Transcript An introduction to multiple antenna systems
MIMO Antenna Systems for Wireless Communication
Prakshep Mehta
(03307909) Guided By:
Prof. R.K. Shevgaonkar
Outline
Introduction...Why MIMO??
What is MIMO ??
From SISO to MIMO The ”pipe” interpretation To exploit the MIMO channel
Foschini, Bell Labs 1996
BLAST
Tarokh, Seshadri & Calderbank 1998
Space Time Coding Special Cases Still to Conquer
What is MIMO ??
Initial Assumptions
Flat fading channel ( B coh >> 1/ T symb ) Slowly fading channel ( T coh >> T symb ) n r receive and n t transmit antennas Noise limited system (no CCI) Receiver estimates the channel perfectly We consider space diversity only
”Classical” receive diversity
H 21 H 11
C
log 2 det
I
P T σ
2
n t
HH
* = log 2 [1+(P T /s 2 ) ·|
H
| 2 ] [bit/(Hz·s)] Capacity increases logarithmically with number of receive antennas...
H =
[ H 11 H 21 ]
Multiple Input Multiple Output systems
H 11
H
H H
11 21
H
12
H
22 H 21 H 12 H 22 C = log 2 det[
I
+(P T /2s 2
)
·
HH
† ]= log 2 1
P T
2 s 2 1 log 2 1
P T
2 s 2 2 Where the i are the eigenvalues to
HH
†
Interpretation:
1 Transmitter 2 m=min(n r , n t ) parallel channels, equal power allocated to each ”pipe” Receiver
MIMO capacity in general
H unknown at TX
C
i m
1 log log 2 2 det
I
1 s
P T
2 s
P T
2
n t
i
n t HH
*
m
min(
n r
,
n t
) H known at TX
C
i m
1 log 2 1
p i
s 2
i
Where the power distribution over ”pipes” are given by a water filling solution
P T
i m
1
p i
i m
1 1
i
p 1 p 2 p 3 p 4 1 2 3 4
The Channel Eigenvalues Orthogonal channels HH
† =
I
, 1 = 2 = …= m = 1
C
diversity
i m
1 log 2 1 s
P T
2
n t
i
min(
n t
,
n r
) log 2 ( 1
P T
/ s 2
n t
) • Capacity increases linearly with min( n r , n t ) • An equal amount of power P T /n t is allocated to each ”pipe” Transmitter Receiver
To Exploit the MIMO Channel
B ell Labs La yered S pace T ime Architecture Time s1 s1 s1 s1 s1 s1 s2 s2 s2 s2 s2 s2 s3 s3 s3 s3 s3 s3 V-BLAST s0 s1 s2 s0 s1 s2 s0 s1 s2 s0 s1 s0 s1 s2 s0 D-BLAST • n r n t 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 ...
{G.J.Foschini, Bell Labs Technical Journal 1996 }
Solution: BLAST algorithm
Idea: NON-LINEAR DETECTOR Step 1:
H +
= (
H
H
H
) -1
H
H Step 2: Find the strongest signal (Strongest = the one with the highest post detection SNR) Step 3: Detect it (Nearest neighbor among Q) Step 4: Subtract it Step 5: if not all yet detected, go to step 2
Space Time Coding
• Use parallel channel to obtain diversity spectral efficiency as in BLAST not • Space-Time trellis codes : coding and diversity gain (require Viterbi detector) • Space-Time block codes : diversity gain (use MMSE at Decoder) *{V.Tarokh, N.Seshadri, A.R.Calderbank
Space-time codes for high data rate wireless communication: Performance Criterion and Code Construction , IEEE Trans. On Information Theory March 1998 }
Orthogonal Space-time Block Codes
Block of T symbols Data in Constellation mapper STBC n t transmit antennas Block of K symbols • K input symbols, T output symbols T • R=K/T is the code rate • If R=1 the STBC has full rate • If T= n t the code has minimum delay • Detector is linear !!!
K *{V.Tarokh, H.Jafarkhani, A.R.Calderbank
Space-time block codes from orthogonal designs, IEEE Trans. On Information Theory June 1999 }
STBC for 2 Transmit
Antennas
[ c 0 c 1 ]
c
0
c
1
c c
* 1 * 0 Time Antenna Full rate and minimum delay Assume 1 RX antenna: Received signal at time 0 Received signal at time 1
r
0
r
1
h
1
c
0
h
1
c
1 *
h
2
c h
2 1
c
0 *
n
0
n
1
Still to Conquer !!
Backward Compatibility Antenna Spacing Complexity at Receiver