Patent Publication Number: US-2003227888-A1

Title: Method and apparatus for pilot estimation using suboptimum expectation maximization

Description:
RELATED APPLICATIONS  
     [0001] 1. Claim of Priority under 35 U.S.C. §119(e)  
     [0002] The present Application for Patent claims priority of U.S. Provisional Application No. 60/386,840, Jun. 5, 2002, assigned to the assignee hereof and hereby expressly incorporated by reference herein.  
     [0003] 2. Reference to Co-Pending Applications for Patent  
     [0004] The present invention is related to the following Applications for Patent in the U.S. Patent &amp; Trademark Office:  
     [0005] “Method and Apparatus for Pilot Estimation Using a Wiener Filter” by Farrokh Abrishamkar et al, having Attorney Docket No. 020099, filed concurrently herewith and assigned to the assignee hereof, and which is expressly incorporated by reference herein;  
     [0006] “Method And Apparatus For Pilot Estimation Using A Prediction Error Method With A Kalman Filter And Pseudo-Linear Regression”, by Farrokh Abrishamkar et al., having Attorney Docket No. 020201, filed concurrently herewith and assigned to the assignee hereof;  
     [0007] “Method And Apparatus For Pilot Estimation Using A Prediction Error Method With A Kalman Filter And A Gauss-Newton Algorithm”, by Farrokh Abrishamkar et al., having Attorney Docket No. 020205, filed concurrently herewith and assigned to the assignee hereof; and  
     [0008] “Method And Apparatus For Pilot Estimation Using An Adaptive Prediction Error Method With a Kalman Filter and A Gauss-Newton Algorithm,” by Farrokh Abrishamkar et al., having Attorney Docket No. 020232, filed concurrently herewith and assigned to the assignee hereof.  
    
    
     
       FIELD  
       [0009] The present invention relates to wireless communication systems generally and specifically, to methods and apparatus for estimating a pilot signal in a code division multiple access system.  
       BACKGROUND  
       [0010] In a wireless radiotelephone communication system, many users communicate over a wireless channel. The use of code division multiple access (CDMA) modulation techniques is one of several techniques for facilitating communications in which a large number of system users are present. Other multiple access communication system techniques, such as time division multiple access (TDMA) and frequency division multiple access (FDMA) are known in the art. However, the spread spectrum modulation technique of CDMA has significant advantages over these modulation techniques for multiple access communication systems.  
       [0011] The CDMA technique has many advantages. An exemplary CDMA system is described in U.S. Pat. No. 4,901,307, entitled “Spread Spectrum Multiple Access Communication System Using Satellite Or Terrestrial Repeaters”, issued Feb. 13, 1990, assigned to the assignee of the present invention, and incorporated herein by reference. An exemplary CDMA system is further described in U.S. Pat. No. 5,103,459, entitled “System And Method For Generating Signal Waveforms In A CDMA Cellular Telephone System”, issued Apr. 7, 1992, assigned to the assignee of the present invention, and incorporated herein by reference.  
       [0012] In each of the above patents, the use of a forward-link (base station to mobile station) pilot signal is disclosed. In a typical CDMA wireless communication system, such as that described in EIA/TIA IS-95, the pilot signal is a “beacon” transmitting a constant data value and spread with the same pseudonoise (PN) sequences used by the traffic bearing signals. The pilot signal is typically covered with the all-zero Walsh sequence. During initial system acquisition, the mobile station searches through PN offsets to locate a base station&#39;s pilot signal. Once it has acquired the pilot signal, it can then derive a stable phase and magnitude reference for coherent demodulation, such as that described in U.S. Pat. No. 5,764,687 entitled “Mobile Demodulator Architecture For A Spread Spectrum Multiple Access Communication System,” issued Jun. 9, 1998, assigned to the assignee of the present invention, and incorporated herein by reference.  
       [0013] Recently, third-generation (3G) wireless radiotelephone communication systems have been proposed in which a reverse-link (mobile station to base station) pilot channel is used. For example, in the currently proposed cdma2000 standard, the mobile station transmits a Reverse Link Pilot Channel (R-PICH) that the base station uses for initial acquisition, time tracking, rake-receiver coherent reference recovery, and power control measurements.  
