Patent Publication Number: US-8982980-B2

Title: Full and partial compressed feedback formats for WLAN

Description:
CROSS-REFERENCES TO RELATED APPLICATIONS 
     This disclosure claims the benefit of U.S. Provisional Patent Application Nos. 61/647,114, entitled “Simple Compressed Beamforming Feedback Single Stream,” filed on May 15, 2012, and 61/678,523, entitled “Simple Compressed Beamforming Feedback Single Stream,” filed on Aug. 1, 2012, the disclosures of which are hereby incorporated by reference herein in their entirety. 
    
    
     FIELD OF THE DISCLOSURE 
     The present disclosure relates generally to communication networks and, more particularly, to frame format for compressed feedback for beamforming applications. 
     BACKGROUND 
     Development of wireless local area network (WLAN) standards such as the Institute for Electrical and Electronics Engineers (IEEE) 802.11a, 802.11b, 802.11g, and 802.11n Standards, has improved single-user peak data throughput. For example, the IEEE 802.11b Standard specifies a single-user peak throughput of 11 megabits per second (Mbps), the IEEE 802.11a and 802.11g Standards specify a single-user peak throughput of 54 Mbps, and the IEEE 802.11n Standard specifies a single-user peak throughput of 600 Mbps. Work has begun on a new standard, IEEE 802.11ac, that promises to provide even greater throughput. 
     Work has begun on a two new standards, IEEE 802.11ah and IEEE 802.11af, each of which will specify wireless network operation in sub-1 GHz frequencies. Low frequency communication channels are generally characterized by better propagation qualities and extended propagation ranges compared to transmission at higher frequencies. In the past, sub-1 GHz ranges have not been utilized for wireless communication networks because such frequencies were reserved for other applications (e.g., licensed TV frequency bands, radio frequency band, etc.). There are few frequency bands in the sub-1 GHz range that remain unlicensed, with different specific unlicensed frequencies in different geographical regions. The IEEE 802.11ah Standard will specify wireless operation in available unlicensed sub-1 GHz frequency bands. The IEEE 802.11af Standard will specify wireless operation in TV White Space (TVWS), i.e., unused TV channels in sub-1 GHz frequency bands. 
     SUMMARY 
     In an embodiment, a method of providing, from a first communication device to a second communication device, channel state information determined at the first communication device, includes determining, with the first communication device, a channel estimate matrix H describing a forward communication channel between the first communication device and the second communication device. The method also includes generating, with the first communication device and based on the channel estimate matrix H, feedback descriptive of the forward communication channel. When operating in a multi user mode or in a single user mode and with multiple spatial streams, generating the feedback comprises generating full compressed feedback, wherein full compressed feedback includes φ angle values and ψ angle values corresponding to each of one or more columns of the channel estimate matrix. When operating in the single user mode and with a single spatial stream, generating the feedback comprises generating partial compressed feedback, wherein partial compressed feedback includes φ angle values, and omits ψ angle values, corresponding to the channel estimate matrix. The method further comprises transmitting the feedback from the first communication device to the second communication device. 
     In another embodiment, an apparatus comprises a network interface configured to determine a channel estimate matrix H describing a forward communication channel between a first communication device and a second communication device. The network interface is also configured to generate feedback descriptive of the forward communication channel. When operating in a multi user mode or in a single user mode and with multiple spatial streams, the network interface is configured to generate full compressed feedback, wherein full compressed feedback includes φ angle values and ψ angle values corresponding to each of one or more columns of the channel estimate matrix. When operating in the single user mode and with a single spatial stream, the network interface is configured to generate partial compressed feedback, wherein partial compressed feedback includes φ angle values, and omits ψ angle values, corresponding to the channel estimate matrix. The network interface is further configured to transmit the feedback to the second communication device. 
     In yet another embodiment, a method of beamforming in a communication system that includes a first communication device and a second communication device includes receiving, at the first communication device from the second communication device, feedback describing a forward communication channel between the first communication device and the second communication device. Feedback corresponds to one of (i) full compressed feedback when the forward communication channel includes multiple spatial streams or when the forward communication channel includes a single spatial stream and the first communication device operates in a multi-user mode, wherein full compressed feedback includes φ angle values and ψ angle values corresponding to each of one or more columns of a channel estimate matrix determined for the forward communication channel at the second communication device, or (ii) partial compressed feedback when the forward communication channel includes a single spatial stream and the first communication device operates in a single user mode, wherein partial compressed feedback includes φ angle values and omits ψ angle values corresponding to the channel estimate matrix determined for the forward communication channel at the second communication device. The method also includes determining, based on the feedback, a steering matrix to be applied to signals to be transmitted from the first communication device to the second communication device. The method additionally includes applying the steering matrix to a signal to be transmitted to the second communication device as the signal is provided to multiple transmit antennas at the first communication device. 
     In still another embodiment, an apparatus comprises a network interface configured to receive, from a first communication device, feedback describing a forward communication channel between the first communication device and a second communication device. Feedback corresponds to one of (i) full compressed feedback when the forward communication channel includes multiple spatial streams or when the forward communication channel includes a single spatial stream and the first communication device operates in a multi-user mode, wherein full compressed feedback includes φ angle values and ψ angle values corresponding to each of one or more columns of a channel estimate matrix determined for the forward communication channel at the second communication device, or (ii) partial compressed feedback when the forward communication channel includes a single spatial stream and the first communication device operates in a single user mode, wherein partial compressed feedback includes φ angle values and omits ψ angle values corresponding to the channel estimate matrix determined for the forward communication channel at the second communication device. The network interface is also configured to determine, based on the feedback, a steering matrix to be applied to signals to be transmitted to the second device. The network interface is additionally configured to apply the steering matrix to a signal to be transmitted to the second device as the signal is provided to multiple transmit antennas at the first communication device. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a block diagram of an example wireless local area network (WLAN)  10  in which channel state information feedback is utilized, according to an embodiment. 
         FIGS. 2A-2B  illustrate an example technique for generating full compressed feedback information for a 4×3 channel configuration, according to an embodiment. 
         FIG. 3  illustrates an example technique for QR decomposition of a steering matrix for a 3×3 channel configuration, according to an embodiment. 
         FIG. 4  illustrates an example technique for QR decomposition of a steering matrix for a 2×2 channel configuration, according to an embodiment. 
         FIG. 5  illustrates a technique for reconstructing a steering matrix for a 4×3 channel configuration, according to an embodiment. 
         FIG. 6  illustrates an example technique for reconstructing a steering matrix for a 3×3 channel configuration, according to an embodiment. 
         FIG. 7  illustrates an example technique for reconstructing a steering matrix for a 2×2 channel configuration, according to an embodiment. 
         FIGS. 8A-8B  illustrate an example technique for generating partial compressed feedback for a 4×1 channel configuration, according to an embodiment. 
         FIG. 9  is a table listing an ordering of compressed feedback angles for different channel configurations when full compressed feedback is utilized, according to some embodiments. 
         FIG. 10  is a table listing an ordering of compressed feedback angles for different channel configurations when full compressed feedback or partial compressed feedback is utilized, according to some embodiments. 
         FIG. 11  is a diagram illustrating a control field of a data unit used to transmit full or partial compressed feedback from a beamformee to a beamformer, according to an embodiment. 
         FIG. 12  is a flow diagram of an example method of providing, to a second communication device, channel state information determined at a first communication device, according to an embodiment. 
         FIG. 13  is a flow diagram of an example method of beamforming in a communication system that includes a first communication device and a second communication device, according to an embodiment 
     
    
    
