course id: 240123 advanced communication...

Course ID: 240123Advanced Communication Systems

Multi-user MIMO and precoding techniques

Prof. Manar MohaisenDepartment of EEC Engineering

Korea University of Technology and Education (KUT)

Lecture ContentMulti user MIMOMulti-user MIMO

Dirty paper coding (DPC)

Linear precoding techniques

Tomlinson-Harashima precoding

V t t b ti t h iVector perturbation techniques♦ Sphere encoder (SE)♦ QRD-M encoder (QRDM-E)♦ Fixed-complexity sphere encoder (FSE)♦ Parallel QRD-M encoder (P-QRDME)

Simulation results and comparisons2Korea University of Technology and Education (KUT)

Multi-user MIMO: UplinkCollaborative MIMO (Virtual MIMO system)Collaborative MIMO (Virtual MIMO system)♦ Several users are assigned the same time and frequency resources♦ They are synchronized by the BS to send their data in the UL such that their

signals combine at the BS’s receive antennasignals combine at the BS s receive antenna♦ The BS uses detection techniques to de-multiplex users’ data

user 1

base station

user 2

3Korea University of Technology and Education (KUT)user 3

Multi-user MIMO: DownlinkMulti user MIMOMulti-user MIMO♦ A base station (BS) communicates simultaneously with multiple users

Each user should receive its designated data without (or with low) IUIU ( ll ) t tiUsers are (usually) not cooperative

♦ How could that be possible?S l ti U i th i i l f di t di (DPC)!Solution: Using the principle of dirty paper coding (DPC)!

user 1

base station

user 2

4Korea University of Technology and Education (KUT)

stat o

user 3

inter-user interference

user data

Multi-user MIMO: DownlinkDirty paper coding (DPC)Dirty paper coding (DPC)♦ General idea

If you know the locations of the dirt on a paper, write on the clean places

♦ In MU-MIMO systemsBS knows the designated data to its own users

S f f (CS )BS has knowledge of DL channel station information (CSI)■ Either by feedback from users or using the reciprocity principle

BS precodes data such that IUI is minimized or even cancelledGi en both the data and the CSI■ Given both the data and the CSI

♦ AssumptionsA i l BS i d ith tA single BS equipped with nT antennasnU users each equipped with nR antennas such that nT ≥ (nU×nR)Users are decentralized (no cooperation between them)BS h f ll k l d f th CSI if t th i i di t dBS has full knowledge of the CSI, if not otherwise indicated


Linear PrecodingSystem modelSystem model♦ System model

H

1s

s x 1rH

ˆUns

x

Unr

( )1 2, , TR U RT

U

Tn n n nn T T Tni C C ⎡ ⎤

⎢ ⎥⎣ ⎦

× ×∈Ω ∈ ∈ =s r H H H HL

♦ Receiver structure

1γ

=x Ps1γ

= + = +y Hx n HPs n( )i iQ=s r

γ is a scaling factor that limits the transmit power to PT

γγ→ = = +r y HPs v

i i

11 ⎧ ⎫⎛ ⎞⎪ ⎪

−


11 Tr H

TPγ

⎧ ⎫⎛ ⎞⎪ ⎪⎨ ⎬⎜ ⎟⎝ ⎠⎪ ⎪⎩ ⎭

= HH

Linear PrecodingLinear ZF precoding (channel inversion)Linear ZF precoding (channel inversion)

†

*E

γ

⎡ ⎤

= → = +P H r s n)1 (

1 1 1TrU Rn n

Hγ⎧ ⎫ ⎛ ⎞⎛ ⎞⎪ ⎪ ⎜ ⎟⎨ ⎬

×−

∑HHantenna 2

ESNR

n

ss

σγ

⎡ ⎤⎢ ⎥⎣ ⎦→ =

21

1 1 1Tr( )

H

iT TP P σγ ⎛ ⎞⎪ ⎪ ⎜ ⎟⎨ ⎬⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎜ ⎟⎪ ⎪ ⎝ ⎠⎩ ⎭ == = ∑H

HH

⎡ ⎤⎛ ⎞

♦ When the channel matrix H is ill-conditionedTh i SNR i d d d d th it i tl d d

2ZF ( ) E log 1 /U RC n n ρ γ⎡ ⎤⎛ ⎞⎢ ⎥⎜ ⎟

⎝ ⎠⎢ ⎥⎣ ⎦= × ⋅ +

The receive SNR is degraded and the capacity is consequently reduced.

