mattias wennström signals & systems group mattias wennström uppsala university sweden promises...
Post on 19-Dec-2015
226 views
TRANSCRIPT
Mattias WennströmSignals & Systems Group
Mattias WennströmUppsala University
Sweden
Promises of Wireless Promises of Wireless MIMO SystemsMIMO Systems
Mattias WennströmSignals & Systems Group
Outline• Introduction...why MIMO??• Shannon capacity of MIMO systems • The ”pipe” interpretation• To exploit the MIMO channel
– BLAST– Space Time Coding– Beamforming
• Comparisons & hardware issues• Space time coding in 3G & EDGE
Telatar, AT&T 1995
Foschini, Bell Labs 1996
Tarokh, Seshadri & Calderbank 1998
Release ’99
Mattias WennströmSignals & Systems Group
Why multiple antennas ????Why multiple antennas ????
• Frequency and time processing are at limits• Space processing is interesting because it does not increase bandwidth
Adaptive Antennasinterference cancellation
Phased array range extension,
interference reduction MIMO Systems
(diversity)
”Specular”channels
”Scattering”channels
outdoor indoor
Mattias WennströmSignals & Systems Group
Initial AssumptionsInitial Assumptions
• Flat fading channel (Bcoh>> 1/ Tsymb)• Slowly fading channel (Tcoh>> Tsymb)• nr receive and nt transmit antennas• Noise limited system (no CCI)• Receiver estimates the channel
perfectly• We consider space diversity only
Mattias WennströmSignals & Systems Group
H11
H21
””Classical” receive diversityClassical” receive diversity
= log2[1+(PT2)·|H|2] [bit/(Hz·s)]
H = [ H11 H21] Capacity increases logarithmically with number of receive antennas...
*
22 detlog HHIt
T
nσ
PC
Mattias WennströmSignals & Systems Group
Transmit diversity / beamformingTransmit diversity / beamforming
H11
H12
Cdiversity = log2(1+(PT2)·|H|2) [bit/(Hz·s)]
Cbeamforming = log2(1 +(PT2 )·|H|2) [bit/(Hz·s)]
• 3 dB SNR increase if transmitter knows H• Capacity increases logarithmically with nt
Mattias WennströmSignals & Systems Group
H11
H22
Multiple Input Multiple Output systemsMultiple Input Multiple Output systems
H12
H21
2221
1211
HH
HHH
Cdiversity = log2det[I +(PT2 )·HH†]=
222122 2
1log2
1log
TT PP
Where the i are the eigenvalues to HH†
m=min(nr, nt) parallel channels, equal power allocated to each ”pipe”
Interpretation:
ReceiverTransmitter
Mattias WennströmSignals & Systems Group
MIMO capacity in generalMIMO capacity in general
m
ii
t
T
t
T
n
P
HHn
PIC
122
*22
1log
detlog
H unknown at TX H known at TX
m
i
iipC1
22 1log
Where the power distribution over”pipes” are given by a water filling solution
m
i
m
i iiT pP
1 1
1
p1
p2
p3
p4
),min( tr nnm
Mattias WennströmSignals & Systems Group
The Channel EigenvaluesThe Channel Eigenvalues
Orthogonal channels HH† =I, 1= 2= …= m= 1
)/1(log),min(1log 22
122 tTrt
m
ii
t
T nPnnn
PC
diversity
• Capacity increases linearly with min( nr , nt )• An equal amount of power PT/nt is allocated to each ”pipe”
Transmitter Receiver
Mattias WennströmSignals & Systems Group
Random channel models andRandom channel models andDelay limited capacityDelay limited capacity
• In stochastic channels,the channel capacity becomes a random variable
Define : Outage probability Pout = Pr{ C < R }
Define : Outage capacity R0 given a outageprobability Pout = Pr{ C < R0 }, this is the delaylimited capacity.
Outage probability approximates the Word error probability for coding blocks of approx length100
Mattias WennströmSignals & Systems Group
Example : Rayleigh fading channelExample : Rayleigh fading channelHij CN (0,1)
nr=1 nr= nt
Ordered eigenvaluedistribution for nr= nt = 4 case.
Mattias WennströmSignals & Systems Group
To Exploit the MIMO ChannelTo Exploit the MIMO Channel
Time
s0
s0
s0
s0
s0
s0
s1
s1
s1
s1
s1
s2
s2
s2
s2
V-BLAST
D-BLAST
Ante
nna
s1 s1 s1 s1 s1 s1
s2 s2 s2 s2 s2 s2
s3 s3 s3 s3 s3 s3
• nr nt required• Symbol by symbol detection. Using nulling and symbol cancellation• V-BLAST implemented -98 by Bell Labs (40 bps/Hz)• If one ”pipe” is bad in BLAST we get errors ...
