Patent Publication Number: US-2009231196-A1

Title: Mmwave wpan communication system with fast adaptive beam tracking

Description:
RELATED APPLICATION 
     This application claims the benefit under 35 U.S.C. §119(e) to U.S. Provisional Patent Application No. 61/035,480, filed Mar. 11, 2008 and is hereby incorporated by reference in its entirety. 
    
    
     BACKGROUND 
     Description of the Related Art 
     Millimeter-wave (mmWave) wireless personal area network (WPAN) communication systems operating in the 60 Gigahertz (GHz) frequency band are expected to provide several Gigabits per second (Gbps) throughput to distances of about ten meters and will be entering into service in a few years. Currently several standardization bodies (IEEE 802.15.3c, WirelessHD SIG, ECMA TG20, COMPA and others) are considering different concepts for mmWave WPAN systems to define the systems which are the best suited for multi-Gbps WPAN applications. 
     A mmWave communication link is less robust than those at lower frequencies (for example, 2.4 GHz and 5 GHz bands) due to both oxygen absorption, which attenuates the signal over long range, and its short wavelength, which provides high attenuation through obstructions such as walls and ceilings. As a result, the use of directional antennas (such as a beamforming antenna, a sectorized antenna, or a fixed beam antenna) has been envisioned as useful for 60 GHz applications. 
     Inherent in any wireless communication systems is the need for improved throughput and reliability. Thus, a strong need exists for techniques to improve mmWave wireless personal area networks. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The present invention may be better understood, and its numerous features and advantages made apparent to those skilled in the art by referencing the accompanying drawings. 
         FIG. 1  illustrates a system for analog beamforming and tracking according to an embodiment of the present invention. 
         FIG. 2  illustrates a beam tracking packet diagram with dedicated time allocated in a super-frame. 
         FIG. 3  illustrates a beam tracking packet diagram according to an embodiment of the present invention. 
         FIG. 4  illustrates a performance comparison of beamforming gain for 100 channel realizations between a dedicated training approach and a training approach according to an embodiment of the present invention. 
         FIG. 5  illustrates a beam tracking protocol according to an embodiment of the present invention. 
         FIG. 6  illustrates an alternative beam tracking protocol according to an embodiment of the present invention. 
         FIG. 7  illustrates an alternative beam tracking packet diagram according to an embodiment of the present invention. 
     
    
    
