Wireless Communication Systems @CS.NCTU Lecture 5: Multi-User MIMO (MU-MIMO) Instructor: Kate Ching-Ju Lin ( 林靖茹 ) 1
Agenda • Interference Nulling • Zero-forcing Beamforming (802.11ac) • Interference Alignment • Network MIMO 2
Cross-Link Interference • Problem: ⎻ Any two nearby links cannot transmit simultaneously on the same frequency • Solution: ⎻ A transmitter with multiple antennas can actively cancel its interfering signals at nearby receiver(s) 3
Interference Nulling Nulling: make (h 1 α +h 2 β )=0 à α = -(h 2 /h 1 ) β x Alice y = hx + (h 1 α +h 2 β )x’ h 1 α x' y’ = h’x + (h 1a α +h 1b β )x’ h 2 Bob y” = h”x + (h 2a α +h 2b β )x’ β x' à ≠ 0 • Signals cancel each other at Alice’s receiver • Signals don’t cancel each other at Bob’s receiver ⎻ Because channels are different ⎻ Bob’s receiver can remove Alice’s interference via ZF decoding
Agenda • Interference Nulling • Zero-forcing Beamforming (802.11ac) • Interference Alignment • Network MIMO 5
802.11ac Cannot leverage multiplexing gains if clients only have a single antenna • From 802.11a/b/g, to 802.11n, to 802.11ac ⎻ AP can be more and more powerful à supporting multiple antennas ⎻ But, how about mobile devices? à usually light- weight and small size à limited number of antennas 6
802.11ac • 802.11ac adopts multiuser MIMO (MU-MIMO) ⎻ Involve multiple clients in concurrent transmissions ⎻ Extract the multiplexing gain ⎻ Maximal number of clients (streams) = number of antennas at the AP ⎻ Only support downlink MU-MIMO now 7
Cross-Stream Interference x 1 x 2 x 3 Client 1 Client 3 Client 2 • Say the AP send x 1 , x 2 and x 3 to client 1, 2 and 3, respectively ⎻ If the AP simply uses each antenna to send one stream, ⎻ Each client receives the combined signal of x 1 , x 2 and x 3 ⎻ x 2 and x 3 are cross-stream interference for client 1 8
Channel Model x 1 x 2 x 3 h 1 = [ h 11 h 12 h 13 ] T h 2 = [ h 21 h 22 h 23 ] T Client 1 h 1 h 3 = [ h 31 h 32 h 33 ] T h 3 h 2 Client 3 Client 2 Interference y 1 = h 11 x 1 + ( h 12 x 2 + h 13 x 3 ) + n 1 y 2 = h 22 x 2 + ( h 21 x 1 + h 23 x 3 ) + n 2 y 3 = h 33 x 3 + ( h 31 x 1 + h 32 x 2 ) + n 3 9
How to Remove Cross-Stream Interference? • Zero-Forcing Beamforming (ZFBF) ⎻ Also called zero-forcing precoding or null-steering ⎻ Linear precoder that maximizes the output SNR • The AP uses its antennas to actively cancel the interfering streams at a particular client ⎻ In the previous example, the AP cancel x 2 and x 3 at client 1 cancel x 1 and x 3 at client 2 cancel x 1 and x 2 at client 3 ⎻ Steer a beam toward to its intended receiver • How to suppress all the interference using the limited number of antennas? 10
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Zero-Forcing Beamforming (ZFBF) [ w 11 w 12 w 13 ] * x 1 [ w 21 w 22 w 23 ] * x 2 [ w 31 w 32 w 33 ] * x 3 h 1 h 3 h 2 • Use all the antennas to send every stream • Each stream i is precoded using ZFBF weight vector w i = [ w i1 w i2 … w iN ] • The precoded signal w ij x i is sent by the j -th antenna • The j -th antenna transmit the summation of all the precoded signal ( w 1j x 1 + w 2j x 2 + … + w Nj x N ) 12
Zero-Forcing Beamforming (ZFBF) [ w 11 w 12 w 13 ] * x 1 * √ P 1 [ w 21 w 22 w 23 ] * x 2 * √ P 2 [ w 31 w 32 w 33 ] * x 3 * √ P 3 h 1 Client 1 h 3 h 2 Client 3 Client 2 Null the interference: √ X √ y i = P i h i w i x i + P j h i w j x j + n i � à P j h i w j = 0 , � j � = i Interference j 6 = i Let W be the pseudo inverse of H √ à W = H † = H ∗ ( HH ∗ ) − 1 Matrix: y = HW Px + n √ Px + n 0 Then, y = 13
SNR of ZFBF • ZFBF is essentially equivalent to ZF, but just performed by the transmitter y = ( y 1 , y 2 ) ~ ~ h 2 = ( h 12 , h 22 ) antenna 2 x 2 ~ θ h 1 = ( h 11 , h 21 ) x 1 antenna 1 x’ 1 | x 0 1 | = | x 1 | cos(90 − θ ) = | x 1 | sin( θ ) • The achievable SNR is determined by the channel correlation among concurrent clients 14
MU-MIMO Bit-Rate Selection AP h C h A h B Select a proper rate based on SNR ZFBF C A B ant. 1 ant. 1 ant. 1 Alice Alice Bob Bob Chris Chris ant. 2 ant. 2 ant. 2
MU-MIMO User Selection AP h C h A Grouping different subsets of h B clients as concurrent receivers C results in different sum-rates A à Need proper user selection B ant. 1 ant. 1 ant. 1 Alice Alice Bob Bob Chris Chris ant. 2 ant. 2 ant. 2
