Abstract:
A method and apparatus to accomplish fast adaptive equalization of a wireless communication channel is disclosed. The equalization method and apparatus utilize time varying adaptive filter coefficients and time varying convergence parameters in a fast adaptive algorithm to provide fast channel equalization in a wireless communication system.

Description:
BACKGROUND OF THE INVENTION 
     Modern telecommunication has experienced explosive growth in the past decade. Distinguishing from the conventional telecommunication systems, there are two important aspects in modern telecommunication technologies, one being digital, and another being wireless. Wireless communication revolutionarily changes the way of communication and provides possibility of communication to anyone, from anywhere, at anytime. While wireless communication technology significantly changes the way people live and work, it adds tremendous challenges to communication engineering design. It is obvious that when a radio signal is transmitted through the air, the signal quality will largely depend on many variables in communication environments that are beyond our control. For example, the radio signal could be absorbed by or reflected from the buildings, mountains, or other obstacles between two points of communication. In addition, the received signal quality depends on the speed of mobile transmitter and receiver terminals. All of these increase the difficulties of maintaining a quality communication link. Furthermore, unlike a wired communication system, a wireless communication system often has problems with flat or frequency selective fading, and time dispersion. 
     In order to maintain a quality wireless communication signal, the radio channel must be estimated and properly compensated, and one effective means of such channel estimation and compensation is called channel equalization. Due to the time-varying nature of a radio channel, channel equalization is often designed to be adaptive, or time-varying, in order to track dynamic channel variation. 
     PRIOR ART 
     Various equalization techniques have been taught in prior arts for channel estimation and compensation and acoustic echo cancellation applications. Depending upon the application and the system requirements, an adaptive equalizer can be quite straightforward or rather complex in realization. A relatively simple equalization technique is perhaps a linear adaptive equalizer using the least mean square (LMS) algorithm. An LMS adaptive equalization minimizes an error signal, typically the mean square error between the output of an adaptive filter and the desired channel response through an adaptive process. A gradient descent adaptive algorithm is often utilized to minimize the mean square error. In a gradient descent adaptive algorithm, the gradient of the error signal with respect to filter coefficients is estimated and the filter coefficients are updated along the negative gradient direction at each iteration of the adaptive process until the mean square error is minimized. Because of its simplicity and easy implementation, LMS adaptive equalization, either linear or decision feedback, has been widely used in various applications. 
     Another equalization technique can be categorized as probabilistic detection algorithms. The most commonly used techniques within this category include Maximum A Posteriori probability (MAP) and Maximum Likelihood Sequence Estimation (MLSE). These techniques minimize the probability of a signal detection error and therefore require knowledge of channel characteristics and the stochastic property of channel noise. While the MAP technique detects a received signal in a symbol-by-symbol manner, the MLSE algorithm utilizes the Viterbi algorithm to minimize the probability of a sequence error. A more detailed description of equalization techniques based on probabilistic detection algorithms can be found in references such as Digital Communication (2 nd  ed. 1994) by E. A. Lee and D. G. Messerschmitt, Telecommunications Applications with TMS320C5x DSPs (Texas Instruments Application Book, 1994), and Adaptive Equalization for TDMA Digital Mobile Radio (IEEE Trans. On Vehicular Technology, Vol. 40, No. 2, May 1991) by J. G. Proakis. 
     The channel equalization techniques described above have both advantages and shortcomings. A simple linear adaptive equalizer is straightforward and simple to implement. However, it is less effective in severe wireless communication environments. Its limitation for wireless communication lies in the fact that the LMS algorithm is inherently a slow convergence algorithm, especially when the reference signal is highly correlated. Therefore, while the conventional LMS based equalization technique is attractive due to its simple implementation, its slow convergence property makes it difficult to track the rapid change of a radio channel due to the terminal speed and the dynamic operating environment. 
     In contrast to an LMS algorithm, a MAP or MLSE based equalization technique is quite effective in estimating and reducing inter-symbol interference (ISI). However, the complexity of implementing the MAP or MLSE algorithms is significantly higher than a LMS algorithm. In fact, the implementation complexity of the MAP and MLSE techniques prohibit its utility in certain applications. For example, in applications such as Personal Wireless Telecommunication (PWT) or Digital Enhanced Cordless Telecommunication (DECT), where time dispersion is typically not as severe as in cellular applications, a less complex equalization technique is often desirable because it has a lower cost. 
     SUMMARY OF THE INVENTION 
     The present invention relates to an adaptive equalizer design in a wireless communication system. More specifically, this invention describes a novel adaptive equalization method and apparatus that utilizes a fast adaptive algorithm. While the present invention is well suited for applications such as Personal Wireless Telecommunication, Digital Enhanced Cordless Telecommunication, Wireless Local Loop communication, and other cellular communication systems, it will be understood by one skilled in the art that the advantages of this invention will apply to other types of communication systems as well. 