     The use of the same reference symbols in different drawings indicates similar or identical items. 
     DESCRIPTION OF THE EMBODIMENT(S) 
     In the following description, numerous specific details are set forth. However, it is understood that embodiments of the invention may be practiced without these specific details. In other instances, well-known methods, structures and techniques have not been shown in detail in order not to obscure an understanding of this description. 
     References to “one embodiment,” “an embodiment,” “example embodiment,” “various embodiments,” and the like, indicate that the embodiment(s) of the invention so described may include a particular feature, structure, or characteristic, but not every embodiment necessarily includes the particular feature, structure, or characteristic. Further, repeated use of the phrase “in one embodiment” does not necessarily refer to the same embodiment, although it may. 
     As used herein, unless otherwise specified the use of the ordinal adjectives “first,” “second,” “third,” and the like, to describe a common object, merely indicate that different instances of like objects are being referred to, and are not intended to imply that the objects so described must be in a given sequence, either temporally, spatially, in ranking, or in any other manner. 
     Embodiments of the invention may be used in a variety of applications. Some embodiments of the invention may be used in conjunction with various devices and systems, for example, a transmitter, a receiver, a transceiver, a transmitter-receiver, a wireless communication station, a wireless communication device, a wireless Access Point (AP), a modem, a wireless modem, a Personal Computer (PC), a desktop computer, a mobile computer, a laptop computer, a notebook computer, a tablet computer, a server computer, a handheld computer, a handheld device, a Personal Digital Assistant (PDA) device, a handheld PDA device, or even high definition television signals in a personal area network (PAN). 
     Although embodiments of the invention are not limited in this regard, discussions utilizing terms such as, for example, “processing,” “computing,” “calculating,” “determining,” “establishing”, “analyzing”, “checking”, or the like, may refer to operation(s) and/or process(es) of a computer, a computing platform, a computing system, or other electronic computing device, that manipulate and/or transform data represented as physical (for example, electronic) quantities within the computer&#39;s registers and/or memories into other data similarly represented as physical quantities within the computer&#39;s registers and/or memories or other information storage medium that may store instructions to perform operations and/or processes. 
     Although embodiments of the invention are not limited in this regard, the terms “plurality” and “a plurality” as used herein may include, for example, “multiple” or “two or more”. The terms “plurality” or “a plurality” may be used throughout the specification to describe two or more components, devices, elements, units, parameters, or the like. For example, “a plurality of stations” may include two or more stations. 
     According to an embodiment of the present invention, directional communication may be achieved using a novel procedure that may be used with, for example, a phase antenna array system where inputs and outputs to/from antenna elements are multiplied by a weight (phase) vector to form transmit (TX) and receive (RX) beams. Devices with beam steerable antennas require optimal adjustment of TX and RX antenna systems (beamforming/tracking), typically using a dedicated time frame for the beamforming, tracking and adjustment. According to an embodiment of the present invention, the use of a dedicated time for tracking is not used. Further, the quality of the beam-formed transmission may become worse over time due to a non-stationary environment and the novel beam tracking procedure may be used to adjust the TX and RX antenna weight vectors. Antenna training may be performed close to the current beamforming such that antenna weight vectors may be updated using recursive procedures using the current TX and RX antenna weight vectors as initial values. 
       FIG. 1  illustrates a system for analog beamforming and tracking according to an embodiment of the present invention. System  100  may include one or more transmitting devices  102  and/or one or more receiving devices  104 . Transmitting device  102  may include a transmit baseband processing circuitry  112 , multiple power amplifiers  114 , each power amplifier  104  connected to a phase shifter  116  and an antenna  118 . Receiving device  104  may include multiple antennas  122 , each antenna  122  connected to a phase shifter  124  and a low noise amplifier  126 . Low noise amplifiers  126  each are connected to a single receive baseband processing circuitry  128 . Although illustrated as separate devices, transmitting device  102  and receiving device  104  may be encompassed in a single component and may share circuitry, for example, antennas and/or phase shifters. 
     Transmitting device  102  uses a phased array approach to achieve directional transmission. In a phased array approach, transmit beams are formed by changing the phases of the output signals of each antenna element. Transmit power is distributed to multiple power amplifiers  114  and the beam can be adaptively steered. Receiving device  104  also uses a phased array approach to achieve directional reception. Receive beams are detected by changing the phases of the input signal of each antenna element. The receive gain is distributed to the multiple low noise amplifiers  126  and the beam can be adaptively received. 
