WO2010005998A2

WO2010005998A2 - Improved precoder for multiple-subcarrier band feedback

Info

Publication number: WO2010005998A2
Application number: PCT/US2009/049852
Authority: WO
Inventors: Ron Porat; Yi Jiang
Original assignee: Wi-Lan, Inc.
Priority date: 2008-07-07
Filing date: 2009-07-07
Publication date: 2010-01-14
Also published as: WO2010005998A3

Abstract

The subject matter disclosed herein provides methods and apparatus for providing feedback from a client station to a base station. In one aspect, there is provided a method. The method may align a phase of one or more singular vectors. The singular vectors may each represent one of a plurality of subcarriers of a band. Moreover, an average singular vector may be determined for the plurality of subcarriers of the band, the aligned average singular vector representative of the plurality of subcarriers of the band. The aligned average singular vector may be provided, as feedback, to a precoder at a base station. Related systems, apparatus, methods, and/or articles are also described.

Description

IMPROVED PRECODER FOR MULTIPLE-SUBCARRIER BAND FEEDBACK CROSS-REFERENCE TO RELATED APPLICATION

[0001] This application claims priority of U.S. Patent Application Serial No. 61/078,765, filed on July 7, 2008, entitled "IMPROVED PRECODER FOR MULTIPLE- SUBCARRIER BAND FEEDBACK," the disclosure of which is hereby incorporated by reference in its entirety.

FIELD [0002] The subject matter described herein relates to wireless communications.

BACKGROUND

[0003] In signal processing associated with wireless devices, the singular value decomposition is frequently used to process signals. The singular value decomposition is a factorization of a rectangular real or a complex matrix. For example, the singular value decomposition includes determining a pseudoinverse, a least squares fitting of data, a matrix approximation, and determining the rank, the range and/or the null space of a matrix. As such, the singular value decomposition is a computationally intensive operation, which in the case of a wireless device, may be problematic.

[0004] Multiple-input and multiple-output (MIMO) is typically used in wireless communications to enhance performance, when compared to non-MIMO approaches. For example, multiple antennas may be implemented at the transmitter and/or the receiver to improve performance by providing, in some implementations, enhanced throughput and range. Often, these performance enhancements may be obtained without substantial increases in transmitted power and/or bandwidth, hence the appeal of MIMO. However, MIMO typically comes at the cost of complex processing, including complex singular value decomposition processing, at the transmitter and at the receiver.

SUMMARY [0005] The subject matter disclosed herein provides methods and apparatus for providing feedback from a client station to a base station.

[0006] In one aspect, there is provided a method. The method may align a phase of one or more singular vectors. The singular vectors may each represent one of a plurality of subcarriers of a band. Moreover, an average singular vector may be determined for the plurality of subcarriers of the band, the aligned average singular vector representative of the plurality of subcarriers of the band. The aligned average singular vector may be provided, as feedback, to a precoder at a base station.

[0007] In another aspect, there is provided a method. The method may include receiving, at a base station, an aligned average singular vector. Moreover, the received aligned average singular vector may be used when precoding a plurality of signals for transmission using a multiple-input and multiple-output transmission. Furthermore, the precoded plurality of signals may be transmitted as the multiple-input and multiple-output transmission.

[0008] The details of one or more variations of the subject matter described herein are set forth in the accompanying drawings and the description below. Features and advantages of the subject matter described herein will be apparent from the description and drawings, and from the claims.

DESCRIPTION OF DRAWINGS [0009] In the drawings, [0010] FIG. 1 depicts a block diagram of a network including client stations and base stations;

[0011 ] FIG. 2A depicts a block diagram of a client station;

[0012] FIG. 2B depicts a process for determining a phase-aligned average singular vector for a band;

[0013] FIG. 2C depicts another process for determining a phase-aligned average singular vector;

[0014] FIG. 3 A depicts a block diagram of a base station; and

[0015] FIG. 3 B depicts a process for using the phase-aligned average singular vector at the base station.

[0016] Like labels are used to refer to same or similar items in the drawings.

