Beamforming using base and differential codebooks

TECHNICAL FIELD

0001Embodiments of the present disclosure relate generally to wireless communication systems, and more particularly, to methods and apparatuses for beamforming using a base codebook and a differential codebook.

BACKGROUND

0002A mobile station in a closed-loop multi input and/or multi output (MIMO) system generally transmits channel state information to a base station over a feedback path. The channel state information is used to employ beamforming at the base station, to compensate for the current channel conditions. In some of the conventional systems, the mobile station transmits a channel covariance matrix to the base station, from which the base station determines a beamforming matrix that is used to employ beamforming at the base station. In some other conventional systems, a beamforming matrix is generated at the mobile station based on the channel conditions. The generated beamforming matrix is then provided to the base station as feedback. However, transmitting the channel covariance matrix and/or the beamforming matrix from the mobile station to the base station may consume relatively high bandwidth that might otherwise be available for data traffic.

0003<patcit id="pcit0001" dnum="US20070195974A1"><text>US 2007/0195974 A1</text></patcit> describes embodiments of a multiple-input multiple-output (MIMO) communication system and methods for beamforming using polar-cap codebooks. In some of the embodiments, beamforming is based on codewords of a polar-cap codebook which represents deviations in the channel with respect to codewords of a full-manifold codebook.

0004"<nplcit id="ncit0001" npl-type="b"><text>Codebook design for IEEE 802.16m MIMO Schemes; C80216m-08_1182r3", IEEE Draft, IEEE-SA, Piscataway, NJ USA, 12 September 2008, pages 1-14 </text></nplcit>describes a universal codebook for both high and low correlated channels, built on and backward compatible to the 802.16e codebook.

BRIEF DESCRIPTION OF THE DRAWINGS

0005Embodiments of the invention will be described by way of exemplary embodiments, but not limitations, illustrated in the accompanying drawings in which like references denote similar elements, and in which: <ul id="ul0001" list-style="none" compact="compact"><li><figref idref="f0001"><b>Fig. 1</b></figref> schematically illustrates a MIMO system;</li><li><figref idref="f0002"><b>Fig. 2</b></figref> illustrates an exemplary method for determination and quantization of a beamforming matrix;</li><li><figref idref="f0003"><b>Fig. 3</b></figref> illustrates an exemplary method for estimating a beamforming matrix based on feedback received from a mobile station; and</li><li><figref idref="f0004"><b>Fig. 4</b></figref> illustrates an example system capable of implementing a communication device, all in accordance with various embodiments of the present disclosure.</li></ul>

DETAILED DESCRIPTION

0006Illustrative embodiments of the invention include, but are not limited to, methods and apparatuses for generating and/or estimating a beamforming matrix using a base codebook and a differential codebook.

0007Various aspects of the illustrative embodiments will be described using terms commonly employed by those skilled in the art to convey the substance of their work to others skilled in the art. However, it will be apparent to those skilled in the art that alternate embodiments may be practiced with only some of the described aspects. For purposes of explanation, specific numbers, materials, and configurations are set forth in order to provide a thorough understanding of the illustrative embodiments. However, it will be apparent to one skilled in the art that alternate embodiments may be practiced without the specific details. In other instances, well-known features are omitted or simplified in order not to obscure the illustrative embodiments.

0008Further, various operations will be described as multiple discrete operations, in turn, in a manner that is most helpful in understanding the illustrative embodiments; however, the order of description should not be construed as to imply that these operations are necessarily order dependent. In particular, these operations need not be performed in the order of presentation.

0009The phrase "in some embodiments" is used repeatedly. The phrase generally does not refer to the same embodiments; however, it may. The terms "comprising," "having," and "including" are synonymous, unless the context dictates otherwise. The phrase "A and/or B" means (A), (B), or (A and B). The phrase "A/B" means (A), (B), or (A and B), similar to the phrase "A and/or B". The phrase "at least one of A, B and C" means (A), (B), (C), (A and B), (A and C), (B and C) or (A, B and C). The phrase "(A) B" means (B) or (A and B), that is, A is optional.

0010Although specific embodiments have been illustrated and described herein, it will be appreciated by those of ordinary skill in the art that a wide variety of alternate and/or equivalent implementations may be substituted for the specific embodiments shown and described, without departing from the scope of the embodiments of the invention. This application is intended to cover any adaptations or variations of the embodiments discussed herein. Therefore, it is manifestly intended that the embodiments of the invention be limited only by the claims.

