1. MITP 413: Wireless Technologies Week 2
Michael L. Honig
Department of ECE
Northwestern University
April 2005

2. Cellular Concept Enables frequency reuse! Low power Transmitters
Switch
(MTSO)
Location
Database
PSTN
Handoff
Micro-
cells
Enables frequency reuse!

3. Cellular Frequency AssignmentsB A C E D G A C B F D G A C B E F D G C B E F D G A C B E D G A C B
Will cellular layout look this regular in practice? Why not use squares instead of hexagons? F G A D
cell cluster

4. Cellular Model Hexagonal cells Regular spacing
Frequency reuse to limit co-channel interference
Received power decreases as 1/(distance)n, n ¼ 4.
Note: “Freq. i”  group of channels (f1,f2, L , fK)
Actual cell “footprint” will be irregular (depends on terrain, etc.)

5. Cellular Terminology
Cell cluster: group of N neighboring cells which use the complete set of available frequencies.
Cell cluster size: N
Frequency reuse factor: 1/N
Uplink or reverse link: Mobiles  Base station
Downlink or forward link: Base station  mobiles
Co-channel cells: cells which are assigned the same frequencies C D F A B G E
cell cluster

6. Frequency Reuse (Ex) Given
33 MHz for Frequency Division Duplex (FDD) cellular
25 kHz simplex channel (one direction)
Cell cluster size N=7
Channel Bandwidth (BW) = 2 x 25 = 50 kHz
Total available channels = 33,000/50 = 660
Available channels per cell = 660/7 ¼ 95

7. Co-Channel Cells
For hexagonal model, N is restricted: N=i2+ij+j2, where i, j are positive integers A
i=3, j=2
N=i2+ij+j2=19
Other examples:
i= j =1  N=3
i=0, j=2  N=4
i=1, j=2  N=7
i=2, j=2  N=12

8. Interference and Capacity
As N increases:
Interference
Channels per cell
Capacity
As N decreases:

9. Interference and Capacity
As N increases:
Interference decreases
Channels per cell decrease
Capacity decreases
As N decreases:
Interference increases
Channels per cell increase
Capacity increases
Objective: choose the minimum N subject to acceptable interference levels.

10. Sources of Interference

11. Sources of Interference
Other users – Multiple-Access interference
Multipath (reflections of signals)
Other devices or systems (e.g., in unlicensed band)
Categories:
Co-channel (frequency bands coincide)
Adjacent-channel
Note: as transmitted power increases, so does the interference
power
frequency
Channel 1
Channel 2

12. Co-Channel Reuse Ratio1 2 5 4 3 . R 7 6 D
From hexagonal geometry
As D/R increases, interference decreases
(improved isolation between co-channel cells).

13. Co-Channel Reuse Ratio
Small D/R:
Small N, large number of channels/cell
More interference (fixed cell size)
Large D/R:
Small capacity
Less interference (improved call quality)
Numerical examples:
i= j =1  N=3, D/R= 3
i=1, j=2  N=7, D/R= 4.58
i=2, j=2  N=12, D/R= 6
i=1, j=3  N=13, D/R= 6.24

14. Measure of Call Quality: Signal-to-Interference-Plus-Noise Ratio
Expressed in dB (10 log (S/I))
Typically, the interference power dominates (ignore noise)
Total interference power is sum over all interferers:
I = åall interferers k Ik (interference power from mobile k)
Target S/I values:
1G (AMPs): Want S/I ¸ 18 dB ¼ 63.1
2G (GSM): Want S/I ¸ 12 dB ¼ 16
2G (CDMA): Want S/I ¸ 7 dB ¼ 5
If there is no noise, can everyone increase their S/I by raising their powers?

