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Channel Assignment

in Cellular Networks

Ivan Stojmenovic

www.site.uottawa.ca/~ivan

Ivan@site.uottawa.ca

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Overview

Fixed channel assignment

Multicoloringco-channel interference

General problem statement

Genetic algorithms

Results and details Fixed/dynamic channel and power assignment

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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 usersless 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

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Cellular architecture

One low power transmitter per cel

Frequency reuselimited spectrum

Cell splitting to increase capacityA B

Reuse distance:minimum distance betweentwo cells using same channel for satisfactory

signal to noise ratio

Measured in # of cells in between

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Problems

Propagation path loss for signal power: quadratic or higher indistance

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

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Reuse pattern for reuse distance 2?

One frequency can be (re)used in all cells of the same color

Minimize number of frequencies=colors

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Reuse distance 2reuse pattern

One frequency can be (re)used in all cells of the same color

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Reuse pattern for reuse distance 3?

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Reuse distance 3reuse pattern

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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

f4

f5

f1f3

f2

f6

f7

f3f2

f4f5

f1

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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 interferencemeasurements

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3 cell cluster

with 3 sector antennas

f1f1 f1

f2

f3

f2

f3

f2

f3h1

h2

h3g1

g2

g3

h1h2

h3g1

g2

g3g1

g2

g3

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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

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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= Color

Hybrid CA = combination fixed/dyn. frequencies

Graph representation: weighted nodes, two nodesconnected by edge iff their distance is < r

same colors cannot be assigned to edge endpoints

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Hexagon graphs: reuse distance 2

What is the graph for reuse distance 3?

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Lower bounds for hexagonal graphs

D= Maximum total weight on any clique

Lower bound on number of channels: DD/3

D/2 D/6

D/2

D/2 D/2

D/2

D/2

D/2D/2D/2

D/2000

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

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Fixed allocationsreuse distance 2D= 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: 3D Performance ratio: 3

Janssen, Kilakos, Marcotte 95: D/2 red, blue and green each

D/2

D/2

D/2

Each node takes as many channels as neededfrom 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

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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 18r2/(3r2+20)

2: 2.25, 3: 3.44, 4: 4.23, 5: 4.73 (Narayanan)

k-colorable graph perf. ratio k/2(Janssen-Kilakos 95)

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Adjacent channel interference

Receiver filter

f1 f3f2interference

Co-site constraint: channels in the same cell must be

c0 apart

Adjacent-site constraint: channels assigned toneighboring cells must be c1 apart

Inter-site constraint: channels assigned to cells that are

r cells apart must be crapart

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Lower bounds: co-site and adjacent-site

Gamst 86

c0max {w(u), w(v), w(x)}

c1 max{vCw(v) | C is a clique}

max {c0 w(u), (c0c1)w(u)+c1vC,vu w(v) | C is a

clique containing u} when c02c1

u

v x

c0c1c0

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3-colorable graphsDistance between channels = max(c0/3, c1)

Borrowing impossible

Distance between channels = max(c0/2, c1)

Borrowing possible

Borrowed channels = change colordynamic CA=online distributed CA

Channels with ongoing calls can(not) be borrowed = (non)recoloring

k-local algorithm: node changes channels based on weights within kcells

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Desirable qualities of CA algorithms

Minimize connection set-up time

Conserve energy at mobile host

Adapt to changing load distribution

Fault tolerance Scalability

Low computation and communication overhead

Minimize handoffs Maximize number of calls that can be accepted

concurrently

R h bl l l l

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Research problem: several power levels

at mobile hosts

If mobile phone is near base station, it may switchto lower power level

Interference from other hosts increases

Interference of that host to other node decreases Are there benefits of using two power levels?

Fixed or dynamic channel and power assignment

and multicoloring: simplest cases Fixed or dynamic channel and power assignment

with co-site, adjacent-site and inter-site constraints:

Genetic algorithms, simulated annealing,

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Genetic algorithms

Rechenberg 1960, Holland 1975

Part of evolutionary computing in AI Solution to a problem is evolved (Darwins theory)

Represent solutions as a chromosomes = search space

Generate initial population of solutions(chromosomes) at random or from other method

REPEAT

Evaluate the fitness f(x) of each chromosomex Perform crossover, mutation and generate new

population, usingf(x) in selecting probabilities

UNTIL satisfactory solution found or timeout

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Fixed channel assignment problem

INPUT: n = number of cells

Compatibility matrix C, C[i,j]= minimal channelseparation between cells i and j, 1i,jn

d[i] = number of channels demanded by cell i

OUTPUT: S[i,k]= channel # of k-th call of cell i, 1kd[i] CONSTRAINTS: |S[i,k]-S[j,L]|C[i,j],1kd[i], 1Ld[j], (i,k)(j,L)

GOAL: minimize m= max S[i,k] = # channels

reducable to graph coloring problem NP-complete GA solution space: m fixed, F[j,k]=0/1 if channel k

is not assigned/assigned to cellj, 1km, 1jn.

