U.S. patent application number 12/658105 was filed with the patent office on 2010-09-09 for differential codebook for a wireless network, mimo beamforming system using same, and method of reducing a quantization error in a mimo beamforming system for a wireless network using same.
Invention is credited to Qinghua Li, Xintian E. Lin, Yuan Zhu.
Application Number | 20100226357 12/658105 |
Document ID | / |
Family ID | 42678202 |
Filed Date | 2010-09-09 |
United States Patent
Application |
20100226357 |
Kind Code |
A1 |
Li; Qinghua ; et
al. |
September 9, 2010 |
Differential codebook for a wireless network, MIMO beamforming
system using same, and method of reducing a quantization error in a
MIMO beamforming system for a wireless network using same
Abstract
A differential codebook for a wireless network includes a
plurality of codewords and [e.sub.1 . . . e.sub.N.sub.s] G as a
center location of the plurality of codewords, where e.sub.k
represents a column vector comprising a plurality of rows including
a k-th row and in which an entry on the k-th row is one and entries
on each of the plurality of rows except for the k-th row are zero,
where G is any N.sub.s by N.sub.s unitary matrix including the
identity matrix, and where N.sub.s, represents a number of spatial
streams in the wireless network. At least two of the plurality of
codewords are symmetric about the center location.
Inventors: |
Li; Qinghua; (San Ramon,
CA) ; Lin; Xintian E.; (Palo Alto, CA) ; Zhu;
Yuan; (Beijing, CN) |
Correspondence
Address: |
INTEL CORPORATION;c/o CPA Global
P.O. BOX 52050
MINNEAPOLIS
MN
55402
US
|
Family ID: |
42678202 |
Appl. No.: |
12/658105 |
Filed: |
February 2, 2010 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
|
|
61156882 |
Mar 3, 2009 |
|
|
|
Current U.S.
Class: |
370/342 ;
375/260 |
Current CPC
Class: |
H04W 68/08 20130101;
H04B 7/0478 20130101; H04W 68/02 20130101; H04W 84/045
20130101 |
Class at
Publication: |
370/342 ;
375/260 |
International
Class: |
H04B 7/216 20060101
H04B007/216; H04K 1/10 20060101 H04K001/10 |
Claims
1. A differential codebook for a wireless network, the differential
codebook comprising: a plurality of codewords; and [e.sub.1 . . .
e.sub.N.sub.s] G as a center location of the plurality of
codewords, where e.sub.k represents a column vector comprising a
plurality of rows including a k-th row and in which an entry on the
k-th row is one and entries on each of the plurality of rows except
for the k-th row are zero, G is any N.sub.s by N.sub.s unitary
matrix including the identity matrix, and N.sub.s, represents a
number of spatial streams in the wireless network, wherein: at
least two of the plurality of codewords are symmetric about the
center location.
2. The differential codebook of claim 1 wherein: one of the
plurality of codewords is at the center location.
3. The differential codebook of claim 2 wherein: the plurality of
codewords are equidistant from the center location.
4. The differential codebook of claim 3 wherein: the plurality of
codewords are equidistant from each other.
5. The differential codebook of claim 1 wherein: no codeword is at
the center location.
6. The differential codebook of claim 5 wherein: the plurality of
codewords are equidistant from the center location.
7. The differential codebook of claim 6 wherein: the plurality of
codewords are equidistant from each other.
8. The differential codebook of claim 1 wherein: at least one entry
of each column of the codewords is a real number.
9. A MIMO beamforming system for a wireless network, the MIMO
beamforming system comprising: a plurality of differential
codebooks, each of which: has a codebook center and a plurality of
codewords; contains [e.sub.1 . . . e.sub.N.sub.s] G as a center
location of the plurality of codewords, where e.sub.k represents a
column vector comprising a plurality of rows including a k-th row
and in which an entry on the k-th row is one and entries on each of
the plurality of rows except for the k-th row are zero, G is any
N.sub.s by N.sub.s unitary matrix including the identity matrix,
and N.sub.s, represents a number of spatial streams in the wireless
network; and contains at least two codewords that are symmetric
about the center location and that are each separated from the
codebook center by a separation distance, wherein: the separation
distance for each one of the plurality of differential codebooks is
different from the separation distance for each other one of the
plurality of differential codebooks.