       [0014] Pilot signals can be affected by noise, fading and other factors. As a result, a received pilot signal may be degraded and different than the originally transmitted pilot signal. Information contained in the pilot signal may be lost because of noise, fading and other factors.  
       [0015] There is a need, therefore, to process the pilot signal to counter the effects of noise, fading and other signal-degrading factors. 
     
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
     [0016]FIG. 1 is a diagram of a spread spectrum communication system that supports a number of users.  
     [0017]FIG. 2 is a block diagram of a base station and a mobile station in a communications system.  
     [0018]FIG. 3 is a block diagram illustrating the downlink and the uplink between the base station and the mobile station.  
     [0019]FIG. 4 is a block diagram of the channels in an embodiment of the downlink.  
     [0020]FIG. 5 illustrates a block diagram of certain components in an embodiment of a mobile station.  
     [0021]FIG. 6 is a flow diagram of one embodiment of a method for estimating the pilot using a Kalman filter.  
     [0022]FIG. 7 is a block diagram illustrating the use of an offline system identification component to determine the parameters needed by the Kalman filter.  
     [0023]FIG. 8 is a block diagram illustrating the offline system identification operation.  
     [0024]FIG. 9 is a block diagram of the calculation blocks of FIG. 8 illustrating the calculations made in each block.  
     [0025]FIG. 10 is a flow diagram of a method for configuring a Kalman filter for steady state operation to estimate the pilot.  
     [0026]FIG. 11 is a block diagram illustrating the inputs to and outputs from the offline system identification component and pilot estimation component. 
    
    
     DETAILED DESCRIPTION  
     [0027] The word “exemplary” is used exclusively herein to mean “serving as an example, instance, or illustration.” Any embodiment described herein as “exemplary” is not necessarily to be construed as preferred or advantageous over other embodiments. While the various aspects of the embodiments are presented in drawings, the drawings are not necessarily drawn to scale unless specifically indicated.  
     [0028] The following discussion develops the exemplary embodiments of a data-driven pilot estimator by first discussing a spread-spectrum wireless communication system. Then components of an embodiment of a mobile station are shown in relation to providing a pilot estimate. Before the pilot is estimated, a pilot estimation component is trained. Details regarding the offline system identification used to train the pilot estimation component are set forth. Included in the specification relating to the offline system identification are illustrations and mathematical derivations for a maximum likelihood parameter estimation. The iterative process of generating state estimates and calculating new parameters is discussed. Formulas for both offline system identification and real-time pilot estimating are illustrated.  
     [0029] Note that the exemplary embodiment is provided as an exemplar throughout this discussion; however, alternate embodiments may incorporate various aspects without departing from the scope of the present invention.  
     [0030] The exemplary embodiment employs a spread-spectrum wireless communication system. Wireless communication systems are widely deployed to provide various types of communication such as voice, data, and so on. These systems may be based on CDMA, TDMA, or some other modulation techniques. A CDMA system provides certain advantages over other types of systems, including increased system capacity.  
     [0031] A system may be designed to support one or more standards such as the “TIA/EIA/IS-95-B Mobile Station-Base Station Compatibility Standard for Dual-Mode Wideband Spread Spectrum Cellular System” referred to herein as the IS-95 standard, the standard offered by a consortium named “3rd Generation Partnership Project” referred to herein as 3GPP, and embodied in a set of documents including Document Nos. 3G TS 25.211, 3G TS 25.212, 3G TS 25.213, and 3G TS 25.214, 3G TS 25.302, referred to herein as the W-CDMA standard, the standard offered by a consortium named “3rd Generation Partnership Project 2” referred to herein as 3GPP2, and TR-45.5 referred to herein as the cdma2000 standard, formerly called IS-2000 MC. The standards cited hereinabove are hereby expressly incorporated herein by reference.  
     [0032] Each standard specifically defines the processing of data for transmission from base station to mobile, and vice versa. As an exemplary embodiment the following discussion considers a spread-spectrum communication system consistent with the CDMA2000 standard of protocols. Alternate embodiments may incorporate another standard. Still other embodiments may apply the compression methods disclosed herein to other types of data processing systems.  