     DETAILED DESCRIPTION 
     In embodiments described below, a wireless network device, such as an access point (AP) of a wireless local area network (WLAN), transmits data streams to one or more client stations. In some embodiments, the WLAN supports multiple input multiple output (MIMO) communication in which the AP and/or the client stations include more than one antenna, thereby creating a plurality of spatial (or space-time) streams over which data can be transmitted simultaneously. In an embodiment in which a transmitting device (e.g., the AP or a client station) employs multiple antennas for transmission, the transmitting device utilizes various antennas to transmit the same signal while phasing (and amplifying) this signal as the signal is provided to the various transmit antennas to achieve beamforming or beamsteering. In order to implement a beamforming technique, the transmitting device generally requires knowledge of certain characteristics of the communication channel (also referred to as “channel characteristics” herein) between the transmitting device and the one or more receiving devices for which a beamforming pattern is to be created. To obtain channel characteristics, according to one embodiment, the transmitting device transmits, to one or more receiving devices, a sounding packet including a number of training fields that allow the receiving devices to accurately estimate the MIMO channel. The one or more receiving devices then transmit or feed-back, in some form, the obtained channel characteristics to the transmitting device, for example by including information characterizing the channel in a management or a control frame transmitted to the transmitting device. Upon receiving, from one or more of the receiving devices, information characterizing the corresponding communication channels, the transmitting device is able to generate desired beam patterns to be used in subsequent transmissions to one or more stations. 
     Channel state information is generally transmitted by a beamformee in one of several forms, in various embodiments and/or scenarios. For example, the beamformee feeds back channel state information directly, for example by feeding back coefficients of a channel estimate matrix determined at the beamformee. In another embodiment and/or scenario, the beamformee computes a steering matrix, and feeds back coefficients of the steering matrix to the beamformer. Further, in some embodiments or situations, to reduce the amount of feedback that a receiving device needs to transmit to the transmitting device, and to thereby reduce overhead associated with beamforming in the communication network, the beamformee utilizes compressed feedback, in which the steering matrix is transmitted in the form of angles representing, fully or partially, compressed versions of the feedback steering matrix. 
       FIG. 1  is a block diagram of an example wireless local area network (WLAN)  10  in which channel state information feedback is utilized, according to an embodiment. The WLAN  10  supports downlink (DL) multiuser (MU) multiple-input and multiple-output (MIMO) communication between an AP  14  and a plurality of client stations  25 - i . Additionally, the WLAN  10  supports DL single-user (SU) communication between the AP  14  and each of the client stations  25 - i . The AP  14  includes a host processor  15  coupled to a network interface  16 . The network interface  16  includes a medium access control (MAC) processing unit  18  and a physical layer (PHY) processing unit  20 . The PHY processing unit  20  includes a plurality of transceivers  21 , and the transceivers  21  are coupled to a plurality of antennas  24 . Although three transceivers  21  and three antennas  24  are illustrated in  FIG. 1 , the AP  14  can include different numbers (e.g., 1, 2, 4, 5, etc.) of transceivers  21  and antennas  24  in other embodiments. In an embodiment, if the AP  14  performs beamforming or beamsteering, and/or if the AP  14  operates in multiuser mode, the AP  14  includes at least two antennas  24 . The WLAN  10  includes a plurality of client stations  25 . Although four client stations  25  are illustrated in  FIG. 1 , the WLAN  10  can include different numbers (e.g., 1, 2, 3, 5, 6, etc.) of client stations  25  in various scenarios and embodiments. 
     The client station  25 - 1  includes a host processor  26  coupled to a network interface  27 . The network interface  27  includes a MAC processing unit  28  and a PHY processing unit  29 . The PHY processing unit  29  includes a plurality of transceivers  30 , and the transceivers  30  are coupled to a plurality of antennas  34 . Although three transceivers  30  and three antennas  34  are illustrated in  FIG. 1 , the client station  25 - 1  can include different numbers (e.g., 1, 2, 4, 5, etc.) of transceivers  30  and antennas  34  in other embodiments. In an embodiment, if the client station  25 - 1  performs beamforming or beamsteering, the client station  25 - 1  includes at least two antennas  34 . 
     In an embodiment, one or all of the client stations  25 - 2 ,  25 - 3  and  25 - 4  has a structure the same as or similar to the client station  25 - 1 . In these embodiments, the client stations  25  structured the same as or similar to the client station  25 - 1  have the same or a different number of transceivers and antennas. For example, the client station  25 - 2  has only two transceivers and two antennas (not shown), according to an embodiment. 
     In various embodiments, the PHY processing unit  20  of the AP  14  is configured to generate data units conforming to a first communication protocol. The transceiver(s)  21  is/are configured to transmit the generated data units via the antenna(s)  24 . Similarly, the transceiver(s)  24  is/are configured to receive data units via the antenna(s)  24 . The PHY processing unit  20  of the AP  14  is configured to process received data units conforming to the first communication protocol, according to an embodiment. 
     In various embodiments, the PHY processing unit  29  of the client device  25 - 1  is configured to generate data units conforming to the first communication protocol. The transceiver(s)  30  is/are configured to transmit the generated data units via the antenna(s)  34 . Similarly, the transceiver(s)  30  is/are configured to receive data units via the antenna(s)  34 . The PHY processing unit  29  of the client device  25 - 1  is configured to process received data units conforming to the first communication protocol, according to an embodiment. 
     In some embodiments, the AP  14  and/or a client station  25  (e.g., the client station  25 - 1 ) is capable of performing beamforming, or steering transmissions in the direction of a receiving device. In general, steered transmissions from a first communication device (e.g., Station A) to a second communication device (e.g., Station B) increase signal directivity, thereby providing a higher signal to noise ratio (SNR) at Station B, and further exploit spatial diversity gain from Station A to Station B. Thus, system configurations that employ steered transmissions generally outperform open loop (or unsteered) system configurations, especially in situations in which the number of transmit antennas used to transmit a signal from Station A is greater than the number of spatial streams over which the signal is transmitted from Station A to Station B. 
     As used herein, the terms “beamforming” and “beamformed” generally refer to transmit-side beamforming (i.e., applying a beamforming steering matrix at the transmitting device) rather than receive-side beamforming. Moreover, in an embodiment, a transmitting device (e.g., the AP  14 ) supports both single-user (SU) operation and multi-user, multiple-input multiple-output (MU-MIMO) operation, similar to the SU and MU-MIMO operation as defined under IEEE 802.11ac. For convenience, MU-MIMO operation is referred to herein simply as MU operation. While MU operation inherently utilizes beamforming, SU data units generally may be either beamformed (SU-BF data units) or non-beamformed (i.e., “open loop,” or SU-OL data units). 
     In one embodiment, in a single user case, the client station  25 - 1  is the beamformee, or the device to which beamforming is directed, and the AP  14  is the beamformer, or the device performing beamforming or beamsteering. In another embodiment, in MU operation, the AP  14  performs beamforming simultaneously to a plurality of client stations  25 . In this embodiment, each client station  25  to which beamforming is directed is a beamformee, and the AP  14  is the beamformer. In yet another embodiment, the AP  14  is the beamformee and the client station  25 - 1  is the beamformer. 
     Generally speaking, the channel between the AP  14  (Station A) and a client station such as, for example, the client station  25 - 1  (Station B) is, in mathematical terms, characterized by:
 
 y   B   =H   AB   Q   steer   x   A   +n   B   Equation 1
 
where y B  and n B  are the received signal vector and additive noise vector at Station B, respectively; H AB  is the equivalent channel from Station A to Station B; x A  is the signal vector to be transmitted from Station A; and Q steer  is the steering matrix (which may be a vector) at Station A that spreads the signal vector onto actual transmitting chains at Station A. In an embodiment, the channel matrix H AB  has matrix dimensions of N tx ×N rx , where N tx  is the number of transmit antennas at Station A used for communicating with Station B, and N rx  is the number of receive antennas at Station B used for communicating with Station A. In an embodiment, the steering matrix Q steer  has matrix dimensions of N tx ×N ss , where N tx  is the number of transmit antennas at Station A used for communicating with Station B, and N ss  is the number spatial (or space-time) streams corresponding to the communication channel between the Station A and the Station B.
 
     The steering matrix Q steer  is determined based on the current channel state information (CSI) for the channel between Station A and Station B, in an embodiment. The channel state information is obtained using a variety of techniques, in various embodiments and/or scenarios. For example, in explicit beamforming, Station A “sounds” the channel by transmitting a sounding packet, such as a non data packet (NDP) sounding packet, that includes training information that allows Station B to obtain an estimate H AB  of the forward communication channel from Station A to Station B. Then, based on the channel estimate H AB , Station B determines a steering matrix V at station B and, to generate compressed feedback, determines a set of angles characterizing the matrix V. The Station B then transmits, or feeds back to the Station A, the compressed feedback comprising the determined angles. Upon receiving the feedback from Station B, Station A reconstructs, based on the set of angles, the steering matrix V determined at Station B. Then, based on the reconstructed steering matrix V, Station A generates a steering matrix Q steer  (e.g. Q steer =V), and utilizes the steering matrix Q steer  in subsequent transmissions to Station B. In the case of an orthogonal frequency division multiplexing (OFDM) system, according to an embodiment, channel estimation is conducted at Station B for each subcarrier, a group of adjacent subcarriers, or a subset of “sampled” subcarriers, and a set of angles corresponding to each “sampled” subcarrier frequency is fed back to Station A. 
     The steering matrix V is a unitary matrix computed, for example, using SVD decomposition of the channel estimate matrix H, in an embodiment. In this case, QR decomposition of the steering matrix V results in a matrix Q and a matrix R, where R is an identity matrix, and rotation angles determined during QR decomposition of the matrix V fully characterize the matrix V. Thus, the rotation angles determined during QR decomposition of the matrix V are sufficient to be utilized as feedback from Station B to station A, in this embodiment. In some embodiments, to reduce the amount of feedback that needs to be transmitted to Station A, partial rotation angle information is fed back to Station A, in at least some situations. For example, for single stream channel configurations (e.g., N rx =1), partial angle information is sufficient to produce beamforming gain for transmissions from Station A to Station B, particularly for single user communications between Station A and Station B. Accordingly, in some embodiments, Station B reduces amount of feedback sent to Station A by transmitting only a portion of angles partially characterizing the matrix V, for at least some system configurations, such in single stream single user system configurations. For example, referring to  FIG. 1 , the client station  25 - 4  includes or utilizes only a single antenna for communication with the AP  14 , in an embodiment. In this embodiment, the client  25 - 4  utilizes partial compressed feedback when the AP  14  communicates with the client station  25 - 4  in single user configuration, and utilizes full compressed feedback when the AP  14  communicates with the client station  25 - 4  as part of multi user communication with multiple client stations  25 . In another embodiment, the client station  25 - 4  is a single antenna device configured to always utilize partial compressed feedback to feed channel information back to the AP  14 . 
       FIGS. 2A-2B  illustrate an example technique  200  for generating full compressed feedback information for a 4×3 (N tx =4, N rx =3) channel configuration, according to an embodiment. In this embodiment, angle rotation and QR decomposition is performed on a steering matrix V having dimension of 4×3. One of ordinary skill in the art will recognize that the algorithm described with reference to  FIGS. 2A-2B  can be straightforwardly modified for steering matrices V having other suitable dimensions (e.g., 4×2, 4×1, 3×3, 3×2, 3×1, 2×2, 2×1, or other suitable dimensions). In an embodiment, a client station  25  (e.g., the client station  25 - 1 ) utilizes the technique  200  to generate full compressed feedback when communicating with the AP  14  in a multi-stream (single user or multi-user) configuration. 
     Referring to  FIG. 2A , a steering matrix V to be decomposed is represented by a 4×3 array of elements v. As illustrated in  FIG. 2A , each column of the matrix V is rotated such that each element in the last row of the matrix V becomes a real non-negative value. To this end, in an embodiment, first each element of the first column of the matrix V is rotated by the angle corresponding to the element V 41  (i.e. θ 41 ), then each element of the second column is rotated by the angle corresponding to the element V 42  (i.e. θ 42 ), and finally each element of the third column is rotated by the angle corresponding to the element V 43  (i.e. θ 43 ). In effect, this angle rotation can be represented as a matrix multiplication of the matrix V and a diagonal matrix P, as shown in Equation 2: 
     
       
         
           
             
               
                 