0011For the purpose of this disclosure and unless otherwise mentioned, a conjugate transpose of an m by n matrix A with possibly complex entries is an n by m matrix, represented by A*, obtained by taking the transpose of the matrix A, and then taking the complex conjugate of each entry of the matrix formed by taking the transpose of the matrix A. For the purpose of this disclosure and unless otherwise mentioned, a unitary matrix is an n by n complex matrix B satisfying the condition (B*)B = B(B*) = I_n, where I_n is the identity matrix in n dimensions, and B* is the conjugate transpose of B. Thus, a matrix B is unitary if and only if B has an inverse, wherein the inverse of B is equal to the conjugate transpose of B. For the purpose of this disclosure and unless otherwise mentioned, two vectors are orthogonal if the two vectors are perpendicular to each other (e.g., the two vectors form a right angle, the dot product of the two vectors is 0). For the purpose of this disclosure and unless otherwise mentioned, a hermitian matrix C is a square matrix with possible complex entries, each of which is equal to its own conjugate transpose (e.g., the element in the i^th row and jth column of matrix C is equal to the complex conjugate of the element in the jth row and i^th column of matrix C, for all indices i and j). Thus, if a matrix C is a hermitian matrix, then C* = C. For the purpose of this disclosure and unless otherwise mentioned, for an m by n matrix M, a singular value decomposition of matrix M refers to a factorization of the form M = E A F*, where E is an m by m unitary matrix, A is a m by n diagonal matrix with nonnegative real numbers on its diagonal, and F* denotes the conjugate transpose of matrix F, where matrix F is an n by n unitary matrix.

0012Embodiments of the present disclosure may be used in wireless access networks that employ orthogonal frequency division multiple access (OFDMA) communications as used by multicarrier transmission schemes presented in, e.g., the Institute of Electrical and Electronics Engineers (IEEE) 802.16 - 2009, approved May 13, 2009, along with any amendments, updates, and/or revisions (e.g., 802.16m, which is presently at predraft stage), 3rd Generation Partnership Project (3GPP) long-term evolution (LTE) project, ultra mobile broadband (UMB) project (also referred to as "3GPP2"), etc. In other embodiments, communications may be compatible with additional/alternative communication standards and/or specifications.

0013<figref idref="f0001"><b>FIG. 1</b></figref> schematically illustrates a communication system <b>100,</b> in accordance with various embodiments of the present disclosure. In various embodiments, the communication system <b>100</b> includes a base station <b>104</b> that communicates with a mobile station <b>140</b> over wireless channel <b>130.</b> In various embodiments, the base station <b>104</b> and/or the mobile station <b>140</b> may be MIMO devices. In various embodiments, the communication system <b>100</b> may be a closed-loop system that employs beamforming to increase a signal to noise ratio (SNR) of signals transmitted by base station <b>104</b> to mobile station <b>140.</b>

0014In various embodiments, the base station <b>104</b> may transmit one or more data streams to the mobile station <b>140.</b> For example, <figref idref="f0001"><b>Fig. 1</b></figref> illustrates a data stream <b>S1</b> being transmitted by the base station <b>104</b> to the mobile station <b>140,</b> although in various other embodiments, any other suitable number of data streams may also be provided. Prior to transmission, the data stream <b>S1</b> may be appropriately weighted by one or more components of the base station <b>104</b> as discussed hereinafter.

0015In various embodiments, the base station <b>104</b> may include a beamformer module <b>112</b> to weight data signals (e.g., data signals of data stream <b>S1</b>) by a beamforming matrix. The term beamforming is used herein to describe the application of beamforming coefficients or weights to frequency-domain signals in the data stream(s), prior to transmission. In various embodiments, the beamforming coefficients or weights may be determined from the beamforming matrix.

0016Base station <b>104</b> may comprise a plurality of transmit antennas <b>108a, 108b, 108c</b> and <b>108d,</b> to transmit the weighted data stream. In <figref idref="f0001"><b>Fig. 1</b></figref><b>,</b> four transmit antennas are illustrated, although in various other embodiments, any other suitable number of transmit antennas may be included in the base station <b>104.</b>

0017The base station <b>104</b> may also include one or more receive antennas (e.g., receive antenna <b>110</b>) that may receive, among other information, feedback about the channel condition from the mobile station <b>140.</b>

0018In various embodiments, the base station <b>104</b> may also include a beamforming matrix estimation module <b>116,</b> which may be configured to estimate the beamforming matrix, based at least in part on feedback received from the mobile station <b>140.</b>

0019An order (e.g., number of rows and/or columns) of the beamforming matrix may be based on a number of data stream(s) transmitted by the base station <b>104</b> and a number of transmit antennas included in the base station <b>104.</b> In various embodiments, the beamforming matrix may be of order N_t by N_s, where N_t and N_s are the number of transmit antennas and the number of data stream(s), respectively, of the base station <b>104.</b> For example, in <figref idref="f0001"><b>Fig. 1</b></figref><b>,</b> N_t is 4 (as there are four transmit antennas <b>108a, 108b, 108c</b> and <b>108d</b>) and N_s is 1 (as there is one data stream <b>S1</b>), and hence, a beamforming matrix B is a 4 by 1 vector. In various embodiments, the signal transmitted by the base station <b>104</b> may be represented by <maths id="math0001" num="Equation (1)"><math display="block"><mi>x</mi><mo>=</mo><mi mathvariant="normal">B</mi><mo>.</mo><mi mathvariant="normal">S</mi><mo>,</mo></math><img file="EP3145142B1_D0001.tif" /></maths> where S represents N_s data stream(s) (e.g., data stream <b>S1</b> of <figref idref="f0001"><b>Fig. 1</b></figref>) of the base station <b>104,</b> B is the N_t by N_s beamforming matrix determined by the beamforming matrix estimation module <b>116,</b> and <i>x</i> is an N_t by 1 vector corresponding to the weighted data signals transmitted by the four transmit antennas <b>108a, 108b, 108c</b> and <b>108d.</b>

0020In various embodiments, the base station <b>104</b> may include at least as many transmit antennas as the number of data stream(s) being transmitted by base station <b>104,</b> although the scope of this disclosure may not be limited in this respect. In these embodiments, N_t is at least as high as N_s.