     [0033]FIG. 1 serves as an example of a communications system  100  that supports a number of users and is capable of implementing at least some aspects of the embodiments discussed herein. Any of a variety of algorithms and methods may be used to schedule transmissions in system  100 . System  100  provides communication for a number of cells  102 A- 102 G, each of which is serviced by a corresponding base station  104 A- 104 G, respectively. In the exemplary embodiment, some of the base stations  104  have multiple receive antennas and others have only one receive antenna. Similarly, some of the base stations  104  have multiple transmit antennas, and others have single transmit antennas. There are no restrictions on the combinations of transmit antennas and receive antennas. Therefore, it is possible for a base station  104  to have multiple transmit antennas and a single receive antenna, or to have multiple receive antennas and a single transmit antenna, or to have both single or multiple transmit and receive antennas.  
     [0034] Terminals  106  in the coverage area may be fixed (i.e., stationary) or mobile. As shown in FIG. 1, various terminals  106  are dispersed throughout the system. Each terminal  106  communicates with at least one and possibly more base stations  104  on the downlink and uplink at any given moment depending on, for example, whether soft handoff is employed or whether the terminal is designed and operated to (concurrently or sequentially) receive multiple transmissions from multiple base stations. Soft handoff in CDMA communications systems is well known in the art and is described in detail in U.S. Pat. No. 5,101,501, entitled “Method and system for providing a Soft Handoff in a CDMA Cellular Telephone System”, which is assigned to the assignee of the present invention.  
     [0035] The downlink refers to transmission from the base station  104  to the terminal  106 , and the uplink refers to transmission from the terminal  106  to the base station  104 . In the exemplary embodiment, some of terminals  106  have multiple receive antennas and others have only one receive antenna. In FIG. 1, base station  104 A transmits data to terminals  106 A and  106 J on the downlink, base station  104 B transmits data to terminals  106 B and  106 J, base station  104 C transmits data to terminal  106 C, and so on.  
     [0036]FIG. 2 is a block diagram of the base station  202  and mobile station  204  in a communications system. A base station  202  is in wireless communications with the mobile station  204 . As mentioned above, the base station  202  transmits signals to mobile stations  204  that receive the signals. In addition, mobile stations  204  may also transmit signals to the base station  202 .  
     [0037]FIG. 3 is a block diagram of the base station  202  and mobile station  204  illustrating the downlink  302  and the uplink  304 . The downlink  302  refers to transmissions from the base station  202  to the mobile station  204 , and the uplink  304  refers to transmissions from the mobile station  204  to the base station  202 .  
     [0038]FIG. 4 is a block diagram of the channels in an embodiment of the downlink  302 . The downlink  302  includes the pilot channel  402 , the sync channel  404 , the paging channel  406  and the traffic channel  408 . The downlink  302  illustrated is only one possible embodiment of a downlink and it will be appreciated that other channels may be added or removed from the downlink  302 .  
     [0039] Although not illustrated, the uplink  304  may also include a pilot channel. Recall that third-generation (3G) wireless radiotelephone communication systems have been proposed in which an uplink  304  pilot channel is used. For example, in the currently proposed cdma2000 standard, the mobile station transmits a Reverse Link Pilot Channel (R-PICH) that the base station uses for initial acquisition, time tracking, rake-receiver coherent reference recovery, and power control measurements. Thus, systems and methods herein may be used to estimate a pilot signal whether on the downlink  302  or on the uplink  304 .  
     [0040] Under one CDMA standard, described in the Telecommunications Industry Association&#39;s TIA/EIA/IS-95-A Mobile Stations-Base Station Compatibility Standard for Dual-Mode Wideband Spread Spectrum Cellular System, each base station  202  transmits pilot  402 , sync  404 , paging  406  and forward traffic  408  channels to its users. The pilot channel  402  is an unmodulated, direct-sequence spread spectrum signal transmitted continuously by each base station  202 . The pilot channel  402  allows each user to acquire the timing of the channels transmitted by the base station  202 , and provides a phase reference for coherent demodulation. The pilot channel  402  also provides a means for signal strength comparisons between base stations  202  to determine when to hand off between base stations  202  (such as when moving between cells).  
     [0041]FIG. 5 illustrates a block diagram of certain components in an embodiment of a mobile station  504 . Other components that are typically included in the mobile station  504  may not be illustrated for the purpose of focusing on the novel features of the embodiments herein. Many embodiments of mobile stations  504  are commercially available and, as a result, those skilled in the art will appreciate the components that are not shown.  
