Precoding

1

PRECODING In Multi-User MIMO

Syed Khalid Hussain

Department of Electrical and Computer Engineering

2

Outline

Introduction Precoding Dirty-Paper coding Linear And Non-Linear Precoding Dirty-Paper coding In MU-MIMO References

3

Outline


4

• MIMO :

• Transmitting end as well as receiving end is equipped with multiple antennas .

• Space-time signal processing in which time is complemented with spatial dimension(due to the use of multiple spatially distributed antennas).

Introduction

TransmitterWith Nt TX AntennasTotal TX Power = P

ReceiverWith Nr RX Antennas

X nHXY

rttt

r

NNNN

r

N

hhh

Nhhhhhh

H

21

22221

11211

5

Introduction

)1,0(~, CNhmkkkk nxHy

PtrE H )]([ xx

N tmm mPxE ,,1,]|[| 2

6

Introduction

RX

Diversity

TX

RX

Beamforming SDMA

TX

RX

Interferencecancellation

RX

SpatialMUX

TXTX

RX

RX

TX TX

A MIMO system has 3 basic features:• Beam-forming (diversity

gain)• Diversity (diversity gain) • Spatial

multiplexing(increase data

rates) Coordination of

processing exist among all transmitters or receivers.

Turn multipath propagation into a benefit for the user

Improvement of many order of magnitude at no cost of extra spectrum is the success of MIMO.

7

Introduction

MU-MIMO :• When MIMO is used to

communicate with several antennas at the same time.

• No Coordination among the users.

• For Uplink , BS needs to separate received signals from all users.

• For DL , there always exist some interference among the users (MUI) as BS broadcast on the same channel.

Illustration of MU-MIMO DL

8

Single User vs Multiuser MIMO

Improvedlink

performance

Time-duplexedtransmit diversity

Time-duplexedspatial

multiplexingHigher

peak rate

SDMA:

Beamforming(Precoding) and Dirty-Paper coding

Highersystem

throughput

Transmission Technique

Primary Benefit ADV:

• Increased Data rate

• Enhanced Reliability

• Improved Energy Efficiency

• Reduced Interference

• Extensive use of Inexpensive Low-Power Component

• Simplification of Media Access Control LayerDIS-ADV:

• Radio Propagation and Orthogonality of channel response.

• Channel Reciprocity• Pilot Contamination

9

Introduction

System Configuration of MU-MIMO

In MU-MIMO , it is assumed that BS has CSI (in practice the channel estimation is impaired by Pilot contamination).

• CSI is helpful in achieving high SNR and in reducing interference.

• Methods for obtaining CSI is using Pilots or training symbols or via feedback of the receiver's channel estimate.

• In DL, there is always exist MUI.

• By using Multiuser Detection , it is possible to reduce MUI but it is too costly to use at the receiver.

• Ideally , MUI is mitigated by intelligent designing of the transmitted signal at BS considering the co-channel interference.

10

MU-MIMO Non-Degraded BC

Traditional Broadcast : TX sending same information to multiple RX.

MIMO Broadcast : Multiple antennas at BS sending information (same or different ) to multiple RX.

• Single antenna AWGN channel is degraded (channel matrix can be ordered according to channel strength).

• By using the superposition , the capacity region of degraded BC can be find.

• When single antenna upgraded to multiple antenna (MIMO BC),it looses it’s degradedness and capacity of this channel can not be find using superposition coding.

• a non-linear coding technique is used, known as Dirty Paper Coding[] (DPC_ first proposed by Costa in 1983).

• So in MIMO BC superposition coding or successive decoding is no longer a capacity achieving scheme.

• Duality between MIMO MAC and BC which can be used to achieve the capacity region of MIMO BC by knowing the capacity region of MAC channel

11

Outline


12

Precoding

By having CSI at AP/BS , AP know about MUI . Thus MUI can be mitigated by Intelligent Beamforming (Precoding) or the use of dirty paper codes.

Precoding :• The signal is weighted/perturbed/successive encoded at the

transmit side.• Linear precoders (beamformers) create beams that focus

energy for each user by weighting the phase and amplitude of the antennas.

• Performance limited by interbeam interference

1u

2u

Beam 1

Beam 2

User 1

User 2

13

Precoding

Precoding can be classified by amount of allowed MUI and Linearity

• Linear Precoding : Not complex but low performance

• Examples : Block-Diagonalization, Successive Optimization e.t.c.

• Non-Linear Precoding : complex but high performance

• Examples : Tomlinson-Harashima Precoding

14

Outline


15

Dirty Paper Coding

Dirty paper coding (DPC) is a known-interference cancellation technique for reducing interference in the scalar BC

(Degraded BC).