DETAILED DESCRIPTION [0017] FIG. 1 is a simplified functional block diagram of an embodiment of a wireless communication system 100. The wireless communication system 100 includes a plurality of base stations HOA and HOB, each supporting a corresponding service or coverage area 112A and 112B. The base stations are capable of communicating with wireless devices within their coverage areas. For example, the first base station 11OA is capable of wirelessly communicating with a first client station 114A and a second client station 114B within the coverage area 112 A. The first client station 114A is also within the coverage area 112B and is capable of communicating with the second base station 11 OB. In this description, the communication path from the base station to the client station is referred to as a downlink 116A and the communication path from the client station to the base station is referred to as an uplink 116B.

[0018] Although for simplicity only two base stations are shown in FIG. 1 , a typical wireless communication system 100 includes a much larger number of base stations. The base stations HOA and HOB can be configured as cellular base station transceiver subsystems, gateways, access points, radio frequency (RP) repeaters, frame repeaters, nodes, or any wireless network entry point.

[0019] The base stations 11 OA and 11 OB can be configured to support an omnidirectional coverage area or a sectored coverage area. For example, the second base station HOB is depicted as supporting the sectored coverage area 112B. The coverage area 112B is depicted as having three sectors, 118A, 118B, and 118C. In typical embodiments, the second base station 11 OB treats each sector 118 as effectively a distinct coverage area.

[0020] Although only two client stations 114A and 114B are shown in the wireless communication system 100, typical systems are configured to support a large number of client stations. The client stations 114A and 114B can be mobile, nomadic, or stationary units. The client stations 114A and 114B are often referred to as, for example, mobile stations, mobile units, subscriber stations, wireless terminals, or the like. A client station can be, for example, a wireless handheld device, a vehicle mounted device, a portable device, client premise equipment, a fixed location device, a wireless plug-in accessory or the like. In some cases, a client station can take the form of a handheld computer, notebook computer, wireless telephone, personal digital assistant, wireless email device, personal media player, meter reading equipment or the like and may include a display mechanism, microphone, speaker and memory.

[0021] In a typical system, the base stations 11 OA and 11 OB also communicate with each other and a network control module 124 over backhaul links 122 A and 122B. The backhaul links 122 A and 122B may include wired and wireless communication links. The network control module 124 provides network administration and coordination as well as other overhead, coupling, and supervisory functions for the wireless communication system 100. [0022] In some embodiments, the wireless communication system 100 can be configured to support both bidirectional communication and unidirectional communication. In a bidirectional network, the client station is capable of both receiving information from and providing information to the wireless communications network. Applications operating over the bidirectional communications channel include traditional voice and data applications. In a unidirectional network, the client station is capable of receiving information from the wireless communications network but may have limited or no ability to provide information to the network. Applications operating over the unidirectional communications channel include broadcast and multicast applications. In one embodiment, the wireless system 100 supports both bidirectional and unidirectional communications. In such an embodiment, the network control module 124 is also coupled to external entities via, for example, content link 126 (e.g., a source of digital video and/or multimedia) and two-way traffic link 128.

[0023] The wireless communication system 100 can be configured to use Orthogonal Frequency Division Multiple Access (OFDMA) communication techniques. For example, the wireless communication system 100 can be configured to substantially comply with a standard system specification, such as IEEE 802.16 and its progeny or some other wireless standard such as, for example, WiBro, WiFi, Long Term Evolution (LTE), or it may be a proprietary system. The subject matter described herein is not limited to application to OFDMA systems or to the noted standards and specifications. The description in the context of an OFDMA system is offered for the purposes of providing a particular example only.

[0024] As used herein, IEEE 802.16 refers to one or more Institute of Electrical and Electronic Engineers (IEEE) Standard for Local and metropolitan area networks, Part 16: Air Interface for Fixed Broadband Wireless Access Systems, 1 October 2004, IEEE Standard for Local and metropolitan area networks, Part 16: Air Interface for Fixed and Mobile Broadband Wireless Access Systems, 26 February 2006, and any subsequent additions or revisions to the IEEE 802.16 series of standards.

