Impact of Interference Impact of Interference Model on Capacity in Model on Capacity in CDMA Cellular Networks CDMA Cellular Networks Robert Akl, D.Sc. Robert Akl, D.Sc. Asad Parvez Asad Parvez University of North University of North Texas Texas
Dec 28, 2015
Impact of Interference Model on Impact of Interference Model on Capacity in CDMA Cellular Capacity in CDMA Cellular
NetworksNetworks
Robert Akl, D.Sc.Robert Akl, D.Sc.
Asad ParvezAsad Parvez
University of North TexasUniversity of North Texas
OutlineOutline
• Introduction to CDMA networksIntroduction to CDMA networks• Average interference modelAverage interference model• Actual interference modelActual interference model• Optimized capacityOptimized capacity• 2D Gaussian user model2D Gaussian user model• 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
Freq
uenc
y
Time
FDMAFr
eque
ncy
Time
Call 1 Call 2 Call 3
Call 4 Call 5 Call 6
Call 7 Call 8 Call 9
Call 10Call 11Call 12
TDMA CDMA
Frequency
Time
Code
Call 1Call 2
Call 3Call 4
1 bit period
1 chip period
Data Signal
PN-code
Coded Data Signal
PN-code
Decoded data Signal
Spr ea di ng
De- sp re ad in g
f
f
f
f
Data Signal
Interference
Recovered Data
Signal
Spread Spectrum: Direct Spreading
Factors Affecting CapacityFactors Affecting Capacity
d1
d2
Base Station
c1
c2
Distance
Pr2
Pr1
• Power ControlPt1: Power transmitted from c1Pt2: Power transmitted from c2Pr1: Power received at base station from c1Pr2: Power received at base station from c2
Pr1 = Pr2
Pt1
Pt2
Time
• Soft handover of calls
Factors Affecting Capacity (cont.)
• Universal frequency useUniversal frequency use
• Reverse link vs forward linkReverse link vs forward link
• Voice activity factorVoice activity factor
AC
F
GB
ED
AA AA
A
AA
AA
AA
TDMA or FDMA CDMA
Reverse link
Forward link
Factors Affecting Capacity (cont.)
Relative Average Inter-cell Relative Average Inter-cell Interference ModelInterference Model
dA
Cell j
Cell i
jr
ir
yxdAA
n
yxr
yxrji
j
j
Cji
mi
jmjI ,
/,
10,E
2
10
),( ),(
),(2
yxdAyxr
yxrI Cj m
i
mj
A
neji
j
js
jiI Relative average interference at cell i caused by nj users in cell j
A
B
Back
1111 1212 1313 …… …… 1M1M
2121 2222
3131 3232
…… ……
…… ……
M1M1 M2M2 MMMM
ijF ,
Interference Matrix
jn
MjinIijF
j
jji
cellin users ofnumber theis and
,,...,1,for /],[ where
Hence, the total relative average inter-cell interference experienced by cell i is
ijFnIM
j
ji ,1
1111 1212 1313 …… …… 1M1M
2121 2222
3131 3232
…… ……
…… ……
M1M1 M2M2 MMMM
12I
C
]2,1[12 FI
Relative Actual Inter-cell Relative Actual Inter-cell Interference ModelInterference Model
• Interference matrix F cannot be calculated in advance• Instead, a new interference matrix U is computed as follows• For a user k in cell j, the relative actual interference offered by this user to cell i is
m
i
jsk r
rejiU
2
jiUikji
jn
k
M
j
I
for ,11
• Hence, the total relative actual inter-cell interference at cell i caused by every user in the network is
D
E
k users in cell j
Actual Interference Matrix Actual Interference Matrix UU
•Example: for a new call in cell 2, compute row matrix U[2,i] for i = 1,…,M using equation D
]2M ...... 23 22 21[2 iU
• Update 2nd row of interference matrix U by adding the above row matrix to it.
1111 1212 1313 …… …… 1M1M
2121 2222
3131 3232
…… ……
…… ……
M1M1 M2M2 MMMM
iUijU 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
Mi
NWInRE
E
I
E
iib
b
i
b
,...,1for
/1 00
W = Spread signal bandwidth
R = bits/sec (information rate)
α = voice activity factor
ni = users in cell i
N0 = background noise spectral
density
F
,...,1for
1/
11/
0
Mi
cNE
RWIn eff
bii
• Let τ be that threshold above which the bit error rate must be maintained, then by rewriting Eq. F
G
Back
Capacity CasesCapacity Cases
• Equal capacity:Equal capacity: all cells have an equal number of users all cells have an equal number of users
ini allfor n
• Optimized Capacity:Optimized Capacity: A set of users in each cell obtained A set of users in each cell obtained by solving following optimization problemby solving following optimization problem
.,...,1for
, subject to
, max1
n
Mi
cIn
n
effii
M
ii
H
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, m = 4Path loss coefficient, m = 4• Shadow fading standard deviation, Shadow fading standard deviation, σσss = 6 dB = 6 dB• Processing gain, W/R = 21.1 dBProcessing gain, W/R = 21.1 dB• Bit energy to interference ratio threshold, τ = 9.2 dBBit energy to interference ratio threshold, τ = 9.2 dB• Interference to background noise ratio, IInterference to background noise ratio, I00/N/N00 = 10 dB = 10 dB• Voice activity factor, α = 0.375Voice activity factor, α = 0.375
• These values in Eq. G give upper bound on the relative These values in Eq. G give upper bound on the relative interference in every cell, c_eff = 38.25.interference in every cell, c_eff = 38.25.
Simulations – Equal CapacitySimulations – Equal Capacity
• Average interferenceAverage interference• Users in each cell: 18Users in each cell: 18
• Actual interferenceActual interference• Users in each cell: 17Users in each cell: 17
Simulations – Optimized Capacity Vs Actual Simulations – Optimized Capacity Vs Actual Interference CapacityInterference Capacity
• Optimized Capacity using average interference = 559
• Simulated Capacity using actual interference = 554
More Simulations – Actual InterferenceMore Simulations – Actual Interference
• Simulated Capacity = 568• Simulated Capacity = 564
Individual Cell Capacity ComparisonIndividual Cell Capacity Comparison
• Comparison of cell capacity for 3 simulation trials.
• Comparison of average cell capacity for 50 simulation trials.
Extreme Cases Using Actual Interference – Extreme Cases Using Actual Interference – Non-Uniform DistributionNon-Uniform Distribution
• Maximum network capacity of 1026 with best case non-uniform user distribution
• Maximum network capacity of 108 with worst case non-uniform user distribution
Model User Distribution by 2D GaussianModel User Distribution by 2D Gaussian
• Mean = 0 and standard deviation = 200 • Mean = 0 and standard deviation = 500
Model User Distribution by 2D GaussianModel User Distribution by 2D Gaussian
• Mean = 0 and standard deviation = 900 • Non-zero mean, standard deviation between 100-300
ConclusionsConclusions
• Actual interference model is computationally Actual interference model is computationally intensive.intensive.
• Capacity obtained using average interference is Capacity obtained using average interference is close to the capacity obtained using actual close to the capacity obtained using actual interference for uniform user distribution.interference for uniform user distribution.
• Average interference model cannot predict Average interference model cannot predict extreme variations in network capacity under non-extreme variations in network capacity under non-uniform user distribution.uniform user distribution.
• Can use 2D Gaussian distribution to model Can use 2D Gaussian distribution to model uniform and non-uniform user distribution.uniform and non-uniform user distribution.