IEEE C80216m-09_1345
Project
IEEE 802.16 Broadband Wireless Access Working Group <http://ieee802.org/16>
Title
Vector Quantization of the Transmit Correlation Matrix for Codebook Transformation
Date
Submitted
2009-07-06
Source(s)
Ron Porat, Simon Pun, Phil Orlik,
Ramesh Annavajjala, Zhifeng (Jeff) Tao
Voice:
E-mail: poratron@yahoo.com; {mpun, porlik,
annavajjala, tao}@merl.com
Mitsubishi Electric Research Labs
Toshiyuki Kuze
E-mail :
kuze.Toshiyuki@ah.MitsubishiElectric.co.jp
Mitsubishi Electric Corporation
5-1-1 Ofuna Kamakura, Kanagawa
2478501, JAPAN
Category: AWD comments
Re:
Abstract
Purpose
Notice
Release
Patent
Policy
*<http://standards.ieee.org/faqs/affiliationFAQ.
html>
This document describes a proposal to reduce the overhead associated with the feedback of the
transmit correlation matrix for transformation codebook MIMO operations.
To be discussed and adopted by 802.16m
This document does not represent the agreed views of the IEEE 802.16 Working Group or any of its subgroups. It
represents only the views of the participants listed in the “Source(s)” field above. It is offered as a basis for
discussion. It is not binding on the contributor(s), who reserve(s) the right to add, amend or withdraw material
contained herein.
The contributor grants a free, irrevocable license to the IEEE to incorporate material contained in this contribution,
and any modifications thereof, in the creation of an IEEE Standards publication; to copyright in the IEEE’s name
any IEEE Standards publication even though it may include portions of this contribution; and at the IEEE’s sole
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contributor also acknowledges and accepts that this contribution may be made public by IEEE 802.16.
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<http://standards.ieee.org/guides/bylaws/sect6-7.html#6> and
<http://standards.ieee.org/guides/opman/sect6.html#6.3>.
Further information is located at <http://standards.ieee.org/board/pat/pat-material.html> and
<http://standards.ieee.org/board/pat>.
Vector Quantization of the Transmit Correlation Matrix for Codebook Transformation
Ron Porat, Simon Pun, Phil Orlik
Mitsubishi Electric Research Labs
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1. Background
This contribution follows [1] where several vector quantization schemes of the transmit correlation matrix were
proposed and analyzed. The fundamental idea simply follows the logic behind general codebooks construction.
In this contribution a vector quantization scheme for the adaptive mode is proposed and shown to perform well
in MU-MIMO. The proposal is for 4-antenna BS. Extension to 8-antenna BS is straightforward in principle but
requires performance verification.
It is shown in the simulations that vector quantization provides comparable performance and sometimes even
better performance than element-wise quantization at one third to one half the feedback overhead.
Due to the reduced overhead, the same scheme can be utilized in other applications e.g. feedback of the
interference correlation matrix or feedback of a narrowband correlation matrix for improved CL-MIMO (SU or
MU) performance.
2. Proposed Scheme
The proposed scheme uses rank-1 codebooks to quantize the two strongest singular vectors of the transmit
correlation matrix R . Using the rank-2 codebook didn’t perform nearly as well in simulations due to reduced
accuracy.
Algorithm 1:
1. Find the strongest singular vector by maximizing 1  ciH Rci where ci is a rank-1 singular vector taken
from a codebook and 1 is the approximated strongest singular value of R . Denote by m the index of
the winning codeword.
2. Find the second strongest singular vector by maximizing 2  diH Rdi where d i is the orthogonalized
rank-1 singular vector with respect to cm . Orthogonalization is defined in section 15.3.7.2.6.6.3. Denote
by n the index of the winning codeword.
a. An explicit formula that can be used follows Gram-Schmidt di  (ci  (cmH ci )cm ) / || ci  (cmH ci )cm ||
3. Quantize the ratio 2 / 1 into a predefined set of thresholds. Denote by q that value.
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Alternatively, the metric in stage 2 can be replaced by minimization of the error between R and its vector
quantized estimation by following this algorithm 2:
1. As in algorithm1
2. Compute the orthogonalized singular vector d i , the singular vector 2 and the quantized ratio q as in
algorithm 1. Find the codeword that minimizes || R  1 (cm cmH  qdi diH ) ||2
The specific algorithm is left for vendor implementation.
The feedback includes the two indices of the winning singular vectors and the index of the quantized singular
value.
Codebook choice
The fundamental choice of codebook is somewhat different than the typical codeword construction. First, only
rank-1 is used and second, the adaptive mode is used for correlated arrays, hence codebooks that are designed to
perform better in correlated antennas are preferable.
In addition, it was found by simulations that the strongest singular vector has much more importance in
providing accurate vector quantization of R than the second. This is to be expected since correlated arrays
where the adaptive more is useful tend to have low ratio of the singular values 2 / 1 .
Hence, an optimal ‘bit allocation’ will require larger codebook for the first singular vector.
As is shown in [2], the 6bit rank-1 codebook chosen for 802.16m exhibits good performance in correlated and
uncorrelated and is therefore a good choice. The 4bit subset codebook didn’t perform sufficiently well in
simulations.
However, as can be seen in the plots below, a 4 bit steering vector (defined in the proposed text) performs very
well for ULA and is therefore proposed in order to educe computation and feedback overhead eve further.
The BS can send a message to the MS indicating that a closely spaced ULA is used and asking to use the
steering vector as the baseline codebook. Alternatively or additionally the MS can compute the vector quantized
R using the steering vector and if the MSE is below a threshold use that instead of the 802.16m codebook.
3. Simulation Assumptions
MUZF simulations based on rank-1 feedback are used. DL spectral efficiencies are calculated assuming an
MMSE receiver at the MS and assuming the interference is perfectly known.

