ECE 598HH: Advanced Wireless Networks and Sensing Systems
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ECE 598HH: Advanced Wireless Networks and Sensing Systems Lecture 6: MIMO Part 1 Haitham Hassanieh
Transcript of ECE 598HH: Advanced Wireless Networks and Sensing Systems
ECE 598HH: Advanced Wireless Networks and Sensing Systems
Lecture 6: MIMO Part 1Haitham Hassanieh
Version Year Technology Modulation Freq. Bandwidth Maximum Data Rate
WiFi 1 (802.11b) 1999 DSSS DBPSK, DQPSK, 2.4 GHz 22 MHz 11 Mb/s
WiFi Standards from WiFi 1 to WiFi 6
Version Year Technology Modulation Freq. Bandwidth Maximum Data Rate
WiFi 1 (802.11b) 1999 DSSS DBPSK, DQPSK, 2.4 GHz 22 MHz 11 Mb/s
WiFi Standards from WiFi 1 to WiFi 6
Version Year Technology Modulation Freq. Bandwidth Maximum Data Rate
WiFi 1 (802.11b) 1999 DSSS DBPSK, DQPSK, 2.4 GHz 22 MHz 11 Mb/s
WiFi 3 (802.11g) 2003 OFDM (N=64)BPSK, QPSK, 16-QAM, 64-QAM 2.4 GHz 20 MHz 54 Mb/s
WiFi Standards from WiFi 1 to WiFi 6
Version Year Technology Modulation Freq. Bandwidth Maximum Data Rate
WiFi 1 (802.11b) 1999 DSSS DBPSK, DQPSK, 2.4 GHz 22 MHz 11 Mb/s
WiFi 3 (802.11g) 2003 OFDM (N=64)BPSK, QPSK, 16-QAM, 64-QAM 2.4 GHz 20 MHz 54 Mb/s
WiFi 4 (802.11n) 2009 OFDM (N=64)MIMO (4x4)
BPSK, QPSK, 16-QAM, 64-QAM
2.4 GHz 5 GHz
20 MHz 40 MHz 600 Mb/s
WiFi Standards from WiFi 1 to WiFi 6
Version Year Technology Modulation Freq. Bandwidth Maximum Data Rate
WiFi 1 (802.11b) 1999 DSSS DBPSK, DQPSK, 2.4 GHz 22 MHz 11 Mb/s
WiFi 3 (802.11g) 2003 OFDM (N=64)BPSK, QPSK, 16-QAM, 64-QAM 2.4 GHz 20 MHz 54 Mb/s
WiFi 4 (802.11n) 2009 OFDM (N=64)MIMO (4x4)
BPSK, QPSK, 16-QAM, 64-QAM
2.4 GHz 5 GHz
20 MHz 40 MHz 600 Mb/s
WiFi Standards from WiFi 1 to WiFi 6
Version Year Technology Modulation Freq. Bandwidth Maximum Data Rate
WiFi 1 (802.11b) 1999 DSSS DBPSK, DQPSK, 2.4 GHz 22 MHz 11 Mb/s
WiFi 3 (802.11g) 2003 OFDM (N=64)BPSK, QPSK, 16-QAM, 64-QAM 2.4 GHz 20 MHz 54 Mb/s
WiFi 4 (802.11n) 2009 OFDM (N=64)MIMO (4x4)
BPSK, QPSK, 16-QAM, 64-QAM
2.4 GHz 5 GHz
20 MHz 40 MHz 600 Mb/s
WiFi 5 (802.11ac) 2014OFDM (N=64, 128, 256, 512)MIMO (8x8)MU-MIMO (Downlink)
BPSK, QPSK, 16-QAM, 64-QAM256-QAM
5 GHz20 MHz 40 MHz80 MHz160 MHz
6.933 Gb/s
WiFi Standards from WiFi 1 to WiFi 6