     In light of the above mentioned problems associated with both least mean square algorithm and probabilistic detection algorithm equalization techniques in the prior art, it is an object of the present invention to provide an adaptive equalizer with less complexity than the commonly used MLS equalizer or MAP algorithm and a fast convergence property. 
     Another object of the present invention is to provide a fast adaptive algorithm that can be applied to both a linear equalizer and a decision feedback equalizer design. 
     A further object of the present invention is to provide a fast adaptive algorithm with a level of complexity and a structural simplicity that is close to the conventional Least Mean Square algorithm in order to also provide a channel equalization technique that has both a desirable level of accuracy and a low implementation cost. 
     Still another object of the invention is to utilize time-varying convergence parameters in the adaptive algorithm in order to achieve a fast convergence and to minimize the error signal. 
     These and other objects, features, and advantages of the present invention will be apparent from the accompanying drawings and from the detailed description that follows. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     The present invention is illustrated by way of example and not limitation in the figures of the accompanying drawings, in which like references indicate similar elements and in which: 
     FIG. 1 is a block diagram of a prior art communication system with channel equalization; and 
     FIG. 2 is block diagram of an adaptive decision feedback equalizer. 
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     FIG. 1 is a general illustration of a prior art wireless communication system  10 . The current invention, a fast adaptive equalizer, may be used with the wireless communication system  10  as generally described below. Although the invention is described with respect to the preferred embodiment, those skilled in the art will recognize that other versions of the wireless communication system shown in FIG.  1  and of the equalizer shown in FIG. 2 embodying the current invention are possible and that the invention is not limited to a specific embodiment. 
     Although many constructions are possible and well known in the prior art, in the embodiment shown in FIG. 1, the wireless communication system  10  takes a source signal  12  and passes it through a source encoder  14 , a channel encoder  16 , and a modulator  18  before transmitting through a radio channel  20  and a transmit antenna  22 . The transmitted signal is received through the antenna  24  of a receiver. At the receiver, the received channel  26  is passed through a demodulation unit  28 , an equalizer  30 , a decision device  32 , a channel decoder  34  and a source decoder  36  before being output to a user as a recovered signal  38 . 
     There are two types of equalizers  30  that are well known in the prior art. The equalization technique illustrated in FIG. 2 is a decision feedback equalizer. More specifically, FIG. 2 illustrates a fast adaptive decision feedback equalizer  30  that is the subject of the present invention. The other equalization technique that could be used in the communication system illustrated in FIG. 1 is a linear equalizer. The linear adaptive equalizer is considered a special case of the decision feedback equalizer shown in FIG. 2 in which the backward filter is set to zero. 
     As shown in FIG. 2, in the fast adaptive decision feedback equalizer  30  of the present invention, x(k) is the input signal  304  received by the receiver, y(k) is the output signal  303  of the equalizer  30  at the k-th iteration of a signal sampling rate, respectively. The received signal x(k) is the input signal  304  to, and is used as the reference signal of, the forward filter  305 , while the output signal y(k)  303  is fed back as the input signal for the backward filter  306 . The desired signal d(k)  301  is obtained by channel estimation from channel estimator  301   a  in which an appropriate channel model is applied for system identification. The error signal e(k)  302  can be expressed as                e        (   k   )       =       d        (   k   )       -       ∑     i   =   0       I   -   1                w     f   ,   k            (   i   )            x        (     k   -   i     )           -       ∑     j   =   1     J              w     b   ,   k            (   j   )            y        (     k   -   j     )                     (   1   )                                
     where w f,k  and w b,k  represent the equalizer coefficients of the forward filter  305  and the backward filter  306 , respectively. Furthermore, each iteration of the signal sampling rate is indicated in equation 1 through the use of k as the sample index, and I and J as the number of taps for the forward filter  305  and the backward filter  306 , respectively. As further shown in FIG. 2, the fast adaptive algorithm  400  is designed to minimize the channel equalization error signal, e(k),  302  for the forward filter  305  and the backward filter  306  from one iteration to the next. 
     In order to minimize the error signal e(k)  302  in the shortest amount of time possible, it is well known in the prior art that the equalizer coefficients w f,k  and w b,k  should be updated at each iteration of the signal sampling rate. Typically, the gradient descent algorithm has been used to update the equalizer coefficients w f,k  and w b,k  according to the following equations, 
     
       
           w   f,k+1 ( i )= w   f,k ( i )+2  μx ( k−i ) e ( k )  (2) 
       