     According to an embodiment of the present invention, transmitting device  102  transmits data signals using a modified version of predetermined TX antenna settings while receiving device  104  performs the processing of the received signals and is able to estimate the needed channel state information from the received signals. The beamforming may be performed during one or several stages where receiving device  104  feeds back the control messages to transmitting device  102 , the control messages include information about the parameters needing further training. After all the needed channel state information is obtained, receiving device  104  calculates optimal TX and RX antenna settings. Then the RX antenna weight vector is applied by receiving device  104  and the TX antenna weight vector is sent to transmitting device  102 . The TX antenna weight vector is then applied by transmitting device  102 . 
     Alternatively, the RX antenna weight vector may be estimated by receiving device  104  and the channel state information needed for the TX antenna weight vector estimation may be sent to transmitting device  102 . The TX antenna weight vector calculation may be performed by transmitting device  102 . 
     It should be noted that all proposed beamforming/tracking methods may provide unquantized TX and RX antenna weight vectors. However, transmitting device  102  and receiving device  104  may have limitations on the continuity of the magnitude and phase of the weight vectors coefficients applied. As such, the quantization of the antenna weight vectors may be near a closest allowable value, for example π/3 or π/2. Further, the TX and RX antenna weight vectors may be quantized to reduce the amount of data transferred for antenna weight vectors transmission between stations after they are calculated. 
       FIG. 2  illustrates a beam tracking packet diagram with dedicated time allocated in a super-frame. In a normal data exchange, a piconet controller (PNC) issues a beacon  202  and a Channel Access Period (CAP)  204  followed by a data packet  206  to station  1  (STA 1 ). Receiving STA 1  sends acknowledgement  208  indicating reception of data packet  206 . PNC sends a data packet  210  to station  2  (STA 2 ) and receives an ACK  212  from STA 2 . Additional data packets  214  and  216  may be sent and corresponding ACKs  218  and  220  received. These data transmissions are sent and received using static, previously determined TX and RX weight vectors. As part of a dedicated tracking protocol, PNC sends a beam tracking packet  222  to STA 1  and after receiving ACK  224  from STA 1 , sends beam tracking packet  226  to STA 2 , and receives ACK  228  from STA 2 . Beam tracking packets  222  and  226  are formed using training matrices. 
     As the number of stations increase, the time for a dedicated tracking procedure increases significantly, providing a more inefficient system. Further, frequent beam-tracking may be required to track small changes of the channel. Beam-search and beam-tracking each may take multiple iterations of message exchange. As the number of stations increase, for example, in a dense environment, the time allocated for tracking overhead may be large and thus cause efficiency to drop. Beam-tracking overhead may be as much as 100 us per iteration, and may be scheduled very frequently, such as every 1 or 2 ms. 
     In the training approach illustrated in  FIG. 2 , transmit (TX) and receive (RX) antenna weight vectors v and u may be applied to the inputs of the transmit antennas  118  using phase shifters  116  and the outputs of the receive antennas  122  using phase shifters  124 , respectively. A mathematical model of the system shown in  FIG. 1  can be illustrated by the following equations: 
       y 1 =u H HFdiag{x}  (1) 
       y 2 =diag{z}G H Hv   (2) 
     where y is the received signal; x is the transmitted symbol; vectors u and v are the receive and transmit beamforming vectors, respectively and also include quantities for tracking; H is a N r ×N t  frequency non-selective channel transfer matrix; and matrices F and G are training matrices, which can be any full rank matrix. For example, the Hardmard matrix may be used as a training matrix because it is orthogonal and its phase only takes value  0  and π. The transmitted symbol is a training symbol. 
     In the approach illustrated in  FIG. 2 , F or G matrices exist only at one side of transmission. For example, to track and update the transmit beamforming vector u, F is used at the transmitter side (see equation 1). On the other hand, to track the receive beamforming vector v, G matrix is used at the receiver side (see equation 2). The tracking protocol needs to reserve particular time to transmit with each column of F and receive with each column of G matrix. In addition, a training sequence in time domain is used in each transmission. 
     According to an embodiment of the present invention, rather than using dedicated tracking message exchanges as illustrated in  FIG. 2 , training is distributed into data transmission. According to one embodiment, the dedicated training time that is used to send and receive with F and G is no longer needed. In each transmission, a perturbation on the v and u vectors is added sequentially for each packet transmission, which only causes a negligible degradation on the beamforming gain. The N t  perturbed transmit beamforming vectors form beamforming matrix {tilde over (V)}=[{tilde over (v)} 1  {tilde over (v)} 2  Λ {tilde over (v)} N     t   ], where {tilde over (v)} i  is the i-th perturbed beamforming vector. Similarly, the N r  perturbed receive beamforming vectors form beamforming matrix Ũ=[ũ 1  ũ 2  Λ ũ N     r   ], where ũ i  is the i-th perturbed vector. After N r +N t  packet transmissions, the two receive vectors are illustrated as: 
     
