8:MIMO Il:Capacity and Multiplexing Architectures EECS Wireless oundations Capacity Can write: o)-lo det) Slow fading: 0=+ur）s Fast fading: c=8+5r】 Fundamentals of Wireless Communication,Tse&Viswanath 6
8: MIMO II: Capacity and Multiplexing Architectures Fundamentals of Wireless Communication, Tse&Viswanath 6 Capacity Can write: Slow fading: Fast fading:
8:MIMO Il:Capacity and Multiplexing Architectures EECS Vireless oundations Fast Fading Capacity for I.I.D.Rayleigh Fading C[bits/s/Hz]35 30 nt=nr =1 nt=1 nr=4 25 nt=nr=4 20 15 10 5 -10 10 20 30 SNR[dB] Fundamentals of Wireless Communication,Tse&Viswanath 7
8: MIMO II: Capacity and Multiplexing Architectures Fundamentals of Wireless Communication, Tse&Viswanath 7 Fast Fading Capacity for I.I.D. Rayleigh Fading
8:MIMO Il:Capacity and Multiplexing Architectures CS ireless F oundations d.o.f.min(nt,nr)determines the high SNR slope. C[bits/s/Hz]35 C[bits/s/Hz】70 30 nt=nr=1 60 nt=1 nr=4 nt=nr=1 25 nt=nr=4 nt=1nr=8 nt=nr=8 20 40 15 30 10 20 5 10 -10 10 30 -10 10 20 30 SNR[dB] SNRIdB] Fundamentals of Wireless Communication,Tse&Viswanath 8
8: MIMO II: Capacity and Multiplexing Architectures Fundamentals of Wireless Communication, Tse&Viswanath 8 d.o.f. determines the high SNR slope
8:MIMO Il:Capacity and Multiplexing Architectures ireless oundations Fast Fading Capacity:Low SNR n,-fold power gain at low SNR [bits/s/Hz] 4 3.5 nt=1n,=4 nt=n=4 .5 -30 -20 -10 、10 SNR[dB] Fundamentals of Wireless Communication,Tse&Viswanath 9
8: MIMO II: Capacity and Multiplexing Architectures Fundamentals of Wireless Communication, Tse&Viswanath 9 Fast Fading Capacity: Low SNR nr – fold power gain at low SNR
8:MIMO II:Capacity and Multiplexing Architectures ECS ireless oundations Nature of Performance Gain At high SNR (d.o.f.limited):min(nt,n,)-fold d.o.f.gain MIMO is crucial. At low SNR(power limited):n,-fold power gain.Only need multiple receive antennas. At all SNR,min(nt,n,)-fold gain due to a combination of both effects. Fundamentals of Wireless Communication,Tse&Viswanath 10
8: MIMO II: Capacity and Multiplexing Architectures Fundamentals of Wireless Communication, Tse&Viswanath 10 Nature of Performance Gain • At high SNR (d.o.f. limited): min(nt ,nr )-fold d.o.f. gain. MIMO is crucial. • At low SNR (power limited): nr -fold power gain. Only need multiple receive antennas. • At all SNR, min(nt ,nr )-fold gain due to a combination of both effects