• Using coherent channel knowledge ( hk ,k = 1,…,K), users are sequentially encoded; for example, user 1 is encoded first, then user 2, up to user K. A given user experiences interference only from users encoded after it.

• DPC can be extended to the MIMO BC (Non Degraded BC) by incorporating beamforming.

• The MIMO BC capacity region is equivalent to the MIMO dirty paper coding (DPC) region.

16

Dirty Paper Coding

DPC is a technique for efficient transmission of digital data through a channel subjected to some interference known to the transmitter. The technique consists of precoding the data in order to cancel the effect caused by the interference.

The term 'dirty paper coding' comes from Max Costa[11], who imagined a paper which is partially covered with dirt that is indistinguishable from ink, the analogy is if the writer knows where the dirt is to start with, he can convey just as much information by writing on the paper as if it were clean, even though the reader does not know where the dirt is.

In this case the dirt is interference, the paper is the channel, the writer on the paper is the transmitter, and the reader is the receiver.

In information-theoretic terms, dirty-paper coding achieves the channel capacity, without a power penalty and without requiring the receiver to gain knowledge of the interference state.

17

Outline


Linear Precoding

18

))(( λuGx

S

2]['

||)')((||minarg||

λuGλλ

SSjΖ

2]['

||'||minarg,

kkkjΖ

kkkk sdusdux

WuS

sx

19

Linear precoding with multiple receive antennas – basic idea

In single-user MIMO, the number of independent streams is optimally found by using the SVD of channel. The power is optimally allocated to the different streams by using the water filling scheme.

In Multiuser MIMO, the different streams can be allocated to a given user or allocated between different users. We want to design a technique that optimally allocates the streams in order to maximize the sum-rate.A B C Etc…

Zero-Forcing Beamforming (ZF)

20

Zero-forcing (or Null-Steering) precoding : A method of spatial signal processing by which the multiple

antenna transmitter can null MUI. Regularized zero-forcing precoding is enhanced processing to consider the impact on a background noise and unknown user interference. ( beamforming for narrowband signals to compensate delays of received signals from a specific source at different elements of the antenna array).

Only add the weighted version of the signals with appropriate weight values in such a manner that frequency domain output of weighted sum produces a zero result.

In case of perfect CSI at AP, ZF-precoding can achieve almost the system capacity when the number of users is large.

On the other hand, the performance of ZF heavily depends on partial CSI accuracy.

Channel Inversion (CI)

21

HW CI

Regularized CI

22

Block-Diagonalization (BD)

23

CI is not practically an efficient solution since forcing closely spaced antennas of same user would require extra power when channels for these antennas are highly correlated.

Solution to this problem is Block-Diagonalization[1,3].

The BD algorithm is a generalization of the ZF precoder for receivers with multiple antennas. A precoding matrix is used in order to block diagonalize the channel. It can be used with partial or complete CSI.

Decomposes MU-MIMO DL channel into multiple parallel independent single user MIMO DL channels.

Signal of each user is preprocessed at TX using a precoding matrix that lies in the null space of all other user’s channel matrices. Thus nulling the MUI.

BD is attractive if the users are equipped with more than one antenna.

Zero MUI constraint can lead to a large capacity loss when the users subspaces significantly overlap.

24

Both BD and SO are suboptimal in performance but very simple to implement (allowing a trade-off) between complexity and performance.

BD impose a restriction that number of transmitting antennas should be greater than total number of receive antennas.

Involves computation of SVD of equivalent channel matrix (offers low computational cost .)

Block-Diagonalization (BD)

Successive Optimization (SO)

25

Leakage Based Precoding

26

Leakage refers to the amount of interference caused by a specific user on other users.

Maximizing the Signal To Leakage And Noise Ratio (SLNR) of all user simultaneously instead of zeroing out the interference.

Instead of trying to perfectly cancel out the interference at each user (as is with ZF) , leakage based precoding aims at minimizing the interference caused by a signal intended for some user on the remaining users.

Do not impose any restriction on the number of antennas.

On comparing with ZF , this scheme outperforms ZF method

Transmit Preprocessing Using Decomposition Approach

27

A transmit preprocessing technique [5] which decomposes a multiuser MIMO DL channel into multiple parallel independent single user MIMO DL channel.

Thus any technique for single user MIMO, such as VBLAST (Vertical Bell Lab Space Time , MLD or joint transmit and receive MIMO processing (e.g. SVD based technique) can be applied to parallel channel.

Increasing the number of transmitting antenna by one increases the number of spatial channels to each user by one.

MU-MIMO Decomposition

Non-Linear Precoding

28

THP was originally introduced as a non-linear transmitter equalization technique for SISO channel with ISI.