                   
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     Referring now to  FIG. 2B , the technique  200  continues with QR decomposition of the resulting matrix V′, according to an embodiment. In  FIG. 2B , the matrix V′ is illustrated as a 4×3 array of elements X. First, a matrix Q φ11  is determined such that multiplying it by the original matrix V′ will cause the complex element  120  to become a real number. In effect, this process results in a rotation of the complex element  122  by an angle −φ 11 . Then, matrix Q φ21  is determined such that multiplying Q φ21 Q φ11  by the original matrix V′ will cause the complex element  122  to become a real number. In effect, this process results in a rotation of the complex element  122  by an angle −φ 21 . Similarly, Q φ31  is determined such that multiplying Q φ31 Q φ21 Q φ11  by the original matrix V′ will cause the complex element  124  to become a real number. In effect, this process results in a rotation of the complex element  124  by an angle −φ 31 . 
     Next, a matrix Q ψ21  is determined such that multiplying Q ψ21 Q φ31 Q φ21 Q φ11  by the original matrix V′ results in a rotation of the vector including elements  120  and  122  by an angle (−ψ 21 ) that causes the element  122  to go to zero. Then, a matrix Q ψ31  is determined such that Q ψ31 Q ψ21 Q φ31 Q φ21 Q φ11  by the original matrix V′ results in a rotation of the vector including elements  120  and  124  by an angle (−ψ 31 ) that causes the element  124  to go to zero. Similarly, a matrix Q ψ41  is determined such that Q ψ41 Q ψ31 Q ψ21 Q φ31 Q φ21 Q φ11  by the original matrix V′ results in a rotation of the vector including elements  120  and  128  by an angle (−ψ 41 ) that causes the element  128  to go to zero. In subsequent iterations, non-zero elements of each of the next two columns are rotated in the same manner, as illustrated in  FIG. 2B . According to an embodiment, angle rotation and QR decomposition of the steering matrix V can be represented by: 
                     [         1                                                           1                                                             cos   ⁡     (     ψ   43     )             sin   ⁡     (     ψ   43     )                                         -     sin   ⁡     (     ψ   43     )               cos   ⁡     (     ψ   43     )             ]     ×           ⁢   …   ×             [           cos   ⁡     (     ψ   31     )                         sin   ⁡     (     ψ   31     )                                       1                                     -     sin   ⁡     (     ψ   31     )                           cos   ⁡     (     ψ   31     )                                                               1         ]     ×             [           cos   ⁡     (     ψ   21     )             sin   ⁡     (     ψ   21     )                                         -     sin   ⁡     (     ψ   21     )               cos   ⁡     (     ψ   21     )                                                               1                                                           1         ]     ×               [           ⅇ     -     jθ   11                                                                   e     -     jθ   21                                                                   e     -     jθ   31                                                                 1         ]     ×     V   ′       =     [           r   11                                                   r   22                                                   r   33           ]                         Equation   ⁢           ⁢   3               
Thus, the process of angle rotation of the steering matrix V and QR decomposition of the resulting matrix V′ results in a matrix diagonal matrix R and a product of the rotation matrices Q determined during QR decomposition of the matrix V. Further, rotation angles ψ i,j  and φ k,l  determined during decomposition of the matrix V′ are sufficient to reconstruct the original steering matrix V, where the indices i, j, k and l are integers greater than or equal to 1. Accordingly, the beamformee transmits the rotation angels ψ i,j  and φ k,l  to the beamformer to allow the beamformer to conduct beamforming in the direction of the beamformee, in an embodiment. For simplicity, in the descriptions below the indices i, j, k and  1  are sometime dropped, and the rotation angles ψ i,j  and φ k,l  are sometimes referred to herein as simply ψ angles (or ψ angle values) and φ angles (or φ angle values), respectively.
 
       FIG. 3  illustrates an example technique  300  for QR decomposition of a steering matrix V′ for a 3×3 (N TX =3, N RX =3) channel configuration, according to an embodiment. The QR decomposition technique  300  is similar the QR decomposition technique  200 B of  FIG. 2 , except that the decomposition technique  300  is performed for a steering matrix V′ having dimensions of 3×3. Similarly,  FIG. 4  illustrates an example technique  400  for QR decomposition of a steering matrix V′ for a 2×2 (N TX =2, N RX =2) channel configuration, according to an embodiment. The QR decomposition technique  400  is similar the QR decomposition technique  200 B of  FIG. 2 , except that the decomposition technique  300  is performed for a steering matrix V′ having dimensions of 2×2. 
     In an embodiment, upon determining rotation angles ψ i,j  and φ k,l  during QR decomposition process of the matrix V′, the beamformee quantizes the determined values of the rotation angles ψ i,j  and φ k,l , and feeds back the quantized values of the angles ψ i,j  and φ k,l  to the beamformer. In an embodiment, the φ k,l  angles are in the range of φε[0,2π), and each φ k,l  angle is quantized to an integer number k φ . Similarly, the ψ i,j  angles are in the range of 
               ψ   ∈     [     0   ,     π   2       )       ,         
and each ψ i,j  angle is quantized to an integer number k ψ . According to an embodiment, the integers k φ  and k ψ  are given by:
 
                           k   ϕ     =     round   ⁡     [       (     ϕ   -     π     2     b   ϕ           )     ·       2     b   ϕ         2   ⁢           ⁢   π         ]                     k   ψ     =     round   ⁡     [       (     ψ   -     π     2     b   ψ           )     ·       2     b   ψ         2   ⁢           ⁢   π         ]                     Equation   ⁢           ⁢   4               
where b φ  and b ψ  are quantization levels used to quantize rotation angles φ k,l  and rotation angles ψ i,j  respectively. As an example, in one embodiment, b φ =4 and b ψ =2. In this embodiment, the angles φ k,l  are quantized using four bits, and the angles ψ i,j  angles are quantized using two bits. In other embodiments, other suitable quantization levels for the angles φ k,l  and/or the angles ψ i,j  are utilized. For example, in one embodiment, the values for b φ  and b ψ  are selected from sets {b φ ,b ψ }={3,1}, {4,2}, {5,3}, {6,4}. In another embodiment, the values for b φ  and b ψ  are selected from sets {b φ , b ψ }={4,2}, {6, 4} for single user transmissions, and from sets {b φ ,b ψ }={7,5}, {9,7} for multi-user transmissions.
 
     Upon receiving the quantized rotation angles ψ i,j  and φ k,l  from the beamformee, the beamformer de-quantizes the rotation angles ψ i,j  and φ k,l,  and performs angle de-rotation to reconstruct the steering matrix V.  FIG. 5  illustrates a technique  500  for reconstructing the steering matrix V for a 4×3 channel configuration, according to an embodiment. In an embodiment, a beamformer (e.g., the AP  14 ) utilizes the technique  500  to reconstruct a steering matrix V determined for a 4×3 channel configuration at a beamformee (e.g., the client station  25 - 1 ) based on rotation angles ψ i,j  and φ k,l  received from the beamformee. The technique  500  effectively reverses QR decomposition process described above with respect to  FIG. 2B  by rotating elements of an identity matrix using the rotation angles ψ i,j  and φ k,l  determined according to the technique  200 B of  FIG. 2B . In this embodiment, the de-rotation process performed according to the technique  500  can be represented by: 
     
       
         
           
             
               
                 
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                                   ⁡ 
                                   
                                     ( 
                                     
                                       ψ 
                                       21 
                                     
                                     ) 
                                   
                                 
                               
                               
                                 
                                   sin 
                                   ⁡ 
                                   
                                     ( 
                                     
                                       ψ 
                                       21 
                                     
                                     ) 
                                   
                                 
                               
                               
                                 
                                     
                                 
                               
                               
                                 
                                     
                                 
                               
                             
                             
                               
                                 
                                   - 
                                   
                                     sin 
                                     ⁡ 
                                     
                                       ( 
                                       
                                         ψ 
                                         21 
                                       
                                       ) 
                                     
                                   
                                 
                               
                               
                                 
                                   cos 
                                   ⁡ 
                                   
                                     ( 
                                     
                                       ψ 
                                       21 
                                     
                                     ) 
                                   
                                 
                               
                               
                                 
                                     
                                 
                               
                               
                                 
                                     
                                 
                               
                             
                             
                               
                                 
                                     
                                 
                               
                               
                                 
                                     
                                 
                               
                               
                                 1 
                               
                               
                                 
                                     
                                 
                               
                             
                             
                               
                                 
                                     
                                 
                               
                               
                                 
                                     
                                 
                               
                               
                                 
                                     
                                 
                               
                               
                                 1 
                               
                             
                           
                           ] 
                         
                         ⨯ 
                         
                             
                           
                             
                               [ 
                               
                                 
                                   
                                     
                                       cos 
                                       ⁡ 
                                       
                                         ( 
                                         
                                           ψ 
                                           31 
                                         
                                         ) 
                                       
                                     
                                   
                                   
                                     
                                         
                                     
                                   
                                   
                                     
                                       sin 
                                       ⁡ 
                                       
                                         ( 
                                         
                                           ψ 
                                           31 
                                         
                                         ) 
                                       
                                     
                                   
                                   
                                     
                                         
                                     
                                   
                                 
                                 
                                   
                                     
                                         
                                     
                                   
                                   
                                     1 
                                   
                                   
                                     
                                         
                                     
                                   
                                   
                                     
                                         
                                     
                                   
                                 
                                 
                                   
                                     
                                       - 
                                       
                                         sin 
                                         ⁡ 
                                         
                                           ( 
                                           
                                             ψ 
                                             31 
                                           
                                           ) 
                                         
                                       
                                     
                                   
                                   
                                     
                                         
                                     
                                   
                                   
                                     
                                       cos 
                                       ⁡ 
                                       
                                         ( 
                                         
                                           ψ 
                                           31 
                                         
                                         ) 
                                       
                                     
                                   
                                   
                                     
                                         
                                     
                                   
                                 
                                 
                                   
                                     
                                         
                                     
                                   
                                   
                                     
                                         
                                     
                                   
                                   
                                     
                                         
                                     
                                   
                                   
                                     1 
                                   
                                 
                               
                               ] 
                             
                             ⨯ 
                             
                                 
                             
                             ⁢ 
                             … 
                             ⨯ 
                             
                                 
                               
                                 
                                   [ 
                                   
                                     
                                       
                                         1 
                                       
                                       
                                         
                                             
                                         
                                       
                                       
                                         
                                             
                                         
                                       
                                       
                                         
                                             
                                         