0021Referring again to <figref idref="f0001"><b>Fig. 1</b></figref><b>,</b> in various embodiments, the mobile station <b>140</b> may include one or more receive antennas, e.g., receive antennas <b>144a</b> and <b>144b,</b> configured to receive signals transmitted through channel <b>130</b> by the base station <b>104.</b> In <figref idref="f0001"><b>Fig. 1</b></figref><b>,</b> two receive antennas are illustrated, although in various other embodiments, any other suitable number of receive antennas may be used. In various embodiments, the mobile station <b>140</b> may include at least as many receive antennas as the number of data stream(s) being transmitted by base station <b>104,</b> although the scope of this disclosure may not be limited in this respect.

0022In various embodiments, the mobile station <b>140</b> may also include a channel estimation module <b>148</b> to estimate channel conditions of the channel <b>130,</b> based at least in part on signals received from one or more of the transmit antennas <b>108a,</b> ..., <b>108d.</b> For example, the channel estimation module <b>148</b> may determine a channel matrix H which describes the current state of channel <b>130.</b> In various embodiments, the channel matrix H may be indicative of conditions of sub-channels between each of the transmit antennas <b>108a, ..., 108d</b> and each of the receive antennas <b>144a</b> and <b>144b.</b> In various embodiments, the channel matrix H may be of the order N_r by N_t, where N_r may be a number of receive antennas in the mobile station <b>140.</b><figref idref="f0001"><b>Fig. 1</b></figref> illustrates four transmit antennas <b>108a,</b> ..., <b>108d</b> (i.e., N_t = 4) of the base station <b>104</b> and two receive antennas <b>144a</b> and <b>144b</b> (i.e., N_r = 2) of the mobile station <b>140,</b> and accordingly, the channel matrix H may be a 2 by 4 matrix for the MIMO system <b>100.</b>

0023The channel estimation module <b>148</b> may also construct a channel covariance matrix R from the channel matrix H. For example, the channel covariance matrix R may be equal to <maths id="math0002" num="Equation (2)"><math display="block"><mi mathvariant="normal">R</mi><mo>=</mo><mi>E</mi><mfenced open="[" close="]" separators=""><mfenced><msup><mi mathvariant="normal">H</mi><mo>∗</mo></msup></mfenced><mi mathvariant="normal">H</mi></mfenced><mo>,</mo></math><img file="EP3145142B1_D0002.tif" /></maths> wherein H* is the conjugate transpose of the channel matrix H, and <i>E</i>[ ] is an expectation operation. In various embodiments, the channel matrix H may be representative of an instantaneous condition of the channel <b>130,</b> whereas the channel covariance matrix R may be representative of relatively long-term statistics of the channel <b>130.</b> Thus, the channel matrix H may change faster over time and frequency as compared to the channel covariance matrix R. In various embodiments, the channel covariance matrix R may be a Hermitian matrix of order N_t by N_t, where N_t (e.g., the number of transmit antennas of the base station <b>104</b>) is 4 for the MIMO system <b>100.</b>

0024In various embodiments, the mobile station <b>140</b> may also include a matrix decomposition module <b>152</b> configured to decompose the channel covariance matrix R using, for example, singular value decomposition. Singular value decomposition of a matrix refers to factorizing the matrix in three different matrices. For example, the singular value decomposition of the channel covariance matrix R may be of the form: <maths id="math0003" num="Equation (3)"><math display="block"><mi mathvariant="normal">R</mi><mo>=</mo><mi mathvariant="normal">U</mi><msup><mi>ΛV</mi><mo>∗</mo></msup><mo>,</mo></math><img file="EP3145142B1_D0003.tif" /></maths> where U is an unitary square matrix of order N_t, A is a N_t by N_t diagonal matrix with nonnegative real numbers on its diagonal, and V* is the conjugate transpose of an unitary square matrix V of order N_t. In various embodiments, the columns of matrix V may be the eigenvectors of matrix (R*)R, and the diagonal values in matrix A may be the singular values of R.

0025In various embodiments, the matrix V may include the beamforming matrix, and the part of the matrix V that represents the beamforming matrix may be represented by V_b. For example, as previously discussed, for a single data stream (e.g., N_s = 1) and four transmit antennas (e.g., N_t = 4) of the base station <b>104</b> (e.g., as illustrated in <figref idref="f0001"><b>Fig. 1</b></figref>), the beamforming matrix is a 4 by 1 vector. In this case, the matrix V is a 4 by 4 square matrix, and the first column of V (e.g., the principal eigenvector of matrix (R*)R) may form the beamforming matrix V_b. That is, in this case, the beamforming matrix V_b may consist of the first column of the matrix V.

