EE360: Lecture 15 Outline Cellular System Capacity

1. EE360: Lecture 15 OutlineCellular System Capacity • What is capacity? • Defining capacity • Shannon capacity of cellular systems • “Information capacity of symmetric cellular multiple access channels” Hrishikesh Mandyam • Multicell capacity • User capacity • Summary

2. What is capacity? • Shannon capacity • Maximum achievable rate or set of rates with arbitrarily small probability of error • Coding scheme not achievable, and complexity/delay are infinite • Tractable formulas exist for point-to-point links, MAC and degraded broadcast channels, and ad-hoc networks under various assumptions • Other theoretical capacity definitions • Outage capacity • Computation cutoff rate (not very useful) • Capacity definitions used in practice • Achievable rates under practical system assumptions • User capacity under practical system assumptions

3. Defining Cellular Capacity • Shannon-theoretic definition • Multiuser channels typically assume user coordination and joint encoding/decoding strategies • Can an optimal coding strategy be found, or should one be assumed (i.e. TD,FD, or CD)? • What base station(s) should users talk to? • What assumptions should be made about base station coordination? • Should frequency reuse be fixed or optimized? • Is capacity defined by uplink or downlink? • Capacity becomes very dependent on propagation model • Practical capacity definitions (rates or users) • Typically assume a fixed set of system parameters • Assumptions differ for different systems: comparison hard • Does not provide a performance upper bound

4. Approaches to Date • Shannon Capacity • TDMA systems with joint base station processing (Hrish) • Multicell Capacity • Rate region per unit area per cell • Achievable rates determined via Shannon-theoretic analysis or for practical schemes/constraints • Area spectral efficiency is sum of rates per cell • User Capacity • Calculates how many users can be supported for a given performance specification. • Results highly dependent on traffic, voice activity, and propagation models. • Can be improved through interference reduction techniques. (Gilhousen et. al.)

5. User Capacity • Maximum number of users a cellular system can support in any cell. • Can be defined for any system. • Typically assumes symmetric data rates, cells, propagation, and mobility. • Depends on the user specifications and radio design • data rate, BER, modulation, coding, etc.

6. Multicell Capacity • Multiuser rate region per Hertz divided by coverage area given reuse distance • Rate region (R1,…,RN) can be obtained via Shannon analysis • How to treat interference from other cells • Alternatively, can compute under practical system assumptions • ASE sums rates in each cell:

7. Which link dictates capacity? • Reverse link (MAC) • Noncoherent reception • Independent fading of all users • Requires power control • Forward link (Broadcast) • Coherent demodulation using pilot carrier. • Synchronous combining of multipath. • Conclusion: reverse link has lower capacity • Thus, reverse link dictates capacity • Other cell interference will tend to equalize performance in each direction. • In asymmetric traffic, forward link will be bottleneck

8. CDMA User Capacity • Single-Cell System • Similar to MAC user capacity • G=W/R is processing gain (W is bandwidth, R is data rate) • h is interference plus noise (assumed fixed) • Assumes power control • Performance improvement through sectorization and voice activity 8C32810.44-Cimini-7/98

9. Sectorization • Base station omni antenna is divided into M sectors. • Users in other sectors do not cause interference. • Number of users per sector is Ns=N/M (reduces interference by M). • Requires handoff between sectors at the base station

10. Voice Activity • Suppress signal when voice user not active. • Voice activity a=.35-.4 (reduces interference by 60-65%). • Resynchronization for every talk spurt. • Higher probability of dropping users.

11. New Capacity (per cell) • Capacity increased proportional to the number of sectors and inversely proportional to the voice activity (M/a typically around 8). • Claim: CDMA is competitive with TD for a single-cell • Does not include impact of sectorization on out-of-cell interference.

12. Multicell System • Codes reused in every cell. • No power control in forward link • Interference from adjacent cells can be very strong. • Power control in reverse link • All users within a cell have same received signal strength • Interference from other cells have variable power • Fast fading (interference and signal) neglected (S/I statistics). • The interferer’s transmit power depends on distance to his base station. • Received power at desired base depends on distance to base, propagation, and the interferer’s transmit power.

13. Reverse Link Interference • Total path loss: propagation (d-4 falloff) and log-normal shadowing (x is Gaussian, 8 dB STD) • Instantaneous interference power • rm is distance to interferer’s base, r0 is distance to desired base • xmis shadowing to interferer base, x0is shadowing to desired base • S is received power with power control • Power less than 1 since otherwise would handoff to desired base

14. Average interference power • Ais the cell area. • r is the user density (r=2Ns/Sqrt[3]) • g is voice activity term (equals 1 w.p. a, 0 w.p. 1-a) • Must be integrated against distribution of m, r0, rm, x0, xm • Simplify distribution of m by assuming minimum distance. • r0, rm uniformly distributed. • Claim: I Gaussian since it’s a functional of a 2D white random process

15. Mean and Variance • Numerical integration leads to E(I/S)=.247Ns • Second Moment: • Assumes autocorrelation of shadowing is a delta function and STD is 8 dB. • Numerical integration leads to Var(I/S)=.078Ns • Total interference distribution I Gaussian, ci binomial r.v. with probability a

16. Capacity Calculation • Calculate probability Eb/N0below target (BER exceeds target) based on Ns and these statistics.. • Compute outage probability as a function of Ns. • Assumes target Eb/N0 =5 d=30 • Results indicate 60 users/sector with 1% outage

17. An Alternate Approach • Simulation approach • Includes three rings of interfering cells • Capacity for TDMA and CDMA compared • Similar assumptions about voice activity and sectorization • TDMA assumes FH with dynamic channel allocation • Results indicate CD greatly outperforms TD • Not surprising given the authors

18. Capacity degradation • Voice activity changed from .375 to .5, -30% change • Path-loss changed from 4 to 3, -20% change • Multipath fading added, -45% change • Handoff margin changed from 0 to 6 dB, -40% change • Power control error changed from 0 to 1 dB, -35% change

19. Summary • Multiple definitions of cellular system capacity • True Shannon capacity unknown • Shannon capacity under given system assumptions still complicated • Using multiccell capacity formulation allows comparison of apples to apples • User capacity calculations highly dependent on system assumptions • Easy to skew results in a given direction