                                       
                                     
                                     
                                       
                                         
                                             
                                         
                                       
                                       
                                         1 
                                       
                                       
                                         
                                             
                                         
                                       
                                       
                                         
                                             
                                         
                                       
                                     
                                     
                                       
                                         
                                             
                                         
                                       
                                       
                                         
                                             
                                         
                                       
                                       
                                         
                                           ⅇ 
                                           
                                             
                                               - 
                                               j 
                                             
                                             ⁢ 
                                             
                                                 
                                             
                                             ⁢ 
                                             
                                               φ 
                                               33 
                                             
                                           
                                         
                                       
                                       
                                         
                                             
                                         
                                       
                                     
                                     
                                       
                                         
                                             
                                         
                                       
                                       
                                         
                                             
                                         
                                       
                                       
                                         
                                             
                                         
                                       
                                       
                                         1 
                                       
                                     
                                   
                                   ] 
                                 
                                 × 
                                 
                                     
                                   
                                     
                                       [ 
                                       
                                         
                                           
                                             1 
                                           
                                           
                                             
                                                 
                                             
                                           
                                           
                                             
                                                 
                                             
                                           
                                           
                                             
                                                 
                                             
                                           
                                         
                                         
                                           
                                             
                                                 
                                             
                                           
                                           
                                             1 
                                           
                                           
                                             
                                                 
                                             
                                           
                                           
                                             
                                                 
                                             
                                           
                                         
                                         
                                           
                                             
                                                 
                                             
                                           
                                           
                                             
                                                 
                                             
                                           
                                           
                                             
                                               cos 
                                               ⁡ 
                                               
                                                 ( 
                                                 
                                                   ψ 
                                                   43 
                                                 
                                                 ) 
                                               
                                             
                                           
                                           
                                             
                                               sin 
                                               ⁡ 
                                               
                                                 ( 
                                                 
                                                   ψ 
                                                   43 
                                                 
                                                 ) 
                                               
                                             
                                           
                                         
                                         
                                           
                                             
                                                 
                                             
                                           
                                           
                                             
                                                 
                                             
                                           
                                           
                                             
                                               - 
                                               
                                                 sin 
                                                 ⁡ 
                                                 
                                                   ( 
                                                   
                                                     ψ 
                                                     43 
                                                   
                                                   ) 
                                                 
                                               
                                             
                                           
                                           
                                             
                                               cos 
                                               ⁡ 
                                               
                                                 ( 
                                                 
                                                   ψ 
                                                   43 
                                                 
                                                 ) 
                                               
                                             
                                           
                                         
                                       
                                       ] 
                                     
                                     × 
                                     
                                       [ 
                                       
                                         
                                           
                                             1 
                                           
                                           
                                             
                                                 
                                             
                                           
                                           
                                             
                                                 
                                             
                                           
                                         
                                         
                                           
                                             
                                                 
                                             
                                           
                                           
                                             1 
                                           
                                           
                                             
                                                 
                                             
                                           
                                         
                                         
                                           
                                             
                                                 
                                             
                                           
                                           
                                             
                                                 
                                             
                                           
                                           
                                             1 
                                           
                                         
                                         
                                           
                                             
                                                 
                                             
                                           
                                           
                                             
                                                 
                                             
                                           
                                           
                                             
                                                 
                                             
                                           
                                         
                                       
                                       ] 
                                     
                                   
                                 
                               
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   5 
                 
               
             
           
         
       
     
       FIG. 6  illustrates an example technique  600  for reconstructing the steering matrix V for a 3×3 channel configuration, according to an embodiment. The technique  600  is similar the technique  500  of  FIG. 5 , except that the decomposition technique  600  is performed for a steering matrix V′ having dimensions of 3×3. The technique  600  effectively reverses QR decomposition technique  300  illustrated in  FIG. 3  by rotating elements of an identity matrix using rotation angles ψ i,j  and φ k,l  determined according to the technique  300  of  FIG. 3 . Similarly,  FIG. 7  illustrates an example technique  700  for reconstructing the steering matrix V for a 2×2 channel configuration, according to an embodiment. The technique  700  is similar the technique  500  of  FIG. 5 , except that the decomposition technique  700  is performed for a steering matrix V′ having dimensions of 2×2. The technique  700  effectively reverses QR decomposition technique  400  illustrated in  FIG. 4  by rotating elements of an identity matrix using rotation angles ψ i,j  and φ k,l  determined according to the technique  400  of  FIG. 4 . 
     As discussed above, in some embodiments, one or more of the client stations  25  are configured to generate partial compressed feedback, and to transmit partial compressed feedback to the AP  14 , in at least some situations (e.g., for single stream, single user system configurations). Partial compressed feedback includes a partial description of the channel, sufficient to obtain suitable beamforming gain when conducting beamforming in the direction of a beamformee using a steering matrix (Q steer ) determined based on the partial compressed feedback received from the beamformee, according to an embodiment. For example, all or most beamforming gain is achieved by utilizing phase information of a computed beamsteering matrix (or vector, in the case of single stream channel), and omitting the magnitude information, in at least some system configurations, such as in single stream system configurations. As an example, consider a steering matrix computed using single value decomposition (SVD) for a 4×1 channel case. In this example, the beamformee determines a channel matrix H (e.g., based on a sounding packet received from the beamformer), and performs SVD decomposition of the channel matrix to generate a steering matrix V. The channel matrix H for a 4×1 channel can be represented as H=[h 11  h 12  h 13  h 14 ]. Then, the beamformee determines a steering matrix V based on the channel matrix H based on SVD of the channel matrix H, in an embodiment. In this embodiment, the steering matrix V is given by 
     
       
         
           
             
               
                 
                   V 
                   = 
                   
                     
                       
                         H 
                         H 
                       
                       
                          
                         H 
                          
                       
                     
                     = 
                     
                       
                         
                           1 
                           
                              
                             H 
                              
                           
                         
                         ⁡ 
                         
                           [ 
                           
                             
                               
                                 
                                   h 
                                   11 
                                   * 
                                 
                               
                             
                             
                               
                                 
                                   h 
                                   12 
                                   * 
                                 
                               
                             
                             
                               
                                 
                                   h 
                                   13 
                                   * 
                                 
                               
                             
                             
                               
                                 
                                   h 
                                   14 
                                   * 
                                 
                               
                             
                           
                           ] 
                         
                       
                       = 
                       
                         
                           1 
                           
                              
                             H 
                              
                           
                         
                         ⁡ 
                         
                           [ 
                           
                             
                               
                                 
                                   
                                      
                                     
                                       h 
                                       11 
                                     
                                      
                                   
                                   ⁢ 
                                   
                                     ⅇ 
                                     
                                       - 
                                       
                                         jw 
                                         11 
                                       
                                     
                                   
                                 
                               
                             
                             
                               
                                 
                                   
                                      
                                     
                                       h 
                                       12 
                                     
                                      
                                   
                                   ⁢ 
                                   
                                     ⅇ 
                                     
                                       - 
                                       
                                         jw 
                                         12 
                                       
                                     
                                   
                                 
                               
                             
                             
                               
                                 
                                   
                                      
                                     
                                       h 
                                       13 
                                     
                                      
                                   
                                   ⁢ 
                                   
                                     ⅇ 
                                     
                                       - 
                                       jw13 
                                     
                                   
                                 
                               
                             
                             
                               
                                 
                                   
                                      
                                     
                                       h 
                                       14 
                                     
                                      
                                   
                                   ⁢ 
                                   
                                     ⅇ 
                                     
                                       - 
                                       jw14 
                                     
                                   
                                 
                               
                             
                           
                           ] 
                         
                       
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   6 
                 
               
             
           
         
       
     
     Having determined the steering matrix V, the beamformee performs a partial de-compression of the determined V matrix, as described in more detail below, and feeds the quantized φ angle values back to the beamformer. The beamformer receives the feedback and de-quantizing the φ angle values provided in the feedback. Then, based on the de-quantized φ angle values, the beamformer computes a phase only approximation V′ of the steering matrix V 
                       V   ′     ≈     [           ⅇ     j   ⁢           ⁢     ϕ   11                   ⅇ     j   ⁢           ⁢     ϕ   21                   ⅇ     j   ⁢           ⁢     ϕ   31                 1         ]       =     [           ⅇ     j   ⁡     (       w   11     -     w   41       )                   ⅇ     j   ⁡     (       w   21     -     w   41       )                   ⅇ     j   ⁡     (       w   31     -     w   41       )                 1         ]             Equation   ⁢           ⁢   7               
The beamformer then utilizes the approximation V′ to perform beamsteering in the direction of the beamformee. In this case, the beamformed channel to the beamformee can be represented by
 
     
       
         
           
             
               
                 
                   
                     
                       
                         
                           HV 
                           ′ 
                         
                         = 
                           
                         ⁢ 
                         
                           
                             [ 
                             
                               
                                 h 
                                 11 
                               
                               ⁢ 
                               
                                 h 
                                 12 
                               
                               ⁢ 
                               
                                 h 
                                 13 
                               
                               ⁢ 
                               
                                 h 
                                 14 
                               
                             
                             ] 
                           
                           ⨯ 
                           
                             [ 
                             
                               
                                 
                                   
                                     ⅇ 
                                     
                                       j 
                                       ⁡ 
                                       
                                         ( 
                                         
                                           
                                             w 
                                             11 
                                           
                                           - 
                                           
                                             w 
                                             41 
                                           
                                         
                                         ) 
                                       
                                     
                                   
                                 
                               
                               
                                 
                                   
                                     ⅇ 
                                     
                                       j 
                                       ⁡ 
                                       
                                         ( 
                                         
                                           
                                             w 
                                             21 
                                           
                                           - 
                                           
                                             w 
                                             41 
                                           
                                         
                                         ) 
                                       
                                     
                                   
                                 
                               
                               
                                 
                                   
                                     ⅇ 
                                     
                                       j 
                                       ⁡ 
                                       
                                         ( 
                                         
                                           
                                             w 
                                             31 
                                           
                                           - 
                                           
                                             w 
                                             41 
                                           
                                         
                                         ) 
                                       
                                     
                                   