Version Year Technology Modulation Freq. Bandwidth Maximum Data Rate
WiFi 1 (802.11b) 1999 DSSS DBPSK, DQPSK, 2.4 GHz 22 MHz 11 Mb/s
WiFi 3 (802.11g) 2003 OFDM (N=64)BPSK, QPSK, 16-QAM, 64-QAM 2.4 GHz 20 MHz 54 Mb/s
WiFi 4 (802.11n) 2009 OFDM (N=64)MIMO (4x4)
BPSK, QPSK, 16-QAM, 64-QAM
2.4 GHz 5 GHz
20 MHz 40 MHz 600 Mb/s
WiFi 5 (802.11ac) 2014OFDM (N=64, 128, 256, 512)MIMO (8x8)MU-MIMO (Downlink)
BPSK, QPSK, 16-QAM, 64-QAM256-QAM
5 GHz20 MHz 40 MHz80 MHz160 MHz
6.933 Gb/s
WiFi 6 (802.11ax) 2019
OFDM (N=256, 512, 1024, 2048)MIMO (8x8)MU-MIMO (Up & Down)OFDMA
BPSK, QPSK, 16-QAM, 64-QAM256-QAM, 1024-QAM
2.4 GHz5 GHz
20 MHz 40 MHz80 MHz160 MHz
9.608 Gb/s
WiFi Standards from WiFi 1 to WiFi 6
Version Year Technology Modulation Freq. Bandwidth Maximum Data Rate
WiFi 1 (802.11b) 1999 DSSS DBPSK, DQPSK, 2.4 GHz 22 MHz 11 Mb/s
WiFi 3 (802.11g) 2003 OFDM (N=64)BPSK, QPSK, 16-QAM, 64-QAM 2.4 GHz 20 MHz 54 Mb/s
WiFi 4 (802.11n) 2009 OFDM (N=64)MIMO (4x4)
BPSK, QPSK, 16-QAM, 64-QAM
2.4 GHz 5 GHz
20 MHz 40 MHz 600 Mb/s
WiFi 5 (802.11ac) 2014OFDM (N=64, 128, 256, 512)MIMO (8x8)MU-MIMO (Downlink)
BPSK, QPSK, 16-QAM, 64-QAM256-QAM
5 GHz20 MHz 40 MHz80 MHz160 MHz
6.933 Gb/s
WiFi 6 (802.11ax)WiFi 6E 2020
OFDM (N=256, 512, 1024, 2048)MIMO (8x8)MU-MIMO (Up & Down)OFDMA
BPSK, QPSK, 16-QAM, 64-QAM256-QAM, 1024-QAM
2.4 GHz5 GHz6 GHz
20 MHz 40 MHz80 MHz160 MHz
9.608 Gb/s
WiFi Standards from WiFi 1 to WiFi 6
WiFi Standards from WiFi 1 to WiFi 6
WiFi 1 More MIMO Antennas WiFi 5/6
More Channels &
Bandw
idth
So far: single input single output
MIMO: multiple input multiple output
Increase capacity of channel using multiple transmit and receive antennas.
MIMO: Multiple Input Multiple Output
So far: single input single output
MIMO: multiple input multiple output
Increase capacity of channel using multiple transmit and receive antennas.
MIMO: Multiple Input Multiple Output
MIMO: Multiple TX-RX streamsπ₯!
π₯"
π¦!
π¦"
β!! = β!!π₯! + β!"π₯"
= β"!π₯! + β""π₯"β!"β""
β"!
π¦!
π¦"=
β!!
β"!
β!"
β""
π₯!
π₯"+
π!
π"π² = ππ± + π§
How to recover π₯" and π₯#?
Estimate π, compute π$" and invert the channel!
+π± = π#ππ² = π#πππ± + π#ππ§ = π± + π#ππ§
Transmit 2 packets at the same time!
MIMO: Multiple TX-RX streamsπ₯!
π₯"
π¦!
π¦"
β!! = β!!π₯! + β!"π₯"
= β"!π₯! + β""π₯"β!"β""
β"!
