Patent Publication Number: US-2012033566-A1

Title: Hybrid feedback for closed loop multiple-input multiple- output

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application is a national stage application of PCT Application No. PCT/US2009/055452, filed Aug. 28, 2009, which claims the benefit of U.S. Provisional Application No. 61/092,716, filed Aug. 28, 2008. All of the above referenced applications are hereby incorporated by reference herein. 
    
    
     TECHNICAL FIELD 
     This disclosure relates to communication systems, and more particularly to a method and apparatus providing channel estimation feedback to a base station by a user equipment in a wireless communication system. 
     BACKGROUND 
     In closed loop Multiple-Input and Multiple-Output (MIMO) systems, downlink channel information is provided back to the base station. The channel information, for example the channel matrix or its right singular vectors, are typically analog sources in nature. 
     For single user MIMO applications, this channel information is used at the base station to direct the transmitted power towards the mobile station. Hence accurate channel feedback in single user applications provides a signal-to-noise ratio (SNR) gain, which may result in significant throughput gains. For multi-user (MU) MIMO applications on the other hand, accurate channel state information at the transmitter (CSIT) is more important since having inaccurate CSIT incurs a significant loss in throughput and does not achieve the full multiplexing gain. 
     Traditionally a digital approach is taken for this problem guided by Shannon&#39;s source-channel separation theorem that proves the optimality of separate source and channel coding. In this approach, the source is first quantized and then the quantization bits are coded using a channel code to recover the quantized source with low error probability at the base station. One drawback of a digital scheme however, is the threshold effect, which means that the digital system achieves the desired performance only at the specific designed SNR. At any lower SNR, system performance is typically sacrificed and at any higher SNR, system performance does not improve. Since the exact feedback channel SNR is unknown and belongs to a range, the digital approach for channel feedback is typically suboptimal. Another shortcoming of this approach, even for a single SNR, is that long source and channel codes are needed to achieve an optimal performance, which is not possible over a fast feedback link. It is desirable to design a single transmission scheme that will be simultaneously good for the entire SNR range over a fast link. 
     Analog transmission of the source on the other hand, allows a graceful degradation of performance at low SNR and does not saturate at high SNR. However, it is typically optimal for transmitting a Gaussian source over a Gaussian channel where the source bandwidth is the same as the channel bandwidth. In some cases however, the channel bandwidth may be greater than the source bandwidth and hence a pure analog scheme may be suboptimal as well. 
     SUMMARY 
     Methods and apparatuses of providing channel estimation feedback to a base station by a user equipment in a wireless communication system are described herein. 
     In an exemplary embodiment of the present disclosure, there is a method of providing channel estimation feedback to a base station by a user equipment in a wireless communication system. The method includes receiving downlink data from the base station, calculating a digital portion representing a channel parameter estimation of the downlink data, calculating an analog portion representing an error estimation of the digital portion and providing, as feedback, the digital portion and the analog portion to the base station. 
     In yet another exemplary embodiment, there is a user equipment. The user equipment including a receiving unit configured to receive downlink data from a base station, a processor coupled to the receivers and configured to generate feedback in the form of digital information representing a channel parameter estimation of the downlink data, and analog information representing an error estimation of the channel parameter estimation, and a transmitting unit configured to transmit the feedback to the base station, wherein the digital information is provided in the form of one or more singular vectors to form a matrix of singular vectors. 
     In still another exemplary embodiment, there is an apparatus. The apparatus including a receiving unit for receiving and decoding feedback received from a user equipment in the form of a digital information representing quantized channel estimation information and an analog information representing an error estimation of the digital information, and a transmitting unit adapted to adjust a transmission parameter based on the feedback and configured to transmit downlink data to a user equipment. 
     The details of one or more variations of the subject matter described herein are set forth in the accompanying drawings and the description below. Features and advantages of the subject matter described herein will be apparent from the description and drawings, and from the claims. 
    
    
     
       DESCRIPTION OF DRAWINGS 
       In the drawings, 
         FIG. 1  depicts a block diagram of a network including client stations and base stations; 
         FIG. 2  depicts a block diagram of a client station including a channel estimator; 
         FIG. 3A  depicts a process for hybrid feedback for closed loop MIMO; 
         FIG. 3B  depicts a hybrid data mapping on a single tile; 
         FIG. 4  depicts a block diagram of a channel estimator; 
         FIG. 5  depicts a block diagram of a base station including a channel estimator; and 
         FIG. 6  depicts a process, at the base station, configured to use hybrid feedback for closed loop MIMO. 
     