DL channel – SCM Suburban Macro and Urban Macro (15 degrees angular spread).

Antenna Configuration –
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
4 lambda/2 spaced antennas [| | | |]

2 lambda/2 spaced cross-pols [XX]

DL Band BW – 4 PRB (assuming one precoder per band)

DL speed and feedback delay – 3kmph, 5mS

DL midamble estimation – perfect

User selection: 4 random users with exhaustive selection
Histograms of the ratio of the second to first singular values of the transmit correlation for the antenna
configurations and environments used is shown in the appendix. Note that the Suburban Macro environment
exhibits almost rank-1 R which is due to the narrow angular spread.
4. Simulation Results
The simulations use the 802.16m rank-1 codebook. The ratio of the second to first singular values was
quantized to the nearest point in [0.25, 0.5] and requires 1bit feedback.
A comparison is made relative to the 4bit subset of the rank-1 4-antenna codebook or 4bit 8-antenna codebook.
4.1 4Tx Results
In the legends:
 ‘6 bit’ uses the 6bit PMI
 ‘4bit+R’ uses the 4bit subset transformed by the unquantized R,
 ‘4bit+Quantized R’ uses 16m element wise quantization (28 bits),
 ‘4bit +VQ(6+6+1)’ uses vector quantization of R using the 6bit 16m rank-1 PMI,
 ‘4bit+(4+4+1)’ uses vector quantization of R using a steering vector (defined in the proposed text) and
similar to the 8-antenna rank-1 codebook
 ‘Perfect SV’ uses the strongest unquantized singular vector of the average narrowband transmit
correlation matrix.
The poor performance seen in Suburban Macro of the element wise quantization of R can be attributed to
figure 3 in [1] where it is shown that the MSE of this method is highest for rank-1 R .
On the other hand, it can be seen that in this scenario and antenna configuration, a 4bit steering vector performs
slightly better while reducing the feedback overhead.
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4.2 8Tx Results
In the legends:




‘4bit+R’ uses the 4bit subset transformed by the unquantized R,
‘4bit+Quantized R’ uses 16m element wise quantization for 8Tx (120 bits),
‘4bit +VQ(4+4+1)’ uses vector quantization of R using the 4bit 16m rank-1 PMI,
‘Perfect SV’ uses the strongest unquantized singular vector of the average narrowband transmit
correlation matrix.
The first two plots show results for a closely spaced ULA using the 4bit rank-1 8Tx codebook to quantize R.
It can be seen that a similar performance to element by element quantization is achievable with just 9 total bits
saving 92.5% overhead.
The next plot for [XXXX] configuration requires better rank-1 codebooks to achieve closer to optimal
performance. Shown are



4bit+VQ(Perfect+4+1) – this dashed black line assumes that the strongest singular vector of R was
perfectly fed back and serves as an upper bound on the performance achieved with 4bit rank-1 8Tx 16m
codebook quantizing the second singular vector and 1bit quantization of the singular values.
4bit+VQ(4+2+2)+4+1) – this dashed red line uses a 4Tx steering vector applied to the co-polarized
antennas and a gain and phase offset between them quantized to two bits each
4bit+VQ(4+1+1)+4+1) – this dashed blue line uses a 4Tx steering vector applied to the co-polarized
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antennas and a gain and phase offset between them quantized to one bit each. Using this configuration,
a total of 11bits are required to quantize R with performance that exceeds that of 16m element wise
quantization. A savings of 91% is achieved.
The proposed rank-1 vector used to quantize the strongest singular vector of R is therefore
[r exp( j ) exp( j  (0 : 3) ) exp( j  (0 : 3) )]/ 4  4r 2 where it was assumed that the co-polarized antennas
occupy the first and second half of the singular vector.
The last plot for [XX XX] requires more bits for vector quantization since this configuration has the least
correlation out of all previous configurations.
As before, we can see that if the strongest singular vector of R is perfectly quantized, the performance is close
to optimal.
The codebook used is a combination of a two antenna steering vector common to all 4 groups of closely spaced
co-polarized antennas and the 6bit rank-1 4Tx codebook which is designed for good performance with
uncorrelated antennas.
Shown are:



