Transcript MIMO MULTIUSER schemes for downlink transmissions:

MIMO MULTIUSER schemes for downlink
transmissions: theoretic bounds
and practical techniques
Federico Boccardi
Bell Laboratories
Paris, 29/3/2007
(joint work with Howard Huang)
Outline
- An introduction to SDMA techniques.
- The capacity region of the MIMO-BC and the optimal DPC scheme.
- Suboptimal schemes, the single receive antenna case.
- Extension to multiple receive antennas.
- Imperfect channel state information at the transmitter side.
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Focus of the presentation
Downlink of a narrowband packet data system
 Why downlink? Uplink of a cellular network can be handled using multiantenna
multiuser detection techniques.
 Why narrowband only? Most principles can be extended to multiband (OFDM)
systems.
 Why packet data? Next-generation systems will be predominately packet (not
circuit) data.
Base station
Terminals
User 1
User 1 data stream
User K data stream
Transmitter
processing
User K
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SINGLE USER vs MULTIUSER MIMO
Transmission
Primary benefit
technique
Time-duplexed
Improved
transmit
link performance
diversity
Time-duplexed
Higher
spatial
peak rate
multiplexing
Higher
SDMA:
system
Sectorization or
throughput
Precoding
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SDMA options
Sectorization
 Use physical reflectors behind each
antenna.
 Performance limited by intersector
User 1
u1
u2
User 2
interference.
Precoding
 The signal is
weighted/perturbed/successive
encoded at the transmit side.
 Linear precoders (beamformers)
create beams that focus energy for
u1
u2
Beam 1
User 1
Beam 2
User 2
each user by weighting the phase and
amplitude of the antennas.
 Performance limited by interbeam
interference.
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System model
 A narrowband MIMO downlink with M antennas at the transmitter and K receivers with
N antennas each can be modelled as MIMO Gaussian broadcast channel.
 The received signal for the kth user is given by
y k  Hk x  n k ,
hmk ~ CN (0,1)
 Under a sum-power constraint (SPC) the transmit signal is subject to the following
constraint
E[tr (x H x)]  P
 Under a per-antenna-power constraint (PAPC) the transmit signal is subject to the
following constraint
E[| xm |2 ]  Pm , m  1,, M
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The capacity of the MIMO-GBC and the Dirty Paper Coding (DPC) region
Dirty paper coding (DPC) [C83] is a known-interference cancellation technique for reducing
interference in the scalar 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 by incorporating beamforming.
 The MIMO BC capacity region is equivalent to the MIMO dirty paper coding (DPC) region [WSS06].
 Under perfect channel state information at both transmitter and receiver side, TDMA is
suboptimal.
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Suboptimal linear and non-linear precoding schemes
 Linear precoding
General expression:
x  G(S )u, G(S )  C M |S|
where S is the subset of users for a given channel realization.
 Non linear precoding
- Vector Precoding (VP): A data-dependent perturbation vector is used after the linear precoding
stage
x
G(S )(u  λ )

λ  arg min || G( S )(u  λ ' ) ||2
λ 'Ζ [ j ]|S|
- Tomlinson-Harashima and QR decomposition: Part of the interference is eliminated by using a
QR decomposition of the channel; the other part is eliminate by using the Tomlinson-Harashima
precoder for each subchannel. For the k-th streams:
xk  uk  d k  sk   ,   arg min || uk  d k  sk   ' ||2
 'Ζ [ j ]
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Linear precoding
Sectorization via fixed beamforming
 Fixed beams + correlated antennas.
 Create virtual sectors using fixed beams.
 Turn on all beams simultaneously for increased throughput.
 Turn on beams individually for increased range and coverage. [SH04]
User dependent beamforming
 User-specific beams + uncorrelated antennas.
 Transmitter uses CSI to form simultaneous beams to multiple users.
 Beams are designed so that, under ideal CSI knowledge, users receive no
interbeam interference.
 Can be shown to achieve optimum asymptotic capacity scaling. [YG06]
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ZF linear precoding with user selection
 For a fixed subset of users the general ZF with per-antenna power constraint problem
can be formulated as
R ( S )  max
|S |
vk , k 1,...,| S |