       
         
           
             
               
                 
                   
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     .where v and u are the latest beamforming vectors under tracking; x i  and z i  are transmitted symbols; noises are ignored. The transmitted symbol is a data symbol. {tilde over (v)} i  may be generated by adding a minimum allowed phase rotation to the i-th entry of v. For example, if the phase shifter has eight levels of value, then θ=π/3 can be added to the phase of the i-th entry of v, denoted by φ i , to generate {tilde over (v)} i . {tilde over (V)} is full rank and can be written as {tilde over (V)}=v[1 Λ 1]+cdiag([e φ     l     30 θ  Λe 100      Nt     +θ ]), where c is a constant that depends on θ. The matrix Ũ=[ũ 1  ũ 2  Λ ũ N     r   ] can be generated similarly. 
     It should be noticed that only a single data stream is described. However, the concepts described herein may be applied to multiple data streams. 
       FIG. 3  illustrates a beam tracking packet diagram according to an embodiment of the present invention. A piconet controller (PNC) issues a beacon  302  and a CAP  304  (followed by a data packet  306  to station  1  (STA 1 ) using perturbed antenna weight vector {tilde over (v)} 1  and is receiving by STA 1  using antenna weight vector u. Receiving STA 1  sends acknowledgement  308  indicating reception of data packet  306 . PNC sends additional data packets  310  through  312  using perturbed antenna weight vectors {tilde over (v)} 2  through {tilde over (v)} N     t    which are received by STA 1  using antenna weight vector u. PNC receives additional ACKs  314  through  316  from STA 1 . Note that PNC may be sending additional data to other stations (not illustrated). Next, PNC sends data packets  318  through  320  using new antenna weight vector v new  which is received by STA 1  using perturbed antenna weight vectors ũ 1  through ũ N     r   . STA 1  sends ACKs  322  through  324 . 
     As illustrated in  FIG. 3 , a preserved time slot for training is not used. Data packets are transmitted and received with the modified beamforming vector {tilde over (v)} i  and ũ i . In this example, PNC and STA 1  conduct beam tracking. The transmit beamforming vector at PNC is tracked before the receive beamforming vector at STA 1  is tracked. 
       FIG. 4  illustrates a performance comparison of beamforming gain for  100  channel realizations between an iterative training approach and a training approach according to an embodiment of the present invention. (Graph  404  illustrates channel realization results using an optimal beamforming vector, for example, using the protocol as illustrated in  FIG. 2 . Graph  406  illustrates channel realization results using a modified vector for tracking, for example, using the protocol as illustrated in  FIG. 3 . The performance difference using perturbed training matrices {tilde over (v)} i  and ũ i  instead of the optimal training matrices v and u is less than 0.2 dB. 
     An iterative training protocol excites each column of F and G that are full rank in a dedicated training slot to update the beamforming vector, reducing efficiency. According to an embodiment of the present invention, the transmitter and receiver use {tilde over (V)}=[{tilde over (v)} 1  {tilde over (v)} 2  Λ {tilde over (v)} N     t   ] and Ũ=[ũ 1  ũ 2  Λ ũ N     r   ] for data transmission and reception respectively, which is also full rank matrix, resulting in a more efficient system. The full rank feature captures the beamforming variation in all directions. 
     Using equations (3) and (4) and an update method, the beamforming vector can be updated as 
     
       
         
           
             
               
                 
                   
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     After the transmit beamforming vector is updated to v new , v new  is used for the update of the receive beamforming vector. The inversion may be performed with low complexity as follows. The equation may be converted to find the inversion of a rank-one update. Because only the i-th element of v is modified to get {tilde over (v)} i , we have {tilde over (V)}=[v v Λ v]+diag(·), where diag(·) is a diagonal matrix. 
     
