Corrections: A QoS-Based Cross-Tier Cooperation Resource Allocation Scheme over Ultra-Dense HetNets (IEEE Access (2019) 7 (27086-27096) DOI: 10.1109/ACCESS.2019.2901506)

In our previous analysis in [1], in order to calculate the number of MUEs, we defined SHole to represent the region occupied by MUEs. Due to an editing error, this formula was expressed as SHole D PrfNS D 0g, where the right- hand side of the equation expresses the probability of having no small cell at this point. The correct number of MUEs cannot be obtained by this equation. Next, we give the correct calculation method for the number of MUEs. The distributions of UEs and SBSs are treated as PPP (Poisson Point Process) with density U and S , respectively. In our definition in [1], UEs are divided into three types, i.e., MUEs, SUEs and CUEs. The number of MUEs can be obtained by the product of the area occupied by MUEs and the UEs density. Thus, the number of MUEs can be obtained by UM D SHole = U. Next, we derive the area that is occupied by the MUEs, which can also be described as the area out of small cells in macrocell. So SHole can be expressed as SHole D PrfNS D 0g = SM [2], where NS D 0 expresses there is no small cell at this point and PrfNS D 0g indicates the probability of having no small cell cover this point, SM is the area of macrocell and SM D πD2. The associate editor coordinating the review of this manuscript and approving it for publication was Giovanni Pau. Since the distribution of SBSs is a PPP with density S , the probability distribution for n points falling into region S is a Poisson distribution [2], i.e. (formula presented) Thus, the probability of no small cell cover this point is expressed as Pr fNS D 0g D exp .S SO/, where SO is the area of a small cell and SO D d2. The number of MUEs is (formula presented) In fact, we let UM D dexp(S SO) SM Ue to satisfy the integer constraint, where dxe maps x to the least integer greater than or equal to x.