Multi-Input Multi-Output Systems (MIMO) Channel Model for MIMO MIMO Decoding MIMO Gains Multi-User MIMO Systems

Transcription

1 Multi-Input Multi-Output Systems (MIMO) Channel Model for MIMO MIMO Decoding MIMO Gains Multi-User MIMO Systems

2 MIMO Each node has multiple antennas Capable of transmitting (receiving) multiple streams concurrently Exploit antenna diversity to increase the capacity h 3 h h h 3 h h 33 h3 h h 3 " $ $ H N M = $ $ # $ h h h 3 h h h 3 h 3 h h 33 % ' ' ' ' &'

3 Channel Model (x) x h h h h x y = h x +h x +n y = h x +h x +n y = Hx +n Can be extended to N x M systems

4 Antenna Space M-antenna node receives in M-dimensional space x! # " y $! & = h $! # % " h & x + h # % " h y = h x + h x + n $! & x + n # % " n $ & % h = (h,h ) y = (, y ) antenna antenna x x h = (h,h ) antenna antenna 3 antenna

5 MIMO Decoding (algebra) Orthogonal vectors + )! # " y $! & = h # % " h $! & x + h # % " h $! & x + n # % " n $ & % * h * - h h y h = (h h h h )x x = h y h h h h h Given x, solve x To guarantee the full rank of H, antenna spacing at the transmicer and receiver must exceed half of the wavelength

6 MIMO Decoding (antenna space) Zero forcing antenna h = (h,h ) x x y = (, y ) h = (h,h ) antenna x x < x To decode x, decode vector y on the direcgon orthogonal to x To improve the SNR, re- encode the first detected signal, subtract it from y, and decode the second signal

7 Channel Estimation Estimate N x M matrix H h x h = h x +h x +n h h y = h x +h x +n x y Two equagons, but four unknowns Antenna at Tx Access code Stream Antenna at Tx Access code Stream EsGmate h, h EsGmate h, h

8 Multiplex Gain MIMO Gains Exploit antenna diversity to deliver multiple streams concurrently Diversity Gain Exploit antenna diversity to increase the SNR of a single stream

9 x example Diversity Gain x h h = h x +n y y = h x +n Decode the SNR of ( + y ) Uncorrelated whit Gaussian noise with zero mean Packet can be delivered through at least one of the many diver paths

10 x example Diversity Gain x h h = h x +n y y = h x +n SNR= P(X) P(n +n ),(where(p(refers(to(the(power = E[(X) ] E[n +n ] = 4E[X ], (where(σ (is(the(variance(of(awgn σ Increase SNR by 3dB Especially beneficial for the low SNR link = *SNR single(antenna

11 Diversity Gain! # " $# MulGply each y with the conjugate of the channel! = h x +n h * # = h x + h * n " y = h x +n h * # y = h x + h * n $ SNR diversity = E[(( h + h )X) ] E[(h * n +h * n ) ] = ( h + h ) E(X ) ( h + h )σ = ( h + h )E(X ) σ SNR single = E[(( h + h )X) ] E[(h * n +h * n ) ] 4 = h E(X ) ( h )σ = h E(X ) σ gain = ( h + h ) h

12 Trade off Between diversity gain and multiplex gain Say we have a N x N system Degree of freedom: N The transmitter can transmit k streams concurrently, where k <= N The optimal value of k is determined by the tradeoff between the diversity gain and multiplex gain

13 Degree of Freedom For N x M MIMO channel Degree of Freedom (DoF): min {N,M} Maximum diversity: NM

14 Space-Time Code Examples: Channel Repetition Scheme: Alamouti Scheme: X = x 0 0 x time X = x -x * x x * time space space diversity: data rate: / sym/s/hz diversity: data rate: sym/s/hz

15 Space-Time Code Examples: Channel Repetition Scheme: Alamouti Scheme: X = x 0 0 x time X = x -x * x x * time space space diversity: 4 data rate: / sym/s/hz But the channel has degrees of freedom! diversity: 4 data rate: sym/s/hz

16 Interference Nulling Alice Bob αx βx!! h!! h h αx +h βx = 0!! Nulling :!h α = h β (h a α +h a β)x 0 (h b α +h b β)x 0 Signals cancel each other at Alice s receiver Signals don t cancel each other at Bob s receiver Because channels are different

17 Homework Say there exist a 3x link, which has a channel " $ H 3 = $ $ # $ h h h h h 3 h 3 % ' ' ' &' How can a three-antenna transmitter transmit a signal x, but null its signal at two antennas of a two-antenna receiver?

18 Interference Alignment -antenna receiver I I wanted signal N-antenna node can only decode N signals If I and I are aligned, à appear as one interferer à -antenna receiver can decode the wanted signal

19 Interference Alignment -antenna receiver I + I wanted signal N-antenna node can only decode N signals If I and I are aligned, à appear as one interferer à -antenna receiver can decode the wanted signal

20 Rotate Signal. Transmitter can rotate the received signal -antenna receiver y y = Ry To rotate received signal y to y = Ry, transmitter multiplies its transmitted signal by the same rotation matrix R

21 Rotate Signal αx βx = (h α +h β)x y = (h α +h β)x y = (h +h,h +h ) y' = (u, v) (h α +h β) = u (h α +h β) = v How to align the signal along the interference? à Find the direcgon of the interference and rotate the signal to that direcgon