1. Subscriber Maximization in CDMA Cellular Network Robert Akl, D.Sc. University of North Texas

2. Outline Overview of CDMAOverview of CDMA Traffic and Mobility ModelTraffic and Mobility Model Subscriber Optimization FormulationSubscriber Optimization Formulation Numerical ResultsNumerical Results ConclusionsConclusions

3. Code Division Multiple Access (CDMA) Overview Multiple access schemesMultiple access schemes Call 1 Call 3 Call 2 Call 4 Frequency Time FDMA Frequency Time Call 1Call 2Call 3 Call 4Call 5Call 6 Call 7Call 8Call 9 Call 10Call 11Call 12 TDMACDMA Frequency Time Code Call 1 Call 2 Call 3 Call 4

4. Relative Average Inter-cell Interference Model Cell j Cell i Relative average interference at cell i caused by n j users in cell j

5. 111213……1M2122 3132 …… …… M1M2MM Interference Matrix Hence, the total relative average inter- cell interference experienced by cell i is111213……1M2122 3132 …… …… M1M2MM

6. Capacity The capacity of a CDMA network is determined by maintaining a lower bound on the bit energy to interference density ratio, given by  W = Spread signal bandwidth  R = bits/sec (information rate)  α = voice activity factor  n i = users in cell i  N 0 = background noise spectral density Let τ be that threshold above which the bit error rate must be maintained, then by rewriting the equation:

7. Mobility Model Call arrival process is a Poisson process with rate: λCall arrival process is a Poisson process with rate: λ Call dwell time is a random variable with exponential distribution having mean: 1/μCall dwell time is a random variable with exponential distribution having mean: 1/μ Probability that a call in cell i goes to cell j after completing its dwell time: q ijProbability that a call in cell i goes to cell j after completing its dwell time: q ij Probability that a call in progress in cell i remains in cell i after completing its dwell time: q iiProbability that a call in progress in cell i remains in cell i after completing its dwell time: q ii Probability that a call will leave the network after completing its dwell time: q iProbability that a call will leave the network after completing its dwell time: q i

8. Mobility Model – Handoff Calls Handoff calls (v ji ): calls that have moved from cell j to an adjacent cell i.Handoff calls (v ji ): calls that have moved from cell j to an adjacent cell i. B j : Call blocking probability for cell j Aj : Set of cells adjacent to cell i ρ j : Total offered traffic to cell j j New arriving calls Handoff calls i

9. Admissible States A new call is accepted if the following inequality still holds upon acceptance, where N i is the maximum number of calls allowed to be admitted in cell i:A new call is accepted if the following inequality still holds upon acceptance, where N i is the maximum number of calls allowed to be admitted in cell i: The blocking probability for cell i becomes:The blocking probability for cell i becomes:

10. Maximization of Subscribers Solve a constrained optimization problem that maximizes the number of subscribers subject to upper bounds on the blocking probabilities and lower bounds on the bit energy to interference ratios:Solve a constrained optimization problem that maximizes the number of subscribers subject to upper bounds on the blocking probabilities and lower bounds on the bit energy to interference ratios:

11. Simulations 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, σ s = 6 dBShadow fading standard deviation, σ s = 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, I 0 /N 0 = 10 dBInterference to background noise ratio, I 0 /N 0 = 10 dB Voice activity factor, α = 0.375Voice activity factor, α = 0.375

12. Simulations – Network Parameters No mobility probabilities q ij = 0 q ii = 0.3 q i = 0.7 AiAiAiAiqijqiiqi 30.0200.2400.700 40.0150.2400.700 50.0120.2400.700 60.0100.2400.700 AiAiAiAiqijqiiqi30.1000.0000.700 40.0750.0000.700 50.0600.0000.700 60.0500.0000.700 Low mobility probabilities High mobility probabilities

13. Traditional Network Topology and Uniform User Distribution Maximum subscribers is 15,140.Maximum subscribers is 15,140.

14. Traditional Network Topology and Non-Uniform User Distribution Maximum subscribers drops to 14,224.Maximum subscribers drops to 14,224.

15. Optimized Network Topology and Non-Uniform User Distribution Maximum subscribers increases to 15,164.Maximum subscribers increases to 15,164.

16. Summary Calculate the maximum number of subscribers that a CDMA cellular network can handle for a given grade-of-service, quality-of-service, network topology, user distribution profile, and mobility.Calculate the maximum number of subscribers that a CDMA cellular network can handle for a given grade-of-service, quality-of-service, network topology, user distribution profile, and mobility. Solution yields the maximum number of calls that should be admitted in each cell to guarantee the given requirements above.Solution yields the maximum number of calls that should be admitted in each cell to guarantee the given requirements above.