    
    
     DETAILED DESCRIPTION 
     Throughout this description, the examples shown should be considered as exemplars, rather than as limitations on the present disclosure. 
       FIG. 1  is a simplified functional block diagram of an embodiment of a wireless communication system  100 . The wireless communication system  100  includes a plurality of base stations  110 A and  110 B, each supporting a corresponding service or coverage area  112 A and  112 B. The base stations are capable of communicating with wireless devices within their coverage areas. For example, the first base station  110 A is capable of wirelessly communicating with a first client station  114 A and a second client station  114 B within the coverage area  112 A. The first client station  114 A is also within the coverage area  112 B and is capable of communicating with the second base station  110 B. In this description, the communication path from the base station to the client station is referred to as a downlink  116 A and the communication path from the client station to the base station is referred to as an uplink  116 B. 
     Although for simplicity only two base stations are shown in  FIG. 1 , a typical wireless communication system  100  includes a much larger number of base stations. The base stations  110 A and  110 B can be configured as cellular base station transceiver subsystems, gateways, access points, radio frequency (RF) repeaters, frame repeaters, nodes, or any wireless network entry point. 
     The base stations  110 A and  110 B can be configured to support an omni-directional coverage area or a sectored coverage area. For example, the second base station  110 B is depicted as supporting the sectored coverage area  112 B. The coverage area  112 B is depicted as having three sectors,  118 A,  118 B, and  118 C. In typical embodiments, the second base station  110 B treats each sector  118  as effectively a distinct coverage area. 
     Although only two client stations  114 A and  114 B are shown in the wireless communication system  100 , typical systems are configured to support a large number of client stations. The client stations  114 A and  114 B can be mobile, nomadic, or stationary units. The client stations  114 A and  114 B are often referred to as, for example, mobile stations, mobile units, subscriber stations, wireless terminals, or the like. A client station can be, for example, a wireless handheld device, a vehicle mounted device, a portable device, client premise equipment, a fixed location device, a wireless plug-in accessory or the like. In some cases, a client station can take the form of a handheld computer, notebook computer, wireless telephone, personal digital assistant, wireless email device, personal media player, meter reading equipment or the like and may include a display mechanism, microphone, speaker and memory. 
     In a typical system, the base stations  110 A and  110 B also communicate with each other and a network control module  124  over backhaul links  122 A and  122 B. The backhaul links  122 A and  122 B may include wired and wireless communication links. The network control module  124  provides network administration and coordination as well as other overhead, coupling, and supervisory functions for the wireless communication system  100 . 
     In some embodiments, the wireless communication system  100  can be configured to support both bidirectional communication and unidirectional communication. In a bidirectional network, the client station is capable of both receiving information from and providing information to the wireless communications network. Applications operating over the bidirectional communications channel include traditional voice and data applications. In a unidirectional network, the client station is capable of receiving information from the wireless communications network but may have limited or no ability to provide information to the network. Applications operating over the unidirectional communications channel include broadcast and multicast applications. In one embodiment, the wireless system  100  supports both bidirectional and unidirectional communications. In such an embodiment, the network control module  124  is also coupled to external entities via, for example, content link  126  (e.g., a source of digital video and/or multimedia) and two-way traffic link  128 . 
     The wireless communication system  100  can be configured to use Orthogonal Frequency Division Multiple Access (OFDMA) communication techniques. For example, the wireless communication system  100  can be configured to substantially comply with a standard system specification, such as IEEE 802.16 and its progeny or some other wireless standard such as, for example, WiBro, WiFi, Long Term Evolution (LTE), or it may be a proprietary system. The subject matter described herein is not limited to application to OFDMA systems or to the noted standards and specifications. The description in the context of an OFDMA system is offered for the purposes of providing a particular example only. 
     As used herein, IEEE 802.16 refers to one or more Institute of Electrical and Electronic Engineers (IEEE) Standard for Local and metropolitan area networks, Part 16: Air Interface for Fixed Broadband Wireless Access Systems, 1 Oct. 2004, IEEE Standard for Local and metropolitan area networks, Part 16: Air Interface for Fixed and Mobile Broadband Wireless Access Systems, 26 Feb. 2006, and any subsequent additions or revisions to the IEEE 802.16 series of standards. 
     In some embodiments, downlinks  116 A-B and uplink  116 C each represent a radio frequency (RF) signal. The RF signal may include data, such as voice, video, images, Internet Protocol (IP) packets, control information, and any other type of information. When IEEE-802.16 is used, the RF signal may use OFDMA. OFDMA is a multi-user version of orthogonal frequency division multiplexing (OFDM). In OFDMA, multiple access is achieved by assigning to individual users groups of subcarriers (also referred to as tones). The subcarriers are modulated using BPSK (binary phase shift keying), QPSK (quadrature phase shift keying), QAM (quadrature amplitude modulation), and carry symbols (also referred to as OFDMA symbols) including data coded using a forward error-correction code. 