15. First Tier Interference
Cell Site-to-Mobile Interference
(Downlink)
Mobile-to-Cell Site Interference
(Uplink)

16. Signal Attenuation P0 In dB: Pr = P0 (dB) – 10 n log (d/d0)
distance d
reference distance d0
Reference power at reference distance d0
Path loss exponent P0
In dB: Pr = P0 (dB) – 10 n log (d/d0)
slope = -10n,
n ~ 2 to 4 for urban cellular
Pr (dB)
log (d)
log (d0)

17. First Tier Co-Channel Cells
S ¼ P0 (R/d0)-n
I ¼ 6 P0 (D/d0)-n
Therefore S/I = R-n/(6D-n) = (D/R)n/6
S/I (dB) = 10n log (D/R) – 10 log 6
= 10 n log (3N)1/2 – 10 log 6 D
First Tier 1 R
Interfering Cell

18. SIR vs. Frequency Reuse S/I (dB) = 10n log (3N)1/2 – 10 log 6
Cell cluster size N
S/I (dB) = 10n log (3N)1/2 – 10 log 6

19. S/I Example Suppose desired S/I = 18 dB ¼ 63.1, path loss n=4:
D/R = 6(S/I)1/n = [6·(63.1)]1/4 ¼ 4.41
D/R = (3N)1/2  N= (D/R)2/3 ¼ 6.49
Conclusion: To guarantee S/I > 18 dB, we must have N > Therefore need 7-cell reuse pattern.

20. Worst Case InterferenceD
D+R
D-R
Suppose N=7, D/R = (3N)1/2 = 4.6
Recalculating the S/I taking into account
the different distances between co-channel cells
gives S/I ¼ 17.3 dB < 18.
To make sure the S/I > 18 dB, we must
increase N  12 (i=j=2).
In that case S/I ¼ dB, which leaves
margin for additional path loss due to hilly terrain,
imperfect cell site locations…
Drawback?

21. Worst Case InterferenceD
D+R
D-R
Suppose N=7, D/R = (3N)1/2 = 4.6
Recalculating the S/I taking into account
the different distances between co-channel cells
gives S/I ¼ 17.3 dB < 18.
To make sure the S/I > 18 dB, we must
increase N  12 (i=j=2).
In that case S/I ¼ dB, which leaves
margin for additional path loss due to hilly terrain,
imperfect cell site locations…
However, N=7  N=12  capacity reduction 7/12!

22. To Increase Capacity in Cellular Systems:
Service provider pays $20B, each new subscriber generates $1000/year  need 20M subscribers to recover cost in a year!

23. To Increase Capacity in Cellular Systems:
Assign more spectrum
Antenna sectoring
Cell splitting
Different cell configurations (zone microcell)
Power control
Migrate to higher efficiency systems (e.g., 1G  2G  3G)
Service provider pays $20B, each new subscriber generates $1000/year  need 20M subscribers to recover cost in a year!

24. Sectorization (120o) Use directional antennas to reduce the
Two Interferers in
First Ring per Sector
Cell Site-to-Mobile Interference
(Downlink)
Mobile-to-Cell Site Interfaces
(Uplink)
Use directional antennas to reduce the
number of interferers from 6 to 2.
S/I increases by factor of 3 (about 5 dB)

25. 60o Sectorization Number of interferers reduced from 6 to 1.
One Interferer in
First Tier per Sector
Cell Site-to-Mobile Interference
(Downlink)
Mobile-to-Cell Site Interfaces
(Uplink)
60o
Number of interferers reduced from 6 to 1.
S/I increases by factor of 6 (about 8 dB).

26. 60o Sectorization: Worst Case Interference2 .
D R . R . M D . 1
Even larger improvement relative to worst-case omni-directional antennas
(about 11 dB).

27. Disadvantages of Sectoring

28. Disadvantages of Sectoring
Additional complexity
Reduced trunking efficiency
Increased handoffs (can be accomodated at base station instead of cellular switch (MTSO), so not a major concern)
Less effective in dense urban environments due to scattering of radio waves across sectors.

29. “Smart” Antennas (Beamforming)
Narrow “beam” focused on one user
Different beams can use the same frequency!