0026In another example (not illustrated in <figref idref="f0001"><b>Fig. 1</b></figref>), for two data streams (e.g., N_s = 2) and four transmit antennas (e.g., N_t = 4) of the base station <b>104,</b> the matrix V is a 4 by 4 square matrix and the beamforming matrix V_b is a 4 by 2 matrix. In this case, the first two columns of V (e.g., two eigenvectors of matrix (R*)R) may form the beamforming matrix V_b.

0027In various embodiments, the mobile station <b>140</b> may also include a quantization module <b>156.</b> Once the beamforming matrix V_b is generated from the matrix V, the quantization module <b>156</b> may quantize the beamforming matrix V_b using a base codebook C_b. In these embodiments, the base codebook C_b may be used to populate the surface of a manifold to efficiently encode or quantize the beamforming matrix. The base codebook C_b may include a plurality of candidate matrices, each having dimensions similar to the beamforming matrix V_b. A candidate matrix, among the plurality of candidate matrices, that best matches the beamforming matrix V_b may be selected from the base codebook C_b, and a codeword corresponding to the selected candidate matrix may be feedback by the mobile station <b>140</b> to the base station <b>104.</b> Here, the selected candidate matrix may be representative of the beamforming matrix V_b (e.g., the selected candidate matrix may be a quantized version of the beamforming matrix V_b), and the selected candidate matrix may be referred herein as quantized beamforming matrix.

0028For example, referring again to <figref idref="f0001"><b>Fig. 1</b></figref><b>,</b> the quantization module <b>156</b> may quantize the beamforming matrix V_b as follows: <maths id="math0004" num="Equation (4)"><math display="block"><mover accent="true"><mi>V</mi><mo>^</mo></mover><mo>=</mo><munder><mrow><mi>arg</mi><mspace width="1ex" /><mi>max</mi></mrow><mrow><mi mathvariant="italic">Vi</mi><mo>∈</mo><msub><mi>C</mi><mi>b</mi></msub></mrow></munder><msub><mrow><mo>‖</mo><mrow><msubsup><mi>V</mi><mi>b</mi><mo>∗</mo></msubsup><msub><mi>V</mi><mi>i</mi></msub></mrow><mo>‖</mo></mrow><mi>F</mi></msub><mo>,</mo></math><img file="EP3145142B1_D0004.tif" /></maths> where <i>V̂</i> is the quantized beamforming matrix, C_b is the base codebook, Vi represents the candidate matrices in the base codebook C_b, <maths id="math0005" num=""><math display="inline"><msubsup><mi>V</mi><mi>b</mi><mo>∗</mo></msubsup></math><img file="EP3145142B1_D0005.tif" /></maths> is a complex conjugate of the beamforming matrix V_b, and ∥∥_F is the Frobenius-norm operation. Although Frobenius-norm is used in equation 4, in various other embodiments, any other appropriate matrix norm or vector norm (e.g., the spectral norm, the Euclidean norm, or the like) may also be used. Equation 4 selects, from among the plurality of candidate matrices included in the base codebook C_b, the quantized beamforming matrix <i>V̂</i> that is best representative of the beamforming matrix V_b.

0029In various embodiments, although quantized beamforming matrix <i>V̂</i> is representative of the beamforming matrix V_b, there may be possible quantization error (e.g., difference between the quantized beamforming matrix <i>V̂</i> and the beamforming matrix V_b) when the quantized beamforming matrix <i>V̂</i> is selected from the base codebook C_b. The quantization error may be based on several factors including, but not limited to, a number of candidate matrices included in the base codebook C_b and how closely the beamforming matrix V_b matches the selected candidate matrix (e.g., the quantized beamforming matrix <i>V̂</i>) from the base codebook C_b.

0030In various embodiments, to reduce this quantization error, the mobile station <b>140</b> may determine a difference matrix that is representative of a difference between the beamforming matrix V_b and the quantized beamforming matrix <i>V̂</i>. For example, a difference matrix D may be formed such that <maths id="math0006" num="Equation (5)"><math display="block"><mi>D</mi><mo>=</mo><mfenced open="[" close="]"><mtable><mtr><mtd><mover accent="true"><mi>V</mi><mo>^</mo></mover></mtd><mtd><msup><mover accent="true"><mi>V</mi><mo>^</mo></mover><mo>⊥</mo></msup></mtd></mtr></mtable></mfenced><mo>∗</mo><msub><mi>V</mi><mi>b</mi></msub><mo>,</mo></math><img file="EP3145142B1_D0006.tif" /></maths> wherein [<i>V̂ V̂</i>^⊥]* is the conjugate transpose of N_t by N_t matrix [<i>V̂ V̂</i>^⊥]. Also, <i>V̂</i>^⊥ may be a matrix that includes columns that are orthogonal to the columns of the quantized beamforming matrix <i>V̂</i>, and the order of the matrix <i>V̂</i>^⊥ may be N_t by (N_t - N_s). For example, for N_s = 1 and N_t = 4, <i>V̂</i> is a 4 by 1 vector, and <i>V̂</i>^⊥ may be a 4 by 3 matrix that is selected such that each of the columns of <i>V̂</i>^⊥ are orthogonal to the vector <i>V̂</i>. In another example, for N_s = 2 and N_t = 4, <i>V̂</i> is a 4 by 2 matrix, and <i>V̂</i>^⊥ may be a 4 by 2 matrix that is selected such that each of the columns of <i>V̂</i>^⊥ are orthogonal to each of the columns of the matrix <i>V̂</i>. In various embodiments, <i>V̂</i>^⊥ may be selected such that [<i>V̂ V̂</i>^⊥] is a unitary matrix. In various embodiments, the difference matrix D and/or the matrix <i>V̂</i>^⊥ may be calculated by, for example, a householder reflection operation on the quantized beamforming matrix <i>V̂</i>. The difference matrix D may be representative of the difference between the beamforming matrix V_b and the matrix <i>V̂</i>.