     In some embodiments, a base station is implemented using multiple-input and multiple-output (MIMO). When MIMO is used, a base station may include a plurality of antennas. For example, base station  110 A may be configured for MIMO and include a precoder (described further below) coupled to two antennas for the MIMO transmission via downlinks  116 A-B. The precoder is configured to perform “precoding,” which refers to beamforming to support MIMO transmission at each of the antennas (e.g., using singular vectors to weight orthogonal “eigen-beams” transmitted via each of the antennas). A client station may include a plurality of antennas to receive the MIMO transmission sent via downlinks  116 A-B. The client station may also combine the received signals, which may result in fewer errors and/or enhanced data transfer. Although the examples given herein are made in the context of MIMO, other smart antenna techniques may be used as well including MISO (multiple input, single output) and SIMO (single input, multiple output). 
     Moreover, when MIMO is used, the base station may perform precoding (which may use channel estimation information) to code, for each antenna, one or more streams of symbols for transmission over the corresponding antenna. In a closed loop feedback-based approach, the channel estimation information is provided by the client station to the base station. For example, a client station may receive each of the downlinks  116 A-B transmitted by the antennas of the base station, decode the received downlink signals, determine channel estimation information for the decoded channels (e.g., subcarriers) in each of the received downlink signals, and then provide to the base station the determined channel estimation information, which serves as feedback. The channel estimation information provided by the client station may include singular vectors determined by the client station using a singular value decomposition (SVD) and an error signal (which is described further below). Although the information that is used as feedback is described herein as including singular vectors, the feedback may include one or more of the following as well: a channel matrix, a channel covariance matrix, an SV′, an R (i.e., upper matrix from a QR decomposition of the channel), and the like. 
     The singular vectors may be determined for each of the channels (e.g., subcarriers) used by the antennas transmitting from the base station to the client station. For example, the base station may include two antennas, each of which transmits over a channel comprising one or more subcarriers. The client station may then determine singular vectors for the subcarriers. The singular vectors may be configured into a matrix, V, which is also referred to as a matrix of right singular vectors or, more simply, the matrix V. 
       FIG. 2  depicts an exemplary client station, such as client station  114 B. The client station  114 B includes a plurality of antennas  220 A-B for receiving the downlinks  116 A-B, each transmitted by a base station, such as base station  110 A, which implements MIMO as described further below. Although the examples described herein refer to two antennas at the base station and two antennas at the client station, other quantities of antennas can be used at the base station and the client station. The client station  114 B also includes a radio interface  240 , which may include other components, such as filters, converters (e.g., digital-to-analog converters and the like), symbol demappers, an Inverse Fast Fourier Transform (IFFT) module, and the like, to process the received MIMO transmission sent via downlinks  116 A-B, to determine channel estimation information, and to decode any data, such as the symbols, carried by the downlinks. In some implementations, the client station  114 B is also compatible with IEEE 802.16 and MIMO transmissions (which are sent via downlinks  116 A-B), although MIMO implementations using other wireless technologies, such as LTE, WiBro, and the like, may also be implemented using the subject matter described herein. The client station  114 B further includes a channel estimator  260  (described further below), a processor  220  for controlling client station  114 B and for accessing and executing program code stored in memory  225 . 
     For each of the MIMO transmissions sent via downlinks  116 A-B and received at each of antennas  220 A-B, the channel estimator  260  may determine channel estimation information, such as the singular vectors determined using a singular value decomposition, and then feedback that information and other information as part of a closed loop MIMO feedback to the base station. Moreover, the feedback from the client station to the base station may be in the form of a hybrid of analog information and digital information. For example, the digital information may include quantized channel estimation information, such as one or more singular vectors of the matrix V, and the analog information may include an error signal representative of the error of the quantized singular vectors of matrix V, when compared to the original, un-quantized singular vectors of matrix V (which has been aligned as described further below). 
       FIG. 3A  depicts a process  300  for providing hybrid feedback (e.g., analog information and digital information). Although the description herein describes the feedback being sent from a client station to a base station, this implementation is only exemplary as the feedback process  300  can be used by any receiver to feedback information to a transmitter (e.g., a base station may use process  300  to feedback information to a client station, which is transmitting on an uplink to the base station). The description of process  300  will also refer to  FIG. 2 . 
     At  302 , a singular value decomposition is performed of channel matrix, H. For example, channel estimator  260  at client station  114 B may perform a singular value decomposition to form the matrix V including singular vectors, such as vectors v 1 , v 2 , v 3 , and so forth until the last singular vector of that matrix. The singular value decomposition may be performed in a variety of ways and may take the following form: 
       H=USV*, 
     wherein H represents the channel estimation matrix, U represents a matrix of left singular vectors, S represents a diagonal matrix whose diagonal elements are the singular values of H, and V* represents a matrix of right singular vectors. The asterisk (*) represents that the matrix V is a conjugate transpose. 
     It should be noted that alternate methods, such as but not limited to the well known power method and closed form singular value decomposition, may be used to form the matrix V of singular vectors from the channel matrix H. The present Applicant has earlier provided additional details of forming matrix V of singular vectors from the channel matrix H in PCT Patent Application Number PCT/US2009/049851, entitled CLOSED FORM SINGULAR VALUE DECOMPOSITION, filed on Jul. 7, 2009, which is incorporated herein by reference. 
     At  304 , the singular vectors of the matrix V* are used to calculate a transmission rank, r opt , based on a desired criterion. For example, an optimal rank that maximizes capacity can be determined using the following formula: 
     