Linear MMSE precoding (regularized channel inversion)♦ The channel matrix is regularized so that P becomes better-conditioned

IUI is minimized but not fully cancelled, on contrary to the ZF precoding!1

⎛ ⎞−


2( )

, ( ) /U R

H Hn TR Un n

n n Pα α σ⎛ ⎞⎜ ⎟⎜ ⎟⎝ ⎠

×= + = ×P H HH I

Tomlinson-Harashima Precoding (THP)IdeaIdea♦ Reduce the transmit power by limiting the range of the transmit signal

This is done using a non-linear modulus operation

The real modulo operation

max1( ) , with 2 | | /22

aM a a cτ⎢ ⎥ ⎛ ⎞⎢ ⎥ ⎜ ⎟= − + = + Δ

cmax is the constellation point with the largest amplitudeΔ is the spacing between any neighbor constellation points

max( ) , with 2 | | /22

M a a cττ⎢ ⎥ ⎜ ⎟⎢ ⎥ ⎝ ⎠⎣ ⎦+ + Δ

Δ is the spacing between any neighbor constellation points

s a( )M a rx s

( ) di ( ) 1/di ( )H QR B I R R G R


, ( ) diag( ), 1/diag( )= − = − =H QR B I R R G R

Linear Precoding vs. THPSimulation resultsSimulation results,♦ nT = 4, nR = 1, nU = 4, QPSK modulation, perfect CSI at BS

100

10-1

10Linear MMSELinear ZFTHP (MMSE)

10-2

BE

R

10-3

B

0 5 10 15 20 2510

-4


0 5 10 15 20 25SNR (dB)

Vector Perturbation with Linear PrecodingLinear version of the THPLinear version of the THP♦ The problem simplifies to perturbing the data vector with the scaled integer

vector t such that the overall transmit power is reduced.

sx

%s

%s %s x


Vector Perturbation with Linear PrecodingImproving the THPImproving the THP♦ THP is equivalent to QRD-based SIC where the best candidate at each

encoding level not optimum perturbation vector (power is minimized)♦ Further reduction in the transmit power is achieved by optimizing the perturbing♦ Further reduction in the transmit power is achieved by optimizing the perturbing

vector t.

♦ Assumptions♦ AssumptionsnR = 1 and nT = nU

The system is transformed into the real n-Euclidian space (n = 2nT)

The search is then simplified to find s ch that the transmit po er is

real( ) real( ) imag( ) real( ) real( )imag( ) imag( ) real( ) imag( ) imag( )

⎡ ⎤ ⎡ ⎤ ⎡ ⎤ ⎡ ⎤⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥⎣ ⎦ ⎣ ⎦ ⎣ ⎦ ⎣ ⎦

−= + → = +r H H x nr Hx n r H H x x

τ= +s s t%The search is then simplified to find such that the transmit power is minimized, that is

τ= +s s t

1

† ZF

MMSEH H α

⎧⎪⎪⎨ ⎛ ⎞⎪ ⎜ ⎟⎪ ⎝ ⎠

−=+

HPH HH I

2argmin ( )

nZτ

⎛ ⎞⎜ ⎟⎜ ⎟⎜ ⎟

= +t

t P s t

Let P decomposed into Q and L (lower triangular)11Korea University of Technology and Education (KUT)

⎜ ⎟⎪ ⎝ ⎠⎩

nZ ⎜ ⎟⎝ ⎠∈t

Sphere EncoderIdeaIdea♦ Restrict the search inside a hyper-sphere

RootAccumulative

metric22i d

⎧ ⎫⎪ ⎪⎪ ⎪⎛ ⎞⎨ ⎬⎜ ⎟+ ≤t L t

Advantages

0.1 0.70.5

Visited node

Peturbed vector

2

Zargmin .

ndτ⎪ ⎪⎪ ⎪⎛ ⎞

⎨ ⎬⎜ ⎟⎝ ⎠⎪ ⎪

⎪ ⎪⎩ ⎭∈

= + ≤t

t L s t

♦ Optimum performance with low average complexity

Drawbacks

2.31.56.1 0.71.10.3

0 92 10 6Unvisited

NodeDrawbacks♦ High worst-case complexity♦ Sequential nature

Limits efficient hardware implementation

0.92.10.6 Node

time

1n ii T=∑

Limits efficient hardware implementation

♦ User-dependent latencyIUI is removed using block diagonalization

UE1

UE2

UE3IUI is removed using block diagonalizationThen, the latency is the worst case among users.


UE3

QRD-M EncoderIdeaIdea♦ Retain the best M candidates

at each encoding level.Advantages♦ Quasi-optimal performance♦ Fixed complexity and latency

Drawbacks♦ High complexity for large search trees R

2( 1)T n T+ −

♦ High complexity for large search trees♦ Sequential nature

Root

0.1 0.70.5

2.31.56.1 0.71.10.3 2.10.91.4


0.92.10.6 1.11.71.9 1.51.82.5

Fixed-complexity Sphere Encoder (FSE)Two stage searchTwo-stage search♦ Full Expansion

At the first p tree search levels, the retained branches are expanded to allpossible nodes and all the resulting branches are retained for the next levelpossible nodes, and all the resulting branches are retained for the next level.

♦ Single ExpansionAll retained branches in the precedent level are independently expanded to all possible nodes The best candidate is retained for next levelspossible nodes. The best candidate is retained for next levels.