                                 
                               
                               
                                 
                                   1 
                                 
                               
                             
                             ] 
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                         ⁢ 
                         
                           
                             ( 
                             
                               
                                  
                                 
                                   h 
                                   11 
                                 
                                  
                               
                               + 
                               
                                  
                                 
                                   h 
                                   12 
                                 
                                  
                               
                               + 
                               
                                  
                                 
                                   h 
                                   13 
                                 
                                  
                               
                               + 
                               
                                  
                                 
                                   h 
                                   14 
                                 
                                  
                               
                             
                             ) 
                           
                           · 
                           
                             ⅇ 
                             
                               jw 
                               14 
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   8 
                 
               
             
           
         
       
     
     Because a steering matrix determined at a beamformer based on partial compressed feedback received from a beamformee provides sufficient beamforming gain for subsequent transmission to the beamformee, beamforming with sufficient beamforming gain is conducted with a reduced overhead associated with feedback of channel state information to the beamformee, in at least some embodiments. Partial compressed feedback is utilized by devices that conform to long range, low frequency communication protocols, such as IEEE-802.11af and/or IEEE-802.11 ah Standards, for example, in some embodiments. In such embodiments, antenna size needed to operate at low (e.g., sub-1 GHz) frequencies and antenna separation needed to construct an antenna array at the low operating frequencies limit receiving devices (or beamformees) to a single antenna available to communicate with a beamformer. Further, devices that operate according to such long range low frequency communication protocols are often small, power battery devices (e.g., sensors) that are constrained to a single antenna by power available at the device, size of the device and/or cost of the device, in some embodiments. Accordingly, in such embodiments, the beamformer (e.g., the AP  14 ) communicates with the beamformee, and steers transmissions to the beamformee, using a single spatial stream, such as in N tx ×1 channel configurations well suited for partial compressed feedback, in at least some situations, such as for single user communications. In other embodiments, partial compressed feedback is utilized in other communication protocols and/or for other suitable channel configurations. 
       FIGS. 8A-8B  illustrate an example technique  800  for generating partial compressed feedback information for a 4×1 communication channel configuration, according to an embodiment. In this example embodiment, a beamformee obtains a 4×1 channel estimate matrix H (e.g., based on a sounding packet received from a beamformer), and based on the channel estimate matrix H, determines a 4×1 steering vector V. Referring to  FIG. 8A , the steering vector V is represented by a 4×1 vector of elements v. Referring to  FIG. 8A , each element of the steering vector V is rotated such that element  802  of the steering vector V becomes a real non-negative value. As illustrated in  FIG. 8A , each element of the steering vector V is rotated by the angle corresponding to the element  802  (i.e. θ 4 ). Accordingly, in this embodiment, the resulting vector V′ can be represented as: 
     
       
         
           
             
               
                 
                   
                     V 
                     ′ 
                   
                   = 
                   
                     
                       [ 
                       
                         
                           
                             
                               v 
                               11 
                             
                           
                         
                         
                           
                             
                               v 
                               21 
                             
                           
                         
                         
                           
                             
                               v 
                               31 
                             
                           
                         
                         
                           
                             
                               v 
                               41 
                             
                           
                         
                       
                       ] 
                     
                     · 
                     
                       
                         ⅇ 
                         
                           
                             - 
                             
                               jθ 
                               41 
                             
                           
                           = 
                         
                       
                       ⁡ 
                       
                         [ 
                         
                           
                             
                               
                                 v 
                                 11 
                                 
                                   ( 
                                   1 
                                   ) 
                                 
                               
                             
                           
                           
                             
                               
                                 v 
                                 21 
                                 
                                   ( 
                                   1 
                                   ) 
                                 
                               
                             
                           
                           
                             
                               
                                 v 
                                 31 
                                 
                                   ( 
                                   1 
                                   ) 
                                 
                               
                             
                           
                           
                             
                               
                                  
                                 
                                   v 
                                   41 
                                   
                                     ( 
                                     1 
                                     ) 
                                   
                                 
                                  
                               
                             
                           
                         
                         ] 
                       
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   9 
                 
               
             
           
         
       
     
     Referring now to  FIG. 8B , the technique  800  continues with a partial QR decomposition of the resulting vector V′, according to an embodiment. In  FIG. 8B , the vector V′ is illustrated as a 4×1 vector of elements v′. First, a vector Q φ11  is determined such that multiplying it by the original vector V′ will cause the complex element V 11   (1)  to become a real number. In effect, this process results in a rotation of the complex element V 11   (1)  by an angle −φ 11 . Then, matrix matrix Q φ21  is determined such that multiplying Q φ21 Q φ11  by the original vector V′ will cause the complex element V 21   (1)  to become a real number. In effect, this process results in a rotation of the complex element V 21   (1)  by an angle −φ 21 . Similarly, Q determined such that multiplying Q φ31 Q φ21 Q φ11  by the original vector V′ will cause the complex element V 31   (1)  to become a real number. In effect, this process results in a rotation of the complex element V 31   (1)  by an angle −φ 31 . This rotation process can be represented by: 
                     V     (   2   )       =       ⁢         [           ⅇ     -     jϕ   11                                                                   ⅇ     -     jϕ   21                                                                   ⅇ     -     jϕ   31                                                                 1         ]     ⨯     V     (   1   )         =       [             v   11     (   1   )       ⁢     ⅇ     -     jϕ   11                       v   21     (   1   )       ⁢     ⅇ     -     jϕ   21                       v   31     (   1   )       ⁢     ⅇ     -     jϕ   31                          v   41                ]     =       ⁢     [           v   11     (   1   )                 v   21     (   1   )                 v   31     (   1   )                      v   41                ]                 Equation   ⁢           ⁢   10               
In contrast to full compressed feedback techniques described above, in the partial feedback technique  800 , the rotation process is not continued to determine values of ψ angles, in an embodiment. Instead, the determined ψ angle values are quantized and fed back to the beamformer. From Equations 6 and 7, it can be seen that, in this embodiment, ψ angles determined during the angle rotation are represented by:
 
φ 11 =θ 11 −θ 41  
 
φ 21 =θ 21 −θ 41  
 
φ 31 =θ 31 −θ 41   Equation 11
 
     In some embodiments, φ angles for partial compressed feedback are determined directly based on a channel matrix obtained at a beamformee without performing compression of a steering matrix determined based on the channel matrix determined at the beamformee. For example, from Equation 7 for an example 4×1 channel configuration described above, it can be seen that φ angles can be determined from a channel matrix obtained for the 4×1 channel directly according to:
 
φ 11   =w   14   −w   11  
 
φ 21   =w   14   −w   12  
 
φ 31   =w   14   −w   13   Equation 12
 
Accordingly, the beamformee does not perform compression of a steering matrix V′ to determine φ angle values to be fed back to the beamformer when partial compressed feedback is being utilized, in an embodiment. Rather, the beamformee determines φ angle values to be fed back to the beamformer directly from a channel matrix H obtained at the beamformee, when partial compressed feedback is being utilized, in this embodiment.
 
     Upon receiving the quantized φ angle values, the beamformer de-quantizes the quantized φ angle values, and constructs a steering vector V based on the de-quantized angles φ. To generate a steering vector V, in one embodiment, the beamformer performs de-rotation (starting with an identity vector) using the de-quantized angles φ and assumed, or pre-determined, values for angles ψ. For example, in an embodiment, equal gain ψ angles having pre-determined values given in Equation 13 below are utilized. 
                       ψ   21     =     π   4       ,       ψ   31     =     0.196   ⁢   π       ,       ψ   41     =     0.167   ⁢   π               Equation   ⁢           ⁢   13               
In other embodiment, other equal gain values for {ψ EG }={ψ 21 ,ψ 31 ,ψ 41 } are utilized. In general, any suitable values for the ψ angles can be assumed at the beamformer, and other suitable predetermined values for the ψ angles are utilized in other embodiments.
 
     For example, approximations of the ψ angles given in Equation 13, such as quantized values of these ψ angle values are utilized, in some embodiments. As an example, ψ angle values given in Equation 13 are quantized to two bits (b ψ =2), in an embodiment. In this embodiment, {ψ EG } is given by 
               {     ψ   EG     }     =       {       π   4     ,     π   8     ,     π   8       }     .           
In another embodiment, approximations of the values given in Equation 13 using a suitable quantization other than 3 bits are utilized. To provide a few other examples, for a 3×1 communication channel configuration,
 
               {     ψ   EG     }     =       {       π   4     ,     0.196   ⁢           ⁢   π       }     .           
or suitable approximations of these values, are utilized for ψ EG  angle values, in an embodiment. As another example, for 2×1 channel configuration
 
                 {     ψ   EG     }     =     {     π   4     }       ,         
or a suitable approximation of this values, is utilized for ψ EG  angle values, in an embodiment.
 
     In embodiments and/or scenarios with other single stream channel configurations, a corresponding different set of ψ angle values is utilized. For example, in a 3×1 channel configuration, 
                 {     ψ   EG     }     =     {       π   4     ,     0.196   ⁢           ⁢   π       }       ,         
or a suitable approximation of these ψ angel values is utilized. As another example, in a 2×1 channel configuration
 
                 {     ψ   EG     }     =     {     π   4     }       ,         
or a suitable approximation of this value is utilized. In other embodiments, other suitable ψ EG  angle values in single stream channel configurations are utilized.
 