     [0042] If the pilot channel  402  were being sent on the uplink  304 , the components illustrated may be used in a base station  202  to estimate the pilot channel. It is to be understood that the inventive principles herein may be used with a variety of components to estimate a pilot whether the pilot is being received by a mobile station  504 , a base station  202 , or any other component in a wireless communications system. Thus, the embodiment of a mobile station  504  is an exemplary embodiment of the systems and methods but it is understood that the systems and methods may be used in a variety of other contexts.  
     [0043] Referring again to FIG. 5, a spread spectrum signal is received at an antenna  506 . The spread spectrum signal is provided by the antenna  506  to a receiver  508 . The receiver  508  down-converts the signal and provides it to the front-end processing and despreading component  510 . The front-end processing and despreading component  510  provides the received pilot signal  512  to the pilot estimation component  514 . The received pilot signal  512  typically includes noise and usually suffers from fading.  
     [0044] The front-end processing and despreading component  510  also provides the traffic channel  516  to a demodulation component  518  that demodulates the data symbols.  
     [0045] The pilot estimation component  514  provides an estimated pilot signal  520  to the demodulation component  518 . The pilot estimation component  514  may also provide the estimated pilot signal  520  to other subsystems  522 .  
     [0046] It will be appreciated by those skilled in the art that additional processing takes place at the mobile station  504 . The embodiment of the pilot estimation component  514  will be more fully discussed below. Generally, the pilot estimation component  514  operates to estimate the pilot signal and effectively clean-up the pilot signal by reducing the noise and estimating the original pilot signal that was transmitted.  
     [0047] Systems and methods disclosed herein use a Kalman filter to estimate the pilot signal. Kalman filters are known by those skilled in the art. In short, a Kalman filter is an optimal recursive data processing algorithm. A Kalman filter takes as inputs data relevant to the system and estimates the current value(s) of variables of interest. A number of resources are currently available that explain in detail the use of Kalman filters. A few of these resources are “Fundamentals of Kalman Filtering: A Practical Approach” by Paul Zarchan and Howard Musoff, “Kalman Filtering and Neural Networks” by Simon Haykin and “Estimation and Tracking: Principles, Techniques And Software” by Yaakov Bar-Shalom and X. Rong Li, all of which are incorporated herein by reference.  
     [0048]FIG. 6 is a flow diagram  600  of one embodiment of a method for estimating the pilot using a Kalman filter. The system receives  602  the baseband CDMA signal. Then the front-end processing and despreading component  510  performs initial processing and despreading  604 . The received pilot signal is then provided  606  to the pilot estimation component  514 . The received pilot signal has been degraded by various effects, including noise and fading. The pilot estimation component  514  estimates  608  the pilot channel using a Kalman filter. After the pilot has been estimated  608 , it is provided  610  to the demodulation component  518  as well as other subsystems  522 .  
     [0049] Referring now to FIG. 7, before the Kalman filter in the pilot estimation component  514  is used, the parameters of the Kalman filter are determined during a training period. As shown, an offline system identification component  702  is used to determine the parameters needed by the Kalman filter. Offline training data is input to the offline system identification component  702  in order to determine the needed parameters. Once the parameters have converged, they are provided to the pilot estimation component  714  and its Kalman filter, to process the received pilot and estimate the original pilot in real time. In the embodiment disclosed herein, the offline system identification component  702  is used once to set up the parameters. After the parameters have been determined, the system uses the pilot estimation component  714  and no longer needs the offline system identification component  702 .  
     [0050] Typically the offline system identification  702  is used before a component is being used by the end user. For example, if the system and methods were being used in a mobile station  204 , when an end user was using the mobile station  204 , it  204  would be using the pilot estimation component  714  to process the pilot in real-time. The offline system identification component  702  was used before the mobile station  204  was operating in real-time to determine the parameters needed to estimate the pilot.  
     [0051] The following discussion provides details regarding the calculations that will be made in the offline system identification component  702  as well as the pilot estimation component  714 . Additional details and derivations known by those skilled in the art are not included herein.  
     [0052] The received pilot complex envelope after despreading is given by the following formula:  
       {tilde over (y)}   k   ={tilde over (s)}   k   +{tilde over (v)}   k   Formula 1.  
