Abstract:
A system and method for estimating channel characteristics in orthogonal frequency-division multiplexing (OFDM) systems with transmitter diversity is presented. The disclosed approach is compatible with the Institute of Electrical and Electronics Engineers (IEEE) “Wireless Local Area Network (LAN) Medium Access Control (MAC) and Physical Layer (PHY) Specification.” In the disclosed system and method, an additional training symbol is transmitted during the data period. This provides additional information that may be used to more accurately estimate channel characteristics.

Description:
CROSS REFERENCE TO RELATED APPLICATIONS  
       [0001]    This application claims the benefit of U.S. provisional patent application serial No. 60/400,888, filed Aug. 1, 2002, which is incorporated herein by reference in its entirety. 
     
    
     
       FIELD OF INVENTION  
         [0002]    The present invention is directed to communication systems and, more particularly, to systems and methods for estimating channel characteristics in orthogonal frequency-division multiplexing (OFDM) systems with transmitter diversity.  
         BACKGROUND  
         [0003]    Radio-frequency local area network (LAN) systems are highly regulated by the federal government. For example, the frequency bands of approximately 5.15-5.25 GHz, 5.25-5.35 GHz, and 5.725-5.825 GHz unlicensed national information structure (U-NII) bands are regulated by Title 47, Section 15.407 of the United States Code of Federal Regulations (CFR). While the CFR specifies certain limitations on the use of radio-frequency networks, other standards committees, such as the Institute of Electrical and Electronics Engineers (IEEE), specify technical requirements for wireless systems to ensure cross-compatibility of wireless systems from different manufacturers. For example, the IEEE “Wireless LAN Medium Access Control (MAC) and Physical Layer (PHY) Specifications: High-Speed Physical Layer in the 5 GHz Band” (hereinafter “the IEEE 5 GHz standard”) provides several requirements for systems operating in the 5 GHz band.  
           [0004]    One of the requirements set forth in the IEEE 5 GHz standard is an OFDM physical layer convergence procedure (PLCP) sub-layer. Specifically, FIG. 1A shows a Presentation Protocol Data Unit (PPDU) frame in the IEEE 5 GHz standard. As shown in FIG. 1A, the PPDU frame includes a short-training period  110 , a long-training period  120  following the short-training period  110 , a signaling period  130  following the long-training period  120 , and a plurality of data periods  140 ,  142 ,  144  that follow the signaling period  130 . The long-training period  120 , the signaling period  130 , and the plurality of data periods  140 ,  142 ,  144  include a guard interval (GI) as defined in the IEEE 5 GHz standard.  
           [0005]    The short-training period  110  contains ten symbols (e.g., t 1 , t 2  . . . t 9 , t 10 ), which are used for signal detecting, coarse-frequency acquisition, diversity selection, and other functions as defined by the IEEE 5 GHz standard. Since the short-training period  110  is described in detail in the IEEE 5 GHz standard, further discussion of the short-training period  110  is omitted here.  
           [0006]    The long-training period  120  contains a guard interval (GI 2 ) and two long-training symbols, T 1  and T 2 . As specified in the IEEE 5 GHz standard, each of the long-training symbol T 1  and T 2  consists of 53 sub-carriers including a zero value at DC, which are modulated by elements of sequence X, given by:  
             X   =       {     1   ,   1   ,     -   1     ,     -   1     ,   1   ,   1   ,     -   1     ,   1   ,     -   1     ,   1   ,   1   ,   1   ,   1   ,   1   ,   1   ,     -   1     ,     -   1     ,   1   ,   1   ,     -   1     ,   1   ,   1   ,   1   ,   1   ,   0   ,   1   ,     -   1     ,     -   1     ,   1   ,   1   ,     -   1     ,   1   ,     -   1     ,   1   ,     -   1     ,     -   1     ,     -   1     ,     -   1     ,     -   1     ,   1   ,   1   ,     -   1     ,     -   1     ,   1   ,     -   1     ,   1   ,     -   1     ,   1   ,   1   ,   1   ,   1     }     .             [     Eq   .              1     ]                               
 
