HIZone sub-regions not connected to f to prevent the problem from becoming infeasible. The constraint given in Equation (7.13) is adopted to make sure that all HIZone sub-regions connected to an MBS, m ∈ M get SINR greater than λh.
Inf ∗ zh+ghmPm No+ X f ∈F ghfPf ≥ λh ∀h ∈ H (7.13)
Like earlier, Inf filters the HIZone sub-regions not connected to the MBS.
X i∈I diqi mcs(sinrif) xif + X h∈H dhqh mcs(sinrhf) yhf ≤ nR ∀f ∈ F (7.14)
where, R is the number of radio resources available per TTI and n is the number of TTIs in the time interval T . The first summation in Equation (7.14) determines the maximum number of radio resources required by theIU Es connected to HAF f which depends on the user’s individual data requirement di for time interval T and
their MCS obtained from their SINR value (mcs(sinrif)). Similarly, the second term
is the summation of the maximum number of radio resources required by the HIZone users connected tof . The constraint gives an upper bound of nR to the net required radio resources obtained from both the summation terms for the time interval T .
Thus, the OPC takes care of BWA for any combination of SG and NSG user locations by tuning the transmit power of HAFs whenever the demand in a HAF exceedsR. The demand from the IU Es (SG and NSG) itself can exceed R in a HAF operating at Pmax due to presence of large number of indoor NSG users. Then the
BWA is in proportion of the radio resource demand between the SG and NSG (refer Equation (7.15) and Equation (7.16)) as the OPC is not feasible in such a situation.
RS0 = RS RS+RN S R (7.15) R0 N S = RN S RS+RN S R (7.16)
The OPC problem (refer Equation 7.8) is a Mixed Integer Non-linear Program- ming (MINLP) problem and is very hard to solve in polynomial time. Hence, we propose an effective heuristic power control mechanism to solve the above MINLP power control problem in polynomial time.