     In some embodiments, after steering matrix is applied to signals at the beamformer, the signals are provided to a plurality of power amplifiers (PAs), each PA corresponding to a different one of the transmit antennas at the beamformer. Each PA is driven at a maximum power level to maximize transmit power output by the corresponding transmit antenna, in at least some embodiments and/or situations. In some such embodiments, power balancing between the different PAs is performed, for example by determining a maximum signal gain applied to the signals provided to the PAs, and comparing each other signal gain to the maximum signal gain. Then output powers of the PAs are adjusted based on the signal gain comparisons, in an embodiment. As discussed above, in embodiments and/or scenarios in which partial compressed feedback is utilized, a beamformee feeds back φ angle values to a beamformer, and omits feeding back ψ angle values to the beamformer (partial compressed feedback), the magnitude information of the V matrix is effectively lost, and only the phase information is fed back to the beamformer. A steering matrix to be applied a signal transmitted to the beamformee is then determined such that appropriate phases are applied to the signals provided to different antennas, and equal gain is applied to the signals provided to different antennas, in some such embodiments. In such embodiments, beamforming gain is substantially similar to beamforming gain achieved in systems in which full compressed feedback is utilized because magnitudes of signals transmitted from different antennas are balanced to achieve maximum output power even when magnitude information is utilized for determining the steering matrix at the beamformer. Further, in embodiments in which equal gain is assumed for determining the steering matrix at a beamformee, PA control is simplified because equal beamsteering gain is applied to the signal as the signal is provided to each of the PAs, and therefore, output power balancing of the PAs need not be performed. In some embodiments, PA power balancing is enabled at the beamformer for system configurations in which full compressed feedback is utilized, and disabled for system configurations in which partial compressed feedback is utilized. 
     In an embodiment, upon receiving quantized φ angle values from the beamformee, the beamformer reconstructs the steering matrix V without performing decomposition with the received φ angle values. That is, having received and de-quantized the φ angle values, the beamformer constructs an approximate, phase-only version V′ of the steering matrix that was computed at the beamformee. The reconstructed steering matrix V′ can be represented as: 
                       V   ′     ≈     [           ⅇ     jϕ   11                 ⅇ     jϕ   21                 ⅇ     jϕ   31               1         ]       =       [           ⅇ     j   ⁡     (       θ   11     -     θ   41       )                   ⅇ     j   ⁡     (       θ   21     -     θ   41       )                   ⅇ     j   ⁡     (       θ   31     -     θ   41       )                 1         ]     =       ⅇ         -   j     ⁢           ⁢     θ   41       ⁢               ⁡     [           ⅇ     j   ⁢           ⁢     θ   11                   ⅇ     j   ⁢           ⁢     θ   21                   ⅇ     j   ⁢           ⁢     θ   31                   ⅇ     j   ⁢           ⁢     θ   41               ]                 Equation   ⁢           ⁢   14               
The beamformer then utilizes the reconstructed version of the steering matrix V′ to conduct beamforming in the direction of the beamformee, according to an embodiment.
 