           [0007]    Additionally, the IEEE 5 GHz standard requires that the long-training symbols be generated according to:  
                 x        (   t   )       =       w        (   t   )              ∑     k   =   0     53                       X        (   k   )                   j2π        (     k   -   26     )              Δ   F          (     t   -     T     G                 12         )                   ,           [     Eq   .              2     ]                               
 
           [0008]    where x(t) is a time-domain representation of the long training symbol; w(t) is a weighting factor for the purpose of spectral shaping; k is a sub-carrier index; X(k) is a coefficient of the training symbol as defined by Eq. 1; and T G/2  is the guard interval, which is defined by the IEEE 5 GHz standard as 1.6 μs.  
           [0009]    In addition to specifying the content of the long-training symbols according to Eq. 2, the IEEE 5 GHz standard further requires that the number of long-training symbols be two (e.g., T 1  and T 2 ), thereby improving the accuracy of channel estimation.  
           [0010]    The IEEE 5 GHz standard further dictates that the first long training symbol T 1  be identical to the second long training symbol T 2 . Thus, designating the identical long-training symbols as X, the first long-training symbol X  155  and the second long-training symbol X  165  are transmitted consecutively during the long-training period  120 . Hence, for a two-branch transmitter-diversity OFDM system as shown in FIG. 2, a first transmitter  260  transmits:  
           [0011]    (1) two long-training symbols X  155   a  and X  165   a  across a first channel H A  during the long-training period  120 ;  
           [0012]    (2) signaling information S  170   a  across the first channel H A  during the signaling period  130 ; and  
           [0013]    (3) data D 1    180   a  and D 2    190   a  across the first channel H A  for subsequent data periods  140 ,  142 .  
           [0014]    Similarly, a second transmitter  265  transmits:  
           [0015]    (1) two long-training symbols X  155   b  and X  165   b  across a second channel H B  during the long-training period  120 ;  
           [0016]    (2) signaling information S  170   b  across the second channel H B  during the signaling period  130 ; and  
           [0017]    (3) data D 1    180   b  and D 2    190   b  across the second channel H B  for subsequent data periods  140 ,  142 .  
           [0018]    The transmitted signals are received at a receiver  205  as a function of the transmitted symbol and the channel characteristics. After removing the guard interval, each received symbol is inverse Fourier transformed. Thus, for a two-branch transmitter-diversity OFDM system as shown in FIG. 2, the received frequency domain signals Y 1  may be represented as:  
             Y   1 =( H   A   ·X )+( H   9   ·X )+Z 1   [Eq. 3].  
           [0019]    where Z 1  represents the received noise, the channel characteristics H A  and H B  are presumed to be time-invariant during the frame duration, and the propagation delay over these two channels are presumed to be substantially the same. Since the same long-training symbol X is transmitted from both branches of the two-branch transmitter-diversity system, Eq. 3 simplifies to:  
             Y   1 =( H   A   +H   B )· X+Z   2   [Eq. 4].  
           [0020]    Similarly, the subsequent received data blocks are represented by:  
           [0021]    [0021] Y   2 =( H   A   +H   B )·X+Z 2   [Eq. 5],  
             Y   3 =( H   A   +H   B )· S+Z   3   [Eq. 6],  
             Y   4   =H   A ·D AI   +H   B ·D BI +Z 4   [Eq. 7],  
           and:  
             Y   5   =H   A   ·D   A2   +H   B   ·D   B2   +Z   S   [Eq. 8].  
           [0022]    Eqs. 4 and 5, in the aggregate, result in:  
           ( Y   1 +Y 2 )· X *( H   A   +H   B )(2| X|   2 )+( Z   1   +Z   2 )·X*  [Eq. 9],  
           [0023]    which may be re-written as:  
                 H   A     +     H   B       =           (       Y   1     +     Y   2       )     ·   X     2     -       (       Z   1     +     Z   2       )     2                                               
 
