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
 Introduction
 Precoding
 References

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
Transmitter
With Nt TX Antennas
Total TX Power = P
Receiver
With Nr RX Antennas
X nHXY +=














=
rttt
r
NNNN
r
N
hhh
Nhhh
hhh
H




21
22221
11211

5
Introduction
)1,0(~, CNhmkkkk nxHy +=
PtrE H
≤)]([ xx
Ntmm mPxE ,,1,]|[| 2
=≤

6
Introduction
RX
Diversity
TX
RX
Beam
forming
SDMA
T
X
RX
Interference
cancellation
RX
Spatial
MUX
TX
T
X
R
X
R
X
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

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Single User vs Multiuser MIMO
Improved
link performance
Time-duplexed
transmit
diversity
Time-duplexed
spatial
multiplexing Higher
peak rate
SDMA:
Beamforming
(Precoding) and Dirty-Paper coding
Higher
system
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 Layer
DIS-ADV:
• Radio Propagation and
Orthogonality of
channel response.
• Channel Reciprocity
• Pilot Contamination

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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

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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

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Outline
 Introduction
 Precoding
 References

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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

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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

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Outline
 Introduction
 Precoding
 References

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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.

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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.

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Outline
 Introduction
 Precoding
 References

Linear Precoding
18
ρ
))(( λuG
x
−
=
S
2
]['
||)')((||minarg
||
λuGλ
λ
−=
∈
S
S
jΖ
2
]['
||'||minarg, λαλλα
λ
−−+=−−+=
∈
kkk
jΖ
kkkk sdusdux
WuS =
γ
s
x =

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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)
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 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
HWCI
+
=

Block-Diagonalization (BD)
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 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.

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 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)
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Leakage Based Precoding
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 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
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 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
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 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
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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
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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

MMSE THP
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LINEAR REPRESENTATION OF
THE PRECODER

33
Outline
 Introduction
 Precoding
 References

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.

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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.

Precoding

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