π¦!
π¦"=
β!!
β"!
β!"
β""
π₯!
π₯"+
π!
π"π² = ππ± + π§
How to recover π₯" and π₯#?
Estimate π, compute π$" and invert the channel!
+π± = π#ππ² = π#πππ± + π#ππ§ = π± + π#ππ§
Noise amplification
For π antennas, π is πΓπ matrix Γ π π%
MIMO: Vector Representationπ₯!
π₯"
π¦!
π¦"
β!! = β!!π₯! + β!"π₯"
= β"!π₯! + β""π₯"β!"β""
β"!
π¦!
π¦"=
β!!
β"!
β!"
β""
π₯!
π₯"+
π!
π"π² = ππ± + π§
How to recover π₯" and π₯#?
=β!!
β"!
β!"
β""π₯! π₯"π² + = π‘!π₯! + π‘"π₯"
MIMO: Antenna Spaceπ² = π‘!π₯! + π‘"π₯"
Ant. 2: π¦#
Ant. 1: π¦"
π‘"π₯"
π‘!π₯!
π²
MIMO: Antenna Spaceπ² = π‘!π₯! + π‘"π₯"
Ant. 2: π¦#
Ant. 1: π¦"
π‘"π₯"
π‘!π₯!
π²To decode π₯!, project on a vector π‘"
%orthogonal to π‘"
π‘"%π² = π‘"
%π‘!π₯! + π‘"
%π‘"π₯"
= π‘"%π‘!π₯!
=β!!
β"!
β!"
β""π₯! π₯"π² +
π‘"%= β"" β β!"
π‘"%π² = β""β!!π₯! β β!"β"!π₯!+ β""β!"π₯"β β!"β""π₯"
= β""β!! β β!"β"! π₯!
0
0
MIMO: Antenna Spaceπ² = π‘!π₯! + π‘"π₯"
Ant. 2: π¦#
Ant. 1: π¦"
π‘"π₯"
π‘!π₯!
π²To decode π₯", project on a vector π‘!
%orthogonal to π‘!
π‘!%π² = π‘!
%π‘!π₯! + π‘!
%π‘"π₯"
= π‘!%π‘"π₯"
=β!!
β"!
β!"
β""π₯! π₯"π² +
π‘!%= β"! β β!!
π‘!%π² = β"!β!!π₯! β β"!β!!π₯!+ β"!β!"π₯"β β!!β""π₯"
= β"!β!" β β!!β"" π₯"
0
0
MIMO: Antenna Space
π² = π‘!π₯! + π‘"π₯"Ant. 2: π¦#
Ant. 1: π¦"
π‘"π₯"
π‘!π₯!
To decode π₯!, project on a vector π‘"&
%orthogonal to the
plane formed by π‘" and π‘&
What about MIMO with more antennas?
Ant. 3: π¦%
π‘&π₯&π‘"&%= π‘" Γ π‘&
+π‘&π₯&
MIMO: Antenna Space
π² = π‘!π₯! + π‘"π₯" + π‘&π₯&Ant. 2: π¦#
Ant. 1: π¦"
π‘"π₯"
π‘!π₯!
To decode π₯!, project on a vector π‘"&
%orthogonal to the
plane formed by π‘" and π‘&
What about MIMO with more antennas?
Ant. 3: π¦%
π‘&π₯&π‘"&%= π‘" Γ π‘&
π antenna MIMO, receives signals in π dimensional spaceΓ Can decode π parallel signals
Decoding complexity scales π(π#) operations with the number of antennas
MIMO Channelπ₯!
π₯"
π¦!
π¦"
β!! = β!!π₯! + β!"π₯"
= β"!π₯! + β""π₯"β!"β""
β"!
How to estimate the channels: β"", β"#, β#", β##?
TX 1:
TX 2:
Preamble π₯!Preamble π₯"
MIMO Channelπ₯!
π₯"
π¦!
π¦"
β!! = β!!π₯! + β!"π₯"
= β"!π₯! + β""π₯"β!"β""
β"!