           [0024]    or, more specifically, as:  
                     H   A          (   k   )       +       H   B          (   k   )         =           (         Y   1          (   k   )       +       Y   2          (   k   )         )     ·     X        (   k   )         2     -       (         Z   1          (   k   )       +       Z   2          (   k   )         )     2         ,     k   =   1     ,   ⋯              ,   N   ,           [     Eq   .              10     ]                               
 
           [0025]    where N represents the number of OFDM sub-carriers, and k represents the sub-carrier index  
           [0026]    Since, as shown in Eq. 1, X(k)ε{±1} for all k, the complex coefficient X*(k) of the transmitted symbol X(k) will be equal to the transmitted symbol X(k). Furthermore, since X(k)ε{±1}, the square norm |X(k)| 2  of the transmitted symbol X(k) will be 1. Additionally, since X(k)ε|±1| 2 |, the statistics of (Z 1 (k)+Z 2 (k))X(k), without loss of generality, is the same as that of (Z 1 (k)+Z 2 (k)).  
           [0027]    By omitting the noise terms, the aggregate effect of both channels H C H A +H B  can be estimated by:  
                   H   C          (   k   )       ≈         (         Y   1          (   k   )       +       Y   2          (   k   )         )     ·     X        (   k   )         2       ,     k   =   1     ,   ⋯              ,   N   ,           [     Eq   .              11     ]                               
 
           [0028]    While Eq. 11 provides an avenue for calculating the combined channel characteristics for H C , it is evident that the duplicative transmission of X provides very little assistance in distinguishing channel characteristics of the individual channels H A  and H B . In other words, because two branches H A  and H B  are used for transmitting a single X, a classic one-equation two-unknown system is presented in which only the aggregate characteristics H C  may be calculated to any degree of certainty. Furthermore, while the duplicative transmission of X increases the signal-to-noise ratio (SNR), the increase in SNR provides little help in resolving the characteristics of each individual channel.  
           [0029]    Although complex algorithms exist to segregate the individual channel effects from the aggregate channel effect, these algorithms make additional presumptions about the channels in order to properly estimate the characteristics of each channel. Thus, these channel estimation algorithms are only as good as their initial presumptions. Furthermore, due to the complexity of these channel estimation algorithms, when the two-branch transmitter-diversity system is expanded to multiple-branches (e.g., three-branch, four-branch, etc.), the complexity of calculations increases exponentially.  
           [0030]    Thus, a heretofore-unaddressed need exists in the industry to address the aforementioned deficiencies and inadequacies.  
         SUMMARY  
         [0031]    The present invention is directed to systems and methods for estimating channel characteristics in OFDM environments with transmitter diversity.  
           [0032]    Briefly described, in architecture, one embodiment of the system comprises logic components that are adapted to transmit a training symbol over a first channel during a first period; transmit the training symbol over a second channel during the first period; transmit a complex conjugate of the training symbol over the first channel during a second period; and transmit a negative complex conjugate of the training symbol over the second channel during the second period.  
           [0033]    The present disclosure also provides methods for estimating channel characteristics in OFDM environments with transmitter diversity.  
           [0034]    In this regard, one embodiment of the method comprises the steps of transmitting a training symbol over a first channel during a first period; transmitting the training symbol over a second channel during the first period; transmitting a complex conjugate of the training symbol over the first channel during a second period; and transmitting a negative complex conjugate of the training symbol over the second channel during the second period.  
           [0035]    Other systems, methods, features, and advantages will be or become apparent to one with skill in the art upon examination of the following drawings and detailed description. It is intended that all such additional systems, methods, features, and advantages be included within this description.  
       