       
         
           
               
             
               
                 
                   
                     
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     where b=([1 1Λ 1]diag −1 (·) H . The inversions of the two terms of {tilde over (V)} can be computed. The inversion of the first term is (I+vb H )=I−(1+b H v) −1 vb H  and the inversion of the second term is the inversion of each diagonal entry. Therefore, only N t +1 scalar divisions are required to obtain {tilde over (V)} −1 . Decision feedback can be used when the data packet is correctly received, where x i  and z i  in equations (3) and (4) are data symbols. The tracking accuracy can be greatly improved by decision feedback due to the dense population of data symbols. 
       FIG. 5  illustrates a beam tracking protocol according to an embodiment of the present invention where channel reciprocal is not assumed. A piconet controller (PNC) transmits a data packet  502 , using a perturbed transmit antenna weight vector {tilde over (v)} 1  and is received by a station, using the optimal receive antenna weight vector u. Further data packets  504  through  506 , are transmitted using perturbed by transmit antenna weight vectors {tilde over (v)} 2  through {tilde over (v)} N     t   , respectively. STA calculate the updated transmit vector v and transmits the updated vector v in transmission  508  to PNC. PNC transfers N r  data packets,  510  and  512  through  514 . Data packets  510  and  512  through  514  are sent with the updated vector v by PNC, and received with receive antenna weight vectors ũ 1  and ũ 2  through ũ N     r   . The tracking is performed during the data transmission stage. Only the transmission from a piconet controller (PNC) to a station (STA) shown. The acknowledge (ACK) transmission from STA to PNC does not participate the tracking, and is not shown. The ACK may be transmitted following the ACK policy for immediate ACK, delayed ACK or block ACK. The feedback of v new  from STA to PNC can also be piggybacked with ACK or other uplink traffic. 
       FIG. 6  illustrates an alternative beam tracking protocol according to an embodiment of the present invention where a channel reciprocal is assumed. A piconet controller (PNC) transmits a data packet  602  with perturbed antenna weight {tilde over (v)} 1  which is received by a station (STA) with antenna weight vector u. STA transmits a data packet  604  with perturbed antenna weight vector ũ 1  which is received by PNC with antenna weight vector v. The process is repeated, PNC transmits a data packet  606  with perturbed antenna weight {tilde over (v)} 2  which is received by STA with antenna weight vector u. STA transmits a data packet  608  with perturbed antenna weight vector ũ 2  which is received by PNC with antenna weight vector V. The process is repeated multiple times, until PNC transmits a data packet  610  with perturbed antenna weight {tilde over (v)} N     t    which is received by STA with antenna weight vector v. STA transmits a data packet  612  with perturbed antenna weight vector ũ N     r    which is received by PNC with antenna weight vector v. For implicit feedback beamforming, where the channel reciprocal is assumed, both the downlink and uplink transmissions are used to track the beamforming vectors at PNC and STA. The receive beamforming vector in one direction is used as the transit beamforming vector for the other direction. 
     Because the illustrated schemes take about N t +N r  packets, albeit without an interruption in data transmission, the channel may vary if the packet duration is long. In an alternate embodiment, partial tracking may be implemented. Namely, the transmitter and receiver can update their beamforming weights within a subspace. Instead of N t  and N r , we track changes within only   and   transmit and receive vector space respectively. The   perturbed transmit beamforming vectors forms beamforming matrix 
     
       
         
           
             
               
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                   i 
                 
               
               ) 
             
             . 
           