     [0053] The received complex envelope in Formula 1 is represented as {tilde over (y)} k . The original but faded pilot signal is represented as {tilde over (s)} k . The noise component is represented as {tilde over (v)} k . For a single path mobile communication channel, the original pilot signal may be represented by the mathematical model found in Formula 2. The corresponding noise component may be represented by the formula found in Formula 3.  
       {tilde over (s)}   k =ρ k   e   Jφ     k     R   hh (τ)= g   k   N{square root}{square root over (E c   p )}   R   hh (τ) {tilde over (ƒ)}   k   Formula 2.  
     [0054]                 v   ~     k     =         g   k            NI   oc              n   ~     k       +       g   k            NI   or              ∑       m   =     -   ∞       ,     m   ≠   k         +   ∞                           R   hh          (       mT   C     -   τ     )                w   ~     k     .                     Formula                 3                         
     [0055] The variables and parameters in the formulas found in Formulas 2 and 3 are given in Table 1.  
                           TABLE 1                                      {square root over (E p )}:   Pilot Envelope           I oc:     Total AWGN Noise           I or:     Total Transmit PSD           g k:     AGC Control Signal           p k:     Rice (Rayleigh) Fade Process           {tilde over (f)} k :   Complex Gaussian Fade Process with Clark Spectrum           φ k :   Fading Phase           m, k:   Chip and Symbol Counts           N:   Processing Gain           R hh (τ):   Correlation           τ:   Time Offset           ñk, {tilde over (w)}k:   Zero Mean Unit Power Gaussian Noise                      
 
     [0056] The demodulation component  518  requires the phase of the pilot signal. In order to obtain the phase, the signals may be written in a form comprising I and Q components rather than being written in an envelope form. In Formula 4, {tilde over (y)} represents the received pilot comprising its I and Q components. The faded pilot, without any noise, is represented as {tilde over (s)} in Formula 5. The total noise is represented in Formula 6 as {tilde over (v)}. Formula 7 illustrates the fade as {tilde over (ƒ)}.  
       {tilde over (y)}=y   I   +jy   Q   Formula 4.  
       {tilde over (s)}=s   I   +js   Q   Formula 5.  
       {tilde over (v)}=v   I   +jv   Q   Formula 6.  
     {tilde over (ƒ)}=ρ e   Jφ =ƒ I   +j ƒ   Q   Formula 7.  
     [0057] Given the relationships of the formulas above, the I and Q components of the faded pilot symbol without noise may be written as shown in Formulas 8 and 9.  
       s   I ( k )=ƒ I ( k ) N{square root}{square root over (E c   p )}R   hh (τ) g ( k )=α( k )ƒ I ( k )  Formula 8.  
       s   Q ( k )=ƒ Q ( k ) N{square root}{square root over (E c   p )}R   hh (τ) g ( k )=α( k )ƒ Q ( k )  Formula 9.  
     [0058] The I and Q components of the received pilot may be written as shown in Formulas 10 and 11.  
       y   I =α ƒ I   +V   I   Formula 10.  
       y   Q =α ƒ Q   +V   Q   Formula 11.  
     [0059] The pilot estimation component  714  operates to take as input the received pilot signal which is noisy and faded to produce an estimate of the pilot signal. A Kalman filter may be used in real-time to estimate the pilot. In the training state, the Kalman filter is trained on training data. A parameter estimation component estimates parameters, discussed below, and provides the parameters to the Kalman filter. The Kalman filter uses the parameters and provides a state estimate to the parameter estimation component. The process shown is iterated through until the parameters for the Kalman filter have converged. This process will be more fully discussed in relation to FIGS. 8 and 9.  
     [0060] The received pilot complex envelope is represented by the formula in Formula 12. In Formula 12, {tilde over (y)}(l) represents the received pilot. The faded pilot, without any noise, is represented as {tilde over (s)}(l) in Formula 13. The quadrature components are used for demodulation.  
       {tilde over (y)} ( l )= y   I ( l )+ jy   Q ( l )  Formula 12.  
       {tilde over (s)} ( l )= s   I ( l )+ js   Q ( l )  Formula 13.  
     [0061] The received complex envelope may be written in the form found in Formula 14 where the received complex envelope is represented as y(l). The original but faded pilot signal is represented as s(l). The noise component is represented as v(l).  
       y ( l )= s ( l )+ v ( l )  Formula 14.  