10. The MIMO beamforming system of claim 9 wherein: for each one of
the plurality of differential codebooks, one of the codewords is at
the codebook center.
11. The MIMO beamforming system of claim 10 wherein: for each one
of the plurality of differential codebooks, the plurality of
codewords are equidistant from each other.
12. The MIMO beamforming system of claim 9 wherein: no codeword is
at a center of any of the plurality of differential codebooks.
13. The MIMO beamforming system of claim 12 wherein: for each one
of the plurality of differential codebooks, the plurality of
codewords are equidistant from each other.
14. The MIMO beamforming system of claim 9 wherein: for each one of
the plurality of differential codebooks, at least one entry of each
column of the codewords is a real number.
15. A method of reducing a quantization error in a MIMO beamforming
system for a wireless network, the method comprising: defining a
differential codebook comprising: a codebook center and a plurality
of codewords; [e.sub.1 . . . e.sub.N.sub.s] G as a center location
of the plurality of codewords, where e.sub.k represents a column
vector comprising a plurality of rows including a k-th row and in
which an entry on the k-th row is one and entries on each of the
plurality of rows except for the k-th row are zero, G is any
N.sub.s by N.sub.s unitary matrix including the identity matrix,
and N.sub.s, represents a number of spatial streams in the wireless
network; and at least two codewords that are symmetric about the
center location and that are each separated from the codebook
center by a separation distance; and constraining the separation
distance to be less than a predetermined limit.
16. The method of claim 15 wherein: the predetermined limit is 20
degrees.
17. The method of claim 15 wherein: at least one entry of each
column of the codewords is a real number.
18. The method of claim 15 wherein: one of the codewords is at the
center location of the differential codebook; and the plurality of
codewords are equidistant from each other.
19. The method of claim 15 wherein: no codeword is at the center
location; and the plurality of codewords are equidistant from each
other.
Description
PRIORITY CLAIM
[0001] This application claims the benefit of priority under 35
U.S.C. .sctn.119(e) to U.S. Provisional Patent Application Ser. No.
61/156,882, filed Mar. 3, 2009, which is incorporated herein by
reference in its entirety.
FIELD OF THE INVENTION
[0002] The disclosed embodiments of the invention relate generally
to wireless communications, and relate more particularly to
beamforming in wireless communication networks.
BACKGROUND OF THE INVENTION
[0003] In closed-loop multiple input/multiple output (MIMO)
beamforming in a wireless network comprising a subscriber station
and a base station, the subscriber station (also referred to at
times herein as a mobile device or a receiver) quantizes the ideal
beamforming matrix and sends a quantization index corresponding to
the ideal beamforming matrix back to the base station (also
referred to at times herein as a transmitter). The base station
reconstructs the beamforming matrix according to the fed-back index
and conducts the beamforming. It is well known that beamforming
increases the link performance and system throughput.
[0004] The beamforming matrix can be fed back differentially. The
change between the current beamforming matrix and the previous one
can be quantized by a codebook and the corresponding quantization
index can be fed back. The quantization codebook determines the
beamforming accuracy and tracking capability.
[0005] Embodiments of the invention may find application in a
wireless local area network (WLAN) or a wireless Metropolitan area
network (WMAN) including a WiMAX (Worldwide Interoperability for
Microwave Access) network or the like. WiMAX technology is based on
the IEEE 802.16 family of standards, including IEEE 802.16e, IEEE
802.16m, and others.