How to estimate the channels: β"", β"#, β#", β##?
TX 1:
TX 2:
Preamble π₯!Preamble π₯"
MIMO Gains
Multiplexing Gain: β’ Send multiple packets at the same timeβ’ πΓπ MIMO Γ πΓ more packets
Diversity Gain: β’ Send/Receive the same packet on
multiple antennas β’ Increase SNR of the received packets
Γ transmit at higher data rates
Receiver Diversity
π₯ π¦!
π¦"
= β!π₯ + π!
π¦! + π¦" = β!π₯ + π! + β"π₯ + π"
How to best decode π₯?
Option 1: Add the received signals
= β! + β" π₯ + π! + π"
Channels can sum up destructively! β! + β" β 0
= β"π₯ + π"
β!
β"
Receiver Diversity
π₯ π¦!
π¦"
= β!π₯ + π!
How to best decode π₯?
Option 1: Add the received signals
= β"π₯ + π"
β!
β"
Option 2: Decode independently
Sub-optimal!
Receiver Diversity
π₯ π¦!
π¦"
= β!π₯ + π!
How to best decode π₯?
Option 1: Add the received signals
= β"π₯ + π"
β!
β"
Option 2: Decode independently
Optimal Solution: Maximum Ratio Combining (MRC)
Maximum Ratio Combining
π₯ π¦!
π¦"
= β!π₯ + π!
= β"π₯ + π"
β!
β"
= β!βπ¦! + β"βπ¦" = β!ββ!π₯ + β!βπ! + β"ββ"π₯ + β"βπ"
= β! " + β" " π₯ + β!βπ! + β"βπ"
ππππππ πππ€ππ = πΌ β! " + β" " π₯ "
= β! " + β" " " πΌ π₯ "
= β! " + β" " " π
Let π = πΌ π₯ " and π" = πΌ π! " = πΌ π" "
πΌ!π¦!+ πΌ"π¦"
Maximum Ratio Combining
π₯ π¦!
π¦"
= β!π₯ + π!
= β"π₯ + π"
β!
β"
= πΌ β!βπ! " + πΌ β"βπ" "
ππππππ πππ€ππ = β! " + β" " " π
ππππ π πππ€ππ = πΌ β!βπ! + β"βπ" "
= β! "πΌ π! " + β" "πΌ π" " = β! " + β" " π"
Let π = πΌ π₯ " and π" = πΌ π! " = πΌ π" "
= β!βπ¦! + β"βπ¦" = β!ββ!π₯ + β!βπ! + β"ββ"π₯ + β"βπ"
= β! " + β" " π₯ + β!βπ! + β"βπ"
πΌ!π¦!+ πΌ"π¦"
Maximum Ratio Combining
π₯ π¦!
π¦"
= β!π₯ + π!
= β"π₯ + π"
β!
β"
ππππππ πππ€ππ = β! " + β" " " π
ππππ π πππ€ππ = β! " + β" " π"
Let π = πΌ π₯ " and π" = πΌ π! " = πΌ π" "
πππ =β! " + β" " " πβ! " + β" " π" = β! " + β" " π
π"
= β!βπ¦! + β"βπ¦" = β!ββ!π₯ + β!βπ! + β"ββ"π₯ + β"βπ"
= β! " + β" " π₯ + β!βπ! + β"βπ"
πΌ!π¦!+ πΌ"π¦"
Maximum Ratio Combining
π₯ π¦!
π¦"
= β!π₯ + π!
= β"π₯ + π"
β!
β"
With Receiver Diversity: πππ = β! " + β" " ππ"
Single Receiver: πππ = β! " ππ"
= β!βπ¦! + β"βπ¦" = β!ββ!π₯ + β!βπ! + β"ββ"π₯ + β"βπ"
= β! " + β" " π₯ + β!βπ! + β"βπ"
πΌ!π¦!+ πΌ"π¦"
Receiver Diversity Gain
π₯ π¦!