       
         
           
             
               r 
               opt 
             
             = 
             
               
                 
                   argmax 
                   r 
                 
                  
                 
                   C 
                   r 
                 
               
               = 
               
                 
                   argmax 
                   r 
                 
                  
                 
                     
                 
                  
                 log 
                  
                 
                     
                 
                  
                 
                   det 
                    
                   
                     ( 
                     
                       I 
                       + 
                       
                         
                           
                             S 
                              
                             
                                 
                             
                              
                             N 
                              
                             
                                 
                             
                              
                             R 
                           
                           r 
                         
                          
                         
                           HV 
                           
                             1 
                             : 
                             r 
                           
                         
                          
                         
                           V 
                           
                             1 
                             : 
                             r 
                           
                           * 
                         
                          
                         
                           H 
                           * 
                         
                       
                     
                     ) 
                   
                 
               
             
           
         
       
     
     In this example, singular vectors v 1 , v 2 , v 3 , and so forth of matrix V* are the columns of that matrix that provide a maximum capacity on the channel. Rank adaptation may be used in single user MIMO whereby a mobile station decides on the rank r of the precoder and sends back the first r strongest singular vectors. Similarly for MU-MIMO a user can send a hybrid version of the r strongest singular vectors. 
     At  306 , one or more of the singular vectors of matrix V* are quantized using a k bit unitary codebook with the mapping criterion of interest such as maximum capacity criterion. The resulting quantization bits are denoted by (b 1 , . . . ,b k ) and the quantized V by {circumflex over (V)}. 
     At  308 , an alignment is conducted to align the original, un-quantized matrix V* to the quantized matrix V by performing a unitary transformation on V. Since the precoder V is invariant to unitary transformations on the right, a goal is to find the unitary transformation matrix Q opt  such that 
     
       
         
           
             
               Q 
               opt 
             
             = 
             
               
                 argmin 
                 Q 
               
                
               
                 
                   
                      
                     
                       
                         V 
                         ^ 
                       
                       - 
                       VQ 
                     
                      
                   
                   F 
                   2 
                 
                 . 
               
             
           
         
       
     
     Q opt  is given by Q opt =V corr U* corr  where V corr  and U corr  are the right and left singular vectors of the correlation matrix, {circumflex over (V)}*V, respectively, i.e., {circumflex over (V)}*V=U corr ΣV* corr . The aligned V is denoted by V a =VQ opt . It should be noted that for rank-1 precoding, the unitary transformation becomes a phase rotation: 
     
       
         
           
             
                
               jφ 
             
             = 
             
               
                 
                   
                     V 
                     * 
                   
                    
                   
                     V 
                     ^ 
                   
                 
                 
                    
                   
                     
                       V 
                       * 
                     
                      
                     
                       V 
                       ^ 
                     
                   
                    
                 
               
               . 
             