     
     
       
           w   b,k+1 ( j )= w   b,k ( j )+2  μy ( k−j ) e ( k )  (3) 
       
     
     where i=0,1,2, . . . l−1, j=1,2, . . . J, and μ is the convergence parameter that determines the stability and convergence speed of the adaptive equalizer. Furthermore, in the prior art, the conventional technique of utilizing the gradient descent algorithm is to select a constant convergence parameter that is fixed for the entire adaptive process. The selection of step size is also usually a “trial and error” process that is slow and imprecise, as convergence often depends on the characteristics of an input signal. 
     Since fast tracking channel variation is important in wireless communication applications and the use of constant convergence parameters yields slower than desired results, the convergence property of the fast adaptive equalizer of the claimed invention is improved over the prior art by utilizing time-varying convergence parameters in the adaptive process. In the preferred embodiment of the present invention, the fast adaptive algorithm  400  is based on a LMS algorithm with gradient adaptive convergence parameters. The time-varying step sizes in the preferred fast adaptive decision feedback equalizer are designed to minimize the mean square of the error signal e(k)  302  for the forward filter  305  and the backward filter  306  from one iteration of the sampling rate to the next. This is preferably accomplished through dual adaptations. First, appropriate initial values of convergence parameters for the forward and backward filter coefficients are selected such that the adaptive process is stable and channel tracking is performed by updating the forward and backward filter coefficients of the adaptive decision feedback equalizer  30 . The adaptive filter coefficients are preferably updated along the negative gradient direction at each iteration of a sampling rate of the input signal to minimize the error signal. Second, the convergence parameter is updated at each iteration to achieve a fast convergence and to minimize the error at each iteration, thereby also determining the convergence speed and stability of the adaptive process. Therefore, since the convergence parameters of the forward and backward coefficients of the fast adaptive decision feedback equalizer  30  are aimed at minimizing the mean square error at the next iteration, the convergence speed and tracking capability of the fast adaptive equalizer can be improved considerably in comparison to the conventional gradient decent decision feedback equalizer. 
     In one preferred embodiment, the variation of the convergence parameters is proportional to the negative gradient of the mean square error with respect to the previous convergence parameter. Therefore, in a decision feedback equalizer, the update equations for forward and backward coefficients can be expressed as 
     
       
           w   f,k+1 ( i )= w   f,k ( i )+2 μ f ( k ) x ( k−i ) e ( k )  (4) 
       
     
     
       
           w   b,k+1 ( j )= w   b,k ( j )+2 μ b ( k ) y ( k−j ) e ( k )  (5) 
       
     
     where μ f (k) and μ b (k) are time-varying convergence parameters that are a function of a sampling rate iteration k for the forward filter  305  and the backward filter  306 , respectively. Expressing equations (4) and (5) in a vector form yields, 
       w   f,k+1   = 2     f,k +2 μ f ( k ) e ( k ) x   k   =w   f,k +μ f ( k ){circle around (∇)} f,k   (6) 
     
       
           w   b,k+1   =w   b,k +2 μ b ( k ) e ( k ) y   k   =w   b,k +μ b ( k ){circle around (∇)} b,k   (7) 
       
     
     where gradient estimates are given by (8) and (9)                       ∇   ^            f   ,   k       =         ∂       e   2          (   k   )           ∂     w     f   ,   k           =     2        e        (   k   )            x   k                 (   8   )                        ∇   ^            b   ,   k       =         ∂       e   2          (   k   )           ∂     w     b   ,   k           =     2        e        (   k   )            y   k                 (   9   )                                
     and the input and output signal vectors are defined as 
     
       
           x   k   =[x ( k ) x ( k− 1) . . .  x ( k−I+ 1)] T   (10) 
       
     
     
       
           y   k   =[y ( k− 1) y ( k− 2) . . .  y ( k−J )] T   (11) 
       
     
     Accordingly, in the preferred embodiment, the convergence parameters for the forward filter  305  and the backward filter  306  of the fast adaptive decision feedback equalizer  30  can be updated as follows:                        μ   f          (   k   )       =         μ   f          (     k   -   1     )       -     α                     ∂       e   2          (   k   )           ∂       μ   f          (     k   -   1     )                           =         μ   f          (     k   -   1     )       +       α   2                            ∇   ^            f   ,   k     T                 ∇   ^            f   ,     k   -   1                           (   12   )                         μ   b          (   k   )       =         μ   b          (     k   -   1     )       -     β                     ∂       e   2          (   k   )           ∂       μ   b          (     k   -   1     )                           =         μ   b          (     k   -   1     )       +       β   2                            ∇   ^            b   ,   k     T                 ∇   ^            b   ,     k   -   1                           (   13   )                                
     where α and β(0&lt;α,β≦1) are scaling factors and can be properly selected to control the speed of adaptation for the convergence parameters. In practical applications, upper bounds for the scaling factors, and thereby for the convergence parameters, can be used to provide added stability to the equalizer  30 . In addition, the convergence property of the fast adaptive equalizer  30  of the present invention may be further improved by assigning an individual convergence parameter to each filter tap. The step sizes for individual filter taps can be obtained by 
      μ f,k ( i )=μ f,k−1 ( i )+2α e ( k ) x ( k−i ) e ( k− 1) x ( k−i− 1)  (14) 
     