0031In various embodiments, the difference matrix D may be quantized using a differential codebook C_d. The differential codebook C_d may include a plurality of candidate matrices, each having dimensions similar to the difference matrix D. For example, referring again to <figref idref="f0001"><b>Fig. 1</b></figref><b>,</b> the quantization module <b>156</b> may quantize the difference matrix D as follows: <maths id="math0007" num="Equation (6)"><math display="block"><mover accent="true"><mi>D</mi><mo>^</mo></mover><mo>=</mo><munder><mrow><mi>arg</mi><mspace width="1ex" /><mi>max</mi></mrow><mrow><msub><mi>D</mi><mi>i</mi></msub><mo>∈</mo><msub><mi>C</mi><mi>d</mi></msub></mrow></munder><msub><mrow><mo>‖</mo><mrow><msup><mi>D</mi><mo>∗</mo></msup><msub><mi>D</mi><mi>i</mi></msub></mrow><mo>‖</mo></mrow><mi>F</mi></msub><mo>,</mo></math><img file="EP3145142B1_D0007.tif" /></maths> where the quantized difference matrix <i>D̂</i> is a quantization of the difference matrix D, C_d is the differential codebook, Di represents the candidate matrices in the differential codebook C_d, and ∥∥<i>_F</i> is the Frobenius-norm operation. Although Frobenius-norm is used in equation 6, in various other embodiments, any other appropriate matrix norm or vector norm may also be used. Equation 6 selects, from the differential codebook C_d, a candidate matrix <i>D̂</i> that is best representative of the difference matrix D.

0032In various embodiments, the mobile station <b>140</b> may transmit, by way of the transmit antenna <b>160,</b> a first codeword and a second codeword to the base station <b>104.</b> In various embodiments, the first codeword (e.g., from the base codebook C_b) may be associated with the quantized beamforming matrix <i>V̂</i> and the second codeword (e.g., from the differential codebook C_d) may be associated with the quantized difference matrix <i>D̂</i>. The mobile station <b>140</b> may transmit the first codeword and the second codeword to the base station <b>104</b> (e.g., instead of sending the actual matrices <i>V̂</i> and <i>D̂</i>), to enable the base station <b>104</b> to estimate the beamforming matrix V_b from the transmitted first and second codewords.

0033For example, if the quantized beamforming matrix <i>V̂</i> is an n^th matrix of the plurality of candidate matrices in the base codebook C_b and if the quantized difference matrix <i>D̂</i> is a m^th matrix of the plurality of the candidate matrices in the differential codebook C_d, then the numbers n and m may be the first and second codewords, respectively. In various other embodiments, codewords associated with the quantized beamforming matrix <i>V̂</i> and/or the quantized difference matrix <i>D̂</i> may be formed in any other appropriate manner as well.

0034In various embodiments, once the base station <b>104</b> receives the first and second codewords from the mobile station <b>140,</b> the base station <b>104</b> may determine, from the received first and second codewords, the matrices <i>D̂</i> and <i>V̂</i>, respectively, using saved copies of the base codebook C_b and differential codebook C_d. In various other embodiments, the base station <b>104</b> may determine, from the received codewords, the matrices <i>D̂</i> and <i>V̂</i> in any other appropriate manner as well.

