1. Professor Saad Haj Bakry, PhD, CEng, FIEE N ETWORK A RCHITECTURE C APACITY OF C ELLULAR S YSTEMS

2. C ONTENTS Saad Haj Bakry Network ArchitectureCellular P RINCIPLES S UGGESTED W ORK D ESIGN C APACITY E VALUATIONS

3. P RINCIPLES Saad Haj Bakry Network Architecture Cellular / Principles O BJECTIVE C ONCEPT S YSTEM U NIT S YSTEM L AYOUT

4. O BJECTIVE Saad Haj Bakry Network ArchitectureCellular: Principles Enabling Limited Frequency Spectrum “ N [2 Way Frequency Channels] ” to Service Large Traffic Demands “ A [Erlang] ” (Offered) “ K [Erlang] ” (Serviced) within a Limited Area “ Z [km 2 ] ” (A City) With Satisfactory Performance “ G [Blocking Probability] = (A-K) / A ”

5. C ONCEPT Saad Haj Bakry Network ArchitectureCellular: Principles Dividing the Area “ Z ” into “ C ” Small Zones or Cells “ z [km 2 ] ” (per Cell), and Reusing the Same Channels in Non-Adjacent Cells with Acceptable Frequency Reuse Buffering Distance ( 1 or 2 Belts of Cells Around a Cell).

6. S YSTEM U NIT Saad Haj Bakry Network Architecture Cellular / Principles R EUSE F ACTOR: R = C / U Smallest Group of Adjacent Cells “ U [Cells] ” where all Available Frequency Spectrum “ N ” can be Used Simultaneously ( U Depends on Reuse Buffering ) T WO W AY C HANNELS PER C ELL: n = N / U

7. Frequency Distribution for a Cellular System with “ One Belt of Cells ” Frequency Reuse Buffering Distance ( S YSTEM U NIT U = 4 Cells) f1 f3 f4 f2 f1 Saad Haj Bakry Network Architecture Cellular / Principles

8. Frequency Distribution for a Cellular System with “ Two Belt of Cells ” Frequency Reuse Buffering Distance ( S YSTEM U NIT U = 7 Cells) f1f1 f1f1 f1f1 f1 f5 f6f6 f2f2 f4 f1 f3 f7f7 Saad Haj Bakry Network Architecture Cellular / Principles

9. D ESIGN Saad Haj Bakry Network Architecture Cellular G IVEN C ASE S PECTRUM L AYOUT / C APACITY E VALUATION R E- E VAL. Z K N U C/R/ z G Practical State Req. Propagation Problem Final Design

10. C APACITY Saad Haj Bakry Network Architecture Cellular: Capacity L AYOUT U TILIZATION E RLANG- B F ORMULA

11. L AYOUT Saad Haj Bakry Network Architecture Cellular: Capacity I NPUT: Z / K / N / G / U 1 Z ONE (?): Erlang-B “ B(N,A) ” v “ G ” A = K / (1-G) C ELLULAR L AYOUT : n = N / U “ channels per cell ” Find “ k ” “ serviced traffic per cell ” Use Erlang-B: B (n,a) = G k = a. (1-B) Output “ C ”, “ z ”, “ R ” C = K/k, z = Z/C, R = C/U

12. E RLANG- B F ORMULA Saad Haj Bakry Network Architecture B = (A N / N!) / (A i / i!) B = 1 / (N! / (A i (N - i)!)) Cellular: Capacity F OR S MALL “ B / G ” (e.g. 1 %) : A = K

13. U TILIZATION / O CCUPANCY Saad Haj Bakry Network Architecture M ULTI C ELL “ C ELLULAR ” : “ q = (k / n) ”, “ Q C = (K / N) ” “ K = (k. C) ”, “ N = (n. U) ” Q C = (k. C) / (n. U) Q C = q. R > 1 M ULTI C ELL “ C ELLULAR ” : “ q = (k / n) ”, “ Q C = (K / N) ” “ K = (k. C) ”, “ N = (n. U) ” Q C = (k. C) / (n. U) Q C = q. R > 1 Cellular: Capacity S INGLE C ELL: Q S = (K / N) < 1

14. E VALUATIONS Saad Haj Bakry Network Architecture Cellular: Evaluations C ASE S TUDIES M ETHODS: T OOLS F OR O N- L INE E VALUATIONS E VALUATION C URVES M ETHODS: T OOLS F OR O N- L INE E VALUATIONS E VALUATION C URVES

15. C ASE S TUDIES Saad Haj Bakry Network Architecture S YSTEM S TATE: Given: System Parameters Find: Performance S YSTEM C APACITY: Given: Parameters / Performance Find: Traffic Capacity S YSTEM D ESIGN: Discussed Earlier S YSTEM D ESIGN: Discussed Earlier Cellular: Evaluations

16. S UGGESTED W ORK Saad Haj Bakry Network Architecture G ENERAL: D EVELOPMENT OF C OMPUTER T OOLS & C URVES P RACTICAL C ASE S TUDIES Cellular