π¦"
= β!π₯ + π!
= β"π₯ + π"
β!
β"
With Receiver Diversity: πππ = β! " + β" " ππ"
Single Receiver: πππ = β! " ππ"
β’ β! " β β" " Γ Can double SNR!
Receiver Diversity GainDo we care about doubling the SNR?
πΆππππππ‘π¦ β log πππ
Rate
SNR
Receiver Diversity Gain
π₯ π¦!
π¦"
= β!π₯ + π!
= β"π₯ + π"
β!
β"
With Receiver Diversity: πππ "() = β! " + β" " ππ"
Single Receiver: πππ !() = β! " ππ"
β’ β! " β β" "
β’ β! " βͺ β" "
β’ β! " β« β" "
Γ Huge Gain in SNR
Γ Little Gain in SNR
Γ Can double SNR!It is unlikely that both antennas experiencechannel fading.
Transmitter Diversity
π¦ = β!π₯! + β"π₯" + π
What should we transmit on each antenna?
Option 1: transmit the same thing π₯ on both antennas
π¦ = β! + β" π₯ + π
Channels can sum up destructively! β! + β" β 0
β!
β"
π₯!
π₯"
Total transmit power = 2πΓ Doubled TX powerΓ Why not use 1 TX with 2π
Transmitter Diversity
π¦ = β!π₯! + β"π₯" + π
What should we transmit on each antenna?
Option 1: transmit the same thing π₯ on both antennas
π¦ = β! + β" π₯ + π
Channels can sum up destructively! β! + β" β 0
β!
β"
π₯!
π₯"
Total transmit power = 2πΓ Doubled TX powerΓ Why not use 1 TX with 2π
β’ Must ensure signals sum up constructively.
β’ Must ensure total TX power = πΌ π₯! " + πΌ π₯" "
= πΌ π₯ " = π
Transmitter Diversity
π¦ = β!π₯! + β"π₯" + π
What should we transmit on each antenna?
Option 2: Maximum Ratio Combining (MRC)
π₯! = πΌ!π₯
β!
β"
π₯!
π₯"
π₯" = πΌ" π₯π¦ = πΌ!β! + πΌ"β" π₯ + π
Set: πΌ! = β!β , πΌ" = β"β Γ π¦ = β!ββ! + β"ββ" π₯ + π
= β! " + β" " π₯ + π
Transmitter Diversity
π¦ = β!π₯! + β"π₯" + π
What should we transmit on each antenna?
Option 2: Maximum Ratio Combining (MRC)
π₯! =β!β
β! " + β" "π₯
β!
β"
π₯!
π₯"
π₯" =β"β
β! " + β" "π₯
πππ‘ππ ππ πππ€ππ = πΌ π₯! " + πΌ π₯! "
=β! "
β! " + β" " π +β" "
β! " + β" " π = π
Transmitter Diversity
π¦ = β!π₯! + β"π₯" + π
What should we transmit on each antenna?
Option 2: Maximum Ratio Combining (MRC)
π₯! =β!β
β! " + β" "π₯
β!
β"
π₯!
π₯"
π₯" =β"β
β! " + β" "π₯
π¦ =β!β!β
β! " + β" "π₯ +
β"β"β
β! " + β" "π₯ + π
Transmitter Diversity
π¦ = β!π₯! + β"π₯" + π
What should we transmit on each antenna?
Option 2: Maximum Ratio Combining (MRC)
π₯! =β!β
β! " + β" "π₯
β!
β"
π₯!
π₯"
π₯" =β"β
β! " + β" "π₯
π¦ =β! " + β" "
β! " + β" "π₯ + π = β! " + β" " π₯ + π
Transmitter Diversity
π¦ = β!π₯! + β"π₯" + π
What should we transmit on each antenna?
Option 2: Maximum Ratio Combining (MRC)
β!
β"
π₯!