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       [0036]    Many aspects of the disclosure can be better understood with reference to the following drawings. The components in the drawings are not necessarily to scale, emphasis instead being placed upon clearly illustrating the principles of the present disclosure. Moreover, in the drawings, like reference numerals designate corresponding parts throughout the several views.  
         [0037]    [0037]FIGS. 1A and 1B are diagrams illustrating Presentation Protocol Data Unit (PPDU) frame structure in the IEEE 5 GHz standard.  
         [0038]    [0038]FIG. 2 is a diagram illustrating a two-branch transmitter-diversity OFDM system that operates within the specification of the IEEE 5 GHz standard.  
         [0039]    [0039]FIGS. 3A and 3B are diagrams illustrating one embodiment of a system for estimating channel characteristics.  
         [0040]    [0040]FIG. 4 is a diagram illustrating a two-branch transmitter-diversity OFDM system in which channel characteristics are estimated according to one embodiment of the invention.  
         [0041]    [0041]FIG. 5 is a flowchart showing an embodiment of a method for estimating channel characteristics, which is employed by a transmitter in a two-branch transmitter-diversity OFDM system.  
         [0042]    [0042]FIG. 6 is a flowchart showing an embodiment of a method for estimating channel characteristics, which is employed by a receiver in a multiple-branch transmitter-diversity OFDM system.  
     