k 1
k
log(1 vk )
subject t o vk  0, k  1,  , | S |
beamforming coefficients
|S|
and
| g
k 1
mk
scheduling coefficients
|2 vk  Pm , m  1,  , M
power allocation
 This is a convex constrained optimization problem and in general can be solved by using
an interior point method. For the particular case of sum-power constraint the optimum
power allocation is given by the so-called waterfilling power allocation.
 An external optimization has to be used for the choice of the transmitting user subset
max R ( S )
S 1,, K 
 The optimal solution requires a brute force search over all possible sets S of users. A
practical greedy algorithm can be used. [YG06, BH06]
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SDMA for single antenna receivers – full CSI
cmp. between linear precoders
linear vs. non-linear precoders
ZF with greedy user selection gives good performance with low complexity! [BTC06]
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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 waterfilling 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 [BH07].
A
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B
C
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Etc…
Block diagonalization based algorithms
 The BD algorithm [SSH04,VVH03] is a generalization of the ZF precoder for receivers with
multiple antennas. A precoding matrix is used in order to block diagonalize the channel.
 Some improvements are proposed in [S06,W05,P04].
 The problem of block diagonalization is that the choice of the active eigenmodes belonging
to different users can not be optimized.
 The multiuser eigenmode transmission (MET) [BH07] technique tries to solve this problem.
-The following equivalent channel is considered
Hk  WkH ( Ek )Hk
where WkH ( Ek ) is a submatrix of Wk whose columns correspond to the selected
eigenmodes of user k, according to the SVD
Hk  Wk Σk Vk
H
- H k is |Ek| x M, where Ek is the set of selected eigenmodes.
-How do we choose the set of users and eigenmodes?
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Choosing users and eigenmodes for MET
 For a given transmission interval, we need to determine the set T of users and
eigenmodes to allocate so that the weigheted sum rate performance metric R(T) is
maximized:
QoS weights.
max R(T )  max max   j log(1   j 2v j )
T
T
vj
jT
v j  0, j  T
subject to 
 F (v j )  P
Power allocation, function
precoding matrix and T
of
MET
 Given M transmit antennas and K users, each with N antennas (assume N<M), there are
up to KN eigenmodes to choose from, but the base can only provide M. Finding the
optimum set requires a brute-force search over all possible allocation of 1,2,…,M
eigenmodes.
The following greedy algorithm is proposed (based on [DS05]) algorithm works in a greedy
manner and chooses up to M modes for transmission.
1. For a given set of eigenmodes, find the eigenmode among the unallocated ones that
maximizes the metric.
2. If the metric is higher with the new eigenmode, keep it and goto step 1. Otherwise,
exit.
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Average sum rate performance, fixed SNR
M = 4, K = 20, N = 4
 MET-SPC is within 2dB of
optimum DPC
 Even under the more
restrictive PAPC,
MET-PAPC outperforms
BD-RAS-SPC and
BD-GUS-PSC.
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Allocation of eigenmodes for each user under MET
M = 4 or 12, K = 20, N = 4
For M = 4 and large number of
users, scheduler chooses to
transmit to each user on its single
largest mode.
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For M = 12 and large number of
users, scheduler could choose to
transmit on smaller modes or
multiple modes for high SNR.
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SDMA schemes with partial CSI
SDMA with estimated or partial CSI:
 Jindal, Love, Honig, Heath, Caire, Cioffi, Goldsmith, Huang, Boccardi,
Trivellato.
Random beamforming techniques:
 Sharif, Hassibi, Viswanath, Tse, Laroia Papadias, Avidor.
Multiuser multiplexing with interference cancellation at the receiver:
 Heath, Andrews, Airy,…
Beamforming with fixed codebook:
 PU2RC: Samsung proposal for UMTS LTE, grid of beams: Alcatel, Ericsson.
Sectorization.
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ZF with partial CSI
 Each receiver sends to the transmitter a channel direction information (CDI) and a channel quality
information (CQI) [J06].
 Each receiver quantizes the “direction” of its channel vector to a unit norm vector, selected from a
quantization codebook formed by 2B unit norm column vectors
 The quantization criterion is minimum chordal distance
 Each user feeds back the channel quantization index to the transmitter, which requires B bits.
Moreover, each user is assumed to use an independently generated codebook.
 We assume a random vector quantization (RVQ) scheme, where the 2B quantization codewords are
independently chosen from an isotropic distribution on the unit sphere.
 RVQ gives a lower bound in terms of performance!
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Beamforming design
 The beamformer is calculated at the transmitter side by using the CDIs collected from the K users
where the channel of the selected users is given by
 The power allocated to each user is the same (no waterfilling!)
 The SINR at the kth receiver is given by
 The SINR cannot be exactly computated neither at the TX side nor at the RX side!
 A good estimation of the SINR is very important for the user selection task.
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CQI feedback/SINR estimation
A first approach is to consider no quantization error (perfect cancellation of the interference with ZF
precoding) and approximate the channel with its projection along the quantized direction
A second approach takes into account the quantization error by averaging with respect to the statistic of
the quantization codebooks (that affect the interference term)
A third approach considers a worse lower bound, but with only one CQI feedback
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ZF with partial CSI – user selection schemes
 Original user selection scheme [JGJ06]
ITERATE:
1) Identification of a quasi-orthogonal set of users
2) Selection of best candidate in the quasi-orthogonal set
 the following lower bound for the SINR estimation is used
 drawback: The parameter
is difficult to optimize. If it is chosen too small,
chances are that very few users are scheduled for transmission. If it is large,
the transmitter may select unwanted users that cause too much interference.
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ZF with partial CSI – user selection schemes
 Algorithm 1: It’s a simple extension of the scheme proposed by Dimic and Sidiropoulus for the
case of perfect CSI. The users are added successively one at a time, up to a maximum of Ntx if
the estimated achievable throughput is increased. Any of previous described CQI
feedbackmethods can be used to estimate the users’ SINRs.
 Algorithm 2: The drawback of Algorithm 1 is that, under imperfect CSI, it use SINR estimates that
are lower bounds of the real SINRs. The consequence of this is that it allocates too a few users.
Representing the possible sets of selected users as paths in a tree, a modified scheme just
consider more “candidates leaves”.
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Simulation results – narrow band, Rayleigh i.i.d. channel
Ntx=4, K=20
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Extension to multiple receive antennas (MET-MMSE)
An extension of the previous ZF with partial CSI scheme is represented by a modified

