Post on 06-Jan-2016
description
NEWCOM – SWP2 MEETING 1
Impact of the CSI on the Design of a Multi-Antenna Transmitter
with ML Detection
Antonio Pascual Isertetonip@gps.tsc.upc.es
Dpt. Signal Theory and CommunicationsTechnical University of Catalonia (UPC)
NEWCOM – SWP2 MEETING 2
Outline
• Introduction
• Classical Solutions• ML Detection:
• Signal model• Different degrees of CSI at the transmitter:
• No CSI• Perfect CSI• Statistical CSI• Imperfect CSI
• Some Conclusions
NEWCOM – SWP2 MEETING 3
Introduction
• Transmission through MIMO channels:
– Problem: design of the transmitter and the receiver
– The adopted figure of merit or cost function depends of the detection strategy at the receiver
– The design strategy depends on the quantity and the quality of the CSI available at the transmitter
NEWCOM – SWP2 MEETING 4
Classical Solutions
• Classical designs:– They are based on the use of linear
transmitters and receivers– Adopted figures of merit: mean square errormean square error
(MSE), signal to noise ratio signal to noise ratio (SNR), … …
B MIMO radio
channel AHs s
linear transmitter linear receiver
NEWCOM – SWP2 MEETING 5
Maximum Likelihood Detection
• Optimum receiver:– It is based on the application of the ML detector– Signal model: for a linear transmitter
– Received signal:
– Optimum ML detection:
, 1, ,n n n n N x HB s w
Bn MIMO radio
channel MLs s
nB s nx
2
1
ˆ arg minN
n nn
s
s x HB s
NEWCOM – SWP2 MEETING 6
• Transmitter architecture:• Temporal processing and modulation construction:• Power allocation:• Spatial processing:
Transmitter Architecture
1/ 2 Hn n nB UP V
HnV
1/ 2nPU
they depend on the available CSI
Hn c n n x H V s w
1
1/ 2
R M
R
n nc
H c cc n
H Hn n n
C
H HU
H h h
V P
V
Modified signal model:
ns streams nM spatial modes
nT antennas
NEWCOM – SWP2 MEETING 7
Pairwise Error Probability
• Pairwise Error Probability (PEP):– Probability of deciding in favor of sb when the
vector sa has been actually transmitted:
– If there is only one error in the s-th stream and the symbols are BPSK
010
1
PEP Pr( ) exp2
,
R
M M
nab c H cs
a b e p ab pp
Nn nn n H n H
ab ab ab ab n b an
EP K
N
C
s s h A h
A φ φ φ V s s
, ,1
4N
Hs n s n s
n
A v vvn,s: s-th column of VnH
NEWCOM – SWP2 MEETING 8
• Objective:– Design of the transmitter subject to a power
constraint in order to minimize the worst PEP
• Impact of the CSI:– The design depends on the available CSI at the
transmitter:– Possible cases:
• No CSI• Perfect CSI• Statistical CSI• Imperfect CSI
Transmitter Design
NEWCOM – SWP2 MEETING 9
No CSI
• Situation:– There is no CSI at the transmitter– The minimization of the maximum PEP implies
that the PEP is equal for all the possible positions of error:
, , 01
4N
Hs n s n s M
n
N n
A v v I
00
2 ( )PEP exp , HT H
H c cS M
E N TrK
N n n
RR H H
for BPSK streams
The matrices VnH can be based on OSTBC or FFT-like matrices
NEWCOM – SWP2 MEETING 10
Perfect CSI (I)
• Situation:– There is a perfect CSI at the transmitter– The minimization of the worst PEP implies the
maximization of the minimum distance at the receiver:
– A closed-form solution exists for the case of 2 QPSK streams (ns=2)
2
,,min max max min
a ba b
abe a bP
B s ss s BHBs HBs
NEWCOM – SWP2 MEETING 11
– Transmission through the two maximum eigenvectors of the MIMO channel (nM=2)
– The configuration depends on the eigenvalues-ratio
Perfect CSI (II)
HH H
2 1/ 0.097
1 2 2 0 1
0
,
0.17
p k p k
2 1/ 0.097
N = 1 channel access
NEWCOM – SWP2 MEETING 12
Perfect CSI (III)
• Constellations:
1 mode 2 modes
2 1/ 0.097 2 1/ 0.097
0 10
PEP exp 0.4232TEKN
1 20
0 2 1
PEP exp 1.1722 0.172TEKN
NEWCOM – SWP2 MEETING 13
Statistical CSI (I)
• Situation:– Only the channel statistics are known
– Channel model:
• are i.i.d. with Gaussian distribution:
– Transmitter design: power allocation
1
Rncp ph
0 1
2 21 , ,
T
T
Tcp n
Hc cp p n
E h h
E diag
h h
h h Σ
mean value: LOS
covariance
, , 0 11
4 · , , ,T
NH
s n s n s n Tn
diag s N n
A v v
NEWCOM – SWP2 MEETING 14
Statistical CSI (II)
– Design objective: minimization of the mean PEP averaged over the channel statistics
– Solution: optimum power allocation:
2
21
021 0
1
| |exp
1 2PEP ,
1
T
R
T
nq q
nq q q T
np S T
q qq
h
E NE K
N n n
2
2 4
1 1 1max 0, 1 4
2 2q
qq q
h
PEPE
NEWCOM – SWP2 MEETING 15
Imperfect CSI (I)
• Situation:– Only a channel estimate, which can be noise or
imperfect, is available– Possible solutions:
• Bayesian designsBayesian designs: the error is modelled statistically• Maximin designsMaximin designs: the error is assumed to belong to
an uncertainty region R, and the worst system performance for any possible error is optimized
– Maximin approach:• Transmission through the estimated eigenvectors• Optimization of the power allocation among the
estimated eigenmodes• Combination with OSTBC
ip
NEWCOM – SWP2 MEETING 16
Imperfect CSI (II)
– Solution: it can be calculated numerically using convex optimization procedures
11
max minSNR ,M
nMi i
n
i iRpp
ΔΔ
TN n
NEWCOM – SWP2 MEETING 17
Some Simulations (I)
Comparison between:
- Optimum linear transmitter-receiver with perfect CSI
- Optimum linear transmitter with ML detection with optimum CSI
- QPSK VBLAST
- 16-QAM Alamouti
NEWCOM – SWP2 MEETING 18
Some Simulations (II)
Comparison between:
- Uniform power allocation (no CSI)
- Optimum power allocation with statistical CSI and different levels of LOS
NEWCOM – SWP2 MEETING 19
Some Simulations (III)
Robust design
Comparison in terms of achievable throughput (using adaptive modulation adaptive modulation with maximum BER constraints):
- Alamouti (nM=2)- Full OSTBC (nM=nT)
NEWCOM – SWP2 MEETING 20
Conclusions
• When using an optimum ML detector, the figure of merit should be based on the PEP, and not on the MSE
• The design of the transmitter depends on the available CSI and its quality:
• No CSINo CSI: equal error probability for all the possible positions of the error
• Perfect CSIPerfect CSI: the eigenmodes of the channel are used with a convenient power allocation and a new signal constellation
• Statistical CSIStatistical CSI: a power allocation is performed taking into account the LOS and the Rayleigh components
• Imperfect CSIImperfect CSI: a robust maximin power allocation is performed