1 5: Capacity of Wireless Channels Fundamentals of Wireless Communication, Tse&Viswanath 5. Capacity of Wireless Channels 2 5: Capacity of Wireless Channels Fundamentals of Wireless Communication, Tse&Viswanath Information Theory • So far we have only looked at specific communication schemes. • Information theory provides a fundamental limit to (coded) performance. • It succinctly identifies the impact of channel resources on performance as well as suggests new and cool ways to communicate over the wireless channel. • It provides the basis for the modern development of wireless communication. 3 5: Capacity of Wireless Channels Fundamentals of Wireless Communication, Tse&Viswanath Historical Perspective • Wireless communication has been around since 1900’s. • Ingenious but somewhat adhoc design techniques Claude Shannon Gugliemo Marconi • Information theory says every channel has a capacity. • Many recent advances based on understanding wireless channel capacity. New points of views arise. 1901 1948 4 5: Capacity of Wireless Channels Fundamentals of Wireless Communication, Tse&Viswanath Multipath Fading: A Modern View Classical view: fading channels are unreliable Modern view: multipath fading can be exploited to increase spectral efficiency. 16dB 5 5: Capacity of Wireless Channels Fundamentals of Wireless Communication, Tse&Viswanath Capacity of AWGN Channel Capacity of AWGN channel If average transmit power constraint is watts and noise psd is watts/Hz, 6 5: Capacity of Wireless Channels Fundamentals of Wireless Communication, Tse&Viswanath Power and Bandwidth Limited Regimes Bandwidth limited regime capacity logarithmic in power, approximately linear in bandwidth. Power limited regime capacity linear in power, insensitive to bandwidth. 7 5: Capacity of Wireless Channels Fundamentals of Wireless Communication, Tse&Viswanath 8 5: Capacity of Wireless Channels Fundamentals of Wireless Communication, Tse&Viswanath Example 1: Impact of Frequency Reuse • Different degree of frequency reuse allows a tradeoff between SINR and degrees of freedom per user. • Users in narrowband systems have high link SINR but small fraction of system bandwidth. • Users in wideband systems have low link SINR but full system bandwidth. • Capacity depends on both SINR and d.o.f. and can provide a guideline for optimal reuse. • Optimal reuse depends on how the out-of-cell interference fraction f(ρ) depends on the reuse factor ρ. 9 5: Capacity of Wireless Channels Fundamentals of Wireless Communication, Tse&Viswanath Numerical Examples Linear cellular system Hexagonal system 10 5: Capacity of Wireless Channels Fundamentals of Wireless Communication, Tse&Viswanath Example 2: CDMA Uplink Capacity • Single cell with K users. • Capacity per user • Cell capacity (interference-limited) [...]... Domain Fundamentals of Wireless Communication, Tse&Viswanath 18 5: Capacity of Wireless Channels Slow Fading Channel h random There is no definite capacity Outage probability: −outage capacity: Fundamentals of Wireless Communication, Tse&Viswanath 19 5: Capacity of Wireless Channels Outage for Rayleigh Channel Pdf of log(1+|h|2SNR) Outage cap as fraction of AWGN cap Fundamentals of Wireless Communication,...5: Capacity of Wireless Channels Example 2 (continued) • If out -of- cell interference is a fraction f of in-cell interference: Fundamentals of Wireless Communication, Tse&Viswanath 11 5: Capacity of Wireless Channels Uplink and Downlink Capacity • CDMA and OFDM are specific multiple access schemes • But information theory tells us what is the capacity of the uplink and downlink channels and... Communication, Tse&Viswanath 20 5: Capacity of Wireless Channels Receive Diversity Diversity plus power gain Fundamentals of Wireless Communication, Tse&Viswanath 21 5: Capacity of Wireless Channels Transmit Diversity Transmit beamforming: Alamouti (2 Tx): Diversity but no power gain Fundamentals of Wireless Communication, Tse&Viswanath 22 5: Capacity of Wireless Channels Repetition vs Alamouti Repetition:... be done Coding across sub -channels becomes now necessary Fundamentals of Wireless Communication, Tse&Viswanath 25 5: Capacity of Wireless Channels Fast Fading Channel Channel with L-fold time diversity: As Fast fading channel has a definite capacity: Tolerable delay >> coherence time Fundamentals of Wireless Communication, Tse&Viswanath 26 5: Capacity of Wireless Channels Capacity with Full CSI Suppose... Fundamentals of Wireless Communication, Tse&Viswanath 28 5: Capacity of Wireless Channels Transmit More when Channel is Good Fundamentals of Wireless Communication, Tse&Viswanath 29 5: Capacity of Wireless Channels Performance At high SNR, waterfilling does not provide any gain But transmitter knowledge allows rate adaptation and simplifies coding Fundamentals of Wireless Communication, Tse&Viswanath 30 5: Capacity. .. request a rate Fundamentals of Wireless Communication, Tse&Viswanath 34 5: Capacity of Wireless Channels SINR Prediction Uncertainty 3 km/hr 30 km/hr accurate prediction conservative of instantaneous prediction of SINR SINR 120 km/hr accurate prediction of average SINR for a fast fading channel Fundamentals of Wireless Communication, Tse&Viswanath 35 5: Capacity of Wireless Channels Incremental ARQ •... achieves a delay-limited capacity Fundamentals of Wireless Communication, Tse&Viswanath 32 5: Capacity of Wireless Channels Example of Rate Adaptation: 1xEV-DO Downlink Multiple access is TDMA via scheduling (More on this later.) Each user is rate-controlled rather than power-controlled (But no waterfilling.) Fundamentals of Wireless Communication, Tse&Viswanath 33 5: Capacity of Wireless Channels Rate Control... Loss in degrees of freedom under repetition Fundamentals of Wireless Communication, Tse&Viswanath 23 5: Capacity of Wireless Channels Time Diversity (I) Coding done over L coherence blocks, each of many symbols This is a parallel channel If transmitter knows the channel, can do waterfilling Can achieve: Fundamentals of Wireless Communication, Tse&Viswanath 24 5: Capacity of Wireless Channels Time Diversity... Fundamentals of Wireless Communication, Tse&Viswanath 12 5: Capacity of Wireless Channels Frequency-selective Channel 's are time-invariant OFDM converts it into a parallel channel: where is the waterfilling allocation: with λ chosen to meet the power constraint Can be achieved with separate coding for each sub-carrier Fundamentals of Wireless Communication, Tse&Viswanath 17 5: Capacity of Wireless Channels. .. CSI Suppose now transmitter has full channel knowledge What is the capacity of the channel? Fundamentals of Wireless Communication, Tse&Viswanath 27 5: Capacity of Wireless Channels Fading Channel with Full CSI This is a parallel channel, with a sub-channel for each fading state where is the waterfilling power allocation as a function of the fading state, and λ is chosen to satisfy the average power . 1 5: Capacity of Wireless Channels Fundamentals of Wireless Communication, Tse&Viswanath 5. Capacity of Wireless Channels 2 5: Capacity of Wireless Channels Fundamentals of Wireless Communication,. sub-carrier. 18 5: Capacity of Wireless Channels Fundamentals of Wireless Communication, Tse&Viswanath Waterfilling in Frequency Domain 19 5: Capacity of Wireless Channels Fundamentals of Wireless Communication,. fraction of AWGN cap. 21 5: Capacity of Wireless Channels Fundamentals of Wireless Communication, Tse&Viswanath Receive Diversity Diversity plus power gain. 22 5: Capacity of Wireless Channels Fundamentals