Advantages♦ Fixed complexity and latency

Root

♦ Fixed complexity and latency♦ Parallel tree-search method

Efficient HW implementation♦ Achieves the optimum diversity

0.1 0.70.5Peturbed

vector

nT

♦ Achieves the optimum diversity

Drawback

2.31.56.1 0.71.10.3 2.10.91.4

0.92.10.62.2 1.51.82.51.71.9

UnvisitedNode

♦ Degradation in the performance


Parallel QRD-M EncoderGoalGoal♦ Achieve a tradeoff between encoding throughput and achieved performance

Faster than QRDM-E but slower than FSEO t f FSE d f l t QRDM EOutperforms FSE and performs close to QRDM-E

Step I: The set of candidates for t is divided into G disjoint subsets, , for

G

i i jA D D D i j= ∩ =∅ ≠UStep II: ♦ The search tree is divided into G partial vector perturbation processes (PVP)♦ In the i-th PVP

1i i j

i =U

♦ In the i th PVP, The candidates for t1 are drawn from DiThe candidates for t2 ~ tK are drawn from the full set AFull-expansion: At the first p tree search levels tall hypotheses are retainedFull expansion: At the first p tree search levels, tall hypotheses are retained.Select best M/G: In the remaining levels, the best M/G candidates at each PVP are retained for next level.

Step III:Step III:♦ Select the best perturbed vector by the G PVPs


Parallel QRD-M EncoderExamples of the PQRDM EExamples of the PQRDM-E♦ p = 1 and p = 2, G = 2

0root root

1 42 3

0VP

level

1

0VP

level

11 2

1 3 12 branches are retained at each

l l22

1

21 2 1 2

43

level

33 4 31 2 21

32 432

partial VP #1 partial VP #24

partial VP #1 partial VP #222 1 2


p p partial VP #1 partial VP #2

Simulation ResultsParametersParameters♦ p = 1, nT = nU = 4, QPSK modulation, perfect CSI at transmitter

100

10-1

10Linear MMSETHP, T = 5FSE-p1, T = 7PQRDME-p1, T = 7, G = 4

10-2

ER

p , ,PQRDME-p1, T = 7, G = 2QRDME, T = 8

-4

10-3

B

0 5 10 15 20 25 30

104


0 5 10 15 20 25 30SNR (dB)

Simulation ResultsParametersParameters♦ p = 2, nT = nU = 4, QPSK modulation, perfect CSI at transmitter


Simulation ResultsParametersParameters♦ p = 2, nT = nU = 4, QPSK modulation♦ Imperfect CSI at transmitter (Quantized version of it)

Ll d M ti ti (B bit f l d B bit i i t 2B)Lloyd-Max quantization: (B bits for real and B bits imaginary parts 2B)Phase quantization: amplitude is known at transmitter, only phase is quantized

100

100

QRDM E P QRDM E ( 2)

10-1

2

10-1

B 3

QRDM-E vs. P-QRDM-E (p = 2)

10-3

10-2

BE

R

10-3

10-2

BE

R

B = 3

10-4 PQRDME-p2, B = 4

PQRDME-p2, B = 5PQRDME-p2, B = 6

10-4

B = 4

B 6


0 10 20 30SNR (dB)

PQRDME-p2, perfect

0 5 10 15 20 25 30SNR (dB)

B = 6

Simulation ResultsFinal comparisonFinal comparison♦ Probability of increasing the transmit power using VP (possible?)


ReferencesPapersPapers♦ M. Costa, Writing on dirty paper. IEEE Trans. on Information Theory, vol. 29, 1983, pp.

439-441.♦ M. Tomlinson, New automatic equalizer employing modulo arithmetic. Electronics Letters,

vol 7 1971 138 139vol. 7, 1971, 138-139.♦ H. Harashima and H. Miyakawa, Matched-transmission technique for channels with inter-

symbol interference. IEEE Trans. on Communications, vol. 20, no. 4, 1972, pp. 774-780.♦ C. Peel, B. Hochwald, and L. Swindlehurst, A vector-perturbation technique for near-

Ccapacity multiantenna multiuser communication - Part I: Channel inversion and regularization. IEEE Trans. on Communications, vol. 53, no. 1, 2005, pp.195-202.

♦ Hochwald, B., Peel, C., & Swindlehurst, L., A vector-perturbation technique for near-capacity multi-antenna multiuser communication - Part II: Perturbation. IEEE Trans. on Communications, vol. 53, no. 3, 2005, pp. 537-544.

♦ Zhang, J. Z., & Kim, K.J. (2005). Near-capacity MIMO multiuser precoding with QRD-M algorithm. In Proc. of IEEE ACSSC, 2005, pp. 1498-1502.

♦ M. Mohaisen et al., Fixed-complexity vector perturbation with block diagonalization for , p y p gMU-MIMO systems. In Proc. IEEE MICC, 2009, pp. 238-243.

♦ M. Mohaisen et al., Parallel QRD-M encoder for decentralized multi-user MIMO systems, in Proc. IEEE ICC, 2011, pp. 1-5.

♦ M Mohaisen A Mohaisen and M Debbah Parallel QRD-M encoder for multi-user MIMO♦ M. Mohaisen, A. Mohaisen, and M. Debbah, Parallel QRD M encoder for multi user MIMO systems, submitted in Nov. 2011.


SummaryIntroduced multi user MIMOIntroduced multi-user MIMO

Introduced idea of the dirty paper coding

Introduced linear precoding and THP

Introduced several vector perturbation techniques


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