    
     DETAILED DESCRIPTION OF THE EMBODIMENTS  
       [0043]    Reference is now made in detail to the description of the embodiments as illustrated in the drawings. While several embodiments are described in connection with these drawings, there is no intent to limit the invention to the embodiment or embodiments disclosed herein. On the contrary, the intent is to cover all alternatives, modifications, and equivalents.  
         [0044]    Several embodiments of the invention are described below, in which additional training symbols may be used to further estimate channel characteristics. Thus, unlike prior systems and methods, which required enormous processing power or additional presumptions about a multi-branch transmitter-diversity system, the embodiments below provide for simpler calculations and fewer presumptions in characterizing multi-branch transmitter-diversity systems.  
         [0045]    [0045]FIGS. 3A and 3B are diagrams illustrating one embodiment of a system for estimating channel characteristics. FIG. 3A is a diagram showing symbols to be transmitted from a first transmitter, while FIG. 3B is a diagram showing symbols to be transmitted from a second transmitter. FIGS. 3A and 3B show a physical layer convergence procedure (PLCP) preamble field for use in synchronization (SYNC) is shown for one embodiment of the invention. As shown in FIGS. 3A and 3B, the PLCP preamble includes a short-training period  310 , a long-training period  320  following the short-training period  310 , a signaling period  330  following the long-training period  320 , and a plurality of data periods  340 ,  342 ,  344  that follow the signaling period  330 . The long-training period  320 , the signaling period  330 , and the plurality of data periods  340 ,  342 ,  344  each include a guard interval as defined in the IEEE 5 GHz standard.  
         [0046]    Thus, as shown in FIG. 3A, the first transmitter transmits symbols during the short-training period  310  in accordance with the IEEE 5 GHz standard. Once the short-training symbols have been transmitted, long-training symbols X  355   a  and X  365   a  are transmitted during the long-training period  320 . Here, the capital symbol X denotes a set of the frequency domain quantities in an orthogonal frequency division multiplexing (OFDM) system. Thus, X can be viewed as a vector containing N elements, where N is the number of sub-carriers in the OFDM system. Each element X(k) of X is carried by its corresponding kth sub-carrier. It should be appreciated that X is inverse Fourier transformed to a time domain signal, added with a cyclic prefix, and converted to a radio-frequency (RF) analog signal by an RF module prior to being radiated from a transmit antenna.  
         [0047]    The duplicative transmission of X is followed by transmission of signaling information S  370   a  during the signaling period  330 . Upon transmitting the signaling information S  370   a , a complex conjugate X*  385   a  of the long-training symbol is transmitted during a first data period  340 . Since, as described above, each element in X is real, it is axiomatic that each element in X* is also real. Additionally, since each element in X is real, it is also axiomatic that X* is identical to X. It should, however, be understood that, outside of the context of the IEEE 5 GHz standard, X need not be wholly real-valued, and that X may contain complex numbers having imaginary components.  
         [0048]    Similarly, as shown in FIG. 3B, the second transmitter transmits symbols during the short-training period  310  in accordance with the IEEE 5 GHz standard. Once the short-training symbols have been transmitted, long-training symbols X  355   b  and X  365   b  are transmitted during the long-training period  320 . The duplicative transmission of X is followed by transmission of signaling information S  370   b  during the signaling period  330 . Upon transmitting the signaling information S  370   b , a negative complex conjugate −X  385   b  of the long-training symbol is transmitted during a first data period  340 . Since each element in X is real, each element in −X is also real. Again, it should be understood that, outside of the context of the IEEE 5 GHz standard, X need not be wholly real-valued and may contain complex numbers having imaginary components. In this regard, if X is generally complex-valued, then the training symbols transmitted during  385   a  and  385   b  may be the symbol pairs of (−X, X), (X, −X), (−X*, X*), or (X*, −X*). For simplicity, the description below show non-limiting examples using symbol pairs (−X*, X*) and (X*, −X*).  
         [0049]    As described here, rather than merely duplicating the transmission of X, the system of FIGS. 3A and 3B supplements the duplicative transmission of X with X* at the first channel, and supplements the duplicative transmission of X with −X* at the second channel. Several advantages of supplementing the long-training symbols with X* and −X* are described below with reference to FIG. 4.  
         [0050]    [0050]FIG. 4 is a diagram illustrating a two-branch transmitter-diversity OFDM system as a wireless device  470  and a receiver  405 . The wireless device  470  may be a wireless local area network (LAN) access point unit, a wireless LAN card, a cellular telephone, a wireless personal digital assistant (PDA), a portable computer having wireless transmission capabilities, etc. As shown in FIG. 4, the wireless device  470  comprises two transmitters  460 ,  465  that are adapted to transmit data in an orthogonal frequency-division multiplexing (OFDM) environment. The receiver  405  is adapted to receive signals from the two transmitters  460 ,  465 . As shown in FIG. 4, a first channel transfer function H A  alters signals that are transmitted from the first transmitter  460  while a second channel transfer function H B  alters signals that are transmitted from the second transmitter  465 .  
         [0051]    Thus, if the first transmitter  460  and second transmitter  465  transmits X (i.e., inverse Fourier transforms X to generate a time domain signal x, adds a cyclic prefix to generate x cp , converts x cp  to a radio-frequency (RF) analog signal X RF  by an RF module, and radiates x RF  at the transmit antenna), then the received symbol Y 1  is represented in the frequency domain by:  
         Y 1 =( H   A   ·X )+( H   B   ·X )+Z 1   [Eq. 12].  
         [0052]    where Z 1  represents the noise for first received symbol. Since the same training symbol X is transmitted from both branches of the two-branch transmitter-diversity system, Eq. 12 may be simplified to:  
           Y   1 =( H   A   +H   B )· X+Z   1   [Eq. 13].  
         [0053]    Similarly, since the same training symbol is transmitted again, the second transmission from the two transmitters  460 ,  465  may be seen as:  
           Y   2 =( H   A   +H   B )· X+Z   2   [Eq. 14].  
         [0054]    Also, if signaling information  370   a  is transmitted as a third transmitted symbol T 3 , then:  
           Y   3 =( H   A   +H   B )· S+Z   3   [Eq. 15],  
         [0055]    where S represents the frequency-domain signaling information. In one embodiment, upon transmitting the signaling information S, the complex conjugate X*  385   a  of the long-training symbol is transmitted from the first transmitter  460  as the fourth symbol T 4 , and a negative complex conjugate −X* is transmitted from the second transmitter  465  as the fourth symbol T 4 . As described above, since X is real, both the complex conjugate X* and the negative complex conjugate −X* are real. Additionally, since X is real:  
         X*=X  [Eq. 16],  
         −X*=−X  [Eq. 17],  
         and:  
         | X ( k )| 2 =1  [Eq. 18].  
         [0056]    Thus, in the context of the IEEE 5 GHz standard, the fourth received symbol may be represented as:  
           Y   4 =( H   A   ·X )+( H   B ·(− X ))+ Z   4   [Eq. 19],  
         [0057]    or simply:  
           Y   4 =( H   A −H B )· X+Z   4   [Eq. 20].  
         [0058]    Combining Eqs. 13 and 20 provides an approach in which H A  and H B  may be isolated. In other words, unlike prior-art approaches in which an aggregate effect H C =H A +H B  of the channels is calculated, individual channel characteristics of H A  and H B  may be calculated since:  
                 (       Y   1     +     Y   4       )     ·     X   *       =           (         (       H   A     +     H   B       )     ·   X     +     Z   1       )     ·     X   *       +       (         (       H   A     -     H   B       )     ·   X     +     Z   4       )     ·     X   *              
                =       2                   H     A   ′                 X        2       +       (       Z   1     +     Z   4       )     ·       X   *     .                   [     Eq   .              21     ]                               
 