Optimization: Minimize number of interferences and satisfy demand

O bl t ti d

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Our problem representation and

solution space

Each row F[j,k], 1km, is a combination ofd[j] outofm elements (# of 1s is = d[j])

Cost function to minimize: C(F)= A+B

A= total number of co-site constraint violations B= total number of adjacent and inter-site violations

= parameter; C(F)=0 for optimal solution

Initial population: generate restricted combinations:

generate random combination ofd[j] Xs and m-

(c0+1)d[j] 0s; replace each X by 100..0 (c0 0s);

shift circularly by random number in [0,c0]

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Mutation

Each row=cell is mutated separately

Combinations in bit representation: x 1s out ofm bits

Mutation with equal probability for each bit: choose one out

ofx 1s and one out ofm-x 0s at random, swap: Ngo-Li 98

Mutation with different probability for each bit:b[i]= # of conflicts ofi-th selected channel

with other channels in this and other cells

p[i]=b[i]/(b[1]++b[x])

Repeat for 0s: # of conflicts if that channel turned on Choosing bit with given probability:

Generate at random r, 0 r1, and choose i,

p[1]+p[i-1] r

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Crossover Regular GA crossover:

1011000110 10011110000101111000 0111000110

Ngo-Li 98:A and B two parents, each row separately,

preserve # of 1s in each row:push 10 and 01 columns in stack if top same;

pop for exchange if top different

1011000110 1001101000

0101111000 0111010110

Problem: # of swaps varies

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New crossover

t= number of desired swaps in a row

Mark positions in two combinations that differ

let s 10s and s 01s are found

Choose tout ofs 10 at random and

01 Choose tout ofs 01 at random and 10

Example: 1011000110 1001010010

0101111000

0111110110s=4 t=2 $^$ ^^^$$ # **#

# **# offspring

selected columns

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Crossover needs further study

Problem: independent changes in each row=cell will

destroy good channel assignments of parents

Two good solutions may have nothing in common

Try experiments with mutation only

(may be crossover has even negative impact !?)

Evaluate impact of each column change by cost

function and apply weighted probabilities for

column selections

Best value for tas function ofs? t=s/2? Small t?

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Combinatorial evolution strategy

Sandalidis, Stavroulakis and Rodriguez-Tellez 98

Generate individuals and evaluate them byf

Select best individualindiv; indiv1=indiv; counter=0; t=0;

REPEAT t=t+1 IF counter=max-countTHENapply increased mutation rate

(destabilize to escape local minimum)

Generate individuals from indiv1 and evaluate them byf

Select best individual indiv2 IF indiv2 better than indiv1 THEN {counter=0; indiv=indiv2} ELSE

{counter=counter+1; indiv1=indiv2}

UNTILtermination

Applied for fixed, dynamic and hybrid CA

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CES for dynamic channel assignment

n=49 cells, m=49 channels, call arrives at cell k

F[j,i]=0/1 if channel i is not assigned/assigned to

cellj, 1im, 1jn: current channel assignment for ongoing calls

Reassignment of all ongoing calls at cell k(channel foreach call may change) to accommodate new call

V[k,i] = new channel assignment for cell k CES minimizes energy function that includes: interference of new

assignment, reusing channels used in nearby cells, reusing channelsaccording to base coloring scheme, and number of reassignments

Centralized controller

CES for Hybrid CA and for borrowing CA in FCA

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Simple heuristics for FCA

Borndorfer, Eisenblatter, Grotschel, Martin 98

(4240 total demand, m=75 channels, Germany)

DSATUR: key[i]= # acceptable channels remained in cell i,cost[i,j]= total interference in cell i if channel j is selected

Initialize key[i]= m; cost[i,j]=0; i,j WHILE cells with unsatisfied demand exist DO {

Extract cell iwith unsatisfied demand and minimumkey[i];

Let j be available channel which minimizes cost[i,j];

Update cost[x,y] x,y by adding interference (i,j)

Update key[x] x, reduce demand at cell i }

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Hill climbing heuristic for FCA Borndorfer, Eisenblatter, Grotschel, Martin 98

Two channel assignments are neighbors if one can be obtained fromthe other by replacing one channel by another in one of cells.

PASS procedure for assignmentA={(cell,channel)}:

Sort all (i,j)A by their interference in decreasing order

FOR each (i,j)A in the order DO

Replace (i,j) by (i,j)if later has same or lower interference

Hill climbing for FCA: initializeA; A=A REPEAT

A=A; A= PASS(A)

UNTIL A A i t f (A)i t f (A)