[0025] In some embodiments, downlinks 116A-B and uplink 116C each represent a radio frequency (RF) signal. The RF signal may include data, such as voice, video, images, Internet Protocol (IP) packets, control information, and any other type of information. When IEEE-802.16 is used, the RF signal may use OFDMA. OFDMA is a multi-user version of orthogonal frequency division multiplexing (OFDM). In OFDMA, multiple access is achieved by assigning to individual users groups of subcarriers (also referred to as subchannels or tones). The subcarriers are modulated using BPSK (binary phase shift keying), QPSK (quadrature phase shift keying), QAM (quadrature amplitude modulation), and carry symbols (also referred to as OFDMA symbols) including data coded using a forward error-correction code.

[0026] In some embodiments, a base station is implemented using multiple-input and multiple-output (MIMO). When MIMO is used, a base station may include a plurality of antennas. For example, base station HOA may be configured for MIMO and include a precoder coupled to two antennas for transmitting the MIMO transmission via downlinks 116A-B. A client station may include a plurality of antennas to receive the MIMO transmission sent via downlinks 116A-B. The client station may also combine the received signals, which may result in fewer errors and/or enhanced data transfer. Although the examples given herein are made in the context of MIMO, other smart antenna techniques may be used as well including MISO (multiple input, single output) and SIMO (single input, multiple output).

[0027] Moreover, when MIMO is used, the base station may perform precoding, which may use additional information, such as channel estimation information, to code, for each antenna, a stream of symbols for transmission over the corresponding antenna. In a closed loop feedback-based approach, the channel estimation information is provided by the client station. For example, a client station may receive each of the downlinks 116A-B transmitted by the antennas of the base station, decode the received downlink signals, determine channel estimation information about the decoded channels (e.g., subcarriers) in each of the received downlink signals, and then provide to the base station the determined channel estimation information. The channel estimation information provided by the client station may include the singular vectors determined by the client station using a singular value decomposition (SVD). Although the channel estimation information is described as including singular vectors, the channel estimation information may also include other channel information, such as the signal to noise ratio, carrier to noise ratio, and the like.

[0028] To determine the singular vectors, the client station may perform a singular value decomposition (SVD) and provide, as feedback, the singular vectors determined using the singular value decomposition. The singular vectors may be determined in a variety of ways, but in some embodiments, a channel estimator at the client station may determine the singular vectors V₁ and v₂ (also referred to as U₁ and u₂), as described below. Although the following describes determining singular vectors V₁ and v₂ for the case of an N x 2 matrix (i.e., when the client station has 2 antennas), the closed form may be extended to client stations have other quantities of antennas.

[0029] Generally, analog feedback may provide advantages, such as low complexity at the client station (e.g., a mobile station) and unbounded feedback accuracy which may be particularly important for multi-user MIMO with uncorrelated antennas or multi-base station MIMO.

[0030] In any case, there are several options for feedback, such as using a full channel matrix H, a covariance matrix H^H H , a strongest (e.g., largest) right singular vector, and two strongest right singular vectors. While feeding back the full channel matrix or channel covariance provides sufficient information for single user and/or multi-user MIMO, feeding back just the first or two strongest eigenvectors may reduce feedback overhead.

[0031] For example, a 4 antenna base station requires 8 complex values for feedback consisting of a full channel matrix or a covariance matrix, and only 3 complex values for the strongest right singular vector option and 5 complex values for two strongest right singular vectors option. An 8 antenna base station or two 4 antenna base stations in multi-base station MIMO will require 16, 7, and 13 values for the full channel matrix option, the strongest right singular vector option, and the two strongest right singular vectors option respectively. In addition, a typical operation of closed loop MIMO in frequency division duplex may require the client station (e.g., a mobile station) to send an initial estimate of the post precoding carrier-to-interference-plus-noise ratio (CINR).

[0032] To further illustrate, the following provides an example of how the singular values of the channel be calculated as these will determine the post precoding SNR (signal to noise ratio).