         [0059]    It should be appreciated that each item in Eq. 21 is a frequency domain representation of an OFDM symbol. From the perspective of the sub-carrier, Eq. 21 may be rewritten as:  
         ( Y   1 ( k )+ Y   4 ( k ))· X ( k )*=2 H   A ( k )·| X ( k )| 2 +( Z   1 ( k )+ Z   2 ( k ))· X *( k ), k=1, . . . N [Eq. 22],  
         [0060]    where N represents the number of OFDM sub-carriers, and k represents the sub-carrier index.  
         [0061]    The channel transfer function H A  (k) may be obtained by:  
                 H   A          (   k   )       =           (         Y   1          (   k   )       +       Y   4          (   k   )         )     ·     X        (   k   )         2     -           (         Z   1          (   k   )       +       Z   4          (   k   )         )     ·     (   k   )       2     .               [     Eq   .              23     ]                               
 
         [0062]    Thus, based on Eq. 23, H A  can be estimated as:  
                   H   A          (   k   )       ≈         (         Y   1          (   k   )       +       Y   4          (   k   )         )     ·     X        (   k   )         2       ,     k   =   1     ,   ⋯              ,   N   ,           [     Eq   .              24     ]                               
 
         [0063]    or, more simply:  
               H   A     ≈           (       Y   1     +     Y   4       )     ·   X     2     .             [     Eq   .              25     ]                               
 
         [0064]    It should be appreciated that an estimation error proportional to the noise term (Z 1 +Z 4 )X/2 is inherent in Eqs. 24 and 25. Generally, the mean of the estimation error is equal to E(Z 1 +Z 4 )/ 2 =0, where E represents the statistical-expected-value function. Correspondingly, the variance of the estimation error is equal to var ((Z 1 +Z 4 )X/2)=var((Z 1 +Z 4 )/2)=var((Z 1 +Z 4 )/2)=σ Z   2 / 2 , where var() represents the statistical-variance function, and Z 1  and Z 4  are presumed to have variance σ z   2 .  
         [0065]    The characteristics of the second channel H B  may similarly be obtained using:  
                   (       Y   1     -     Y   4       )     ·     X   *       =           (         (       H   A     +     H   B       )     ·   X     +     Z   1       )     ·     X   *       -       (         (       H   A     -     H   B       )     ·   X     +     Z   4       )     ·     X   *              
                =       2                   H     B   ′                 X        2       +       (       Z   1     -     Z   4       )     ·     X   *             ,           [     Eq   .              26     ]                               
 
         [0066]    or, more simply:  
               H   B     =           (       Y   1     -     Y   4       )     ·   X     2     -           (       Z   1     -     Z   4       )     ·   X     2     .               [     Eq   .              27     ]                     H   B          (   k   )       =           (         Y   1          (   k   )       -       Y   4          (   k   )         )     ·     X        (   k   )         2     -         (         Z   1          (   k   )       -       Z   4          (   k   )         )     ·     X        (   k   )         2         ,     
          k   =   1     ,              …              ,     N   .             [     Eq   .              28     ]                               
 
         [0067]    or:  
         [0068]    Therefore, H B  may be estimated as:  
               H   B     ≈           (       Y   1     -     Y   4       )     ·   X     2     .             [     Eq   .              29     ]                               
 