MET, where a CDI and CQI are fed back for each eigenmode.
For practical systems (ex.: 3 sectors with 4 transmit antennas each and receivers

with 2 antennas), even though multiple streams could be sent to a single user (and
these streams could be jointly detected), the dominant eigenmode it is almost always
the one scheduled for the transmission to a given user.
This effect is even more pronounced in the case of imperfect CSI at the transmitter

side, because weaker modes would be the most affected by the effect of the
quantization error.
For this reason, for the case of partial CSI at the transmitter side, we only consider

the case of dominant eigenmode transmission [BHT 07].
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MET-MMSE: brief description
Phase I
Processing at the transmit side
-Send common pilots to the K users in the systems
Processing at the kth receive side
-Calculate the SVD of single user channel matrix and select the Hermitian of
the left eigenvector associated to the dominant eigenmode as combining
vector.
-Calculate and send to the transmitter CDI and the CQI.
Phase II
Processing at the transmit side
-Use CQI and CDI to select a set of active users, and the precoding matrix
associated to this set.
-Send a dedicated pilot for each selected user, in order to estimate the
equivalent channel (channel+precoder).
Processing at the kth receive side
-MMSE detector.
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MET-MMSE, simulation results
-Rayleigh fading channel model
-sum-rate vs SNR
-M=4 transmit antennas
-K=20 users
-B=10 feedback bits
-baseline: Beamforming with fixed
precoding unitary matrix
(DFT), and MMSE receiver.
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-Rayleigh fading channel model
-sum-rate vs number of
feedback bits
-M=4 transmit antennas
-K=20 users
-SNR = 12dB
-baseline: Beamforming with fixed
precoding unitary matrix
(DFT), and MMSE receiver.
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-Rayleigh fading channel model
-sum-rate vs number of users
-M=4 transmit antennas
-SNR = 12 dB
-baseline: Beamforming with fixed
precoding unitary matrix
(DFT), and MMSE receiver.
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Thanks for your attention!
contacts:
Federico Boccardi
Wireless/Broadband Access Networks
Bell Labs Research
e-mail: [email protected]
Tel: +44-(0)1793-776670
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