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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

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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

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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

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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

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• 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

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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

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• 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

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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

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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

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– 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

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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

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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

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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

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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

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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

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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

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Some Simulations (II)

Comparison between:

- Uniform power allocation (no CSI)

- Optimum power allocation with statistical CSI and different levels of LOS

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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)

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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