         
       
     
     After 
     
       
         
           
             
               
                 N 
                 ( 
               
               r 
             
             + 
             
               
                 N 
                 ( 
               
               t 
             
           
         
       
     
     packet transmissions, we will have two receive vectors 
     
       
         
           
             
               
                 
                   
                     
                       y 
                       ( 
                     
                     1 
                   
                   = 
                   
                     
                       u 
                       H 
                     
                      
                     H 
                      
                     
                       
                         V 
                         ( 
                       
                        
                       
                         [ 
                         
                           
                             
                               
                                 x 
                                 1 
                               
                             
                             
                               
                                   
                               
                             
                             
                               
                                   
                               
                             
                           
                           
                             
                               
                                   
                               
                             
                             
                               O 
                             
                             
                               
                                   
                               
                             
                           
                           
                             
                               
                                   
                               
                             
                             
                               
                                   
                               
                             
                             
                               
                                 x 
                                 
                                   
                                     N 
                                     ( 
                                   
                                   t 
                                 
                               
                             
                           
                         
                         ] 
                       
                     
                   
                 
               
               
                 
                   ( 
                   7 
                   ) 
                 
               
             
             
               
                 
                   
                     
                       y 
                       ( 
                     
                     2 
                   
                   = 
                   
                     
                       [ 
                       
                         
                           
                             
                               z 
                               1 
                             
                           
                           
                             
                                 
                             
                           
                           
                             
                                 
                             
                           
                         
                         
                           
                             
                                 
                             
                           
                           
                             O 
                           
                           
                             
                                 
                             
                           
                         
                         
                           
                             
                                 
                             
                           
                           
                             
                                 
                             
                           
                           
                             
                               z 
                               
                                 
                                   N 
                                   ( 
                                 
                                 r 
                               
                             
                           
                         
                       
                       ] 
                     
                      
                     
                       
                         U 
                         ( 
                       
                       H 
                     
                      
                     Hv 
                   
                 
               
               
                 
                   ( 
                   8 
                   ) 
                 
               
             
           
         
       
     
     where v and u are the latest beamforming vectors under tracking; x i  and z i  are transmitted symbols; noises are ignored. The transmitted symbol is a data symbol. Equations (7) and (8) may be simplified by removing the effect of training symbols as 
     
       
         
           
             
               
                 
                   
                     q 
                     1 
                   
                   = 
                   
                     
                       
                         
                           y 
                           ( 
                         
                         1 
                       
                        
                       
                         Λ 
                         x 
                       
                     
                     = 
                     
                       
                         u 
                         H 
                       
                        
                       H 
                        
                       
                         V 
                         ( 
                       
                     
                   
                 
               
               
                 
                   ( 
                   9 
                   ) 
                 
               
             
             
               
                 
                   
                     q 
                     2 
                   
                   = 
                   
                     
                       
                         Λ 
                         z 
                       
                        
                       
                         
                           y 
                           ( 
                         
                         2 
                       
                     
                     = 
                     
                       
                         
                           U 
                           ( 
                         
                         H 
                       
                        
                       Hv 
                     
                   
                 
               
               
                 
                   ( 
                   10 
                   ) 
                 
               
             
           
         
       
     
     where 
     
       
         
           
             
               Λ 
               x 
             
             = 
             
               
                 
                   [ 
                   
                     
                       
                         
                           x 
                           1 
                           
                             - 
                             1 
                           
                         
                       
                       
                         
                             
                         
                       
                       
                         
                             
                         
                       
                     
                     
                       
                         
                             
                         
                       
                       
                         O 
                       
                       
                         
                             
                         
                       
                     
                     
                       
                         
                             
                         
                       
                       
                         
                             
                         
                       
                       
                         
                           x 
                           
                             N 
                             t 
                           
                           
                             ( 
                             
                               - 
                               1 
                             
                           
                         
                       
                     
                   
                   ] 
                 
                  
                 
                     
                 
                  
                 and 
                  
                 
                     
                 
                  
                 
                   Λ 
                   z 
                 
               
               = 
               
                 
                   [ 
                   
                     
                       
                         
                           z 
                           1 
                           
                             - 
                             1 
                           
                         
                       
                       
                         
                             
                         
                       
                       
                         
                             
                         
                       
                     
                     
                       
                         
                             
                         
                       
                       
                         O 
                       
                       
                         
                             
                         
                       
                     
                     
                       
                         
                             
                         
                       
                       
                         
                             
                         
                       
                       
                         
                           z 
                           
                             N 
                             t 
                           
                           
                             ( 
                             
                               - 
                               1 
                             
                           
                         
                       
                     
                   
                   ] 
                 
                 . 
               