π₯"
π¦ = β! " + β" " π₯ + π
πππ = β! " + β" " ππ"
Γ Similar SNR Gain to RX Diversity
Caveat: MRC at TX Requires Feedback from the Receiver!
Transmitter Diversity
π¦ = β!π₯! + β"π₯" + π
What should we transmit on each antenna?
Solution: Use Space-Time Codes
β!
β"
π₯!
π₯"
TX1: π₯!
TX2: π₯"
π‘ = 1 π‘ = 2
π₯ 1
π₯ 1
π₯ 2
π₯ 2
MRC codes across space only (Requires Channel Feedback):
πΌ! =β!β
β! " + β" "
πΌ" =β"β
β! " + β" "
πΌ" πΌ"
πΌ! πΌ!
Transmitter Diversity
π¦ = β!π₯! + β"π₯" + π
What should we transmit on each antenna?
β!
β"
π₯!
π₯"
TX1: π₯!
TX2: π₯"
π‘ = 1 π‘ = 2
π₯ 1
π₯ 2
βπ₯β 2
π₯β 1
Alamouti Codes:
π¦[1] = β!π₯[1] + β"π₯[2]
π¦ 2 = ββ!π₯β[2] + β"π₯β[1]
Solution: Use Space-Time Codes
Transmitter Diversity
π¦ = β!π₯! + β"π₯" + π
What should we transmit on each antenna?
β!
β"
π₯!
π₯"
Alamouti Codes:
π¦[1] = β!π₯[1] + β"π₯[2] π¦ 2 = ββ!π₯β[2] + β"π₯β[1]
β!βπ¦ 1 + β"π¦β 2 = β!ββ!π₯ 1 + β!ββ"π₯ 2ββ"β!βπ₯ 2 + β"β"βπ₯ 1= β! " + β" " π₯ 1
Solution: Use Space-Time Codes
Transmitter Diversity
π¦ = β!π₯! + β"π₯" + π
What should we transmit on each antenna?
β!
β"
π₯!
π₯"
Alamouti Codes:
π¦[1] = β!π₯[1] + β"π₯[2] π¦ 2 = ββ!π₯β[2] + β"π₯β[1]
β"βπ¦ 1 β β!π¦β 2 = β"ββ!π₯ 1 + β"ββ"π₯ 2+β!β!βπ₯ 2 β β!β"βπ₯ 1= β! " + β" " π₯ 2
Solution: Use Space-Time Codes
Transmitter Diversity
π¦ = β!π₯! + β"π₯" + π
What should we transmit on each antenna?
β!
β"
π₯!
π₯"
TX1: π₯!
TX2: π₯"
π‘ = 1 π‘ = 2
π₯ 1
π₯ 2
βπ₯β 2
π₯β 1
Alamouti Codes: β!βπ¦ 1 + β"π¦β 2
= β! " + β" " π₯ 1
β"βπ¦ 1 β β!π¦β 2
= β! " + β" " π₯ 2
Solution: Use Space-Time Codes
MIMO Gains
Multiplexing Gain: β’ Send multiple packets at the same timeβ’ πΓπ MIMO Γ Γπ more packetsβ’ Data Rate: β π log πππ /π
Diversity Gain: β’ Increase SNR of the received packetsβ’ πΓπ MIMO Γ Γ logπ" data rateβ’ Data Rate β log πππ Γπ"
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WiFi 802.11ac MCS (Modulations and Coding Schemes)
48
WiFi 802.11ac MCS (Modulations and Coding Schemes)
49
WiFi 802.11ac MCS (Modulations and Coding Schemes)
MIMO: Multiple TX-RX streamsWiFi Access Points 2 to 8 MIMO WiFi Devices 1 to 2 MIMO
β’ Powerβ’ Form Factor & Antenna
Separationβ’ Most mobile phones
support 2 MIMO
MIMOπ₯!
π₯"
π¦!
π¦"
β!! = β!!π₯! + β!"π₯"
= β"!π₯! + β""π₯"β!"β""
β"!
