EE360: Lecture 15 Outline Cellular 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

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

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

Approaches to Date Shannon Capacity Multicell Capacity User 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.)

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.

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:

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

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

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

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.

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.

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.

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 xm is shadowing to interferer base, x0 is shadowing to desired base S is received power with power control Power less than 1 since otherwise would handoff to desired base

Average interference power A is 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

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

Capacity Calculation Calculate probability Eb/N0 below 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

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

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

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