BRIEF DESCRIPTION OF THE DRAWINGS
[0006] The disclosed embodiments will be better understood from a
reading of the following detailed description, taken in conjunction
with the accompanying figures in the drawings in which:
[0007] FIG. 1 is a stylized representation of a differential
codebook according to an embodiment of the invention;
[0008] FIGS. 2 and 3 are depictions of quantization codebooks that
make use of input symmetry according to embodiments of the
invention;
[0009] FIG. 4 is a concise representation of orthogonal matrices on
Grassmannian manifold according to an embodiment of the invention;
and
[0010] FIG. 5 is a flowchart illustrating a method of reducing a
quantization error in a MIMO beamforming system for a wireless
network according to an embodiment of the invention.
[0011] For simplicity and clarity of illustration, the drawing
figures illustrate the general manner of construction, and
descriptions and details of well-known features and techniques may
be omitted to avoid unnecessarily obscuring the discussion of the
described embodiments of the invention. Additionally, elements in
the drawing figures are not necessarily drawn to scale. For
example, the dimensions of some of the elements in the figures may
be exaggerated relative to other elements to help improve
understanding of embodiments of the present invention. The same
reference numerals in different figures denote the same elements,
while similar reference numerals may, but do not necessarily,
denote similar elements.
[0012] The terms "first," "second," "third," "fourth," and the like
in the description and in the claims, if any, are used for
distinguishing between similar elements and not necessarily for
describing a particular sequential or chronological order. It is to
be understood that the terms so used are interchangeable under
appropriate circumstances such that the embodiments of the
invention described herein are, for example, capable of operation
in sequences other than those illustrated or otherwise described
herein. Similarly, if a method is described herein as comprising a
series of steps, the order of such steps as presented herein is not
necessarily the only order in which such steps may be performed,
and certain of the stated steps may possibly be omitted and/or
certain other steps not described herein may possibly be added to
the method. Furthermore, the terms "comprise," "include," "have,"
and any variations thereof, are intended to cover a non-exclusive
inclusion, such that a process, method, article, or apparatus that
comprises a list of elements is not necessarily limited to those
elements, but may include other elements not expressly listed or
inherent to such process, method, article, or apparatus.
[0013] The terms "left," "right," "front," "back," "top," "bottom,"
"over," "under," and the like in the description and in the claims,
if any, are used for descriptive purposes and not necessarily for
describing permanent relative positions. It is to be understood
that the terms so used are interchangeable under appropriate
circumstances such that the embodiments of the invention described
herein are, for example, capable of operation in other orientations
than those illustrated or otherwise described herein. The term
"coupled," as used herein, is defined as directly or indirectly
connected in an electrical or non-electrical manner. Objects
described herein as being "adjacent to" each other may be in
physical contact with each other, in close proximity to each other,
or in the same general region or area as each other, as appropriate
for the context in which the phrase is used. Occurrences of the
phrase "in one embodiment" herein do not necessarily all refer to
the same embodiment.
DETAILED DESCRIPTION OF THE DRAWINGS
[0014] In many cases, the input to a quantization codebook is
symmetric about a center [e.sub.1 . . . e.sub.N.sub.s]. The
codebook may therefore be designed to make use of this symmetry,
such as by selecting codeword locations in order to reduce
quantization error. Accordingly, in at least one embodiment of the
invention, a differential codebook for a wireless network comprises
a plurality of codewords and [e.sub.1 . . . e.sub.N.sub.s] G as a
center location of the plurality of codewords, where e.sub.k
represents a column vector comprising a plurality of rows including
a k-th row and in which an entry on the k-th row is one and entries
on each of the plurality of rows except for the k-th row are zero,
where G is any N.sub.s by N.sub.s unitary matrix including the
identity matrix, and where N.sub.s represents a number of spatial
streams in the wireless network. At least two of the plurality of
codewords are symmetric about the center location. When G is the
identity matrix, [e.sub.1 . . . e.sub.N.sub.s] G=[e.sub.1 . . .
e.sub.N.sub.s].