π² = ππ± + π§
Nπ± = π%ππ² = π%πππ± + π%ππ§ = π± + π%ππ§
Multi-User MIMOπ₯!
π₯"
π¦!
π¦"
β!! = β!!π₯! + β!"π₯"
= β"!π₯! + β""π₯"β!"β""
β"!
π² = ππ± + π§
Nπ± = π%ππ² = π%πππ± + π%ππ§ = π± + π%ππ§
Does not work. Receivers do not have access to each otherβs signals
Precoding π₯!
π₯"
π¦!
π¦"
β!! = β!!π₯! + β!"π₯"
= β"!π₯! + β""π₯"β!"β""
β"!
Receive: π² = π.π± + π§ = ππ#ππ± + π§ = π± + π§
Send: .π± = π#ππ±
Also known as Beamforming or Zero-Forcing
Requires Channel Feedback!
What about distributed transmitters?π₯!
π₯"
π¦!
π¦"
β!! = β!!π₯! + β!"π₯"
= β"!π₯! + β""π₯"β!"β""
β"!
Receive: π² = π.π± + π§ = ππ#ππ± + π§ = π± + π§
Send: .π± = π#ππ±
Does not work. Transmitters do not have access to each otherβs signals
False: what if transmitters are APs connected over Ethernet?
Clock Synchronization in MIMOπ₯!
π₯"
π¦!
π¦"
β!!
= β!!π₯!π#*"+,-!!. + β!"π₯"π#*"+,-!".
= β"!π₯!π#*"+,-"!. + β""π₯"π#*"+,-"".
β!"β""
β"!
π¦!
π¦"
π¦!
π¦"=
β!!
β"!
β!"
β""
π₯!
π₯"+
π!
π"
Clock Synchronization in MIMOπ₯!
π₯"
π¦!
π¦"
β!!
β!"β""
β"!
π¦!
π¦"=
β!! π#*"+,-!!.
β"!π#*"+,-"!.
β!"π#*"+,-!".
β""π#*"+,-"".
π₯!
π₯"+
π!
π"
On chip MIMO: Ξπ!!= Ξπ"!= Ξπ!"= Ξπ""= Ξπ
π¦!
π¦"=
β!!
β"!
β!"
β""
π₯!
π₯"+
π!
π"π#*"+,-.
Clock Synchronization in MIMOπ₯!
π₯"
π¦!
π¦"
β!!
β!"β""
β"!
π¦!
π¦"=
β!! π#*"+,-!!.
β"!π#*"+,-"!.
β!"π#*"+,-!".
β""π#*"+,-"".
π₯!
π₯"+
π!
π"
MU-MIMO: Ξπ!!= Ξπ!" and Ξπ"!= Ξπ""
π¦!
π¦"=
β!! π#*"+,-!.
β"!π#*"+,-".
β!"π#*"+,-!.
β""π#*"+,-".
π₯!
π₯"+
π!
π"
Clock Synchronization in MIMOπ₯!
π₯"
π¦!
π¦"
β!!
β!"β""
β"!
π¦!
π¦"=
β!! π#*"+,-!!.
β"!π#*"+,-"!.
β!"π#*"+,-!".
β""π#*"+,-"".
π₯!
π₯"+
π!
π"
MU-MIMO: Ξπ!!= Ξπ!" and Ξπ"!= Ξπ""
π¦!
π¦"=
β!!
β"!
β!"
β""
π₯!
π₯"+
π!
π"
π#*"+,-!.
0
0
π#*"+,-".
Clock Synchronization in MIMOπ₯!
π₯"
π¦!
π¦"
β!!
β!"β""
β"!
π¦!
π¦"=
β!! π#*"+,-!!.
β"!π#*"+,-"!.
β!"π#*"+,-!".
β""π#*"+,-"".
π₯!
π₯"+
π!
π"
Distributed MIMO: Ξπ!! β Ξπ!" β Ξπ"! β Ξπ""
Next Lecture!
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