Transcript Uplink Throughput in a Single-Macrocell/Single

Uplink Throughput in a
Single-Macrocell/Single-Microcell
CDMA System,
with Application to Data Access
Points
Shalinee Kishore (Lehigh University)
[email protected]
Stuart C. Schwartz (Princeton University)
Larry J. Greenstein (WINLAB-Rutgers University)
H. Vincent Poor (Princeton University)
VTC Fall 2003
Two-Tier Cellular CDMA System
Macrocell with embedded microcell (used to enhance data capabilities)
• Macrocell serves NM (large number) users at fixed data rate RM.
• Microcell serves n (small number) users one-at-a-time at higher data
rate, Rm,  resembles a Data Access Point (DAP).
• Both base stations employ CDMA in the same frequency channel 
cross-tier interference.
• Microcell user can vary its spreading gain according to path gain and
interference conditions.
Goal: Analyze achievable uplink throughputs for DAP.
Per-user throughput
Total DAP throughput
Per-user Throughput: Uplink throughput for a single DAP user.
Total DAP Throughput: Uplink throughput over all n DAP users.
Problem Statement
Given:
• Single-Macrocell/Single-Microcell CDMA System with system
bandwidth W and fixed chip rate 1/W.
• Probability distribution of user locations
• Transmission gain model between user j and base station i (i = M,m)
 b
H i  i
  d ji
T ji  
  bi
H i  d
  ji
2
i

 10 10 , d ji  b


4
i

 10 10 , d ji  b


w here,
d ji  distance betw eenuser j and base i
H i  antenna height, gain, etc. at base i
bi  breakpoint distance of base i
i
1010  lognormal shadow fading w ith i for base i
Problem Statement (Cont’d)
• N total users who are assigned base stations according to path gains.
User j elects macrocell when TjM > dTjm, otherwise it elects DAP.
d = desensitivity factor
d  1  small DAP coverage area
• NM macrocell users who simultaneously transmit with rate RM = W/G
(G is fixed macrocell processing gain) and achieve minimum SINR GM.
• Remaining n = N - NM DAP users who transmit one-at-a-time and can
adapt their processing gain (thus their data rate, Rm).
Objective: Determine Rm for DAP users with minimum SINR of Gm.
Calculation of DAP Single-User Data Rate
Using the SINR requirements, it can be shown for n random DAP users,
r (n ) 
w hereK 
Rm (n )
W
 (K  N  n ) 
 min 
,1
 GI I

m
M
m


W
 1 (the single - cell pole capacity) and
RM GM
Normalized interference at
macrocell due to DAP user
Normalized interference at
DAP due to macrocell users
TM
IM 
Tm
Im 
Tmk
T
k M
random
variables
Mk
Our results show that the distribution of IMIm can be well modeled as lognormal.
Calculation of DAP Single-User Data Rate (Cont’d)
• Consequently, cumulative distribution function (CDF) of r given n DAP
users, F(r|n), is that of a truncated lognormal random variable.
• The distribution of r is:
N
F (r ) 
 p F (r | n )
n 1
n
1  p0
where pn is the probability that there are n DAP users.
• Thus, distribution of r can be well-approximated using weighted sum of
CDF’s of truncated lognormal random variables.
• Single-user data rates can be used to compute data throughputs.
Data Throughputs: Time-Averaged Data Rates
Per User Throughput, tu, takes into account time-limited access when more
than one DAP user in the system. Distribution can be computed as:
N
Ft u (t u ) 
 p F (nt
n 1
n
u
| n)
1  p0
E{tu} can be computed from this distribution.
Total DAP Throughput, t, measure of DAP utilization. For a given n, t is the
sum of throughputs for the n users. Average value can be computed as
N
E{t }   pnE{ r | n}
n 0
where E{r|n} can be approximated assuming a truncated lognormal
distribution.
CDF
Accuracy of Truncated Lognormal Approximation
tu/W, Normalized Per-User Throughput
(K=26, Gm=7, NM=25, HM / Hm = 10)
Normalized Average Throughput
Normalized Average Throughput (E{ t / W }) Versus d
Total DAP
Throughput
Per-User
Throughput
d, Desensitivity
(K=26, Gm=7, NM=25, HM / Hm = 10)
Conclusion
• Demonstrated that by controlling the desensitivity factor, a microcell
can be converted to a DAP.
• Analyzed uplink data rate for a single DAP user and demonstrated
that it can be well-approximated as a truncated lognormal
random variable.
• Developed throughput statistics for both single DAP users and overall
DAP users.
• Found the value of desensitivity for which per-user throughput and
total DAP throughput are both high.
• Future work: multiple DAP’s, downlink throughputs, effect of mobility
(time-varying channel conditions), etc.