           
         
       
     
     Alternatively for rank-2 or higher, one can use a diagonal unitary rotation matrix whereby each column of V is independently phase aligned. 
     During the alignment, the phase of un-quantized matrix V* is adjusted to attempt alignment to the quantized matrix {circumflex over (V)}. The resulting aligned, un-quantized matrix is referred to as Va. 
     At  310 , an analog error signal is generated. The analog error signal represents the error between the quantized, matrix {circumflex over (V)} and the un-quantized, aligned matrix Va (also referred to as V aligned ). In some embodiments, the error signal may be determined based on the following equation: 
       error signal E={circumflex over (V)}-V a . 
     At  312 , the quantized matrix {circumflex over (V)} is encoded. For example, channel estimator  260  may use a short algebraic code, such as Reed-Muller code, to encode the quantization bits (b 1 , . . . ,b k ) of quantized matrix {circumflex over (V)} into a codeword, such as (c 1 , . . . ,c n ), wherein c 1  represents the first bit of the codeword and c n  represents the last bit of the codeword. 
     At  314 , the analog error signal generated at  310  and the codeword of the quantized matrix {circumflex over (V)} formed at  312 , are provided (e.g., sent), as feedback, by the channel estimator  260  from the client station  114 B to a base station. This feedback is a hybrid feedback, which includes an analog portion (e.g., the analog error signal generated at  310 ) and a digital portion (e.g., codeword of the quantized matrix {circumflex over (V)} formed at  312 ). Moreover, this feedback information enables the base station to configure precoding for MIMO transmission at the base station. For the plurality of subcarriers of a band, an average singular vector may be determined, the aligned average singular vector representative of the plurality of subcarriers of the band. The aligned average singular vector may be provided, as the hybrid feedback to a precoder at a base station. Further detail on creating an average singular vector was described earlier by the Applicant in PCT Patent Application Number PCT/US2009/049852, filed Jul. 7, 2009, entitled IMPROVED PRECODER FOR MULTIPLE-SUBCARRIER BAND FEEDBACK, herein incorporated by reference in its entirety. 
     In an embodiment, the digital data is constructed by using a 4 or 6 bit codebook quantizers for both rank 1 and rank 2 transmissions. To encode the 4 bits, for example, the (8,4,4) extended Hamming, i.e., Reed-Muller code RM (3,1), is used. The digital part of hybrid information which consists of 8 coded bits will occupy 4 subcarriers, i.e., QPSK symbols. 
     Furthermore, 2 tiles are used as the basic uplink transmission unit. If rank 2 transmission is used the analog error will have 8 analog symbols occupying 8 subcarriers. If rank 1 transmission is used, the analog error will have 4 analog symbols which will occupy 4 subcarriers. 
     In rank 1 transmission, the digital and analog data are mapped into the first tile as shown in  FIG. 3B  and then repeated over the second tile. For rank 2 transmission, the digital data is repeated and sent over the 2 tiles just as in rank 1 transmission. Specifically, the first 4 symbols of the analog error are sent on the analog positions of the first tile as shown in  FIG. 3B  and the last 4 symbols are sent on the analog positions of the second tile. 
     Before placing the 8 analog symbols on the tiles, a unitary transformation is applied on them using an 8 dimensional rotational unitary matrix, φ 8 , constructed according to 
     
       
         
           
             
               Φ 
               n 
             
             = 
             
               [ 
               
                 
                   
                     
                       
                         Φ 
                         
                           n 
                           / 
                           2 
                         
                       
                        
                       cos 
                        
                       
                           
                       
                        
                       θ 
                     
                   
                   
                     
                       
                         Φ 
                         
                           n 
                           / 
                           2 
                         
                       
                        
                       sin 
                        
                       
                           
                       
                        
                       θ 
                     
                   
                 
                 
                   
                     
                       
                         - 
                         
                           Φ 
                           
                             n 
                             / 
                             2 
                           
                         
                       
                        
                       sin 
                        
                       
                           
                       
                        
                       θ 
                     
                   
                   
                     
                       
                         Φ 
                         
                           n 
                           / 
                           2 
                         
                       
                        
                       cos 
                        
                       
                           
