Autonomous algorithms for centralized and distributed interference coordination: a virtual layer-based approach

Kasparick, Martin; Wunder, Gerhard

doi:10.1186/1687-1499-2014-120

EURASIP Journal on Wireless Communications and Networking

Table 1 Important notation

From: Autonomous algorithms for centralized and distributed interference coordination: a virtual layer-based approach

Notation	Definition
$P_{jb}^{m}$	Power assigned to beam b on PRB j insector m
${\bar{P}}_{jb}^{m}$	Average power constraint (‘target’ power) of beam b on PRB j in sector m
${\bar{P}}^{m} (t)$	Current total allocated power in sector m
P _max	Maximum total base station power
$c_{jb} (k, {\bar{P}}_{j}^{m})$	Power cost/consumption of beam b on PRB j in sector m
$C_{jb}^{m} (k)$	Virtual power cost/consumption of sector m on beam b and PRB j
π(l)	Probability of fading state l
$K (l)$	Set of possible scheduling decisions given fading state l
$h_{ij}^{m} (t)$	Channel vector from base station m to user i on PRB j at time t
${\bar{h}}_{ij}^{m}$	Average channel from base station m to user i on PRB j
$μ_{jb}^{l} (k)$	Vector of user rates on PRB j and beam b given decision k and fading state l
${\bar{X}}^{m}$	Vector of average total rates of users insector m
$ϕ_{jk}^{lm}$	Fraction of time that scheduling decision k is chosen on PRB j given fading state l
$ϕ_{ijb}^{m}$	Fraction of time that user i in sector m is scheduled using beam b on PRB j
$G_{ij}^{m}$	Long-term gain of user i to base station m for his best beam on PRB j
$G_{ijb}^{m}$	Long-term gain of user i to base station m for beam b on PRB j
$R_{ij}^{m} (k)$	Virtual rate of user i on PRB j given decision k
R _j	Vector of virtual user rates in PRB j
$R_{ijb}^{m}$	Virtual rate of user i on PRB j and beam b
$X_{i}^{m}$	Virtual average rate of user i in sector m
X(t/n_v)	Vector of virtual average rates at t th virtual scheduling run
$F_{ijb}^{m}$	SINR of user i on beam b and PRB j
$D_{jb}^{(\hat{m}, m)}$	Sensitivity of sector m to a power change of beam b on PRB j in sector $\hat{m}$
$D_{jb}^{m}$	Sum sensitivity to a power change of beam b on PRB j in sector m
n_j(k)	Number of beams that are activated on PRB j if decision k is chosen
λ_{j b}(t)	Dual parameter: deviation of power on PRB j and beam b from the target value
$α_{jb}^{m} (k)$	Scales target beam powers to instantaneous powers ‘costs’
$α_{ijb}^{m}, β_{ijb}^{m}$	Approximation constants in concave lower bound

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