       FIG. 9  is a table  900  listing an ordering of compressed feedback angles for different channel configurations, according to some embodiments. Ordering listed in the table  900  is utilized for various channel configurations when the AP  14  operates in multi user mode, i.e., when the AP  14  transmits to multiple ones of the client stations  25 - i  simultaneously. The table  900  corresponds to system configurations in which full compressed feedback is utilized for the listed channel configurations, according to an embodiment. Accordingly, the table  900  includes ordering for both φ and ψ angles for each of the listed channel configurations.  FIG. 10  is a table  1000  listing an ordering of compressed feedback angles for different channel configurations, according to some embodiments. Ordering listed in the table  1000  is utilized for various channel configurations when the AP  14  operates in single user mode, i.e., when the AP  14  transmits to only one of the client stations  25 - i  at a time. The table  1000  corresponds to system configurations in which partial compressed feedback is utilized for some of the listed channel configurations, according to an embodiment. The table  1000  is similar to the table  900  of  FIG. 9 , except that ψ angles are “struck out” or “punctured” from the table  1000  for channel configurations for which partial compressed feedback is utilized. 
     In some embodiments, partial compressed feedback is utilized for single user beamforming in additional channel configurations not indicated in  FIG. 10 . For example, in some embodiments, partial compressed feedback is utilized for a 2×2 channel configuration when single user mode of operation is being utilized. In such embodiments, y angles are additionally punctured from the table  1000  for the 2x2 channel configuration listed in the table  1000 . In some such embodiments, a steering matrix V′ reconstructed at the beamformer includes phase—only version of the first column of the steering matrix V′ computed at the beamformee, and a distorted version of the second column of the steering matrix V′ computed at the beamformee. In an embodiment, the beamformer utilizes the first column of the steering matrix V′ reconstructed at the beamformer to steer a single stream in the direction of the beamformee. 
     Further, in some embodiments, partial compressed feedback is additionally utilized for some or all multi-stream channel configurations listed in table  1000  of  FIG. 10 . In some such embodiments, ψ angles corresponding to only the first column of the steering matrix V′ are punctured from the ordering listed for these channel configurations the table  1000  of  FIG. 10 . For example, for the 4×1 channel configuration, angles {ψ 21 ,ψ 31 , ψ 41 } are struck out from table  1000 , in an embodiment. In this embodiments, predetermined equal gain values {ψ 21 ,ψ 31 ,ψ 41 } as described above, for example, are utilized at the beamformer to reconstruct the first column of the steering matrix V′, and ψ angles fed back from the beamformee are utilized to reconstruct the second and the third columns of the steering matrix V′. In this case, a phase-only version of the first column of the steering matrix V′ is obtained at the beamformee, and the second and third columns of the steering matrix V′ reconstructed at the beamformer are distorted versions of the corresponding columns of the steering matrix V′ computed at the beamformee. Referring to  FIG. 1 , such partial compressed feedback in which ψ angles corresponding to only the first column of a steering matrix V′ computed at a client station  25  are punctured from feedback from the client station  25  is utilized by the AP  14  to steer single stream pilot tones in subsequent multi-stream transmissions to the client station  25 , such as in an embodiment in which the first column of the steering matrix V′ is utilized to beamform pilot tones for each of the spatial streams. 
     Alternatively, in some embodiments, full compressed feedback is transmitted for all channel configurations for both single user and multi user system configurations. For example, angle orderings listed in table  900  of  FIG. 9  are utilized for both single user and multi user system configurations, in some such embodiments. However, the beamformer ignores ψ angle values fed back from the beamformee, for at least some system configurations, such as single stream single user system configurations. For example, the beamformer utilizes pre-determined equal gain values (e.g., ψ EG  values discussed above) for ψ angle values when reconstructing the steering matrix V′ rather than using the ψ angle values received from the beamformee, in some embodiments. In such embodiments, the beamformer need not perform PA balancing, as discussed above, when ψ EG  values are utilized to reconstruct the steering matrix V′ at the beamformer. 
       FIG. 11  is a diagram illustrating a MIMO control field  1100  of a data unit used to transmit compressed feedback (full or partial) from a beamformee to a beamformer, according to an embodiment. The control field  1100  is used to transmit various information describing the compressed feedback included in the data unit, in an embodiment. In one embodiment, the control field  1100  is included in a data unit that a client station  25  transmits to the AP  14  to feed back channel state information for a single stream channel to the AP  14  when WLAN  10  operates in a single user mode, i.e., when the AP  14  transmits to only one of the client stations  25 - i  at a time. In another embodiment, the control field  1100  is included in a data unit that a client station  25  transmits to the AP  14  to feed back channel state information for a multi-stream channel or for a single stream channel when the AP  14  when WLAN  10  operates in a multiuser mode, i.e., when the AP  14  transmits (and beamforms) to more than one of the client stations  25 - i  simultaneously. The control field  1100  includes elements, or subfields, common to both system configurations, where certain elements are interpreted differently based on the particular system configuration being utilized, in some embodiments 
     The control field  1100  includes an MU subfield  1102  to indicate whether a single user or a multiuser mode is being utilized (“a mode indicator”). In an example embodiment, the MU subfield  1102  is set to a logic “0” to indicate single user feedback (SU FB), and is set to a logic “1” to indicate multiuser feedback “MU FB.” Alternatively, in another embodiment, a logic “0” indicates MU FB and a logic “1” indicates SU FB. 
     The control field  1100  also includes an Nc subfield  1104  and an Nr subfield  1106  to indicate a number of columns and a number of rows, respectively, in a steering matrix corresponding to the feedback communication channel (i.e., the communication channel between the beamformer and the beamformee). More specifically, in an embodiment, a steering matrix has dimensions corresponding to (number of transmit antennas)×(number of spatial (or space-time) streams) forming a steering matrix suitable for use with the communication channel to which the channel feedback corresponds. Accordingly, in this embodiment, the Nc subfield  1104  indicates the number of spatial streams (or space-time streams if space-time encoding is utilized) corresponding to the communication channel, and the Nr subfield  1106  indicates the number of transmit antennas used at the beamformer for steering transmissions to the beamformee. In an embodiment, the particular number of spatial/space-time streams to which the steering matrix corresponds is determined at the beamformee. As an example, in an embodiment, a maximum of four transmit antennas and a maximum of four receive antennas are utilized, forming a maximum of four spatial/space-time streams. In this embodiment, depending on the particular channel configuration to which the feedback corresponds, the Nc subfield  1104  and the Nr subfield  1106  each contains a value in the range of 0 to 3 to indicate a corresponding number of spatial/space-time streams and a corresponding number of transmit antennas, respectively. In other embodiments, other suitable channel configurations are supported, and, accordingly, the Nc subfield  1104  and/or the Nr subfield  1106  contain other suitable values in at least some situations. 
     The control field  1100  also includes BW subfield  1108  to indicate the channel bandwidth to which the feedback data corresponds. In one embodiment, the bandwidth subfield  1108  includes two bits that are set to the value of 0 to indicate a 2 MHz BW, the value of 1 to indicate a 4 MHz BW, the value of 2 indicate an 8 MHz, and the value of 3 to indicate a 16 MHz BW. In other embodiments, the BW subfield  1108  includes other suitable number of bits and/or is used to indicate other suitable bandwidths. The control field  1100  also includes Ng subfield  1110  to indicate a tone grouping used to transmit the channel feedback. 
     The control field  1100  also includes a codebook info subfield  1112  used to indicate the number of bits used to quantize and/or encode the angles corresponding to the compressed feedback. In an embodiment, a codebook is composed of entries of from (x, y), where the x value corresponds to the number of bits used to quantize the φ angle value, and the y value corresponds to the number of bits used to quantize the ψ angle value. In an embodiment, the specific codebook information depends on whether the single stream SU configuration or multi stream (SU or MU) configuration is being utilized. Accordingly, in this embodiment, the value of the subfield  1112  is interpreted differently depending on the particular system configuration being utilized. 
     In an embodiment, the subfield  1112  includes one bit allowing indication of one of two suitable codebook entries, and the one bit indication is interpreted differently based on the system configuration being utilized. For example, in an embodiment, for multi stream (SU or MU) channel configurations (indicated by Nc subfield  1104  set to indicate a number of columns greater than 1), or for multi-user (single stream or multi stream) system configurations (indicated by SU/MU subfield  1102  set to “MU”), a value of logic “0” in the codebook info field indicates (4, 2) quantizing bits for SU mode (e.g., indicated by a value of 0 in SU/MU subfield  1102 ), and (7, 5) quantizing bits in MU mode (e.g., indicated by a value of 1 in SU/MU subfield  1102 ). Similarly, in an embodiment, for multi stream (SU or MU) channel configurations (indicated by Nc subfield  1104  set to indicate a number of columns greater than 1), or for multi-user (single stream or multi stream) system configurations (indicated by SU/MU subfield  1102  set to “MU”), a logic “1” in subfield  1112  indicates (6, 4) quantizing bits in SU mode and (9, 7) quantizing bits in MU mode. 
     On the other hand, for single stream, single user system configurations (e.g., indicated by SU/MU subfield  1102  set to “SU” and Nc subfield  1104  set to indicate Nc=1), partial compressed feedback that includes φ angle values and omits ψ angle values is utilized, and the codebook info subfield  1112  needs to indicate quantization used for the φ angle feedback and need not indicate quantization for ψ angle values, which are not included in the feedback, in some embodiments. Further, in some embodiments in which ψ angle values are fed back to the beamformer but are ignored by the beamformer, codebook info subfield  1112  is interpreted as if the ψ angle values were omitted from the feedback transmitted by the beamformee. In some embodiments, due to a higher tolerance on inaccuracy of φ angle values for single stream channel configurations, the number of bits used to quantize the φ angle values is reduced compared to the number of bits used in multi-stream system configurations. For example, in one such embodiment, a logic “0” in the codebook info subfield  1112  indicates that 2 bits are utilized for quantization of the φ angle feedback, and a logic “1” indicates that 3 bits are utilized for quantization of the φ angle feedback. In other embodiments, logic “0” and/or logic “1” in the codebook info subfield  1112  indicate that other suitable numbers of bits (e.g., 1 bit, 4 bits, 5 bits, etc.) are utilized for quantization of the φ angle feedback. 
     In yet another embodiment, a logic “0” in the codebook info subfield  1112  indicates that partial compressed feedback is utilized, while a logic “1” in the codebook info subfield  1112  indicates that full compressed feedback is utilized, or vice versa. For example, a logic “0” in the codebook info subfield  1112  indicates that 2 bits are utilized for quantization of the φ angle feedback, and also indicates omission of the ψ angle values in the feedback (i.e., indicates that partial compressed feedback is being utilized), in one such embodiment. On the other hand, a logic “1” in the codebook info subfield  1112  indicates (x, y) (e.g., (4,2)) quantizing bits for full compressed feedback, i.e. x bits utilized to quantize the φ angle values and y bits utilized to quantize the ψ angle values in the feedback, in this embodiment. 
       FIG. 12  is a flow diagram of an example method  1200  of providing, to a second communication device, channel state information determined at a first communication device, according to an embodiment. With reference to  FIG. 1 , the method  1200  is implemented by the network interface  27  of the client station  25 - 1 , in an embodiment. For example, in one such embodiment, the PHY processing unit  29  is configured to implement the method  1200 . According to another embodiment, the MAC processing  28  is also configured to implement at least a part of the method  1200 . With continued reference to  FIG. 1 , in yet another embodiment, the method  1200  is implemented by the network interface  16  (e.g., the PHY processing unit  20  and/or the MAC processing unit  18 ). In other embodiments, the method  1200  is implemented by other suitable network interfaces. 
     At block  1202 , a channel estimate matrix H describing a forward communication channel between the first communication device and the second communication device is determined at the second communication device. The channel estimate matrix H is determined at block  1202  based, for example, on a sounding packet transmitted by the first communication device to the second communication device, in an embodiment. The channel estimate matrix H determined at block  1202  has dimensions of N tx ×N rx , where N tx  corresponds to a number of transmit antennas used at the first communication device for communicating with the second communication device, and N rx  corresponds to a number of receive antennas used at the second communication device for communicating with the first communication device, in an embodiment. Accordingly, when the communication channel between the first communication device and the second communication device includes a single spatial stream (e.g., when N rx =1), the channel estimate matrix determined at block  1202  is a vector. 
     At block  1204 , feedback descriptive of the forward communication channel is generated at the second communication device. Block  1204  includes blocks  1206  and  1208 . At block  1206 , full compressed feedback is generated. Block  1206  is performed when the communication system is operating in a multi-user mode or when the communication system is operating in a single user mode and the forward communication channel includes multiple spatial streams (e.g., N tx &gt;1 and N rx &gt;1). Full compressed feedback includes φ angle values and ψ angle values corresponding to each of one or more columns of the channel estimate matrix H determined at block  1202 . In an embodiment, full compressed feedback is generated as described above in connection with  FIGS. 2A-2B , in an embodiment. In another embodiment, full compressed feedback is generated as described above in connection with one of  FIGS. 3-4 . In other embodiments, full compressed feedback is determined at block  1206  using other suitable techniques. 
     At block  1208 , partial compressed feedback is generated. Block  1208  is performed when the communication system is operating in a single-user mode and when the forward communication channel includes a single spatial streams (e.g., N rx =1 and N rx &gt;1). Partial compressed feedback generated at block  1208  includes φ angle values and omits ψ angle values corresponding to the channel estimate matrix H determined at block  1202 . In an embodiment, partial compressed feedback is generated as described above in connection with  FIGS. 8A-8B , in an embodiment. In another embodiment, partial compressed feedback is generated as described above in connection with one of Equations 11 and 12. In other embodiments, partial compressed feedback is determined at block  1208  using other suitable techniques. 
     At block  1210 , the feedback generated at block  1210  is transmitted from the second communication device to the first communication device. In an embodiment, feedback is first quantized (e.g., as described above in connection with Equation 4, or using another quantization scheme), and the quantized feedback is transmitted to the first communication device at block  1210 . In an embodiment, a data unit that includes the feedback is generated at block  1210 , and the data unit is transmitted to the first communication device. In an embodiment, the data unit generated at block  1210  includes a control field, such as the control field  1100  of  FIG. 11 . The control field is used to indicate, among other things, codebook information indicating a set of one or more quantization bit values used for quantizing feedback included in the data unit, in an embodiment. In other embodiments, suitable data units other than a data unit that includes the control field  1100  of  FIG. 11  are generated and transmitted to the first communication device at block  1210   
       FIG. 13  is a flow diagram of an example method  1300  of beamforming in a communication system that includes a first communication device and a second communication device, according to an embodiment. With reference to  FIG. 1 , the method  1300  is implemented by the network interface  16  of the AP  14 , in an embodiment. For example, in one such embodiment, the PHY processing unit  20  is configured to implement the method  1300 . According to another embodiment, the MAC processing  18  is also configured to implement at least a part of the method  1300 . With continued reference to  FIG. 1 , in yet another embodiment, the method  1300  is implemented by the network interface  27  (e.g., the PHY processing unit  29  and/or the MAC processing unit  28 ). In other embodiments, the method  1300  is implemented by other suitable network interfaces. 