     [0062] As known in the art, stationary signals may be modeled using a Gauss-Markov state space format amenable to Kalman filtering, as shown in Formula 15.  
               s        (   l   )       =         ∑     i   =   1     M                       A        (   i   )            s        (     l   -   i     )           +       B        (   l   )              w        (   l   )       .                 Formula                 15                       
 
     [0063] The received complex envelope may be written in the form found in Formula 16 where the received complex envelope is represented as y(l). The original pilot signal is represented as x(l). The noise component is represented as v(l). In the equation in Formula 15 M=1, which means that the pilot is being modeled with the first order Gauss-Markov process. The clean pilot may be written in the form shown in Formula 17.  
       y ( l )= x ( l )+ v ( l )  Formula 16.  
       x ( l )= Ax ( l− 1)+ Bw ( l )  Formula 17.  
     [0064] In order to estimate  x   N , given  Y   N ={y 0 , y 1 , . . . y N }, the formulas shown in Formulas 18 and 19 may be used.  
       {circumflex over (x)} ( l )= A{circumflex over (x)} ( l− 1)+ Bw ( l )  Formula 18.  
       y ( l )= {circumflex over (x)} ( l )+ v ( l )  Formula 19.  
     [0065] Given  {circumflex over (X)}   N ={{circumflex over (x)} 0 , . . . , {circumflex over (x)} N }, A and B may be estimated as shown in the derivation and formulas of Formulas 20-22. The method for determining A and B in Formulas 21 and 22 may be referred to as a maximum likelihood parameter estimation.  
                 δ     δ                 A            L        (       A                 and                 B     |         X   _     ^     N       )         ,         δ     δ                 B            L        (       A                 and                 B     |         X   _     ^     N       )         =   0.             Formula                 20                   A   ^     ML     =           ∑     i   =   1     N                         x   ^     i            x   ^       i   -   1                        X   _     ^     N          2       .             Formula                 21                   B   ^     ML     =           ∑     i   =   1     N            (                    x   ^     i     -         x   ^       i   -   1            A   ^         )     2       N     .             Formula                 22                       
 
     [0066] The equations in Formulas 21 and 22 may be used to calculate new values for Ã 1 , Ã 2 , . . . Ã M , {tilde over (B)}. The training may be continued until the Ã 1 , Ã 2 , . . . Ã M , B values converge. As shown below in FIG. 8, the Kalman filter is used to generate state estimates. The formulas shown in Formula 23-26 may be used to derive the state estimates in the Kalman filter.  
       x   k   =Âx   k-1   +{circumflex over (B)}w   k   Formula 23.  
       y   k   =x   k   +v   k   Formula 24.  
     σ k   2 =Var( w )=1  Formula 25.  
     σ v   2 =Var( v )  Formula 26.  
     [0067] The calculations of the Kalman Filter to generate the new state estimates may be made from the formulas shown in Formulas 27-32.  
               k   k     =         P   k         P   k     +     σ   v   2         .             Formula                 27                       
 
       e   k   =y   k   −{circumflex over (x)}   k|k-1   Formula 28.  
       {circumflex over (x)}   k|k   ={circumflex over (x)}   k|k-1   +k   k   e   k   Formula 29.  
       {circumflex over (x)}   k+1|k   =Â{circumflex over (x)}   k|k   Formula 30.  
       P   k+1   =Â   2 (1 −k   k ) P   k   +{circumflex over (B)}   2   Formula 31.  
     k=0, . . . , N−1  Formula 32.  
     [0068]FIG. 8 is a block diagram illustrating the offline system identification operation  802 . Initialized parameters (Ã 1 , Ã 2 , . . . Ã M , {tilde over (B)})  804  are provided to the Kalman filter  806  to generate state estimates. In addition, training data  808  (Y 1 , Y 2 , . . . Y N ) is also provided to the Kalman filter  806 . With the initialized parameters  804  and training data  808 , the Kalman filter  806  generates a state estimate  {circumflex over (X)}   N ={{circumflex over (x)} 0 , . . . , {circumflex over (x)} N } according to the formulas as described above. The new state estimate is provided to the maximum likelihood parameter estimation component  810 . The maximum likelihood parameter estimation component  810  calculates new parameter values using the equations in Formulas 21 and 22. A state space model is formed, and the Kalman filter  806  generates new sequence state estimate. The Kalman filter  806  and the maximum likelihood parameter estimation component  810  continue to operate until the parameters have converged.  