[0015] Referring now to the drawings, FIG. 1 is a stylized
representation of a differential codebook 100 according to an
embodiment of the invention. The previous beamforming matrix
{circumflex over (V)}(t-1) is known at both the transmitter and the
receiver. The current beamforming matrix {circumflex over (V)}(t)
needs to be quantized differentially with respect to {circumflex
over (V)}(t-1). A quantization codebook is deployed around
{circumflex over (V)}(t-1) so that one of the codewords may be
close to {circumflex over (V)}(t). The index of the codeword
closest to {circumflex over (V)}(t) is fed back to the
transmitter.
[0016] A differential feedback scheme that may make use of
differential codebook 100 and the concepts presented above is
discussed in detail in U.S. application Ser. No. 12/584,142, which
is hereby incorporated by reference herein in its entirety. For
convenience, certain details of that exemplary differential
feedback scheme are reproduced below.
[0017] Differential at subscriber station:
D=[{circumflex over (V)}(t-1){circumflex over
(V)}.sup..perp.(t-1)].sup.HV(t). (1)
[0018] Quantization at subscriber station:
D ^ = arg max D i .di-elect cons. C d D H D i F . ( 2 )
##EQU00001##
[0019] Beamforming matrix reconstruction at base station:
{circumflex over (V)}(t)=[{circumflex over (V)}(t-1){circumflex
over (V)}.sup..perp.(t-1)]{circumflex over (D)}. (3)
[0020] Beamforming at base station:
y=H{circumflex over (V)}(t)s+n. (4)
[0021] In (1), the N.sub.t.times.N.sub.s, V(t) and {circumflex over
(V)}(t) are, respectively, the ideal and quantized beamforming
matrices for frame t, and {circumflex over (V)}.sup..perp.(t-1) is
N.sub.t.times.(N.sub.t-N.sub.s) and has the complementary columns
orthogonal to {circumflex over (V)}(t-1). N.sub.t is the number of
transmit antennas at the transmitter. In (2), the differential
codebook C.sub.d may be referred to as a polar cap. In (4), y is
the received vector, H is the channel matrix of size
N.sub.r.times.N.sub.t (where N.sub.r is the number of receive
antennas), {circumflex over (V)}(t) is the reconstructed
beamforming matrix (or vector) of size N.sub.t by N.sub.s, s is the
N.sub.s.times.1 data vector, and n is the complex additive white
Gaussian noise plus interference.
[0022] In practice, (1) and (2), which are illustrative and which
tend to degrade performance, are combined. The receiver maximizes
the beamformed channel capacity (or another performance metric) by
inserting each codeword into the expression of the testing
beamformed channel capacity as
D ^ = arg max D i .di-elect cons. C d det ( I + .gamma. N s D i H Q
( t - 1 ) H H H HQ ( t - 1 ) D i ) , ( 5 ) ##EQU00002##
where Q(t-1)=[{circumflex over (V)}(t-1) {circumflex over
(V)}.sup..perp.(t-1)]. Expression (5) may be simplified as
D ^ = arg max D i .di-elect cons. C d H [ V ^ ( t - 1 ) V ^ .perp.
( t - 1 ) ] H D i 2 . ##EQU00003##
[0023] Since the most probable outcome is for {circumflex over
(V)}(t) to remain the same as {circumflex over (V)}(t-1), the polar
cap C.sub.d should have the N.sub.t.times.N.sub.s
[ 1 1 ] = [ e 1 e N s ] ##EQU00004##
as a codeword so that {circumflex over (V)}(t) remains the same as
{circumflex over (V)}(t-1) after the reconstruction in (3).