[0033] Assume the channel matrix H is of dimension 2 by N (2xN), where N is greater than or equal to 2 (N>=2). The singular values can be found from the eigenvalues of

HH which is of a 2x2 dimension matrix, which can be solved based on the following two

equations:

where Tr is trace and Tr is trace and σi and σ₂ are the two singular values of H.

[0034] To calculate the singular value decomposition, the focus is on the matrix

H which is of size Nx2, and then find the correct singular vectors that are of size 2 and use those singular vectors to find the left singular vectors which are the right singular vectors of

H. [0035] First, the form of is of the following form: , where U

can be generally expressed as follows:

[0036] By the definition of the singular value decomposition, the first column of matrix U is calculated according to the following equation:

where ||x|| represents a Euclidean norm. The maximum Euclidean norm is the maximal singular value

[0037] Denoting by

the

row of matrix H and developing the above expression, the following equation is formed:

which can be expressed (e.g., via substitution) as follows:

[0038] Differentiating and equating to zero, the following equation is formed:

after which a CORDIC rotation is used to calculate cos θ and sin θ . Using the

strongest singular vector is determined by normalizing the following equation:

[0039] At this point, the strongest right singular vector has been finalized. To finalize the two right strongest singular vectors, a solution to the following equation is found:

which may be normalized.

[0040] To illustrate further, the singular value decomposition (SVD) is generally done through iterative procedures. But for the special case of N x 2 matrix, the decomposition may be done via a closed-form solution for singular value decomposition. For example, given a matrix of the following form:

.

, and then calculating the singular value decomposition as follows:

where

is a orthonormal matrix, and

is of the following form:

and V is of the following form:

[0041] By the definition of the singular value decomposition, the first column of V, which is parameterized by θ and φ , is calculated according to the following equation:

where | represents for Euclidean norm, and this maximum Euclidean norm is the maximal

singular value CT₁ . Denoting a_h b, as the zth element of hi and h2, respectively, the solution of the θ and φ equation above can be derived based on the following equation:

[0042] Thus, the optimal which can be expressed as follows:

[0043] Further simplification of the θ and φ equation yields the following:

and further constraining causes no loss of optimality, and equating the derivative

to zero yields the following:

[0044] Hence, the following:

[0045] The value of θ may be calculated based on the above equation, which has only one solution in the interval 0 to π/2. However, since the solution of interest is cos θ and sin θ rather than θ itself, the following may be used to find a solution:

[0046] When α is denoted as follows:

[0047] The following equation results:

which leads to the unique solution in θ over the interval of 0 to

ws:

and

[0048] Given the above cos θ and sin

V may be formed as follows:

and given the following:

[0049] and, given the following:

which is the first column of

the largest singular value has the following form:

wherein represents the Euclidean norm and the second equality follows from the θ symbol above. As such, the corresponding singular vector is

[0050] Given the following equation,

which is the second column of UΣ, and given

, where represents

the Frobenius norm, the smaller singular value is obtained as follows:

[0051] Thus, the corresponding singular vector is

[0052] Table 1 depicts example Matlab pseudo-code for determining the singular vectors as described above.

Table 1 Sample Pseudo-Code

[0053] Once the singular vectors (e.g., V₁ and v₂ which may also be referred to as singular vectors ui and u₂) are determined by channel estimator 260, channel estimator 260 may provide the singular vectors to a precoder at the base station.

[0054] Rather than provide singular vectors for each of the subcarriers of a band (which would result in a considerable amount of the uplink 116C being used for overhead), closed loop MIMO may instead provide, as feedback, one set of singular vectors v_\ and v₂ per band, wherein a typical band is 400-800KHz and spans 36-72 subcarriers. For example, that one set of singular vectors V₁ and v₂ per band may be determined for a central subcarrier of the band. However, this central subcarrier approach may not accurately represent the band. The subject matter described herein relates to determining, at a client station, a phase-aligned, average singular vector for the band. For example, to determine the phase-aligned, average singular vector, the client station aligns the phase of each of the singular vectors of the subcarriers of the band, and then determines the average of the singular vector over the subcarriers of the band. The determined phase-aligned, average singular vector is provided to the base station to configure a precoder for a MIMO transmission via downlinks 116A-B. In some implementations, the determined phase-aligned, average singular vector more accurately represents the band when compared to using the central subcarrier or using an average across the band that is not phase aligned.

