Subscriber Maximization in CDMA Cellular Network

transcript

Subscriber Maximization in CDMA Subscriber Maximization in CDMA Cellular NetworkCellular Network

Robert Akl, D.Sc.Robert Akl, D.Sc.

University of North TexasUniversity of North Texas

OutlineOutline

• Overview of CDMAOverview of CDMA

• Traffic and Mobility ModelTraffic and Mobility Model

• Subscriber Optimization FormulationSubscriber Optimization Formulation

• Numerical ResultsNumerical Results

• ConclusionsConclusions

Code Division Multiple Access Code Division Multiple Access (CDMA) Overview(CDMA) Overview

• Multiple access schemesMultiple access schemes

Call 1

Call 3

Call 2

Call 4

FDMAFr

Call 1 Call 2 Call 3

Call 10Call 11Call 12

TDMA CDMA

Frequency

Call 1Call 2

Call 3Call 4

Relative Average Inter-cell Relative Average Inter-cell Interference ModelInterference Model

Cell j

Cell i

Iji Erj

m x,y 10 j

rim x,y / i

2Cj nj

Aj dA x,y

Iji e s 2 nj

rjm (x,y)

rim (x,y)Cj dA(x,y)

jiI Relative average interference at cell i caused by nj users in cell j

1111 1212 1313 …… …… 1M1M

2121 2222

3131 3232

…… ……

M1M1 M2M2 MMMM

Interference Matrix

where F[ j,i]Iji /nj for i, j 1,..., M,

and nj is the number of users in cell j

Hence, the total relative average inter-cell interference experienced by cell i is

1111 1212 1313 …… …… 1M1M

2121 2222

3131 3232

…… ……

M1M1 M2M2 MMMM

I2 1F[1,2]

CapacityCapacity

• The capacity of a CDMA network is determined by maintaining a lower bound on the bit energy to interference density ratio, given by

REb ni 1 Ii /W N0

for i 1,...,M

W = Spread signal bandwidth

R = bits/sec (information rate)

α = voice activity factor

ni = users in cell i

N0 = background noise spectral

density

ni Ii W /R

Eb /N0

1 ceff

for i 1,...,M

• Let τ be that threshold above which the bit error rate must be maintained, then by rewriting the equation:

Mobility ModelMobility Model

• Call arrival process is a Poisson process with rate: Call arrival process is a Poisson process with rate: λλ

• Call dwell time is a random variable with exponential Call dwell time is a random variable with exponential distribution having mean: distribution having mean: 1/μ1/μ

• Probability that a call in cell Probability that a call in cell ii goes to cell goes to cell jj after after completing its dwell time: completing its dwell time: qqijij

• Probability that a call in progress in cell Probability that a call in progress in cell ii remains in cell remains in cell ii after completing its dwell time: after completing its dwell time: qqiiii

• Probability that a call will leave the network after Probability that a call will leave the network after completing its dwell time: completing its dwell time: qqii

Mobility Model – Handoff CallsMobility Model – Handoff Calls

• Handoff calls (Handoff calls (vvjiji): calls that have moved from cell ): calls that have moved from cell

jj to an adjacent cell to an adjacent cell ii..

ji j 1 B j q ji 1 B j q ji xj

ji 1 B j q ji j

• Bj : Call blocking probability for cell j• Aj : Set of cells adjacent to cell i• ρj : Total offered traffic to cell j

j j xj j j

New arriving calls

Handoff calls

Admissible StatesAdmissible States

• A new call is accepted if the following inequality still holds upon acceptance, A new call is accepted if the following inequality still holds upon acceptance, where where NNii is the maximum number of calls allowed to be admitted in cell is the maximum number of calls allowed to be admitted in cell i:i:

ni N i, for i 1,..., M

• The blocking probability for cell The blocking probability for cell ii becomes: becomes:

N i /N i!

Aik k!

, where Ai

Maximization of SubscribersMaximization of Subscribers

max(1 ,...,M ),(N1 ,...,N M )

subject to Bi ,

N i N jF[ j,i]ceff

for i 1,...,M.

• Solve a constrained optimization problem that maximizes Solve a constrained optimization problem that maximizes the number of subscribers subject to upper bounds on the the number of subscribers subject to upper bounds on the blocking probabilities and lower bounds on the bit energy blocking probabilities and lower bounds on the bit energy to interference ratios:to interference ratios:

SimulationsSimulations

• Network configurationNetwork configuration• COST-231 propagation modelCOST-231 propagation model• Carrier frequency = 1800 MHzCarrier frequency = 1800 MHz• Average base station height = 30 metersAverage base station height = 30 meters• Average mobile height = 1.5 metersAverage mobile height = 1.5 meters• Path loss coefficient, Path loss coefficient, mm = 4 = 4• Shadow fading standard deviation, Shadow fading standard deviation, σσss = 6 dB = 6 dB• Processing gain, Processing gain, W/RW/R = 21.1 dB = 21.1 dB• Bit energy to interference ratio threshold, Bit energy to interference ratio threshold, ττ = 9.2 dB = 9.2 dB• Interference to background noise ratio, Interference to background noise ratio, II00/N/N00 = 10 dB = 10 dB• Voice activity factor, Voice activity factor, αα = 0.375 = 0.375

Simulations – Network ParametersSimulations – Network Parameters

No mobility probabilities• qij = 0• qii = 0.3• qi = 0.7

AAii qijqij qiiqii qiqi

33 0.0200.020 0.2400.240 0.7000.700

44 0.0150.015 0.2400.240 0.7000.700

55 0.0120.012 0.2400.240 0.7000.700

66 0.0100.010 0.2400.240 0.7000.700

AAii qijqij qiiqii qiqi

33 0.1000.100 0.0000.000 0.7000.700

44 0.0750.075 0.0000.000 0.7000.700

55 0.0600.060 0.0000.000 0.7000.700

66 0.0500.050 0.0000.000 0.7000.700

Low mobility probabilities High mobility probabilities

Traditional Network Topology Traditional Network Topology and Uniform User Distributionand Uniform User Distribution

• Maximum subscribers is 15,140.Maximum subscribers is 15,140.

Traditional Network Topology Traditional Network Topology and Non-Uniform User Distributionand Non-Uniform User Distribution

• Maximum subscribers drops to 14,224.Maximum subscribers drops to 14,224.

Optimized Network Topology and Optimized Network Topology and Non-Uniform User DistributionNon-Uniform User Distribution

• Maximum subscribers increases to 15,164.Maximum subscribers increases to 15,164.

SummarySummary

• Calculate the maximum number of subscribers Calculate the maximum number of subscribers that a CDMA cellular network can handle for a that a CDMA cellular network can handle for a given grade-of-service, quality-of-service, given grade-of-service, quality-of-service, network topology, user distribution profile, and network topology, user distribution profile, and mobility.mobility.

• Solution yields the maximum number of calls that Solution yields the maximum number of calls that should be admitted in each cell to guarantee the should be admitted in each cell to guarantee the given requirements above. given requirements above.

Subscriber Maximization in CDMA Cellular Network

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