channel assignment in cellular networks ivan stojmenovic ivan [email protected]
TRANSCRIPT
Channel Assignment in Cellular Networks
Ivan Stojmenovic
www.site.uottawa.ca/~ivan
Overview
• Fixed channel assignment
• Multicoloring – co-channel interference
• General problem statement
• Genetic algorithms
• Results and details
• Fixed/dynamic channel and power assignment
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
Cellular architecture
One low power transmitter per cell
Frequency reuse–limited spectrum
Cell splitting to increase capacityA
B
Reuse distance: minimum distance between two cells using same channel for satisfactory signal to noise ratio
Measured in # of cells in between
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
Reuse pattern for reuse distance 2?
One frequency can be (re)used in all cells of the same color
Minimize number of frequencies=colors
Reuse distance 2 – reuse pattern
One frequency can be (re)used in all cells of the same color
Reuse pattern for reuse distance 3?
Reuse distance 3 – reuse pattern
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
f4
f5
f1
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
3 cell clusterwith 3 sector antennas
f1f1 f1f2f3
f2
f3
f2
f3h1
h2
h3g1
g2
g3
h1h2
h3g1
g2g3
g1g2g3
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
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
Hexagon graphs: reuse distance 2
What is the graph for reuse distance 3?
Lower bounds for hexagonal graphsD= Maximum total weight on any cliqueLower bound on number of channels: D
D/3
D/2 D/6
D/2
D/2 D/2
D/2
D/2
D/2D/2D/2
D/2
000
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
Fixed allocations – reuse 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 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
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<=D/3 (why?)
• In practice, reuse distances 3 or 4 may be used
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)
Adjacent channel interferenceReceiver filter
f1 f3f2interference
Co-site constraint: channels in the same cell must be c0 apart
Adjacent-site constraint: channels assigned to neighboring cells must be c1 apart
Inter-site constraint: channels assigned to cells that are r cells apart must be cr apart
Lower bounds: co-site and adjacent-site
Gamst ’86
c0 max {w(u), w(v), w(x)}
c1 max{vC w(v) | C is a clique}
max {c0 w(u), (c0–c1)w(u)+ c1vC,vu w(v) | C is a clique containing u} when c0 2c1
u
v x
c0c1c0<2c1
Algorithm: interleaving channels of different color classes
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 k cells
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
Research problem: several power levels at mobile hosts
• If mobile phone is ‘near’ base station, it may switch to 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, …
Genetic algorithms• Rechenberg 1960, Holland 1975 …
• Part of evolutionary computing in AI
• Solution to a problem is evolved (Darwin’s 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 chromosome x
• Perform crossover, mutation and generate new population, using f(x) in selecting probabilities
• UNTIL satisfactory solution found or timeout
Fixed channel assignment problem• INPUT: n = number of cells
Compatibility matrix C, C[i,j]= minimal channel separation between cells i and j, 1i,jnd[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 cell j, 1km, 1jn.
• Optimization: Minimize number of interferences and satisfy demand
Our problem representation and solution space
• Each row F[j,k], 1km, is a combination of d[j] out of m elements (# of 1’s 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 of d[j] X’s and m-(c0+1)d[j] 0’s; replace each X by 100..0 (c0 0’s); shift circularly by random number in [0,c0]
Mutation• Each row=cell is mutated separately• Combinations in bit representation: x 1’s out of m bits• Mutation with equal probability for each bit: choose one out
of x 1’s and one out of m-x 0’s at random, swap: Ngo-Li ‘98
• Mutation with different probability for each bit: b[i]= # of conflicts of i-th selected channel with other channels in this and other cellsp[i]=b[i]/(b[1]+…+b[x])Repeat for 0’s: # of conflicts if that channel turned on
• Choosing bit with given probability: Generate at random r, 0 r 1, and choose i, p[1]+…p[i-1] r <p[1]+…+p[i]
Crossover• Regular GA crossover:
1011000110 1001111000 0101111000 0111000110
• Ngo-Li ’98: A and B two parents, each row separately, preserve # of 1’s in each row: push 10 and 01 columns in stack if top same;
pop for exchange if top different1011000110 1001101000 0101111000 0111010110
• Problem: # of swaps varies
New crossover• t= number of desired swaps in a row
• Mark positions in two combinations that differ
• let s 10’s and s 01’s are found
• Choose t out of s 10 at random and 01
• Choose t out of s 01 at random and 10
• Example: 1011000110 1001010010 0101111000 0111110110
s=4 t=2 $^$ ^^^$$ # **# # **# offspring
selected columns
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 t as function of s? t=s/2? Small t?
Combinatorial evolution strategy• Sandalidis, Stavroulakis and Rodriguez-Tellez ’98
• Generate individuals and evaluate them by f• Select best individual indiv; indiv1=indiv; counter=0; t=0;
• REPEAT t=t+1• IF counter=max-count THEN apply increased mutation rate
(destabilize to escape local minimum)
• Generate individuals from indiv1 and evaluate them by f
• Select best individual indiv2
• IF indiv2 better than indiv1 THEN {counter=0; indiv=indiv2} ELSE {counter=counter+1; indiv1=indiv2}
• UNTIL termination
• Applied for fixed, dynamic and hybrid CA
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
cell j, 1im, 1jn: current channel assignment for ongoing calls
• Reassignment of all ongoing calls at cell k (channel for each 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 channels according to base coloring scheme, and number of reassignments
• Centralized controller
• CES for Hybrid CA and for borrowing CA in FCA
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 i with unsatisfied demand and minimum key[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 }
Hill climbing heuristic for FCA• Borndorfer, Eisenblatter, Grotschel, Martin ’98
• Two channel assignments are neighbors if one can be obtained from the other by replacing one channel by another in one of cells.
• PASS procedure for assignment A={(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: initialize A; A’=A
• REPEAT
• A=A’; A’= PASS(A)
• UNTIL A’=A or interference(A’)interference(A)