0035Once the base station <b>104</b> determines the matrices <i>D̂</i> and <i>V̂</i>, the beamforming matrix estimation module <b>116</b> in the base station <b>104</b> may estimate the original beamforming matrix V_b. For example, the beamforming matrix estimation module <b>116</b> may generate the matrix <i>V̂</i>^⊥ from the determined matrix <i>V̂</i>. Subsequently, the beamforming matrix estimation module 116 may determine an estimated beamforming matrix <i>V̂_b</i> as follows: <maths id="math0008" num="Equation (7)"><math display="block"><msub><mover accent="true"><mi>V</mi><mo>^</mo></mover><mi>b</mi></msub><mo>=</mo><mfenced open="[" close="]"><mtable><mtr><mtd><mover accent="true"><mi>V</mi><mo>^</mo></mover></mtd><mtd><msup><mover accent="true"><mi>V</mi><mo>^</mo></mover><mo>⊥</mo></msup></mtd></mtr></mtable></mfenced><mover accent="true"><mi>D</mi><mo>^</mo></mover><mo>.</mo></math><img file="EP3145142B1_D0008.tif" /></maths>

0036Thus, the estimated beamforming matrix <i>V̂_b</i> may be an estimate of the original beamforming matrix V_b. In various embodiments, the base station <b>104</b> (e.g., the beamformer module <b>112</b>) may weight data stream(s) (e.g., as discussed with respect to equation 1) with the estimated beamforming matrix <i>V̂_b</i>, and the transmit antennas <b>108a,</b> ..., <b>108d</b> of the base station <b>104</b> may transmit the weighted data stream(s).

0037<figref idref="f0002"><b>Fig. 2</b></figref> illustrates an exemplary method <b>200</b> for determination and quantization of a beamforming matrix, in accordance with various embodiments of the present invention. One or more operations of the method <b>200</b> may be carried by one or more modules of the mobile station <b>140.</b> Referring to <figref idref="f0001"><b>Figs. 1</b></figref> and <figref idref="f0002"><b>2</b></figref><b>,</b> in various embodiments, the method <b>200</b> includes, at <b>204</b> ("Determining a channel covariance matrix R"), determining, e.g., by the channel estimation module <b>148</b> of the mobile station <b>140,</b> a channel covariance matrix R based on signals received from the base station <b>104.</b> In various embodiments, the channel covariance matrix R may be formed from the channel matrix H, as discussed with respect to equation 2. As previously discussed, the channel matrix H may be representative of conditions of sub-channels between one or more transmit antennas <b>108a,</b> ... <b>108d</b> of the base station <b>104</b> and one or more receive antennas <b>144a, 144b</b> of the mobile station <b>140.</b>

0038The method <b>200</b> may further include, at <b>208</b> ("Decomposing the channel covariance matrix"), decomposing, e.g., by the matrix decomposition module <b>152</b> of the mobile station <b>140,</b> the channel covariance matrix R into a left matrix U, a diagonal matrix A, and a complex conjugate of a right matrix V using singular value decomposition, as previously discussed with respect to equation 3.

0039The method <b>200</b> may further include, at <b>212</b> ("Determining beamforming matrix Vb"), determining, e.g., by the matrix decomposition module <b>152</b> of the mobile station <b>140,</b> the beamforming matrix V_b such that the beamforming matrix V_b comprises one or more columns of the right matrix V. In various embodiments, the beamforming matrix V_b may comprise the first N_s number of columns of the right matrix V.

0040The method <b>200</b> may further include, at <b>216</b> ("Selecting a quantized beamforming matrix"), selecting, e.g., by the quantization module <b>156</b> of the mobile station <b>140,</b> a quantized beamforming matrix <i>V̂</i> from a first plurality of candidate matrices included in base codebook C_b, where the quantized beamforming matrix <i>V̂</i> may be representative of the beamforming matrix V_b. The quantized beamforming matrix <i>V̂</i> may be selected such that the quantized beamforming matrix <i>V̂</i>, among the first plurality of candidate matrices in the base codebook C_b, maximizes a Frobenius norm of a product of a complex conjugate of the beamforming matrix and the quantized beamforming matrix <i>V̂</i>, as discussed with respect to equation 4.

0041The method <b>200</b> may further include, at <b>220</b> ("Determining a difference matrix"), determining, e.g., by the quantization module <b>156</b> of the mobile station <b>140,</b> a difference matrix D that is representative of a difference between the beamforming matrix V_b and the quantized beamforming matrix <i>V̂</i>, as discussed with respect to equation 5. For example, to determine the difference matrix D, matrix <i>V̂</i>^⊥ may be formed (e.g., using householder reflection on the quantized beamforming matrix <i>V̂</i>) based at least in part on the quantized beamforming matrix <i>V̂</i>, such that each of one or more columns of the matrix <i>V̂</i>^⊥ is orthogonal to each of one or more columns of the quantized beamforming matrix <i>V̂</i>. Subsequently, matrix [<i>V̂ V̂</i>^⊥] may be formed, which may be a combination of the quantized beamforming matrix <i>V̂</i> and the matrix <i>V̂</i>^⊥. In various embodiments, the matrix <i>V̂</i>^⊥ may be formed such that the matrix [<i>V̂ V̂</i>^⊥] is an unitary matrix having an order that is equal to a number of rows of the beamforming matrix V_b. The difference matrix D may be determined such that the difference matrix D is a product of a complex conjugate of the matrix [<i>V̂ V̂</i>^⊥] and the beamforming matrix V_b, as discussed with respect to equation 5.

