ECS Vireless oundations 8.MIMO II:Capacity and Multiplexing Architectures Fundamentals of Wireless Communication,Tse&Viswanath 1
8: MIMO II: Capacity and Multiplexing Architectures Fundamentals of Wireless Communication, Tse&Viswanath 1 8. MIMO II: Capacity and Multiplexing Architectures
8:MIMO Il:Capacity and Multiplexing Architectures EECS Wireless oundations Outline Transceiver architectures for fast fading (V-BLAST family) Transceiver architecture for slow fading (D-BLAST) Multiple antennas in networks:SDMA Fundamentals of Wireless Communication,Tse&Viswanath 2
8: MIMO II: Capacity and Multiplexing Architectures Fundamentals of Wireless Communication, Tse&Viswanath 2 Outline • Transceiver architectures for fast fading (V-BLAST family) • Transceiver architecture for slow fading (D-BLAST) • Multiple antennas in networks: SDMA
8:MIMO Il:Capacity and Multiplexing Architectures ECS Nireless oundations Transmitter and Receiver CSI Can decompose the MIMO channel into a bunch of orthogonal sub-channels. Can allocate power and rate to each sub-channel according to waterfilling [n]) AWGN decode coder k information {wn》 streams 交nl AWGN U* In)) decoder coder (o) (o) Fundamentals of Wireless Communication,Tse&Viswanath 3
8: MIMO II: Capacity and Multiplexing Architectures Fundamentals of Wireless Communication, Tse&Viswanath 3 Transmitter and Receiver CSI • Can decompose the MIMO channel into a bunch of orthogonal sub-channels. • Can allocate power and rate to each sub-channel according to waterfilling
8:MIMO Il:Capacity and Multiplexing Architectures ECS Wireless oundations Analogy with OFDM x[1]=d[N-L+1] 山 xL-1]=dW-1 yL-1] d0] Cyelic x[L]=d[o] ☑ Remove yILl Channel 0 prefix prefix IDFT DFT dy-1 dN-1] x[N+L-1]=d[N-1] y[N+L-1] [N+L-1 Major difference: In MIMO,the U and V matrices depend on the channel H. In OFDM,the IDFT and DFT matrices do not. Fundamentals of Wireless Communication,Tse&Viswanath
8: MIMO II: Capacity and Multiplexing Architectures Fundamentals of Wireless Communication, Tse&Viswanath 4 Analogy with OFDM Major difference: In MIMO, the U and V matrices depend on the channel H. In OFDM, the IDFT and DFT matrices do not
8:MIMO Il:Capacity and Multiplexing Architectures vireless oundations Receiver CSI Only The channel matrix H and its singular values 2's are random and unknown to the transmitter. P AWGN coder w[m] rate R x[m] 文y[m] .... H(m] Joint decoder AWGN coder rate Rm Has to fix a Q and a power allocation independent of H. Q=I and uniform power allocation is optimal in many cases. It is not trivial to come up with capacity-achieving architectures. Fundamentals of Wireless Communication,Tse&Viswanath 5
8: MIMO II: Capacity and Multiplexing Architectures Fundamentals of Wireless Communication, Tse&Viswanath 5 Receiver CSI Only The channel matrix H and its singular values i 2 's are random and unknown to the transmitter. Has to fix a Q and a power allocation independent of H. Q=I and uniform power allocation is optimal in many cases. It is not trivial to come up with capacity-achieving architectures
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