30. Growing by Splitting Cell 4 Into
Cell Splitting 2 2 1 5 1 5
(4)
(2)
(3)
(6)
(7)
(5)
(1) 4 1 1 3 7 3 7 6 3 6 3
Growing by Splitting Cell 4 Into
Cells of Small Size
Smaller cells  lower power, more channels available per unit area.

31. Mixed Micro/Macro Cells
How to accommodate both pedestrian (low-mobility) and high-mobility users?
Macro-cell
(1-2 mile radius)
High power (expensive)
Transmitters
Micro-cell
(e.g., city block)
Low power (inexpensive) transmitters
Micro-cell overlay reduces capacity of macro-cellular network!

32. “Umbrella” Cell High mobility users communicate
with large (high power base station).
Must support handoff between macro-
and micro-cells. (Mobile speed must
be estimated at base station.)

33. Zone Microcells Any channel can be assigned to any zone.
Base
Station
Zone Selector
Microwave or
fiber optic link
Any channel can be assigned to any zone.
No handoff between zones.
Radiation localized, improves S/I.
Highways, urban corridors.

34. Zone Microcells: Co-Channel Distance. D DZ RZ R
3 hexagons (zones) per cell
N=7
DZ/RZ = 2(D/R)
(less interference with same
frequency reuse)

35. Power Control and System Migration
Advantages?
Migration to 3G/4G/ extensions…
Target S/I decreases enables increased frequency reuse
IS-136 (2G) requires S/I > 12 dB  N=4
GSM (2G) requires S/I > 9 dB  N=3
IS-95 requires S/I > 7 dB (N=1)
CDMA 2000 requires S/I > 3-5 dB (depending on mobility)

36. Power Control and System Migration
Minimizes interference
Saves battery power
Solves “near-far” problem (crucial in CDMA)
Migration to 3G/4G/ extensions…
Target S/I decreases enables increased frequency reuse
IS-136 (2G) requires S/I > 12 dB  N=4
GSM (2G) requires S/I > 9 dB  N=3
IS-95 requires S/I > 7 dB (N=1)
CDMA 2000 requires S/I > 3-5 dB (depending on mobility)

37. Trunking and Grade of Service (GoS)
Idea (trunking): Allocate channels on a per-call basis Select from pool of available channels.

38. Trunking and Grade of Service (GoS)
Idea (trunking): Allocate channels on a per-call basis Select from pool of available channels.
Example: set of channels is (f1, f2, f3)
Number of
Calls in progress
service times 4
System
capacity 3 2 1
time f3 f2 f2 f1 f1
blocked or
delayed call
call arrival f1 f2

39. Grade of Service (GoS) GoS measures: Blocking probability
Probability that delay > time T (e.g., maximum acceptable delay for voice call)
GoS pertains to busiest hour (e.g., rush hour)
GoS depends on: ??
Contrast with queuing model (toll booth). What about GoS for data services?

40. Grade of Service (GoS) GoS measures: Blocking probability
Probability that delay > time T (e.g., maximum acceptable delay for voice call)
GoS pertains to busiest hour (e.g., rush hour)
GoS depends on:
Number of channels
Call arrival rate 
Average holding time H
Contrast with queuing model (toll booth). Ask about GoS for data
Traffic engineering problem: determine the number of channels so that that GoS
meets some target performance (e.g., Prob of blocking < 2%).

41. Traffic Intensity
Traffic intensity is defined as  H, and measured in Erlangs.
Example: =1 call/minute, H= 1 minute,
 H = 1 Erlang  on average, users request 1 channel
 H = ½ Erlang  there are no requests for channels more than % of the time
Departing, or “carried” traffic f1
Offered traffic (“load”)
 H = A
What does \lambda H = ½ mean – why more than 50%? Applies to circuit-switched (voice) service.
Channel
assignment f2
C channels fC
Offered traffic is not the same as the carried traffic, due to blocking!