0042The method <b>200</b> may further include, at <b>224</b> ("Selecting a quantized beamforming matrix"), selecting, e.g., by the quantization module <b>156</b> of the mobile station <b>140,</b> a quantized difference matrix <i>D̂</i> from a second plurality of candidate matrices included in differential codebook C_d, where the quantized difference matrix D may be representative of the difference matrix D. The quantized difference matrix <i>D̂</i> may be selected such that the quantized difference matrix D, among all the second plurality of candidate matrices in the difference codebook C_d, maximizes a Frobenius norm of a product of a complex conjugate of the difference matrix and the quantized difference matrix <i>D̂</i>, as discussed with respect to equation 6.

0043The method <b>200</b> may further include, at <b>228</b> ("Transmitting a first codeword and a second codeword"), transmitting, e.g., by the transmit antenna <b>160</b> of the mobile station <b>140,</b> to the base station <b>104,</b> a first codeword and a second codeword associated with the quantized beamforming matrix and the quantized difference matrix, respectively, as previously discussed.

0044<figref idref="f0003"><b>Fig. 3</b></figref> illustrates an exemplary method <b>300</b> for estimating, by base station <b>104,</b> the beamforming matrix based on feedback received from the mobile station <b>140,</b> in accordance with various embodiments of the present invention. One or more operations of the method <b>300</b> may be carried by one or more modules of the base station <b>104.</b> Referring to <figref idref="f0001"><b>Figs. 1</b></figref> and <figref idref="f0003"><b>3</b></figref><b>,</b> in various embodiments, the method <b>300</b> includes, at <b>304</b> ("Receiving a first codeword and a second codeword"), receiving, e.g., by the receive antenna <b>110,</b> from the mobile station <b>140,</b> e.g., from the transmit antenna <b>160,</b> a first codeword and a second codeword associated with the quantized beamforming matrix <i>V̂</i> and the quantized difference matrix <i>D̂</i>, respectively.

0045The method <b>300</b> may further include, at <b>308</b> ("Determining the quantized beamforming matrix and the quantized difference matrix"), determining, e.g., by the beamforming matrix estimation module <b>116,</b> the quantized beamforming matrix <i>V̂</i> and the quantized difference matrix <i>D̂</i> based at least in part on the received first codeword and the second codeword, respectively.

0046The method <b>300</b> may further include, at <b>312</b> ("Estimating a beamforming matrix"), estimating, e.g., by the beamforming matrix estimation module <b>116,</b> the beamforming matrix (e.g., the estimated beamforming matrix <i>V̂_b</i>) from the determined quantized beamforming matrix <i>V̂</i> and the quantized difference matrix <i>D̂</i>, as discussed with respect to equation 7.

0047The method <b>300</b> may further include, at <b>316</b> ("Weighing one or more data streams"), weighing, e.g., by the beamformer module <b>112,</b> one or more data streams (e.g., data stream <b>S1</b>) using the estimated beamforming matrix <i>V̂_b</i>. The method <b>300</b> may further include, at <b>320</b> ("Transmitting the weighed data streams"), transmitting, e.g. by one or more transmit antennas (e.g., transmit antennas <b>108a,</b> ..., <b>108d</b>) of the base station <b>104,</b> the weighed data stream(s) to the mobile station <b>140.</b>

0048Quantizing the beamforming matrix using two codebooks C_b and C_d has several advantages relative to quantizing a beamforming matrix using a single codebook. For example, quantizing the beamforming matrix into the quantized beamforming matrix <i>V̂</i> and the quantized difference matrix <i>D̂</i> may reduce a quantization error. Accordingly, the estimation of the beamforming matrix, formed at the base station <b>104,</b> may be more accurate.

0049In various embodiments discussed so far, a base codebook and a differential codebook is used to quantize the beamforming matrix. However, in various embodiments, more than one differential codebook may also be used. For example, once the difference matrix D and the quantized difference matrix <i>D̂</i> are generated, a second difference matrix may be generated (e.g., using an equation that is at least in part similar to equation 5), which may be representative of a difference between the difference matrix D and the quantized difference matrix <i>D̂</i>. The second difference matrix may then be quantized using a second differential codebook to generate a second quantized difference matrix. The mobile station <b>140</b> may transmit, to the base station <b>104,</b> a codeword corresponding to the second quantized difference matrix, in addition to transmitting codewords corresponding to the quantized beamforming matrix and the quantized difference matrix. The base station <b>104</b> may estimate the beamforming matrix <i>V̂_b</i> using codewords corresponding to the quantized beamforming matrix, the quantized difference matrix, and the second quantized difference matrix.