                       
                        
                       θ 
                     
                   
                 
               
               ] 
             
           
         
       
     
     where φ 2  is the standard 2 dimensional rotation matrix 
     
       
         
           
             
               Φ 
               2 
             
              
             
               [ 
               
                 
                   
                     
                       cos 
                        
                       
                           
                       
                        
                       θ 
                     
                   
                   
                     
                       sin 
                        
                       
                           
                       
                        
                       θ 
                     
                   
                 
                 
                   
                     
                       
                         - 
                         sin 
                       
                        
                       
                           
                       
                        
                       θ 
                     
                   
                   
                     
                       cos 
                        
                       
                           
                       
                        
                       θ 
                     
                   
                 
               
               ] 
             
           
         
       
     
     and θ is a properly chosen angle. These rotational matrices can be reversed at the user equipment and provide more diversity gain on the analog data over 2 tiles and protect it from deep fades. It should be noted that for 
     
       
         
           
             
               θ 
               = 
               
                 Π 
                 4 
               
             
             , 
           
         
       
     
     the rotational matrices reduce to the well-known Walsh-Hadamard matrices. 
     The mobile can alternatively decide to transmit on 4 or 6 tiles in which case the 2 tile structure will just be repeated for 4 and 6 tile transmissions. This will result in increased diversity. Furthermore, repeating the digital data on two different tiles as opposed to the same tile provides more diversity gain. 
     To satisfy the power constraint, the average power per subcarrier is set to 1 (or equivalently per tile to be 8). Furthermore, the same scaling factor for both digital and analog data is used. However, since the digital data is mapped to a QPSK constellation and has constant power of 1 per subcarrier and the analog data is an error term and has much lower average power, the analog error is first boosted by a known factor, β, which is a design parameter that could be selected based on the application. 
     In an embodiment, the resulting analog average power is the same as the digital power as it provides good balance between the detection of the digital and analog portions. Hence, writing the power equation for the basic transmission unit of 2 tiles provides: 
     
       
         
           
             
               16 
               = 
               
                 
                   
                     α 
                     2 
                   
                    
                   
                     ( 
                     
                       
                         P 
                         digital 
                       
                       + 
                       
                         
                           β 
                           2 
                         
                          
                         
                           
                              
                             E 
                              
                           
                           F 
                           2 
                         
                       
                     
                     ) 
                   
                 
                 = 
                 
                   
                     α 
                     2 
                   
                    
                   
                     ( 
                     
                       8 
                       + 
                       
                         
                           β 
                           2 
                         
                          
                         
                           
                              
                             E 
                              
                           
                           F 
                           2 
                         
                       
                     
                     ) 
                   
                 
               
             
             , 
             wherein 
           
         
       
       
         
           
             α 
             = 
             
               
                 
                   16 
                   
                     8 
                     + 
                     
                       
                         β 
                         2 
                       
                        
                       
                         
                            
                           E 
                            
                         
                         F 
                         2 
                       
                     
                   
                 
               
               . 
             
           
         
       
     
     At the receiver, this factor can be estimated by finding the ratio of the average power of the pilot signal to the average power of the digital part of the data since the pilots all have power 1. 
     At the receiver, the digital part of the feedback data is first combined using a Maximal Ratio Combiner (MRC) and then a Maximum Likelihood (ML) decoder is used to decode the Hamming code. Assuming that the ith coded bit sees an equivalent vector channel k (resulting from both the SIMO channel and repetition), i.e., {right arrow over (y)} i ={right arrow over (h)} i {right arrow over (c)} i +{right arrow over (n)}, then the corresponding MRC performs the following operation on the ith received vector: 
     
       
         
           
             
               
                 y 
                 ^ 
               
               i 
             
             = 
             
               
                 
                   
                     h 
                     -&gt; 
                   
                   i 
                   * 
                 
                 
                    
                   
                     
                       h 
                       -&gt; 
                     
                     i 
                   
                    
                 
               
                
               
                 
                   
                     y 
                     -&gt; 
                   
                   i 
                 
                 . 
               