[0055] FIG. 2A depicts an exemplary client station, such as client station 114B. The client station 114B includes a plurality of antennas 220 A-B for receiving the downlinks 116A-B, each transmitted by a base station, such as base station HOA, which implements MIMO as described further below. Although the examples described herein refer to two antennas at the base station and two antennas at the client station, other quantities of antennas can be used at the base station and the client station. The client station 114B also includes a radio interface 240, which may include other components, such as filters, converters (e.g., digital-to-analog converters and the like), symbol demappers, an Inverse Fast Fourier Transform (IFFT) module, and the like, to process the received MIMO transmission sent via downlinks 116A-B and to decode any data carried by the downlinks. In some implementations, the client station 114B is also compatible with IEEE 802.16, OFDMA, and MIMO. The client station 114B further includes a channel estimator 260 (described further below), a processor 220 for controlling client station 114B and for accessing and executing program code stored in memory 225.

[0056] For each of the MIMO transmissions sent via downlinks 116A-B and received at each of antennas 220A-B, the channel estimator 260 may determine channel estimation information. For example, for each of the subcarriers of a band, the channel estimator 260 may determine singular vectors using a singular value decomposition. In some embodiments, rather than perform a traditional, singular value decomposition to determine the singular vectors for each of the subcarriers, the channel estimator 260 performs a closed form singular value decomposition to determine the singular vectors V₁ and v₂, as described above. For each of the subcarriers, channel estimator 260 determines one or more of the singular vectors V₁ and v₂.

[0057] To determined the phase-aligned, average singular vector_; channel estimator 260 may select one of the subcarriers and then use that subcarrier's singular vector vi to phase align the other subcarrier's singular vectors vi. Once phase-aligned, the channel estimator 260 determines the average of the singular vectors vl across all of the subcarriers of the band, and then normalizes the average. In some embodiments, the channel estimator 260 may repeat the above process using the determined phase-aligned average singular vector Vi (e.g., rather than selecting one of the subcarriers to align the phases of the other subcarriers, using the determined average, and then aligning the phase of all the other subcarriers relative to the determined average singular vector, and so forth.) To determine the phase-aligned average singular vector for singular vector v_2i channel estimator 260 repeats the above-described process using the singular vector v₂ of each of the subcarriers.

[0058] The following describes an exemplary implementation for determining average singular vectors including phase-aligned average singular vector for singular vectors vi and v₂.

[0059] Specifically, rather than using the central subcarrier of the band, the following four algorithms are described for designing a beamforming vector for a band which contains multiple subcarriers. These algorithms are for one-stream schemes, but they can also be applied to two-stream schemes.

[0060] In the first algorithm, let B be the set of subcarrier indices of the band. Hence, the first algorithm includes the following: 1. compute the matrix

2. Obtain the principle eigen-vector

The vector v is the beamforming vector to be used for the whole band. [0061] The second algorithm includes three steps as follows:

1. Compute the principle right singular vector ,for

2. Obtain the matrix

3. Calculate the principle eigen-vector which is the beamforming vector to be

used for the whole band.

[0062] The third algorithm (which includes phase alignment) comprises the following three steps:

1. Compute the principle right singular vector

2. Pick up a vector v_; for an arbitrary / e B and align the phase of other vectors by replai so that is a positive number.

3. Calculate the norm-1 vector , which is the beamforming vector to be used for

the whole band.