For MU-MIMO , THP precoding[8] pre-subtracts the previously precoded symbols intended for other users thus performing spatial pre-equalization.

This interference pre-subtraction at the transmitter is well-suited to BC channels because the decentralized nature of receiver prevents joint processing of the received signals.

Perfect CSI knowledge is necessary for THP. Perfect CSI enables the TX to precisely pre-subtract the

term that would interfere at the RX

Tomlinson-Harashima Precoding

29

At RX Decision Feedback Equalization (DFE matrix) is used (non-linear equalization technique) to overcome the effect of noise in MU-MIMO.Due to error propagation associated with DFE, a feedforward filter is also used at TX. Based on perfect CSI assumption at TX ,several THP schemes has been proposed FOR BC channels including ZF, MMSE etc.Avoided due to associated higher computational complexity.

TOMLINSON HARASHIMA PRECODING FOR MIMO CHANNELS

SO THP

30

BLCOK DIAGRAM OF S0 THP SYSTEM

The combination SO and THP [1] is used to improve the available subspace of different users and eliminate any residual MUI.

The algorithm comprises of first evaluating the equivalent channel matrix(which is Block Diagonal), then the reordering of users and in the end precoding with THP.

First a precoding matrix is defined successively for all users. The ordering of users in

which they are precoded using THP is the reverse of the order in which their precoding matrices are generated.

Modulo 2 is used at the TX and RX , since THP increases the transmit power.

MMSE THP

31

LINEAR REPRESENTATION OF THE PRECODER

Successive MMSE (SMMSE)

32

33

Outline


34

Dirty-Paper Coding

35

Duality Of MIMO BC Region To MIMO MAC Region

Since MIMO BC channel is non degraded channel, it’s capacity remains an unsolved problem.

In [9], they established a duality between the “Dirty paper” achievable region (the Caire-Shamai achievable region) for MIIMO BC channel and the capacity region of MIMO Multi Access channel, which is easy to compute.

Thus using duality greatly reduces computational complexity required for obtaining the DP achievable region for the MIMO BC.

The duality also allows previously known results for MIMO MAC to MIMO BC.

The DP achievable region achieves the sum rate (maximum capacity ) of the MIMO BC.

36

References

[1] Stankovic, Veljko, and Martin Haardt. "Multi-user MIMO downlink precoding for users with multiple antennas." Proc. of the 12-th Meeting of the Wireless World Research Forum (WWRF), Toronto, ON, Canada. Vol. 10. 2004.

[2] Spencer, Quentin H., and Martin Haardt. "Capacity and downlink transmission algorithms for a multi-user MIMO channel." Signals, Systems and Computers, 2002. Conference Record of the Thirty-Sixth Asilomar Conference on. Vol. 2. IEEE, 2002.

[3] Spencer, Quentin H., A. Lee Swindlehurst, and Martin Haardt. "Zero-forcing methods for downlink spatial multiplexing in multiuser MIMO channels." Signal Processing, IEEE Transactions on 52.2 (2004): 461-471.

[4] Li, Ye Geoffrey, and Gordon L. Stuber. Orthogonal frequency division multiplexing for wireless communications. Springer Science & Business Media, 2006.

[5] Choi, Lai-U., and Ross D. Murch. "A transmit preprocessing technique for multiuser MIMO systems using a decomposition approach." Wireless Communications, IEEE Transactions on 3.1 (2004): 20-24.

37

References

[6] Spencer, Quentin H., et al. "An introduction to the multi-user MIMO downlink."Communications Magazine, IEEE 42.10 (2004): 60-67.

[7] Joham, Michael, Johannes Brehmer, and Wolfgang Utschick. "MMSE approaches to multiuser spatio-temporal Tomlinson-Harashima precoding." ITG FACHBERICHT (2004): 387-394.

[8] Shenouda, Michael Botros, and Timothy N. Davidson. "Tomlinson-Harashima precoding for broadcast channels with uncertainty." Selected Areas in Communications, IEEE Journal on 25.7 (2007): 1380-1389.

[9] Vishwanath, Sriram, Nihar Jindal, and Andrea Goldsmith. "On the capacity of multiple input multiple output broadcast channels." Communications, 2002. ICC 2002. IEEE International Conference on. Vol. 3. IEEE, 2002.

[10] Jindal, Nihar, and Andrea Goldsmith. "Dirty-paper coding versus TDMA for MIMO broadcast channels." Information Theory, IEEE Transactions on 51.5 (2005): 1783-1794.

[11] Costa, Max HM. "Writing on dirty paper (corresp.)." Information Theory, IEEE Transactions on 29.3 (1983): 439-441.