         [0069]    Similar to Eqs. 24 and 25, an estimation error proportional to the noise term (Z 1 −Z 4 )X/2 is inherent in Eqs. 28 and 29. Thus, the mean of the estimation error is equal to E((Z 1 −Z 4 )X/2)=0, and the variance of the estimation error is equal to var((Z 1 −Z 4 )X/2)=var((Z 1 −Z 4 )/2)=σ Z   2 /2.  
         [0070]    Thus, as seen from Eqs. 12 through 29, each individual channel may be accurately characterized by transmitting X and −X* during one of the data periods. Hence, rather than merely characterizing the aggregate of the channels, estimates of each individual channel may be derived from the approach outlined above.  
         [0071]    In another embodiment, greater signal integrity and lower estimation error may be achieved by combining Eqs. 13, 14, and 20. Since Eqs. 13 and 14 represent duplicative transmissions of the same training symbol X, combining Eqs. 13 and 14 may be seen as a further signal averaging. Thus, by exploiting the SNR improvement gained by the duplicative transmission of the training symbol X, the channels may be isolated according to:  
         [0072]    ( Y   1   +Y   2 +2 Y   4 )X=4  H   A   ·|X | 2 +(Z 1   +Z   2 +2 Z   4 )·X*  [Eq. 30],  
         [0073]    and:  
                 H   A     =           (       Y   1     +     Y   2     +     2        Y   4         )     ·   X     4     -         (       Z   1     +     Z   2     +     2        Z   4         )     ·   X     4         ,           [     Eq   .              31     ]                               
 
         [0074]    or, equivalently:  
                   H   A          (   k   )       =           (         Y        (   k   )       1     +       Y   2          (   k   )       +     2          Y   4          (   k   )           )     ·     X        (   k   )         4     -         (         Z   1          (   k   )       +       Z   2          (   k   )       +     2          Z   4          (   k   )           )     ·     X        (   k   )         4         ,     
          k   =   1     ,              …              ,   N   ,           [     Eq   .              32     ]                               
 
         [0075]    Therefore, H A  can be estimated by:  
                   H   A          (   k   )       ≈         (         Y        (   k   )       1     +       Y   2          (   k   )       +     2          Y   4          (   k   )           )     ·     X        (   k   )         4       ,     k   =   1     ,              …              ,     N   .             [     Eq   .              33     ]                               
 
         [0076]    Thus, unlike Eqs. 24, 25, 28, and 29, the estimation error induced by the noise term for Eq. 32 is (Z 1 +Z 2 +2Z 4 )X/4. Here, the mean of the estimation error is equal to E((Z 1 +Z 2 +2Z 4 )X/4)=0, and the variance of the estimation error is equal to var((Z 1 +Z 2 +2Z 4 )X/4)=var((Z 1 +Z 2 +2Z 4 )/4)=3σ Z   2 /8, where Z 1 , Z 2 , and Z 4  are assumed to have variance of σ Z   2 .  
         [0077]    As seen from Eq. 32, the variance of the estimation error is reduced, thereby improving the accuracy of estimation. Similarly, the characteristics of the second channel H B  may be obtained by:  
                   H   B          (   k   )       ≈         (         Y   1          (   k   )       +       Y   2          (   k   )       -     2          Y   4          (   k   )           )     ·     X        (   k   )         4       ,     k   =   1     ,              …              ,   N   ,           [     Eq   .              34     ]                               
 