42. Erlang B Formula (1917)
Formula for computing blocking probability assuming:
Blocked calls disappear
Requests for channel arrive according to a Poisson random process (inter-arrival times are independent, exponentially distributed)
Applies to infinite user population
C channels available
Exponentially distributed service time
Blocking probability formula:
time
Prob(call lasts < t secs) 1
3 minutes
1-e-t/
“Blocked calls cleared” formula

43. Erlang B Curves

44. Erlang C Formula Blocked calls enter a queue First come, first served
Call is blocked if queuing delay D > T
Formula for probability of blocking given in text.

45. Example Take PB · 2%, C=5  Offered load A < 1.7 Erlangs
If each user is busy 1/10 of the time (0.1 Erlang/user), Total # users < 17 (maximum)
For C=10: A < 5 Erlangs or 50 users
For C=100: A=88 or 880 users
Observation: A/C increases with C (e.g., 10 groups of 10 channels can support only 500 users)
Trunking efficiency increases as C increases

46. Trunking Efficiency
Refers to the traffic intensity (Erlangs) that can be supported given a fixed number of channels and a target blocking probability.
For a fixed blocking probability:
Trunking efficiency improves with the number of channels.
Best to pool as many channels as possible.

47. Spectral Efficiency (SE)
Defined as
Example: SE = 0.1 Erlang/MHz/km2  10 MHz needed to support 1 Erlang/km2 (Note that 1 km2 may correspond to a cell.)
To convert Erlangs to users, must estimate traffic per user, e.g., if on average, each user is active 1/10 of the time, then 1 Erlang corresponds to 10 users.
With uniformly distributed traffic, the SE is
Traffic per cell depends on…

48. Spectral Efficiency (SE)
Defined as
Example: SE = 0.1 Erlang/MHz/km2  10 MHz needed to support 1 Erlang/km2 (Note that 1 km2 may correspond to a cell.)
To convert Erlangs to users, must estimate traffic per user, e.g., if on average, each user is active 1/10 of the time, then 1 Erlang corresponds to 10 users.
With uniformly distributed traffic, the SE is
Traffic per cell depends on:
Number of channels
Grade of Service (e.g., typically 2%)
S/I requirement (determined by cluster size N)
What is a reasonable performance measure for a data service?

49. Effect of Sectorization
Does sectorization increase spectral efficiency?

50. Effect of Sectorization
For fixed N, sectorization
Increases the S/I
Reduces trunking efficiency
For example, with 99 channels per cell, 120o sectors divides this into 33 channels per sector, which reduces the number of Erlangs that can be supported for a given blocking probability.
Can we use sectorization to increase SE?
Yes, must also reduce N
Example: suppose the target S/I = 18 dB  N=7 for omni-directional antennas. With 120o sectors, the S/I increases to about 23 dB. Can reduce N from 7 to 4, and still maintain S/I > 18 dB.

51. Channel Allocation
Objective: equalize grade of service (blocking probability) over coverage area  Allows increase in subscriber pool.
Fixed Channel Assignment (FCA): channels assigned to each cell are predetermined.
Separate channels within a cell to avoid adjacent-channel interference
Nonuniform FCA: distribute channels among cells to match averaged traffic load over time.
Channel borrowing: borrow channels from neighboring cell
Temporary: high-traffic cells return borrowed channels
Static: channels are non-uniformly distributed and changed in a predictive manner to match anticipated traffic
Dynamic Channel Assignment (DCA): channels are assigned to each call from the complete set of available channels
Must satisfy S/I constraint
Channels returned to pool after call is completed
Can be centralized (supervised by MSC) or distributed (supervised by BS)
Distributed DCA used in DECT

52. FCA vs. DCA FCA DCA Low complexity Better under heavy traffic
Sensitive to changes in traffic
Variable grade of service
Higher probability of outage
Suitable for macro-cellular systems (e.g., cellular)
Low call setup delay
Requires careful frequency planning
Centralized assignment
Moderate/High complexity
Must monitor channel occupancy, traffic distribution, S/I (centralized)
Better under light/moderate traffic
Insensitive to changes in traffic
Stable grade of service
Low probability of outage (call termination)
Suitable for micro-cellular systems (e.g., cordless)
Moderate/high call setup delay
No frequency planning
Assignment can be centralized or distributed