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Mar 31, 2015

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Channel Assignment in Cellular Networks Ivan Stojmenovic www.site.uottawa.ca/~ivan [email protected] Slide 2 Overview Fixed channel assignment Multicoloring co-channel interference General problem statement Genetic algorithms Results and details Fixed/dynamic channel and power assignment Slide 3 Cell structure Implements space division multiplex: base station covers a certain transmission area (cell) Mobile users communicate only via the base station Advantages of cell structures: higher capacity, higher number of users less transmission power needed more robust, decentralized base station deals with interference locally Cell sizes from some 100 m in cities to, e.g., 35 km on the country side (GSM) - even more for higher frequencies Slide 4 Cellular architecture One low power transmitter per cell Frequency reuselimited spectrum Cell splitting to increase capacity A B Reuse distance: minimum distance between two cells using same channel for satisfactory signal to noise ratio Measured in # of cells in between Slide 5 Problems Propagation path loss for signal power: quadratic or higher in distance fixed network needed for the base stations handover (changing from one cell to another) necessary interference with other cells: Co-channel interference: Transmission on same frequency Adjacent channel interference: Transmission on close frequencies Slide 6 Reuse pattern for reuse distance 2? One frequency can be (re)used in all cells of the same color Minimize number of frequencies=colors Slide 7 Reuse distance 2 reuse pattern One frequency can be (re)used in all cells of the same color Slide 8 Reuse pattern for reuse distance 3? Slide 9 Reuse distance 3 reuse pattern Slide 10 Frequency planning I Frequency reuse only with a certain distance between the base stations Standard model using 7 frequencies: Note pattern for repeating the same color: one north, two east-north f4f4 f5f5 f1f1 f3f3 f2f2 f6f6 f7f7 f3f3 f2f2 f4f4 f5f5 f1f1 Slide 11 Fixed and Dynamic assignment Fixed frequency assignment: permanent certain frequencies are assigned to a certain cell problem: different traffic load in different cells Dynamic frequency assignment: temporary base station chooses frequencies depending on the frequencies already used in neighbor cells more capacity in cells with more traffic assignment can also be based on interference measurements Slide 12 3 cell cluster with 3 sector antennas f1f1 f1f1 f1f1 f2f2 f3f3 f2f2 f3f3 f2f2 f3f3 h1h1 h2h2 h3h3 g1g1 g2g2 g3g3 h1h1 h2h2 h3h3 g1g1 g2g2 g3g3 g1g1 g2g2 g3g3 Slide 13 Cell breathing CDM systems: cell size depends on current load Additional traffic appears as noise to other users If the noise level is too high users drop out of cells Slide 14 Multicoloring Weight w(v) of cell v = # of requested frequencies Reuse distance r Minimize # channels used: NP hard problem Multi-coloring = multi-frequencing Channel= Frequency= ColorChannel= Frequency= Color HybridHybrid CA = combination fixed/dyn. frequencies Graph representation: weighted nodes, two nodes connected by edge iff their distance is < r same colors cannot be assigned to edge endpoints Slide 15 Hexagon graphs: reuse distance 2 What is the graph for reuse distance 3? Slide 16 Lower bounds for hexagonal graphs D= Maximum total weight on any clique Lower bound on number of channels: D D/3 D/2D/6 D/2 0 00 Odd cycle bound: induced 9-cycle, each weight D/2 Channels needed in this cycle: 9D/2 Each channels can be used at most 4 times. Needs 9/8D channels Slide 17 Fixed allocations reuse distance 2 D= maximum number of channels in a node or 3-cycle Red : 1, 4, 7, 10, Green: 2, 5, 8, 11, Blue: 3, 6, 9, 12, Total # channels: 3DPerformance ratio: 3 Janssen, Kilakos, Marcotte 95: D/2 red, blue and green each D/2 Each node takes as many channels as needed from its own set If necessary, RED borrow from GREEN BLUE borrow from RED GREEN borrow from BLUE If a node has D/2+x channels, no neighbor has more than D/2-x channels 3D/2 channels used, performance ratio: 3/2 Slide 18 4/3 approximation for reuse distance 2 McDiarmid-Reed 97, Narayanan-Shende 97, Scabanel-Ubeda-Zerovnik 98 Base color graph RED, GREEN, BLUE D/3 RED, GREEN, BLUE, PURPLE channels Each vertex uses at most D/3 channels from own set Certain heavy vertices (>D/3 colors) borrow from light neighbors: red from green, green from blue, blue from red Purple channels used if/when needed; at most one vertex in 3-cycle will need them (why?) If only one heavy vertex then how it borrows? max 2 nodes borrow (why?); G=D/3+x, B=D/3+y, green borrows from ?, blue from ? x+y Feder-Shende algorithm-reuse dist. 3 Base color underlying graph with 7 colors Assign L channels to each color class Every node takes as many channels as it needs from its base color set Heavy node (>L colors) borrows any unused channels from its neighbors L=D/3 algorithm with performance ratio 7/3 Reuse distance r perform. ratio 18r 2 /(3r 2 +20) 2: 2.25, 3: 3.44, 4: 4.23, 5: 4.73 (Narayanan) k-colorable graph perf. ratio k/2 (Janssen-Kilakos 95) Slide 20 Adjacent channel interference Receiver filter f1 f3f2 interference Co-site constraint: channels in the same cell must be c 0 apart Adjacent-site constraint: channels assigned to neighboring cells must be c 1 apart Inter-site constraint: channels assigned to cells that are r cells apart must be c r apart Slide 21 Lower bounds: co-site and adjacent-site Gamst 86 c 0 max {w(u), w(v), w(x)} c 1 max{ v C w(v) | C is a clique} max {c 0 w(u), (c 0 c 1 )w(u)+ c 1 v C,v u w(v) | C is a clique containing u} when c 0 2c 1 u v x c0c0 c1c1 c 0

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