       
         μ b,k ( i )=μ b,k−1 ( j )+2β e ( k ) y ( k−j− 1) e ( k− 1) y ( k−j− 2)  (15) 
       
     
     whereby the update equations for the equalizer are then given by 
     
       
           w   f,k+1   =w   f,k + μ   f,k {circumflex over (∇)} f,k   (16) 
       
     
     
       
           w   b,k+1   =w   b,k + μ   b,k {circumflex over (∇)} b,k   (17) 
       
     
     and 
     
       
           μ   f,k =diag[μ f,k (1)μ f,k (2) . . . μ f,k ( i ) . . . μ f,k ( I )]  (18) 
       
     
     
       
           μ   b,k =diag[μ b,k (1)μ b,k (2) . . . μ b,k ( j ) . . . μ b,k ( J )]  (19) 
       
     
     are diagonal convergence parameter matrices whose components are given by (14) and (15). 
     In another embodiment of a fast adaptive algorithm  400 , the convergence parameters can be obtained by taking the second derivative of the error signal and setting it to zero as in equation 20.                  ∂       e   2          (     k   +   1     )           ∂       μ   f          (   k   )           =   0           (   20   )                   ∂       e   2          (     k   +   1     )           ∂       μ   b          (   k   )           =   0           (   21   )                                
     By expressing the error signal at the (k+1 )-th sample as a function of the error at the k-th sample using Taylor&#39;s expansion, and omitting the higher order terms, the following relation holds                e        (     k   +   1     )       =       e        (   k   )       +       ∑     i   =   0       I   -   1                ∂     e        (   k   )           ∂       w   k          (   k   )                         δ                     w   f          (   i   )           +       ∑     j   =   1       J   -   1                ∂     e        (   k   )           ∂       w   b          (   k   )                         δ                     w   b          (   j   )                     (   22   )                                
     Expressed in a vector form,                      e        (     k   +   1     )       =       e        (   k   )       =           ∂     e   k         ∂     w     f   ,   k                         δ                   w     f   ,   k         +         ∂     e   k         ∂     w     b   ,   k                         δ                   w     b   ,   k                         =       e        (   k   )       +         μ   f          (   k   )            x   k                            ∇   ^            f   ,   k         +         μ   b          (   k   )            y   k                 ∇   ^            b   ,   k                         (   23   )                                
     Using the gradient estimates from (8), (9), (10), and (11), and taking the square of both sides of (23) yields, 
     
       
           e ( k+ 1) 2   =e   2 ( k )[1−2μ f ( k ) x   k   T   x   k 2μ b ( k ) y   k   T   y   k ] 2   (24) 
       
     
     From (20), (21), and (24), 
     
       
         μ f ( k ) x   k   T   x   k +μ b ( k ) y   k   T   y   k =0.5=constant  (25) 
       
     
     The convergence parameters for the forward and backward equalizers can be generally obtained by                  μ   f          (   k   )       =     α       x   k   T          x   k                 (   26   )                   μ   b          (   k   )       =     β       y   k   T          y   k                 (   27   )                                
     where α and β are preferably positive constants with certain upper bounds to provide added stability to the equalizer  30 . 
     Both preferred embodiments of the fast adaptive equalizers and algorithms described above improve the convergence behavior of the prior art decision feedback equalizer with variable step sizes. The current invention is considerably simpler in implementation than many non-LMS based equalizers but provides better convergence characteristics than conventional LMS based decision feedback equalizers. The current invention is therefore desirable for equalizer design in personal wireless telecommunications and other cellular applications where fast channel tracking is important. Although additional complexity is required in computing the time-varying convergence parameters, the complexity increment is small compared to other equalization techniques. Furthermore, these techniques can be applied to both channel estimation and channel tracking as well as both decision feedback and linear equalizer design. 
     In the foregoing specification, the invention has been described with reference to specific embodiments thereof. It will, however, be evident that various modifications and changes may be made thereto without departing from the broader spirit and scope of the invention as set forth in the appended claims. Those skilled in the art to which the invention pertains may make modifications and other embodiments employing the principles of this invention without departing from its spirit or essential characteristics, particularly after considering the foregoing teachings. The described embodiments are to be considered in all respects only as illustrative and not restrictive and the scope of the invention is, therefore, indicated by the appended claims rather than by the foregoing description.