         [0078]    thereby resulting in the mean of the estimation error being equal to E((Z 1 +Z 2 −2Z 4 )X/4)=0, and the variance of the estimation error being equal to var((Z 1 +Z 2 −2Z 4 )X/4)=var((Z 1 +Z 2 2Z 4 )/4)=3σ Z   2 /8, where Z 1 , Z 2 , and Z 4  are assumed to have variance of σ Z   2 ;  
         [0079]    In a more general sense, the variance of the estimation error can be further reduced with the transmission of additional long training symbols X or the transmission of additional complex conjugates X* and negative complex conjugates −X* of the long training symbol X.  
         [0080]    While multiple-branch transmitter-diversity systems have been shown above, another embodiment of the invention may be seen as a method for estimating channel characteristics. Embodiments of such a method is shown in FIGS. 5 and 6.  
         [0081]    [0081]FIG. 5 is a flowchart showing method steps that are performed by the wireless device  470  in a two-branch transmitter-diversity OFDM system. If the signal transmission follows the IEEE standard, then the transmission of the signals during the guard interval is implicit in the embodiment of FIG. 5. As shown in FIG. 5, a training symbol is transmitted ( 520 ) over both the first and second channels during a first period. In one embodiment, the wireless device  470  comprises first channel transmit logic  555  and second channel transmit logic  565 , which are adapted to transmit information over the first and second channels, respectively. After transmitting ( 520 ) the training symbol during the first period, a complex conjugate of the training symbol is transmitted ( 530 ) over the first channel during a second period. Substantially simultaneously, during the second period, a negative complex conjugate of the training symbol is transmitted ( 540 ) over the second channel.  
         [0082]    If the channel estimation is performed in accordance with the IEEE 5 GHz standard, then the first period is one of the long-training periods in the preamble of the physical layer convergence procedure (PLCP), and the second period is one of the subsequent data periods. FIG. 6 is a flowchart showing a method for estimating channel characteristics, which is performed by the receiver  405 . As shown in FIG. 6, the symbols are received ( 620 ) at a receiver  405 . Upon receiving ( 620 ) the symbols, individual channel effects are isolated ( 630 ) from the received symbols. These isolated ( 630 ) individual channel effects are used to estimate ( 640 ) characteristics of the individual channels. In one embodiment, the receiver  405  comprises receive logic  625 , isolate logic  635 , and estimate logic  645 , which are adapted to perform the receiving ( 620 ), isolating ( 630 ), and estimating ( 640 ) steps, respectively, as shown in FIG. 6. Also, in an example embodiment, the received symbols may be analogous counterparts to the transmitted signals as shown in FIG. 5. Thus, for an n-branch transmitter-diversity system, the receiver  405  receives ( 620 ) n symbols, each of which has a different permutation of training symbols to form a true n-equation n-unknown system, thereby permitting isolation of each channel as described with reference to Eqs. 12 through 34.  
         [0083]    As seen from FIGS. 5 and 6, the embodiments of the method permit more accurate estimates of the individual channel characteristics, rather than merely estimating the aggregate characteristics of the channel, or making additional presumptions that affect the channel characteristics.  
         [0084]    Although exemplary embodiments have been shown and described, it will be clear to those of ordinary skill in the art that a number of changes, modifications, or alterations to the invention as described may be made. For example, while a two-branch transmitter-diversity system has been shown for purposes of illustration, it will be clear to one of ordinary skill in the art that the disclosed approach may be extended to multiple-branch transmitter-diversity systems having three, four, or more branches. Additionally, while FIG. 4 simply shows antennas in a wireless device  470 , it will be clear to one of ordinary skill in the art that the transmitters may be a part of a wireless LAN access point unit, a wireless LAN card, a cellular telephone, a wireless personal digital assistant (PDA), or other similar wireless devices that are adapted to transmit and receive data. Furthermore, while one embodiment of the invention shows an additional training symbol being transmitted during the time period allotted for D 1 , it will be clear to one of ordinary skill in the art that the additional training symbol may also be transmitted during any of the subsequent data periods. Also, while only one additional training symbol (e.g., the complex conjugate of the long-training symbol, the negative complex conjugate of the long training symbol, etc.) is shown in FIGS. 3A and 3B, it will be clear to one of ordinary skill in the art that additional training symbols may be transmitted to increase the signal-to-noise ratio in channel estimation, or, additionally, to characterize multiple-branch transmitter-diversity systems having more than two branches. Also, while several embodiments of the invention are described within the framework of the IEEE 5 GHz standard, it will be clear to one of ordinary skill in the art that the methods and systems described herein may be extended to any environment in which orthogonal frequency-division multiplexing (OFDM) is used. Additionally, while the IEEE 5 GHz standard is used to more clearly describe several aspects of the invention, it should be understood that the systems and methods described above are compatible with the IEEE 2.4 GHz standard (IEEE 802.11g) or other similar wireless standards, regardless of the operating frequency band. These, and other such changes, modifications, and alterations, should therefore be seen as being within the scope of the disclosure.