             
           
         
       
     
     The transmit vector may be computed within the subspace spanned by the columns of   as 
     
       
         
           
             
               
                 
                   
                     
                       
                         v 
                         ( 
                       
                       new 
                     
                     = 
                     
                       norm 
                       ( 
                       
                         
                           ( 
                           
                             
                               V 
                               ( 
                             
                             H 
                           
                           ) 
                         
                          
                         
                           q 
                           1 
                           H 
                         
                       
                       ) 
                     
                   
                    
                   
                     
 
                   
                    
                   where 
                    
                   
                     
 
                   
                    
                   
                     
                       A 
                       + 
                     
                     = 
                     
                       { 
                       
                         
                           
                             
                               
                                 
                                   
                                     A 
                                     H 
                                   
                                    
                                   
                                     ( 
                                     
                                       AA 
                                       H 
                                     
                                     ) 
                                   
                                 
                                 
                                   - 
                                   1 
                                 
                               
                               , 
                             
                           
                           
                             
                               
                                 number 
                                  
                                 
                                     
                                 
                                  
                                 of 
                                  
                                 
                                     
                                 
                                  
                                 columns 
                               
                               ≥ 
                               
                                 number 
                                  
                                 
                                     
                                 
                                  
                                 of 
                                  
                                 
                                     
                                 
                                  
                                 rows 
                               
                             
                           
                         
                         
                           
                             
                               
                                 
                                   
                                     ( 
                                     
                                       
                                         A 
                                         H 
                                       
                                        
                                       A 
                                     
                                     ) 
                                   
                                   
                                     - 
                                     1 
                                   
                                 
                                  
                                 
                                   A 
                                   H 
                                 
                               
                               , 
                             
                           
                           
                             otherwise 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   11 
                   ) 
                 
               
             
           
         
       
     
     is the pseudo inverse of A. Similarly, the receive vector within the subspace spanned by the columns of   is computed by 
     
       
         
           
             
               
                 
                   
                     
                       y 
                       ( 
                     
                     2 
                   
                   = 
                   
                     
                       [ 
                       
                         
                           
                             
                               z 
                               1 
                             
                           
                           
                             
                                 
                             
                           
                           
                             
                                 
                             
                           
                         
                         
                           
                             
                                 
                             
                           
                           
                             O 
                           
                           
                             
                                 
                             
                           
                         
                         
                           
                             
                                 
                             
                           
                           
                             
                                 
                             
                           
                           
                             
                               z 
                               
                                 N 
                                 r 
                               
                               ( 
                             
                           
                         
                       
                       ] 
                     
                      
                     
                       
                         U 
                         ( 
                       
                       H 
                     
                      
                     
                       
                         
                           H 
                            
                           
                               
                           
                            
                           v 
                         
                         ( 
                       
                       new 
                     
                   
                 
               
               
                 
                   ( 
                   12 
                   ) 
                 
               
             
             
               
                 
                   
                     q 
                     2 
                   
                   = 
                   
                     
                       Λ 
                       z 
                     
                      
                     
                       y 
                       2 
                     
                   
                 
               
               
                 
                   ( 
                   13 
                   ) 
                 
               
             
             
               
                 
                   
                     
                       u 
                       ( 
                     
                     new 
                   
                   = 
                   
                     norm 
                     ( 
                     
                       
                         
                           ( 
                           
                             
                               U 
                               ( 
                             
                             H 
                           
                           ) 
                         
                         + 
                       
                        
                       
                         q 
                         2 
                       
                     
                     ) 
                   
                 
               
               
                 
                   ( 
                   14 
                   ) 
                 
               
             
           
         
       
     