4bit+VQ(Perfect+4+1) – this dashed black line assumes that the strongest singular vector of R was
perfectly fed back and serves as an upper bound on the performance achieved with 4bit rank-1 8Tx 16m
codebook quantizing the second singular vector and 1bit quantization of the singular values.
4bit+VQ(6+3)+4+1) – this dashed blue line uses a 2Tx 3bit steering vector and a 4Tx 6bit rank-1
codebookapplied to the co-polarized antennas and a gain and phase offset between them quantized to
two bits each
4bit+VQ(6+3)+(6+3)+1) – this dashed red line uses the same rank-1 precoder as before but applies it to
the second singular vector as well. This helps compensating for the performance loss from the
‘inaccurate’ quantization of the strongest singular vector. It can be seen that using this configuration,
performance similar to the element wise quantization can be achieved at 84% overhead savings.
The proposed rank-1 codebook is therefore of the structure:
[ M 4(1, i ) M 4(1, i ) exp( j) M 4(2, i) M 4(2, i) exp( j) M 4(3, i) M 4(3, i ) exp( j) M 4(4, i ) M 4(4, i ) exp( j)]
Where M4(j,i) is the j’th element of the i’th codeword of the 6bit 4Tx codebook and where the following
antenna numbering was assumed [ 1 X 3 2 X 4 5 X 7 6 X 8 ] .
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References
1. C802.16m-09/516r1 – “Reduced-Overhead Covariance Matrix Feedback”
2. C802.16m-09/588 –“ Performance Evaluation of Codebooks Proposed for IEEE 802.16m Amendment”
Appendix
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Proposed text
15.3.7.2.6.6.3 Adaptive codebook based feedback mode
Add at the end of the section:
The R matrix for 4-antenna BS can be vector quantized into its singular vectors and values. The two strongest
singular vectors and the ratio of the second to first singular values are fed back.
The singular vectors are quantized using the 6bit rank-1 codebooks as defined in section 15.3.7.2.6.6.2.2.1.
The ratio of singular values is quantized to the nearest element in [ 0.25 , 0.5 ].
The total feedback overhead is 13bits.
The BS can signal the MS to use a 4-bit steering vector based approach such that the feedback overhead
associated with the signaling of the two singular vectors and their ratio is reduced to 9bits.
The steering vector is defined as:
 1 
 e j sin(i ) 
svi  0.5   j 2 sin(i ) 
e

 j 3 sin(i ) 
e

i  (i  0.5)   / 24   / 3
i  1,...,16
The R matrix for 8-antenna BS can be vector quantized into its singular vectors and values. The two strongest
singular vectors and the ratio of the second to first singular values are fed back.
Different rank-1 codebooks are used to quantize R depending on the antenna configuration as follows:
1. ULA of  / 2 spaced 8 vertically polarized antennas [ | | | | | | | | ].
In this case the 8 antenna rank-1 codebook as defined in section (?) is used to quantized the two
strongest singular vectors
2.  / 2 spaced 4 cross polarized antennas [ XXXX ] or two widely spaced clusters of antenna
configuration 1.
In this case the strongest singular vector is quantized using a 6bit codebook. The precoder takes the form
[r exp( j ) svi ; svi ] / 4  4r 2 where:

svi is a 4bit 4Tx steering vector as defined above

r is quantized to one bit using the values [1/ 2
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  is quantized to one bit using the values [1 5]*pi/4
The second singular vector uses the 4bit 8Tx rank-1 codebook as before
3. Two widely spaced clusters of antenna configuration two closely spaced cross-pols (XX XX).
In this case both singular vectors are quantized using a 9bit codebook comprised of a 6bit rank-1 4Tx
codebook and a 3bit 2Tx steering vector.
The rank-1 codebook has the structure:
[ M 4(1, i ) M 4(1, i ) exp( j) M 4(2, i) M 4(2, i) exp( j) M 4(3, i) M 4(3, i ) exp( j) M 4(4, i ) M 4(4, i ) exp( j)]


M4(j,i) is the j’th element of the i’th codeword of the 6bit 4Tx codebook
   sin(i ) i  (i  0.5)   /12   / 3 i  1,...,8

The antenna numbering is [ 1 X 3 2 X 4
5
X 7 6X 8].
1
4