Bell Labs Layered Space Time Architecture
{G.J.Foschini, Bell Labs Technical Journal 1996 }
Mattias WennströmSignals & Systems Group
Space Time CodingSpace Time Coding
• Use parallel channel to obtain diversitydiversity not spectral efficiency as in BLAST• Space-Time trellistrellis codes : coding and and diversity gain (require Viterbi detector)• Space-Time blockblock codes : diversity gain
(use outer code to get coding gain)• nr= 1 is possible• Properly designed codes acheive diversity of nr nt
*{V.Tarokh, N.Seshadri, A.R.CalderbankSpace-time codes for high data rate wireless communication: Performance Criterion and Code Construction, IEEE Trans. On Information Theory March 1998 }
Mattias WennströmSignals & Systems Group
Orthogonal Space-time Block Orthogonal Space-time Block CodesCodes
STBC
Block of K symbols
• K input symbols, T output symbols T K• R=K/T is the code rate code rate • If R=1 the STBC has full rate full rate • If T= If T= nt the code has minimum delayminimum delay• Detector is Detector is linearlinear !!! !!!
Block of T symbols
nt transmit antennas
Constellation mapper
Data in
*{V.Tarokh, H.Jafarkhani, A.R.CalderbankSpace-time block codes from orthogonal designs, IEEE Trans. On Information Theory June 1999 }
Mattias WennströmSignals & Systems Group
STBC for 2 Transmit STBC for 2 Transmit AntennasAntennas
[ c0 c1 ]
*01
*10
cc
cc
Time
Antenna
Full rateFull rate andminimum delayminimum delay
1*02
*111
012010
nchchrnchchr
Assume 1 RX antenna:
Received signal at time 0
Received signal at time 1
Mattias WennströmSignals & Systems Group
ncHr
1
0*1
0*1
*2
21*
1
0 ,,,c
c
n
n
hh
hh
r
rcnHr
ncHnHcHHrHr ~~ 2*** F
Diagonal matrix due to orthogonality
The MIMO/ MISO system is in fact transformed to an equivalent SISO system with SNR
SNReq = || H ||F2 SNR/nt
|| H ||F2 =
Mattias WennströmSignals & Systems Group
The existence of Orthogonal STBCThe existence of Orthogonal STBC
• Real symbols : Real symbols : For nt =2,4,8 exists delay optimalfull rate codes.For nt =3,5,6,7,>8 exists full ratecodes with delay (T>K)
• Complex symbols : Complex symbols : For nt =2 exists delay optimalfull rate codes.For nt =3,4 exists rate 3/4 codesFor nt > 4 exists (so far) rate 1/2 codes
Example: nt =4, K=3, T=4 R=3/4
*12
*3
*13
*2
*2
*31
321
321
0
0
0
0
sss
sss
sss
sss
sss
Mattias WennströmSignals & Systems Group
Outage capacity of STBCOutage capacity of STBC
2
2 1logF
t
Hn
SNRCSTBC
HHn
SNRIC
t
detlog2diversity
Optimal capacity
STBC is optimal wrt capacity if HH† = || H ||F
2 which is the case for• MISO systems• Low rank channels
Mattias WennströmSignals & Systems Group
Performance of the STBC… Performance of the STBC… (Rayleigh faded channel)
|| H ||F2 = m
nt=4 transmit antennas andnr is varied.
The PDF of Assume BPSK modulation BER is then given by
tr
trnn
b nn
nn
SNRP
tr 12
4
1
Diversity gainnrnt which is same as fororthogonal channels
Mattias WennströmSignals & Systems Group
MIMO With BeamformingMIMO With Beamforming
Requires that channel H is known at the transmitterIs the capacity-optimal transmission strategy if
Cbeamforming = log2(1+SNR·1) [bit/(Hz·s)]
SNR12
11
Which is often true for line of sight (LOS) channels
Only one ”pipe” is used
Mattias WennströmSignals & Systems Group
Comparisons...Comparisons...2 * 2 system. With specular component (Ricean fading)
One dominatingeigenvalue. BF putsall energy into that ”pipe”
Mattias WennströmSignals & Systems Group
Correlated channels / Mutual Correlated channels / Mutual coupling ...coupling ...
When angle spread () is small, we have a dominating eigenvalue.The mutual coupling actuallyimprovesimproves the performance of the STBC by making the eigenvalues ”more equal”in magnitude.
Mattias WennströmSignals & Systems Group
WCDMA Transmit diversity conceptWCDMA Transmit diversity concept(3GPP Release ’99 with 2 TX antennas)
•2 modes• Open loop (STTD)• Closed loop (1 bit / slot feedback)
• Submode 1 (1 phase bit)• Submode 2 (3 phase bits / 1 gain bit)
Open loop mode is exactly the 2 antenna STBC
*01
*10
ss
ss
The feedback bits (1500 Hz) determines the beamformer weightsSubmode 1 Equal power and bit chooses phase between {0,180} / {90/270}
Submode 2 Bit one chooses power division {0.8 , 0.2} / {0.2 , 0.8} and 3 bits chooses phase in an 8-PSK constellation
Mattias WennströmSignals & Systems Group
GSM/EDGE Space time coding proposalGSM/EDGE Space time coding proposal
• Frequency selective channel …• Require new software in terminals ..• Invented by Erik Lindskog
Time Reversal Space Time Coding Time Reversal Space Time Coding (works for 2 antennas)(works for 2 antennas)
Time reversal Complex conjugate
Time reversal Complex conjugate -1
S(t)
S1(t)
S2(t)
Block
Mattias WennströmSignals & Systems Group
””Take- home message”Take- home message”• Channel capacity increases linearlylinearly
with min(nr, nt)
• STBC is in the 3GPP WCDMA proposal