             
           
         
       
     
     An ML decoder is then used on the combined symbols to decode the digital code as follows: 
     
       
         
           
             
               ( 
               
                 
                   c 
                   1 
                   opt 
                 
                 , 
                 … 
                  
                 
                     
                 
                 , 
                 
                   c 
                   n 
                   opt 
                 
               
               ) 
             
             = 
             
               
                 argmax 
                 
                   
                     ( 
                     
                       
                         c 
                         1 
                       
                       , 
                       
                           
                       
                        
                       … 
                        
                       
                           
                       
                       , 
                       
                         c 
                         n 
                       
                     
                     ) 
                   
                   ∈ 
                   
                     RM 
                      
                     
                       ( 
                       
                         3 
                         , 
                         1 
                       
                       ) 
                     
                   
                 
               
                
               
                 ∑ 
                 
                   
                      
                     
                       
                         
                           y 
                           ^ 
                         
                         i 
                       
                       - 
                       
                         
                            
                           
                             
                               h 
                               -&gt; 
                             
                             i 
                           
                            
                         
                          
                         
                           c 
                           i 
                         
                       
                     
                      
                   
                   2 
                 
               
             
           
         
       
     
     The analog portion of the data is reconstructed using a linear estimator. Assuming the equivalent vector channel on the ith analog symbol, e i , is given by {right arrow over (h)} i , i.e., {right arrow over (y)} i ={right arrow over (h)} i e i +{right arrow over (n)}, the estimator is given by 
     
       
         
           
             
               
                 e 
                 ^ 
               
               i 
             
             = 
             
               
                 
                   
                     h 
                     -&gt; 
                   
                   i 
                   * 
                 
                 
                   
                     
                        
                       
                         
                           h 
                           -&gt; 
                         
                         i 
                       
                        
                     
                     2 
                   
                   + 
                   
                     
                       1 
                       / 
                       S 
                     
                      
                     
                         
                     
                      
                     N 
                      
                     
                         
                     
                      
                     R 
                   
                 
               
                
               
                 
                   
                     y 
                     -&gt; 
                   
                   i 
                 
                 . 
               
             
           
         
       
     
     The precoder V is then reconstructed by adding the reconstructed analog error to the decoded quantized precoder. 
     In an alternate embodiment, the hybrid algorithm could send other quantities such as H, SV, QR, or P. This can be achieved with proper vector or scalar quantizers for these quantities. For example a scalar quantizer can be designed for the elements of a Raleigh faded H by using 1 quantization bit for the real and 1 quantization bit for the imaginary of each element. Since the elements of H, i.e., h ij &#39;s, are Gaussian, the following scalar quantizer for the Gaussian variables can be used: 
     
       
         
           
             
               q 
                
               
                 ( 
                 x 
                 ) 
               
             
             = 
             
               { 
               
                 
                   
                     
                       
                         
                           2 
                           Π 
                         
                       
                        
                       σ 
                     
                   
                   
                     
                       
                         if 
                          
                         
                             
                         
                          
                         x 
                       
                       ≥ 
                       0 
                     
                   
                 
                 
                   
                     
                       
                         - 
                         
                           
                             2 
                             Π 
                           
                         
                       
                        
                       σ 
                     
                   
                   
                     
                       
                         if 
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                          
                         x 
                       
                       &lt; 
                       0 
                     
                   
                 
               
             
           
         
       
     