Namely,
{circumflex over (V)}(t-1)=[{circumflex over (V)}(t-1){circumflex
over (V)}.sup..perp.(t-1)][e.sub.1 . . . e.sub.N.sub.s]. (6)
This allows the beamforming matrix to stay in the optimal point for
low mobility channels. (Without the [e.sub.1 . . . e.sub.N.sub.s]
codeword the codebook would tend to vibrate around the optimum
point.) Furthermore, the locations of {circumflex over (V)}(t) are
symmetric about {circumflex over (V)}(t-1). Therefore, besides the
center codeword [e.sub.1 . . . e.sub.N.sub.s], the e remaining
quantization codewords should be symmetric about [e.sub.1 . . .
e.sub.N.sub.s].
[0024] One simple configuration is as follows. The remaining
codewords have equal distance to the center. Note that all codeword
are on the appropriate (including but not limited to Grassmannian,
Stiefel) manifold. There are multiple definitions for the distance
between two codewords, e.g., chordal distance and average channel
capacity loss. For a low signal to noise ratio (SNR) region, the
distance may be
d(A,B)=trace(A.sup.HBB.sup.HA), (7)
where A and B are two N.sub.t.times.N.sub.s, codewords. For other
SNR regions, the distance may be
d ( A , B ) = det ( I + .gamma. N s A H BB H A ) , ( 8 )
##EQU00005##
where .gamma. is the signal to noise ratio or a predetermined
scalar. For simplicity, (8) may be simplified as
d(A,B)=det(A.sup.HBB.sup.HA) (9)
[0025] The realization that the input to the quantization codebook
is symmetric about a center [e.sub.1 . . . e.sub.N.sub.s] permits
the design of a codebook that makes use of this symmetry. FIGS. 2
and 3 depict two such designs according to embodiments of the
invention. Both of the depicted codebooks are designed to minimize
quantization error.
[0026] FIG. 2 depicts a differential codebook 200 according to an
embodiment of the invention. The center of differential codebook
200 is [e.sub.1 . . . e.sub.N.sub.s], but no codeword is located at
the center. In this case, all the codewords are set around a center
at [e.sub.1 . . . e.sub.N.sub.s]. This configuration may be
desirable for at least the following two reasons. First, the
distance between any two codewords may be greater than the distance
between any codeword and the center [e.sub.1 . . . e.sub.N.sub.s].
In other words, the quantization error is greater outside the
center than near the center. Therefore, no codeword is set on the
center for reducing the large quantization error outside the
center. Second, the beamforming matrix may tend to change
substantially between adjacent feedbacks in some situations.
Therefore, there is no need for the codeword [e.sub.1 . . .
e.sub.N.sub.s] that keeps the beamforming matrix at the same place.
The codewords have an equal distance d.sub.0 to the center. The
distance between any pair of codewords is d.sub.1. This structure
may be desirable when the number of codewords is not much greater
than the degree of freedom of differential codebook 200 and the
radius of the codebook is relatively large. For example, the
differential codebook for tracking a 4.times.2 beamforming matrix
has 7 degrees of freedom. If the distance between the codeword and
the codebook center is 20 degrees and the number of codewords is 8,
then differential codebook 200 may be desirable.
[0027] FIG. 3 depicts a differential codebook 300 according to an
embodiment of the invention. Unlike differential codebook 200,
differential codebook 300 has a center codeword. The distance from
the center codeword to the other codewords is d.sub.0. The
non-center codewords are each equidistant from each other, having
separation distance d.sub.1, as illustrated.
[0028] The wireless network may define several differential
codebooks with different sizes of d.sub.0. The smaller d.sub.0, the
smaller the quantization error. Thus, in one embodiment, as further
discussed below, a method of reducing a quantization error in a
MIMO beamforming system comprises minimizing d.sub.0, or in other
words, constraining d.sub.0 to be less than some predetermined
limit. However, for small d.sub.0, the feedback may not be able to
track the fast variation of a beamforming matrix that may vary more
than d.sub.0 between two adjacent feedbacks. On the other hand,
large d.sub.0 tracks the channel variation well, but at the cost of
greater quantization error.