MU-MIMO User Selection AP h C h A Grouping different subsets of h B clients as concurrent receivers C results in different sum-rates A à Need proper user selection B • Exhaustive search: � N � ⎻ Calculate the sum-rate for each of groups k ⎻ Pick the one with the maximal sum-rate • Greedy: ⎻ sequentially add a user producing the maximal rate after projecting on the subspace of the users that have been selected
MU-MIMO Power Allocation • Achievable sum-rate for a set of user S � log(1 + p i | h i w i | 2 ) R = max p i i ∈ S subject to � � w i � 2 p i � P max i ∈ S Power allocated to user i 18
MU-MIMO Power Allocation � � log(1 + p i | h i w i | 2 ) s.t. � w i � 2 p i � P max R = max p i i ∈ S i ∈ S • Optimal power allocation: Waterfilling � + � µ p i = � w i � 2 � 1 , where ( x ) + = max { x, 0 } ( µ � � w i � 2 ) + = P � µ is the water level satisfying i ∈ S [1] Yoo et.al. “On the optimality of multiantenna broadcast scheduling using zero-forcing beamforming,” IEEE JSAC, 24(3):528–541, March 2006. [2] Huang et.al., "User Selection for Multiuser MIMO Downlink With Zero-Forcing Beamforming," in 19 IEEE TVT, vol. 62, no. 7, pp. 3084-3097, Sept. 2013.
Waterfilling Power Allocation � + � µ power allocated to user i : p i = � w i � 2 � 1 water level µ such that ( µ � � w i � 2 ) + = P � i ∈ S � w i � 2 user • Good channels get more power than poor channels • Fairness is a concern 20
Agenda • Interference Nulling • Zero-forcing Beamforming (802.11ac) • Interference Alignment • Network MIMO 21
Interference Alignment 2-antenna receiver I 1 I 2 wanted signal N-antenna node can only decode N signals If I 1 and I 2 are aligned, à appear as one interferer à 2-antenna receiver can decode the wanted signal x and the combined interference (I 1 +I 2 ) à No need to decode I 1 and I 2 since the Rx does not care
Rotate Signal • A multi-antenna transmitter can rotate the received signal 2-antenna receiver y’ y = Ry • To rotate received signal y to y’ = Ry , the transmitter precodes the transmitted signal by multiplying it with the rotation matrix R
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Rotate Signal (2x2 Example) • Say an interfering transmitter wants to align its signal at the interfered receiver along the direction (u,v) • The interferer precodes its signal x with a weight vector (w 1 , w 2 ) ant2 h 11 (h 11 +h 12 , h 21 +h 22 ) (u, v) x y 1 =(h 11 +h 12 )x h 12 h 21 h 22 y 2 =(h 21 +h 22 )x x ant1
Rotate Signal (2x2 Example) • Find (w 1 , w 2 ) such that ⎻ (w 1 h 11 +w 2 h 12 , w 1 h 21 +w 2 h 22 ) ∥ (u, v) (1) w 1 h 11 + w 2 h 12 = u Alignment w 1 h 21 + w 2 h 22 v q Power constraint w 2 1 + w 2 (2) 2 = 1 h 11 (h 11 +h 12 , h 21 +h 22 ) (u, v) w 1 x y 1 =(w 1 h 11 +w 2 h 12 )x h 12 h 21 h 22 w 2 x y 2 =(w 1 h 21 +w 2 h 22 )x
Interference Alignment Alignment direction 2-antenna receiver I 1 I 2 wanted signal I 3 N-antenna node can only decode N signals How to align interfering signals? à Find the direction of any interference (e.g., I 1 ) à All the remaining interferers (e.g., I 1 and I 2 ) rotate their signals to that direction
Agenda • Interference Nulling • Zero-forcing Beamforming (802.11ac) • Interference Alignment • Network MIMO 28
Network MIMO • Also known as virtual MIMO, cooperative MIMO, distributed MIMO • Why we need network MIMO? ⎻ Maximal number of concurrent packets is limited by the number of antennas per AP ⎻ It is hard to equip with a large number of antennas in a single AP • How to build a network MIMO node? 29
Network MIMO vAP • Combine multiple APs as a giant virtual AP • Distributed antennas are connected via backhual wired network • Process signals by one or multiple backend servers 30
Open Issues of Network MIMO • Salability • Latency • Synchronization 31
Scalability • Forwarding raw complex signals through the Ethernet requires an extremely large backhual bandwidth ⎻ Ethernet capacity might now become a bottleneck • Complexity of precoding/decoding a large scale of streams is fairly high ⎻ A single server can only support a limited number of concurrent packets ⎻ Software-based precoding/decoding at the servers is less efficient than hardware-based processing at APs 32
Latency • Servers need to collect the received signals from distributed antennas • The latency between antennas and servers might be longer than symbol duration ⎻ For example, the symbol duration of 802.11n is only 4 microseconds (us) • A packet might not be able to be acknowledged immediately after data transmission ⎻ The MAC protocol might need to be re-designed 33
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