     where σ is the standard deviation of the real and imaginary parts of h ij &#39;s and in the case of Raleigh fading channel is equal to √{square root over (0.5)}. 
       FIG. 4  depicts an example implementation of the algorithm  260 . In the depicted implementation, algorithm  260  includes a codebook quantizer  405  for receiving the unquantized matrix V and quantizing that matrix into bits b 1 -b k  using a codebook. The algorithm  260  further includes a code  410  for encoding the bits b 1 -b k  into a digital codeword. The code could be, for example, an algebraic code, a convolutional code or any related code. An example, of an algebraic code is the Reed-Muller code. The algorithm also includes an alignment module  415  to perform the alignment described above with respect to  320 . The algorithm further includes a difference module  418  to generate the error signal based on the aligned matrix Va and the quantized matrix formed at  306 . The codebook index lookup  420  transforms back the transmitted bits (which are the index to the codebook table) into the actual codeword. 
       FIG. 5  depicts a base station, such as base station  110 A. The base station  110 A includes antennas  320 A-B configured to transmit via downlinks  116 A-B and configured to receive uplink  116 C via at least one of antennas  320 A-B. The base station  110 A further includes a radio interface  340  coupled to the antennas  320 A-B, a precoder  360  (described further below), a processor  330  for controlling base station  110 A and for accessing and executing program code stored in memory  335 . The radio interface  340  further includes other components, such as filters, converters (e.g., digital-to-analog converters and the like), mappers, a Fast Fourier Transform (FFT) module, and the like, to generate a MIMO transmission via downlinks  116 A-B to receive the channel estimation information provided via uplink  116 C, and to receive feedback from client station  114 B. The received feedback is used at precoder  360 . In some implementations, the base station  110 A is also compatible with IEEE 802.16 and the RF signals of the MIMO downlinks  116 A-B and uplink  116 C are configured in accordance with OFDMA. 
     The radio interface  340  decodes the uplink  116 C carrying the feedback, such as a hybrid feedback including an analog portion (e.g., the analog error signal generated at  310 ) and a digital portion (e.g., codeword of the quantized matrix P formed at  312 ). The radio interface  340  may also decode uplink  116 C carrying any feedback information (e.g., the hybrid analog and digital feedback information sent at  335  from the client station to the base station), which are provided to the precoder  360 . The precoder  360  is configured in accordance with the hybrid feedback information, which is received. 
       FIG. 6  depicts a process  600  to configure a base station to use the hybrid feedback information, which is provided as feedback from the client station to the base station. The description of process  600  will refer to  FIG. 5  as well. 
     At  692 , a base station, such as base station  110 A, receives from a client station hybrid feedback information, such as the information sent at  314  above. In some embodiments, the hybrid feedback information (e.g., including an analog portion, such as the analog error signal generated at  310 , and a digital portion, such as a codeword of the quantized matrix P formed at  312 ) may be received in a tile format. 
     At  694 , the received hybrid feedback information is provided to a precoder, such as precoder  360  to configure the precoder  360  for MIMO transmission. The precode  360  combines the received information (e.g., the received analog error and the received quantized V to form the matrix V, which includes singular vectors v 1  and v 2 ). These singular vectors v 1  and v 2  (as well as any other channel estimation information provided as feedback by the client station to the base station) enable the precoder  360  to precode, based on a singular value decomposition using matrix V, one or more symbols streams for MIMO transmission via antennas  320 A-B. Although the description refers to using two singular vectors v 1  and v 2 , other quantities of singular vectors may be used as well. 
     At  696 , the base station  110 A transmits to the client station based on the precoded symbols via MIMO. 
     Although the above describes the embodiments using vectors and matrixes, the vectors and matrixes may be implemented as any type of data container and/or data structure, as well. 
     The subject matter described herein may be embodied in systems, apparatus, methods, and/or articles depending on the desired configuration. Base station  110 A (or one or more components therein) can be implemented using one or more of the following: a processor executing program code, an application-specific integrated circuit (ASIC), a digital signal processor (DSP), an embedded processor, a field programmable gate array (FPGA), and/or combinations thereof. Client station  114 B (or one or more components therein) can be implemented using one or more of the following: a processor executing program code, an application-specific integrated circuit (ASIC), a digital signal processor (DSP), an embedded processor, a field programmable gate array (FPGA), and/or combinations thereof. These various implementations may include implementation in one or more computer programs that are executable and/or interpretable on a programmable system including at least one programmable processor, which may be special or general purpose, coupled to receive data and instructions from, and to transmit data and instructions to, a storage system, at least one input device, and at least one output device. These computer programs (also known as programs, software, software applications, applications, components, program code, or code) include machine instructions for a programmable processor, and may be implemented in a high-level procedural and/or object- oriented programming language, and/or in assembly/machine language. As used herein, the term “machine-readable medium” refers to any computer program product, computer-readable medium, apparatus and/or device (e.g., magnetic discs, optical disks, memory, Programmable Logic Devices (PLDs)) used to provide machine instructions and/or data to a programmable processor, including a machine-readable medium that receives machine instructions as a machine-readable signal. Similarly, systems are also described herein that may include a processor and a memory coupled to the processor. The memory may include one or more programs that cause the processor to perform one or more of the operations described herein. 
     Although a few variations have been described in detail above, other modifications or additions are possible. In particular, further features and/or variations may be provided in addition to those set forth herein. Moreover, the implementations described above may be directed to various combinations and subcombinations of the disclosed features and/or combinations and subcombinations of several further features disclosed above. In addition, the logic flow depicted in the accompanying figures and/or described herein does not require the particular order shown, or sequential order, to achieve desirable results. Other embodiments may be within the scope of the following claims.