Energy-Aware Base Stations: The Effect of Planning, Management, and Femto Layers

Table 1

Main notation.

Symbol	Explanation	Value
𝐴	Area under investigation	1.8  ×1.8 Km
CRD	Set of possible coordinates	Equally spaced points of distance 50 m
𝑆	Set of sites	Cartesian coordinates inside A
𝑀𝑎	Set of macrocells	23 possible sites
𝑀𝑖	Set of microcells	43 possible sites
𝑁Tx	Number of base stations (macrocells and microcells)	69
𝐹	Set of femtocells access points	Cartesian coordinates inside 𝐴
𝑁FTx	Number of femtocells access points	25–75
𝑥𝑓,𝑦𝑓	Cartesian coordinates of femtocell 𝑓	Coordinates inside 𝐴
𝐻𝑓	Height of femtocell 𝑓	1.5 m above floor
𝑃𝑓	Maximum transmit power level for femtocell 𝑓	{0,0.5} W
𝑃𝑗	Maximum transmit power level for base station 𝑗	{0,10,20,30,40,50} W (macro); {0,1,2,3,4,5} W (micro)
𝐺𝑓	Antenna gain for femtocell 𝑓	2 dBi
𝑈	Set of users	Cartesian coordinates inside 𝐴,with |𝑈|=847
𝛿𝑖	Signal to noise ratio threshold for user 𝑖	5 dB for voice, 2.5 dB for video, and 2 dB for web service
𝐺(𝑈,𝑆)	Affinity graph for users and base stations	Set of edges between 𝑈and 𝑆
𝐺(𝑈,𝐹)	Affinity graph for users and femtocells	Set of edges between 𝑈 and 𝐹
𝐵𝑗	Best server site	Identifier of the site
𝑝^𝑐𝑗	Power associated with the control channel of base station 𝑗	15% of the total power
HN𝑗	Soft handoff site	Identifier of the site
𝑞	Soft handoff margin	5 dB
𝑙𝑖𝑗	Path loss from user 𝑖 to base station 𝑗	Variable
CV𝑗	Coverage umbrella of base station 𝑗	Variable
𝑥𝑖𝑗	Variable indicating if user 𝑖 is associated with base station 𝑗	{0, 1}
𝐺𝑖	Antenna gain of base station 𝑖	10 dB (macro), 3 dB (micro)
𝐺𝑖	Antenna gain of user 𝑖	2 dBi
𝜔	Orthogonality factor	0.6
𝜈𝑖	Voice activity	0.58
𝜇𝑖	Carrier to interference plus noise ratio for user 𝑖	Variable
𝜋𝑝	Minimum sensitivity threshold	−115 dBm
𝑛	Thermal noise	−174 dBm/Hz
𝑝𝑗	Mean transmit power of base station 𝑗	Variable
𝑟𝑖	Required rate for user 𝑖	12 Kbps for voice, 64 Kbps for vide, 144 Kbps for web service
𝐶	Chip rate	3.87×10^6 cps
𝑊𝑗	Total consumed power for base station 𝑗	Equation (8a)
𝑊^𝐹𝑓	Total consumed power for femtocell 𝑓	10 W
𝑅𝑗	Maximum data rate processed by base station 𝑗	14 Mbps (macro), 4 Mbps (micro)
𝑎𝑗	Binary variable indicating if base station 𝑗 is used	{0, 1}
𝑈^max	Set of users during peak hour	Cartesian coordinates inside 𝐴
𝑁^max	Number of users during peak hour	847
𝑁^min	Minimum number of users	40
𝑡	Current time	Variable
𝑡𝜁	Decision time	Variable
𝑇	Maximum time	24 h
Ω𝑘	Set of base stations that are controlled by a critical base station 𝑘 in the pseudo distributed algorithm	Variable
𝜀	Load threshold	0.3 for macros and 0.03 for micros