Downlink User Capacity in a CDMA Macrocell with a Hotspot Microcell

1. Downlink User Capacity in a CDMA Macrocell with a Hotspot Microcell 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 • Both macrocell and microcell use CDMA over same • set of frequencies  cross-tier interference. • Goal: Derive analytical methods that compute downlink • user capacity and account for • Finitely dispersive channels • Various methods of downlink power control

3. Downlink Capacity: Background • CDMA downlink: Base stations transmit orthogonal • signals to users. • Channel dispersion causes loss of orthogonality at user • terminals. • Orthogonality factor, b, captures loss-of-orthogonality • of user signals in a channel. • b [0,1], where b = 0 when no dispersion in channel • and b = 1 when infinite dispersion. • b can be computed from channel delay profile.

4. Orthogonality Factor Assuming all Rayleigh fading paths, it has been shown that where rn is instantaneous gain on n-th path s.t. b is time-varying but earlier simulation results show little difference in replacing time variation by its average.

5. Downlink Capacity: Problem Statement • Given: • Single-macrocell/single-microcell system with N =NM+Nm • users, processing gain W/R and minimum SIR requirement G. • Channel delay profile  orthogonality factor, b. • Conventional RAKE receivers at user terminals • Base station k transmits total power PTk, k { M,m} • Macrocell user i assigned fraction xi of PTM • Microcell user j assigned fraction yj of PTm • Downlink power control scheme for allocating xi and yj • Determine: • Downlink user capacity (number of simultaneous voice users)

6. Overview of Analysis Instantaneous interference power to macrocell user k from macrocell base is: ‘ ‘ where TMk is instantaneous path gain between user k and macrocell base. (Similar interference at microcell user.) • We denote: • TMk as the fast-varying path gain and • TMk as the slow-varying (locally-averaged) path gain. ‘

7. Digression: Slow-varying Path Gain Model Fast-varying Path Gain Model ‘ where, Tjk = rTjk rn depends on the channel delay profile.

8. Overview of Analysis (Cont’d) Using SINR requirement for macrocell user i and microcell user j, we show that PTM ≥ 0 and PTm ≥ 0 iff ‘ ‘ Downlink feasibility condition ‘ ‘ where K’ = W/RG . • Feasibility condition must be met some given percentage of • time by all • i UM (set of macrocell users) and • j  Um (set of microcell users) • Feasibility conditions depend on allocations xi & yj.

9. 3 Power Control Schemes • Uniform power control:xi = 1/NM and yj = 1/Nm. • Slow power control: power allocation determined from • slow-varying path gains. • Fast power control: power allocation determined from • fast-varying path gains. • Under fast power control, there exists a single feasibility • condition: ‘ ‘ ‘ ‘

10. Approximating Capacity for Fast Power Control • We can approximate feasibility under fast power control • by substituting LHS of feasibility condition by its average. • We find this average for the uniform multipath channel. • Recall: uniform multipath delay profile power Height of each line is mean- square gain of a Rayleigh fading path. delay Lp Number of Paths

11. Digression: Treating Non-Uniform Delay Profiles • For uniform channels, we can compute LHS of • feasibility condition as a simple function of Lp. • What about non-uniform channels? • In uplink study, we showed approximate equivalence • between uniform and non-uniform channels using the • channel diversity factor. • Diversity factor (DF) can be computed for any profile. • Substituting DF for Lp, we can approximate average of • LHS for non-uniform channels.

12. Approximating Capacity for Fast PC (Cont’d) • Using mean approximation, feasibility condition • depends on b (RHS) and DF (LHS). • We found that for DF > 1, • Therefore, feasibility condition can be written in • terms of b. • For maximum total user capacity, NM = Nm. • Combining these results, we obtain: Closed-form solution for downlink user capacity

13. Uplink User Capacity as a Function of b We can recast uplink user capacity in terms of b :

14. Comparing Uplink and Downlink User Capacities • We have uplink user capacity in terms of b. • We have downlink user capacity for fast PC in terms of b. • We can also obtain downlink user capacity in terms of • b for uniform and slow PC. Major Findings: • Uplink dominates downlink for uniform and slow PC. • Downlink dominates uplink for fast PC.

15. Comparing Uplink and Downlink User Capacities for Fast Power Control Rural Area Hilly Terrain Typical Urban Downlink User Capacity Total Number of Users Uplink User Capacity b, Orthgonality Factor

16. Conclusion • Derived downlink feasibility condition for single-frequency • two-tier CDMA system in finitely-dispersive channels. • Used uniform multipath channel to approximate • downlink user capacity under fast power control. • Found excellent agreements between analytical • approximations and simulation results. • Showed that, for uniform and slow power control, • downlink dominated by uplink. • Showed that, for fast power control, uplink dominated • by downlink, underscoring importance of fast power • control on two-tier CDMA downlinks.