     After the transmit beamforming vector is updated to v new , v new  is used for the update of the receive beamforming vector. The pseudo inversion can be done with low complexity. 
       FIG. 7  illustrates another alternative beam tracking packet diagram according to an embodiment of the present invention. Because a random phase may be introduced during TX and RX switches, a tracking sequence may occur within one data packet. Different perturbed phase vectors may be applied to several OFDM symbols. As illustrated a preamble  702  is transmitted. The decoding of OFDM symbols will use the channel estimation in preamble  702 . OFDM symbols  704  and  706  through  708  are transmitted with perturbed weight vectors {tilde over (v)} 1  and {tilde over (v)} 2  through {tilde over (v)} N     t   . OFDM symbols  710  and  712  through  714  are transmitted with the new updated v new  and received with perturbed weight vectors ũ 1  and ũ 2  through ũ N     r   . Slight performance loss may occur to the data symbol. The decoded information can be used for a decision directed channel estimation, which will be used for beam vector update. To get accurate estimation of {tilde over (V)}=[{tilde over (v)} 1  {tilde over (v)} 2  Λ {tilde over (v)} N     t   ] and Ũ=[ũ 1  ũ 2  Λ ũ N     r   ], several OFDM symbols will use the same phase vector, and the estimation will be average across frequency and time. 
     When using a small number of antennas in a phased array, for example, four antennas, changing the phase shift in one out of four results in an antenna pattern that may fail to provide the required antenna gain. According to an embodiment of the present invention, several alternatives may be used to improve the gain. Beam tracking may be replaced by one iteration of the beam search. Because the number of antennas is small and the initial beamforming vector is close to the optimum, the training time is short. Alternatively, because the number of antennas is small, only a small portion of the data symbols of the packet are used for the beamforming tracking and beamformed by the perturbed beamforming vectors. The rest of the symbols may be sent (or received) with the unperturbed beamforming vector, that is, the optimum vector. A lower modulation coding scheme (MCS) may be applied to the data symbols sent by the perturbed beamforming vectors, and a higher MCS may be used for the unperturbed portion. Therefore the loss from the tracking is minimized. Both mechanisms may also be used for a collection of sectorized antennas. For the case of sectorized antennas, the tracking may be conducted on a selected subset of the antennas for overhead reduction. 
     The techniques described above may be embodied in a computer-readable medium for configuring a computing system to execute the method. The computer readable media may include, for example and without limitation, any number of the following: magnetic storage media including disk and tape storage media; optical storage media such as compact disk media (e.g., CD-ROM, CD-R, etc.) and digital video disk storage media; holographic memory; nonvolatile memory storage media including semiconductor-based memory units such as FLASH memory, EEPROM, EPROM, ROM; ferromagnetic digital memories; volatile storage media including registers, buffers or caches, main memory, RAM, etc.; and data transmission media including permanent and intermittent computer networks, point-to-point telecommunication equipment, carrier wave transmission media, the Internet, just to name a few. Other new and various types of computer-readable media may be used to store and/or transmit the software modules discussed herein. Computing systems may be found in many forms including but not limited to mainframes, minicomputers, servers, workstations, personal computers, notepads, personal digital assistants, various wireless devices and embedded systems, just to name a few. A typical computing system includes at least one processing unit, associated memory and a number of input/output (I/O) devices. A computing system processes information according to a program and produces resultant output information via I/O devices. 
     Realizations in accordance with the present invention have been described in the context of particular embodiments. These embodiments are meant to be illustrative and not limiting. Many variations, modifications, additions, and improvements are possible. Accordingly, plural instances may be provided for components described herein as a single instance. Boundaries between various components, operations and data stores are somewhat arbitrary, and particular operations are illustrated in the context of specific illustrative configurations. Other allocations of functionality are envisioned and may fall within the scope of claims that follow. Finally, structures and functionality presented as discrete components in the various configurations may be implemented as a combined structure or component. These and other variations, modifications, additions, and improvements may fall within the scope of the invention as defined in the claims that follow.