[0029] In reality, the base station may select one of the
differential codebooks according to, for example, its antenna
configuration (or correlation) and the mobile speed. The index of
the selected codebook may then be sent to the mobile station.
Alternatively, the mobile station may select one of the
differential codebooks based on, for example, the correlation (or
variation) of the ideal beamforming matrix. For example, the mobile
station may estimate the channel matrices from the mid-ambles and
compute the ideal beamforming matrices. The variations of the
beamforming matrix are also computed. Based on the variations, the
mobile station selects one differential codebook and sends the
corresponding codebook index to the base station.
[0030] Accordingly, certain embodiments of the invention involve a
MIMO beamforming system for a wireless network that comprises a
plurality of differential codebooks, each of which are similar to
the differential codebook that was described earlier herein, i.e.,
each of which (among other characteristics) has a plurality of
codewords and contains [e.sub.1 . . . e.sub.N.sub.s] G as a center
location of the plurality of codewords, as has been described. Each
differential codebook further contains additional codewords that
are symmetric about the center location and that are each separated
from the codebook center by a separation distance, as has also been
described. Each differential codebook has its own unique separation
distance. In other words, the separation distance for each one of
the plurality of differential codebooks is different from the
separation distance for each other one of the plurality of
differential codebooks. In certain embodiments, for each one of the
plurality of differential codebooks the additional codewords are
equidistant from each other codeword in that codebook.
[0031] For complexity reduction, one entry of each column of each
codeword may be converted to a real number. For example, the first
row of the codeword can be converted to positive numbers or to zero
by subtracting the global phase of each column. For Grassmannian
codebook whose codewords are sub-planes or lines in the
Grassmannian manifold, the storage and computational complexity may
be further reduced. The codeword matrix may be converted to the one
that has a triangle of zeros at one of the four corners of the
codeword matrix, as illustrated in FIG. 4.
[0032] FIG. 5 is a flowchart illustrating a method 500 of reducing
a quantization error in a MIMO beamforming system for a wireless
network according to an embodiment of the invention.
[0033] A step 510 of method 500 is to define a differential
codebook comprising a codebook center, a plurality of codewords,
[e.sub.1 . . . e.sub.N.sub.s] G as a center location of the
plurality of codewords, and additional codewords that are symmetric
about the center location and that are each separated from the
codebook center by a separation distance. As an example, the
differential codebook can be similar to one or more of differential
codebooks 100, 200, and 300 that are shown, respectively, in FIGS.
1, 2, and 3.
[0034] A step 520 of method 500 is to constrain the separation
distance to be less than a predetermined limit. In one embodiment,
the predetermined limit can be 15 or 20 degrees that is the angle
between the center and any outer codeword.
[0035] Although the invention has been described with reference to
specific embodiments, it will be understood by those skilled in the
art that various changes may be made without departing from the
spirit or scope of the invention. Accordingly, the disclosure of
embodiments of the invention is intended to be illustrative of the
scope of the invention and is not intended to be limiting. It is
intended that the scope of the invention shall be limited only to
the extent required by the appended claims. For example, to one of
ordinary skill in the art, it will be readily apparent that the
differential codebook and the related structures and methods
discussed herein may be implemented in a variety of embodiments,
and that the foregoing discussion of certain of these embodiments
does not necessarily represent a complete description of all
possible embodiments.
[0036] Additionally, benefits, other advantages, and solutions to
problems have been described with regard to specific embodiments.
The benefits, advantages, solutions to problems, and any element or
elements that may cause any benefit, advantage, or solution to
occur or become more pronounced, however, are not to be construed
as critical, required, or essential features or elements of any or
all of the claims.
[0037] Moreover, embodiments and limitations disclosed herein are
not dedicated to the public under the doctrine of dedication if the
embodiments and/or limitations: (1) are not expressly claimed in
the claims; and (2) are or are potentially equivalents of express
elements and/or limitations in the claims under the doctrine of
equivalents.
* * * * *