Uplink User Capacity in a CDMA Macrocell with a Hotspot Microcell: Effects of Transmit Power Constraints and Finite Dis

1. Uplink User Capacity in a CDMA Macrocell with a Hotspot Microcell: Effects of Transmit Power Constraints and Finite Dispersion Shalinee Kishore (Lehigh University) skishore@lehigh.edu Larry J. Greenstein (WINLAB-Rutgers University) H. Vincent Poor (Princeton University) Stuart C. Schwartz (Princeton University) IEEE Globecom 2003

2. Two-Tier Cellular CDMA System Macrocell with embedded microcell • Macrocell and microcell use CDMA over same set of • frequencies  cross-tier interference. • Users select their base stations according to (slowly- • changing) local mean path gains. • Ideal power control by each base is assumed.

3. Previous Work: Uplink user capacity quanitifed assuming • 1) No constraint on transmit power • 2) Infinitely dispersive channels* • (S. Kishore, et al., IEEE Trans. On Wireless Communications, March 2003.) • Goal: Determine uplink user capacity for this system for • 1) Finite power constraint • 2) Finitely dispersive channels† • *Infinitely dispersive channel: infinitude of strong • multipaths  received signal has constant output power • after RAKE processing. • †Finitely dispersive channel: finite multipaths  output • power has variable fading.

4. Effect of Transmit Power Constraint

5. Problem Statement Given: • N total users, NM macrocell and Nm microcell. • Distribution of user locations. • Random codes of length W/R, where W is system • bandwidth and R is user data rate. • Minimum SINR requirement, G. • Transmit power constraint, Pmax. • dmax, max. distance over which users are distributed.

6. Problem Statement (Cont’d) • Path gain between a user and a base is modeled as • Users choose base station for which its path gain is higher. • Determine: • Uplink user capacity such that P[Outage] does not exceed • some specified value, as a function of Pmax and dmax.

7. Outage Previously: for no transmit power constraint, SINR requirement can be met if and only if (K - NM)(K - Nm) > IMIm where K = W/RG + 1 (single-cell pole capacity), IM and Im are normalized cross-tier interferences (random variables). We computed the probability of not meeting this condition, given either 1) NM and NmPinf(NM,Nm) 2) N = NM + NmPinf(N)

8. Outage (Cont’d) • System unable to support N users if infeasible and/or if • transmit power (P) of any one user exceeds Pmax. • Pr[Outage|N] = Pinf(N) + (1 - Pinf(N))·Pr[P > Pmax|N], • We determined how to exactly compute and reliably • approximate Pr[P > Pmax|N]. • Result: Pr[Outage|N] can be solved as a function of • dimensionless parameter F:

9. Uplink User Capacity versus Max Power Constraint N, Total Number of Users, 5% Outage F*

10. Effect of Finitely Dispersive Channels

11. Motivation • Thus far: considered infinitely-dispersive uplink channel. • Actual channels have finite number of paths, each with • variable fading  user output signal has variable fading. • Can model fading with modified path gain: Tij’ =rTij, • wherer is a unit-mean random variable. • We examine performance for four channel types: • Rural Area (RA) • Typical Urban (TU) • Hilly Terrain (HT) • Uniform multipath

12. Uniform Multipath Channel Channel Delay Profile power Height of each line is mean- square gain of a Rayleigh fading path. delay Lp Number of Paths • Diversity Factor (DF) measures the amount of multipath • diversity in channel. Computable for any delay profile. • Uniform channel has DF = Lp. • Non-uniform channels with Lp paths have DF < Lp. • For example, DFRA= 1.6, DFHT= 3.3, and DFTU = 4.0.

13. Finite Dispersion: Problem Statement • Given: • Single-macrocell/single-microcell system • Propagation model with variable fading • Pmax = Max transmit power level • dmax = Max distance over which users are distributed • hW = Noise power • Determine: • Uplink user capacity so that Pr[Outage] does not exceed • some given value (e.g., 5%). • for the three standard environments, i.e., RA, TU, and HT, as • functions of F. • for any environment when F > F*.

14. Variable Power Fading: Key Results • Uplink capacity for RA, HT, and TU terrains: constant over • F > 0.1 and decreases sharply in F when F < 0.1. • Capacity reduction relative to infinitely dispersive channel: as much as 15% for the RA environment. • When F > F*, user capacity in uniform multipath channel • can be approximated as: , for Lp > 1. • Showed uplink capacity is the same for channels with same DF. Replace Lp in with DF DF Napprox Non-Uniform Delay Profile

15. Uplink User Capacity under Finite Dispersion N, Total Number of Users, 5% Outage Lp, Number of Paths

16. Conclusion • Studied impact of transmit power constraints and finite • dispersion on uplink user capacity of two-tier cellular • CDMA system. • Developed exact analytical methods and reliable • approximation schemes. • Quantified effect of maximum power constraints on • coverage area and capacity. • Used uniform multipath channel to approximate uplink • user capacity for finitely-dispersive channels. • Excellent agreements between analytical approximations • and simulation results.