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Cellular System Capacity
• Maximum number of users a
cellular system can support in
any cell.
• Can be defined for any system.
• Typically assumes symmetric
data rates, cells, propagation,
and mobility.
• Depends on the user
specifications and radio design
– data rate, BER, modulation,
coding, etc.
Which link dictates capacity?
• Reverse link
– Noncoherent reception
– Independent fading of all users
– Requires power control
• Forward link
– Coherent demodulation using
pilot carrier.
– Synchronous combining of
multipath.
• Conclusion: reverse link is the
limiting factor in capacity.
– Claim: other cell interference will
tend to equalize performance in
each direction.
CDMA Cellular Capacity
• Single-Cell System
– Similar to MAC user capacity
W /R
Eb / N 0 
( N  1)  (h / S )
 N  1
W /R h

Eb / N 0 S
– G=W/R is processing gain (W is
bandwidth, R is data rate)
 h is interference plus noise
- Assumes power control
- Performance improvement
through sectorization and voice
activity
8C32810.44-Cimini-7/98
Sectorization
• Base station omni antenna is
divided into M sectors.
• Users in other sectors do not cause
interference.
• Number of users per sector is
Ns=N/M (reduces interference by M).
• Requires handoff between sectors
at the base station
Voice Activity
• Suppress signal when voice
user not active.
• Voice activity a=.35-.4 (reduces
interference by 60-65%).
• Requires resynchronization for
every talk spurt.
– Higher probability of dropping
users.
New Capacity (per cell)
Eb / N 0 
W /R
( N s  1)a  (h / S )
M  W /R  h
 
 N  MN s  M  
a  Eb / N 0  S
• Capacity increased proportional to
the number of sectors and inversely
proportional to the voice activity
(M/a typically around 8).
• Claim: Thus, CDMA is competitive
with FD/TD for a single-cell
• Does not include impact of
sectorization on out-of-cell
interference.
Multicell System
• Codes reused in every cell.
• No power control in forward link
– Interference from adjacent cells
can be very strong.
• Power control in reverse link
– All users within a cell have same
received signal strength
– Interference from other cells
have variable power
• Fast fading (interference and signal)
neglected (S/I statistics).
• The interferer’s transmit power
depends on distance to his base
station.
• Received power at desired base
depends on distance to base,
propagation, and the interferer’s
transmit power.
Reverse Link Interference
• Total path loss: propagation (d-4
falloff) and log-normal shadowing.
 x is Gaussian, 8 dB STD.
L  10(x /10) r 4
• Instantaneous interference power
4
I (r0 , rm )  rm  (x 0 x m ) /10
   10
1
S
 r0 
– rm is distance to interferer’s base
– r0 is distance to desired base
 xm is shadowing to interferer’s base
 x0 is shadowing to desired base
- S is received power with power control
- Power less than 1 since otherwise
would handoff to desired base
Average interference power
4


 rm  (x 0 x m ) /10
I
  g   10
1 (rm / r0 ) 410(x 0 x m ) /10  1 rdA
S
 r0 
- A is the cell area.
 r is the user density (r=2Ns/Sqrt[3])
 g is voice activity term (equals 1
w.p. a, 0 w.p. 1-a)
- Must be integrated against
distribution of m, r0, rm, x0, xm
- Simplify distribution of m by
assuming minimum distance.
- r0, rm uniformly distributed.
- Claim: I Gaussian since it’s a
functional of a 2D white random
process
Mean and Variance
• Numerical integration leads to
E(I/S)=.247Ns
• Second Moment:
– Assumes autocorrelation of
shadowing is a delta function.
– Numerical integration leads to
Var(I/S)=.078Ns
• Calculations assume 8dB STD.
• Total interference distribution
Eb / N 0 
W /R
N s 1

i 1
i
 ( I / S )  (h / S )
i binomial r.v. with probability a
Capacity Calculation
• Calculate probability Eb/N0
below target (BER exceeds
target) based on Ns and these
statistics. .
Ns


3
P( BER  10 )  P   i  I / S  d 
 i 1

W /R h
d

Eb / N 0 S
• Compute outage probability as
a function of Ns.
– Assumes target Eb/N0 =5..
 d=30
• Similar calculation for uplink
An Alternate Approach
• Simulation approach
• Includes three rings of
interfering cells
• Capacity for TDMA and CDMA
compared
– Similar assumptions about voice
activity and sectorization
– TDMA assumes FH with dynamic
channel allocation
Capacity degradation
• Voice activity changed from
.375 to .5, -30% change
• Path-loss changed from 4 to 3,
-20% change
• Multipath fading added, -45%
change
• Handoff margin changed from
0 to 6 dB, -40% change
• Power control error changed
from 0 to 1 dB, -35% change