[0063] The fourth algorithm (which also includes phase alignment) solves the following optimization problem. Generally, the underlying process is to solve the following minimization problem:

wherein v is the first or second singular vector of the channel in a subcarrier i. The forth algorithm works separately on each singular vector, which are not limited in length. The optimal solution given known phase φ, may be as follows:

Hence, a solution can be found using the alternate minimization (AM) method as follows: (1) pick any subcarrier j and align the phases of all singular vectors in the band relative to that

subcarrier, i.e., ; (2) calculate the average beamforming vector by

normalizing the vector; and (3) repeat step 1 by using the vector calculated in step 2.

Performing more iterations generally leads to better performance, but in some cases one or two iterations of steps (l)-(3) provide sufficient accuracy.

[0064] FIG. 2B depicts a process 200 for determining the phase-aligned average singular vector. The description of process 200 will also refer to FIG. 2 A. Channel estimator 260 at client station 114B may be configured to determine the singular vectors for each of the plurality of subcarriers of a band (e.g., using a singular value decomposition). At 294, channel estimator 260 may align the phase of the singular vectors. At 296, channel estimator 260 may average the aligned singular vectors across the band — thus yielding the phase- aligned average singular vector for the band. In some embodiments, the channel estimator 260 normalizes the singular vectors before determining the average. For example, the channel estimator 260 normalizes the singular vector vi of each of the subcarriers of the band, and then determines the average of the phase-aligned vectors V₁ of the subcarriers of the band. At 298, the phase-aligned average singular vector may be provided (e.g., sent) to the base station to, for example, configure a precoder. In some implementations, process 200 is stored as program code stored at memory 225.

[0065] FIG. 2C depicts a process for 250 for the determining an aligned average singular vector, which is aligned in accordance with the phase of a reference subcarrier. The description of process 250 will also refer to FIG. 2 A. At 252, channel estimator 260 may compute, based on the channel estimate, a v(i) (i.e., either a singular vector V₁ or a singular vector v₂) for each of the i subcarriers of a multi-subcarrier band. At 254, channel estimator 260 selects one of the subcarriers as a so-called "reference subcarrier." Channel estimator 260 aligns the phase (Cp₁) of the singular vectors of the subcarriers in accordance with the phase (φ,) of the singular vector of the reference subcarrier. At 256, channel estimator 260 calculates the average aligned singular vector for the entire multi-subcarrier band from the sum of phase-aligned singular vectors v(i) of all the subcarriers (e.g., all i subcarriers). At 258, channel estimator 260 may repeat 254 and 256 using the average aligned singular vector determined at 256 as the singular vector of the reference subcarrier. In some implementations, the phase alignment is performed as described above with respect to algorithms 3 and 4 above. In some implementations, process 250 is stored as program code stored at memory 225.

[0066] FIG. 3 A depicts a base station, such as base station HOA. The base station HOA includes antennas 320 A-B configured to transmit via downlinks 116A-B and configured to receive uplink 116C via at least one of antennas 320A-B. The base station 11OA further includes a radio interface 340 coupled to the antennas 320A-B, a precoder 360 (described further below), a processor 330 for controlling base station HOA and for accessing and executing program code stored in memory 335. The radio interface 340 further includes other components, such as filters, converters (e.g., digital-to-analog converters and the like), mappers, a Fast Fourier Transform (FFT) module, and the like, to generate symbols for a MIMO transmission via downlinks 116A-B and to receive (e.g., via uplink 116C) the phase- aligned average singular vectors V₁ and v₂ for the band of subcarriers. In some implementations, the base station 11 OA is also compatible with IEEE 802.16 and the RF signals of the MIMO downlinks 116A-B and the uplinks 116C are configured as an OFDMA signal. The precoder 360 uses the determined values of phase-aligned average singular vectors V₁ and v₂ as well as any other channel estimate information (including so-called "side information) about the subcarriers to precode each of the streams to be transmitted as a MIMO transmission by antennas 320A-B.