0050In the embodiments discussed so far, quantized form of the beamforming matrix (which includes the quantized beamforming matrix <i>V̂</i> and the quantized difference matrix <i>D̂</i>) is transmitted by the mobile station <b>140</b> to the base station <b>104.</b> In various embodiments, the mobile station <b>140</b> may also transmit a quantized form of the channel covariance matrix R (e.g., instead of or in addition to transmitting the quantized form of the beamforming matrix) to the base station <b>104,</b> to enable the base station <b>104</b> to reconstruct or estimate the channel covariance matrix and subsequently determine the beamforming matrix by decomposing the estimated channel covariance matrix. For example, the mobile station <b>140</b> may quantize the channel covariance matrix R (e.g., obtained from equation 2) using a base codebook (using a method that is at least in part similar to equation 4) to obtain a quantized channel covariance matrix. The mobile station 140 may then calculate a corresponding difference matrix (using a method that is at least in part similar to equation 5) that is representative of a difference between the channel covariance matrix and the quantized channel covariance matrix. The mobile station <b>140</b> may quantize the corresponding difference matrix using a differential codebook (using a method that is at least in part similar to equation 6) to obtain a corresponding quantized difference matrix. The mobile station <b>140</b> may transmit codewords corresponding to the generated quantized matrices to the base station <b>104,</b> from which the base station <b>104</b> may estimate the channel covariance matrix. The base station <b>104</b> may then estimate the beamforming matrix by decomposing (e.g., using singular value decomposition) the estimated channel covariance matrix.

0051The communication devices described herein may be implemented into a system using any suitable hardware and/or software to configure as desired. <figref idref="f0004"><b>Fig. 4</b></figref> illustrates, for one embodiment, an example system <b>400</b> comprising one or more processor(s) <b>404,</b> system control logic <b>408</b> coupled to at least one of the processor(s) <b>404,</b> system memory <b>412</b> coupled to system control logic <b>408,</b> non-volatile memory (NVM)/storage <b>416</b> coupled to system control logic <b>408,</b> and one or more communications interface(s) <b>420</b> coupled to system control logic <b>408.</b>

0052System control logic <b>408</b> for one embodiment may include any suitable interface controllers to provide for any suitable interface to at least one of the processor(s) <b>404</b> and/or to any suitable device or component in communication with system control logic <b>408.</b>

0053System control logic <b>408</b> for one embodiment may include one or more memory controller(s) to provide an interface to system memory <b>412.</b> System memory <b>412</b> may be used to load and store data and/or instructions, for example, for system <b>400.</b> System memory <b>412</b> for one embodiment may include any suitable volatile memory, such as suitable dynamic random access memory (DRAM), for example.

0054System control logic <b>408</b> for one embodiment may include one or more input/output (I/O) controller(s) to provide an interface to NVM/storage <b>416</b> and communications interface(s) <b>420.</b>

0055NVM/storage <b>416</b> may be used to store data and/or instructions, for example. NVM/storage <b>416</b> may include any suitable non-volatile memory, such as flash memory, for example, and/or may include any suitable non-volatile storage device(s), such as one or more hard disk drive(s) (HDD(s)), one or more compact disc (CD) drive(s), and/or one or more digital versatile disc (DVD) drive(s) for example.

0056The NVM/storage <b>416</b> may include a storage resource physically part of a device on which the system <b>400</b> is installed or it may be accessible by, but not necessarily a part of, the device. For example, the NVM/storage <b>416</b> may be accessed over a network via the communications interface(s) <b>420.</b>

0057System memory <b>412</b> and NVM/storage <b>416</b> may include, in particular, temporal and persistent copies of beamforming matrix logic <b>424,</b> respectively. In various embodiments, the system <b>400</b> may be a part of the mobile station <b>140,</b> and the beamforming matrix logic <b>424</b> may include instructions that when executed by at least one of the processor(s) <b>404</b> result in the system <b>400</b> generating a beamforming matrix and/or quantizing the beamforming matrix (e.g., using a base codebook and a differential codebook), as described herein. In various other embodiments, the system <b>400</b> may be a part of the base station <b>104,</b> and the beamforming matrix logic <b>424</b> may include instructions that when executed by at least one of the processor(s) <b>404</b> result in the system <b>400</b> estimating a beamforming matrix from received codewords (e.g., corewords corresponding to the beamforming matrix) of the base codebook and the differential codebook, as described herein.

0058In some embodiments, the beamforming matrix logic <b>424</b> may additionally (or alternatively) be located in the system control logic <b>408.</b>

0059Communications interface(s) <b>420</b> may provide an interface for system <b>400</b> to communicate over one or more network(s) and/or with any other suitable device. Communications interface(s) <b>420</b> may include any suitable hardware and/or firmware. Communications interface(s) <b>420</b> for one embodiment may include, for example, a network adapter, a wireless network adapter, a telephone modem, and/or a wireless modem. For wireless communications, communications interface(s) <b>420</b> for one embodiment may use one or more antennae.

0060For one embodiment, at least one of the processor(s) <b>404</b> may be packaged together with logic for one or more controller(s) of system control logic <b>408.</b> For one embodiment, at least one of the processor(s) <b>404</b> may be packaged together with logic for one or more controllers of system control logic <b>408</b> to form a System in Package (SiP). For one embodiment, at least one of the processor(s) <b>404</b> may be integrated on the same die with logic for one or more controller(s) of system control logic <b>408.</b> For one embodiment, at least one of the processor(s) <b>404</b> may be integrated on the same die with logic for one or more controller(s) of system control logic <b>408</b> to form a System on Chip (SoC).

0061In various embodiments, system <b>400</b> may have more or less components, and/or different architectures.

0062The invention is solely define by the appended claims.