     At block  1302 , feedback describing a forward communication channel between a first communication device and a second communication device is received at the first communication device from the second communication device. Block  1302  includes block  1304  and block  1306 . At block  1304 , full compressed feedback is received. Block  1206  is performed when the communication system is operating in a multi-user mode or when the communication system is operating in a single user mode and the forward communication channel includes multiple spatial streams. Full compressed feedback includes φ angle values and ψ angle values corresponding to each of one or more columns of a channel estimate matrix H determined for the forward communication channel at the second communication device. 
     At block  1208 , partial compressed feedback is received. Block  1208  is performed when the communication system is operating in a single-user mode and when the forward communication channel includes a single spatial streams. Partial compressed feedback generated at block  108  includes φ angle values and omits ψ angle values corresponding to a channel estimate matrix H determined for the forward communication channel at the second communication device. 
     At block  1308 , a steering matrix to be applied to signals to be transmitted to the second communication device is determined based on feedback received at block  1302 . In an embodiment and/or scenario, when full compressed feedback is received at block  1302 , the steering matrix at block  1308  is determined as described above in connection with  FIG. 5 . In another embodiment and/or scenario, when full compressed feedback is received at block  1302 , the steering matrix is at block  1308  determined as described above in connection with one of  FIGS. 6 and 7 . In an embodiment and/or scenario, when partial compressed feedback is received at block  1302 , the steering matrix at block  1308  is determined using pre-determined equal gain values for ψ angle values as discusses above in connection with Equation 9. In an embodiment and/or scenario, when partial compressed feedback is received at block  1302 , a phase-only steering matrix is determined based on feedback received at block  1302 , for example as described above in connection with Equation 14. In other embodiments and/or scenarios, the steering matrix is determined at block  1308  using other suitable techniques. 
     At block  1310 , the steering matrix determined at block  1308  is applied to a signal to be transmitted to the second communication device as the signal is provided to multiple transmit antennas at the first communication device. In some embodiments, after the steering matrix is applied to the signal at block  1310 , the signal is provided to a plurality of power amplifiers corresponding to the multiple transmit antennas to which the signal is provided at block  1310 . In one such embodiment, balancing of power amplifiers to maximize output power of each power amplifier is enabled when full compressed feedback is received at block  1302  and is disabled when partial compressed feedback is received at block  1302 . In other embodiments, power amplifier balancing is not disabled when partial compressed feedback is received at block  1302 . 
     At least some of the various blocks, operations, and techniques described above may be implemented utilizing hardware, a processor executing firmware instructions, a processor executing software instructions, or any combination thereof. When implemented utilizing a processor executing software or firmware instructions, the software or firmware instructions may be stored in any computer readable memory such as on a magnetic disk, an optical disk, or other storage medium, in a RAM or ROM or flash memory, processor, hard disk drive, optical disk drive, tape drive, etc. Likewise, the software or firmware instructions may be delivered to a user or a system via any known or desired delivery method including, for example, on a computer readable disk or other transportable computer storage mechanism or via communication media. Communication media typically embodies computer readable instructions, data structures, program modules or other data in a modulated data signal such as a carrier wave or other transport mechanism. The term “modulated data signal” means a signal that has one or more of its characteristics set or changed in such a manner as to encode information in the signal. By way of example, and not limitation, communication media includes wired media such as a wired network or direct-wired connection, and wireless media such as acoustic, radio frequency, infrared and other wireless media. Thus, the software or firmware instructions may be delivered to a user or a system via a communication channel such as a telephone line, a DSL line, a cable television line, a fiber optics line, a wireless communication channel, the Internet, etc. (which are viewed as being the same as or interchangeable with providing such software via a transportable storage medium). The software or firmware instructions may include machine readable instructions that, when executed by the processor, cause the processor to perform various acts. 
     When implemented in hardware, the hardware may comprise one or more of discrete components, an integrated circuit, an application-specific integrated circuit (ASIC), a programmable logic device (PLD), etc. 
     While the present invention has been described with reference to specific examples, which are intended to be illustrative only and not to be limiting of the invention, changes, additions and/or deletions may be made to the disclosed embodiments without departing from the scope of the invention. 
     Further aspects of the present inventions relate to one or more of the following clauses. 
     In an embodiment, a method of providing, from a first communication device to a second communication device, channel state information determined at the first communication device, includes determining, with the first communication device, a channel estimate matrix H describing a forward communication channel between the first communication device and the second communication device. The method also includes generating, with the first communication device and based on the channel estimate matrix H, feedback descriptive of the forward communication channel. When operating in a multi user mode or in a single user mode and with multiple spatial streams, generating the feedback comprises generating full compressed feedback, wherein full compressed feedback includes φ angle values and ψ angle values corresponding to each of one or more columns of the channel estimate matrix. When operating in the single user mode and with a single spatial stream, generating the feedback comprises generating partial compressed feedback, wherein partial compressed feedback includes φ angle values, and omits ψ angle values, corresponding to the channel estimate matrix. The method further comprises transmitting the feedback from the first communication device to the second communication device. 
     In other embodiments, the method includes one or more of the following features. 
     Generating partial compressed feedback includes determining a steering matrix V based on the channel matrix H, generating a steering matrix V′ by rotating each element of the steering matrix V such that the last element of the steering matrix V becomes a positive real number, and performing partial QR decomposition of the steering matrix V′ to determine the φ angle values to be included in the partial compressed feedback. 
     Generating the partial compressed feedback includes determining, directly from the channel matrix H, φ angle values to be included in the partial compressed feedback. 
     Generating the feedback further comprises quantizing the feedback. 
     A first set of quantization bits is used for quantizing the feedback when the feedback corresponds to the full compressed feedback. 
     A second set of quantization bits is used for quantizing the feedback when the feedback corresponds to the partial compressed feedback. 
     The second set of quantization bits is different than the first set of quantization bits. 
     Transmitting the feedback comprises generating a data unit to include the feedback. 
     The data unit further includes a codebook information field indicating a set of quantization bits used for quantizing the feedback. 
     The codebook information field is interpreted differently based on whether the feedback corresponds to the full compressed feedback or to the partial compressed feedback. 
     In another embodiment, an apparatus comprises a network interface configured to determine a channel estimate matrix H describing a forward communication channel between a first communication device and a second communication device. The network interface is also configured to generate feedback descriptive of the forward communication channel. When operating in a multi user mode or in a single user mode and with multiple spatial streams, the network interface is configured to generate full compressed feedback, wherein full compressed feedback includes φ angle values and ψ angle values corresponding to each of one or more columns of the channel estimate matrix. When operating in the single user mode and with a single spatial stream, the network interface is configured to generate partial compressed feedback, wherein partial compressed feedback includes φ angle values, and omits ψ angle values, corresponding to the channel estimate matrix. The network interface is further configured to transmit the feedback to the second communication device. 
     In other embodiments, the apparatus includes one or more of the following features. 
     The network interface is configured to generate partial compressed feedback at least by determining a steering matrix V based on the channel matrix H, generating a steering matrix V′ by rotating each element of the steering matrix V such that the last element of the steering matrix V becomes a positive real number, and performing partial QR decomposition of the steering matrix V′ to determine the φ angle values to be included in the feedback. 
     The network interface is configured to generate partial compressed feedback at least by determining, directly from the channel matrix H, φ angle values to be included in the feedback. 
     The network interface is further configured to quantize the feedback prior to transmitting the feedback. 
     The network interface is configured to use a first set of quantization bits for quantizing the feedback when the feedback corresponds to the full compressed feedback. 
     The network interface is configured to use a second set quantization of bits for quantizing the feedback when the feedback corresponds to the partial compressed feedback. 
     The second set of quantization bits is different than the first set of quantization bits. 
     The network interface is further configured to generate a data unit to include the feedback. 
     The data unit further includes a codebook information field indicating a set of quantization bits used for quantizing the feedback. 
     The codebook information field is interpreted differently based on whether the feedback corresponds to the full compressed feedback or to the partial compressed feedback. 
     In yet another embodiment, a method of beamforming in a communication system that includes a first communication device and a second communication device includes receiving, at the first communication device from the second communication device, feedback describing a forward communication channel between the first communication device and the second communication device. Feedback corresponds to one of (i) full compressed feedback when the forward communication channel includes multiple spatial streams or when the forward communication channel includes a single spatial stream and the first communication device operates in a multi-user mode, wherein full compressed feedback includes φ angle values and ψ angle values corresponding to each of one or more columns of a channel estimate matrix determined for the forward communication channel at the second communication device, or (ii) partial compressed feedback when the forward communication channel includes a single spatial stream and the first communication device operates in a single user mode, wherein partial compressed feedback includes φ angle values and omits ψ angle values corresponding to the channel estimate matrix determined for the forward communication channel at the second communication device. The method also includes determining, based on the feedback, a steering matrix to be applied to signals to be transmitted from the first communication device to the second communication device. The method additionally includes applying the steering matrix to a signal to be transmitted to the second communication device as the signal is provided to multiple transmit antennas at the first communication device. 
     In other embodiments, the method includes one or more of the following features. 
     When feedback corresponds to partial compressed feedback, determining the steering matrix comprises determining the steering matrix by reconstructing, based on the received φ angle values and pre-determined ψ angle values, a receiver steering matrix determined for the forward communication channel at the receiving device. 
     When feedback corresponds to partial compressed feedback, determining the steering matrix comprises determining the steering matrix by reconstructing, based on the received φ angle values, a phase only version of a receiver steering matrix determined for the forward communication channel at the second communication device. 
     The method further comprises after applying the steering matrix to the signal, providing the signal to a plurality of power amplifiers corresponding to the multiple transmit antennas, and balancing output powers of the plurality of power amplifiers to maximize output power of each power amplifier of the plurality of power amplifiers. 
     When feedback corresponds to full compressed feedback, balancing of output power amplifiers is enabled. 
     When feedback corresponds to partial compressed feedback, balancing of output power amplifiers is disabled. 
     Determining the steering matrix includes de-quantizing at least the received φ angle values. 
     De-quantizing is performed (i) based on a first number of quantization bits when received feedback is full compressed feedback and (ii) based on a second number of quantization bits when received feedback is partial compressed feedback, wherein the second number of quantization bits is different than the first number of quantization bits. 
     The method further comprising receiving codebook information indicating a number of quantization bits used for generating the feedback at the receiving device. 
     The codebook information is interpreted differently depending on whether the received feedback is full compressed feedback or partial compressed feedback. 
     In still another embodiment, an apparatus comprises a network interface configured to receive, from a first communication device, feedback describing a forward communication channel between the first communication device and a second communication device. Feedback corresponds to one of (i) full compressed feedback when the forward communication channel includes multiple spatial streams or when the forward communication channel includes a single spatial stream and the first communication device operates in a multi-user mode, wherein full compressed feedback includes φ angle values and ψ angle values corresponding to each of one or more columns of a channel estimate matrix determined for the forward communication channel at the second communication device, or (ii) partial compressed feedback when the forward communication channel includes a single spatial stream and the first communication device operates in a single user mode, wherein partial compressed feedback includes φ angle values and omits ψ angle values corresponding to the channel estimate matrix determined for the forward communication channel at the second communication device. The network interface is also configured to determine, based on the feedback, a steering matrix to be applied to signals to be transmitted to the second device. The network interface is additionally configured to apply the steering matrix to a signal to be transmitted to the second device as the signal is provided to multiple transmit antennas at the first communication device. 
     In other embodiments, the apparatus includes one or more of the following features. 
     The network interface is configured to, when feedback corresponds to partial compressed feedback, determine the steering matrix at least by reconstructing, based on the received φ angle values and pre-determined ψ angle values, a receiver steering matrix determined for the forward communication channel at the second communication device. 
     The network interface is configured to, when feedback corresponds to partial compressed feedback, determine the steering matrix at least by reconstructing, based on the received φ angle values, a phase-only version of a receiver steering matrix determined for the forward communication channel at the second communication device. 
     The network interface is further configured to after applying the steering matrix to the signal, provide the signal to a plurality of power amplifiers corresponding to the multiple transmit antennas, and balance output powers of the plurality of power amplifiers to maximize output power of each power amplifier of the plurality of power amplifiers. 
     When feedback corresponds to full compressed feedback, enable balancing of output power amplifiers. 
     When feedback corresponds to partial compressed feedback, disable balancing of output power amplifiers. 
     The network interface is further configured to de-quantize at least the received φ angle values prior to determining the steering matrix. 
     De-quantizing is performed (i) based on a first number of quantization bits when received feedback is full compressed feedback and (ii) based on a second number of quantization bits when received feedback is partial compressed feedback. 
     The second number of quantization bits is different than the first number of quantization bits. 
     The network interface is further configured to receive codebook information indicating a number of quantization bits used for generating the feedback at the second communication device, and interpret the codebook information differently depending on whether the received feedback is full compressed feedback or partial compressed feedback.