[0067] FIG. 3B depicts a process 300, at the base station, for using the phase- aligned average singular vectors determined at the client station. The description of process 300 will refer to FIGs. 2A and 3 A as well. At 393, a base station, such as base station HOA, receives the phase-aligned average singular vector (e.g., for vi and/or v₂) determined at a client station, such a client station 114B. At 394, the received phase-aligned average singular vector may be used at a precoder, such as precoder 360, when precoding signals for transmission using multiple-input and multiple-output transmission. At 396, the base station transmits, as the multiple-input and multiple-output transmission, the precoded plurality of signals (e.g., symbols carried via downlink 116A-B). In some implementations, process 300 is stored as program code stored at memory 335.

[0068] The radio interface 340 decodes the uplink 116C carrying the phase- aligned average singular vectors V₁ and V₂ and then provides the phase-aligned average singular vectors vi and v₂to the precoder 360. The precoder 360 uses the phase-aligned average singular vectors vj and v₂ (as well as any other channel estimation information and/or side information provided by the client station to the base station as feedback) to precode symbols for MIMO transmission via each antenna 320A-B and MIMO downlinks 116A-B. The term "precoding" refers to beamforming to support MIMO transmission at each of the antennas (e.g., using the singular vectors to weight orthogonal "eigen-beams" transmitted via each of the antennas).

[0069] The subject matter described herein may be embodied in systems, apparatus, methods, and/or articles depending on the desired configuration. Base station HOA (or one or more components therein) can be implemented using one or more of the following: a processor executing program code, an application-specific integrated circuit (ASIC), a digital signal processor (DSP), an embedded processor, a field programmable gate array (FPGA), and/or combinations thereof. Client station 114B (or one or more components therein) can be implemented using one or more of the following: a processor executing program code, an application-specific integrated circuit (ASIC), a digital signal processor (DSP), an embedded processor, a field programmable gate array (FPGA), and/or combinations thereof. These various implementations may include implementation in one or more computer programs that are executable and/or interpretable on a programmable system including at least one programmable processor, which may be special or general purpose, coupled to receive data and instructions from, and to transmit data and instructions to, a storage system, at least one input device, and at least one output device. These computer programs (also known as programs, software, software applications, applications, components, program code, or code) include machine instructions for a programmable processor, and may be implemented in a high-level procedural and/or object-oriented programming language, and/or in assembly/machine language. As used herein, the term "machine-readable medium" refers to any computer program product, computer-readable medium, apparatus and/or device (e.g., magnetic discs, optical disks, memory, Programmable Logic Devices (PLDs)) used to provide machine instructions and/or data to a programmable processor, including a machine-readable medium that receives machine instructions as a machine-readable signal. Similarly, systems are also described herein that may include a processor and a memory coupled to the processor. The memory may include one or more programs that cause the processor to perform one or more of the operations described herein.

[0070] Although a few variations have been described in detail above, other modifications or additions are possible. In particular, further features and/or variations may be provided in addition to those set forth herein. For example, the implementations described above may be directed to various combinations and subcombinations of the disclosed features and/or combinations and subcombinations of several further features disclosed above. In addition, the logic flow depicted in the accompanying figures and/or described herein does not require the particular order shown, or sequential order, to achieve desirable results. Other embodiments may be within the scope of the following claims.

Claims

WHAT IS CLAIMED:

1. A method comprising: aligning a phase of one or more singular vectors, the singular vectors each representing one of a plurality of subcarriers of a band; determining, for the plurality of subcarriers of a band, an average singular vector for the aligned singular vectors, the average singular vector representative of the plurality of subcarriers of the band; and providing, as feedback, the aligned average singular vector to a precoder at a base station.

2. The method of claim 1, wherein aligning further comprises: selecting one of the subcarrriers as a reference subcarrier; and aligning a phase of each of the singular vectors of the subcarrier of the band in accordance with a phase of a singular vector of the reference subcarrier, and wherein determining the average singular vector further comprises: calculating the average aligned singular vector for all of the subcarriers of the band based on a sum of the phase-aligned singular vectors.

3. A method comprising: receiving, at a base station, a phase-aligned average singular vector; using the received phase-aligned average singular vector when precoding a plurality of signals for transmission using a multiple-input and multiple-output transmission; and transmitting, as the multiple-input and multiple-output transmission, the precoded plurality of signals.