     [0069] In the embodiment of FIG. 8, the training runs for the length of the pilot symbol record. In addition, the sequence of pilot symbols may be tuned to the target speed and environment of choice.  
     [0070]FIG. 9 is a block diagram of calculation blocks of FIG. 8 that illustrate the calculations made in each block. The Kalman filter state estimation component  806  performs the calculations as shown to generate a new state estimate. The maximum likelihood parameter estimation component  810  performs the calculations as shown to generate new parameters. The offline system identification component  702  iterates through the calculations as shown until the parameters converge.  
     [0071]FIG. 10 is a flow diagram of a method for configuring a Kalman filter  806  for steady state operation to estimate the pilot. Training samples  808  are provided  1002  to the offline system identification component  702 . The parameters  804  are initialized  1004 . In addition, the state is initialized  1006 . Then the Kalman filter  806  is used to generate  1008  a new state estimate. The maximum likelihood parameter estimation  810  is used to generate  1010  new parameters. The generating steps  1008 ,  1010  are repeated  1012  until the filter and parameters have converged. Those skilled in the art will appreciate the various ways in which one may determine that the filter and parameters have converged. After the system has completed training the filter  806 , the converged parameters are provided  1014  for online steady-state (real-time) Kalman filter operation.  
     [0072]FIG. 11 is a block diagram illustrating the inputs to and outputs from the offline system identification component  702  and pilot estimation component  714 . The offline system identification component  702  is provided training samples  Y   N  and initial conditions {circumflex over (x)} 0  and ê 0 . The system identification component  702  operates in an iterative fashion, as described above, until the necessary parameters have converged. After the system identification component  702  has completed training, it  702  provides the state, parameters and initial conditions ({circumflex over (x)} 0 , Â, {circumflex over (B)}, K) to the pilot estimation component  714 . The pilot estimation component  714  comprises the Kalman filter  806  operating in real-time. Thus, at this stage the Kalman filter  806  is no longer training, but is being used to estimate the pilot, given the received pilot as input.  
     [0073] As discussed above, the pilot estimation component  714  uses a Kalman filter to estimate the pilot. The calculations for the Kalman filter  806  operating in real-time are shown in FIG. 11 and are known by those skilled in the art. The Kalman filter  806  is provided the online received pilot symbols and estimates the pilot. As shown, the Kalman filter  806  produces an estimate for both the I and Q components of the pilot signal.  
     [0074] Those of skill in the art would understand that information and signals may be represented using any of a variety of different technologies and techniques. For example, data, instructions, commands, information, signals, bits, symbols, and chips that may be referenced throughout the above description may be represented by voltages, currents, electromagnetic waves, magnetic fields or particles, optical fields or particles, or any combination thereof.  
     [0075] Those of skill would further appreciate that the various illustrative logical blocks, modules, circuits, and algorithm steps described in connection with the embodiments disclosed herein may be implemented as electronic hardware, computer software, or combinations of both. To clearly illustrate this interchangeability of hardware and software, various illustrative components, blocks, modules, circuits, and steps have been described above generally in terms of their functionality. Whether such functionality is implemented as hardware or software depends upon the particular application and design constraints imposed on the overall system. Skilled artisans may implement the described functionality in varying ways for each particular application, but such implementation decisions should not be interpreted as causing a departure from the scope of the present invention.  
     [0076] The various illustrative logical blocks, modules, and circuits described in connection with the embodiments disclosed herein may be implemented or performed with a general purpose processor, a digital signal processor (DSP), an application specific integrated circuit (ASIC), a field programmable gate array (FPGA) or other programmable logic device, discrete gate or transistor logic, discrete hardware components, or any combination thereof designed to perform the functions described herein. A general purpose processor may be a microprocessor, but in the alternative, the processor may be any conventional processor, controller, microcontroller, or state machine. A processor may also be implemented as a combination of computing devices, e.g., a combination of a DSP and a microprocessor, a plurality of microprocessors, one or more microprocessors in conjunction with a DSP core, or any other such configuration.  
     [0077] The steps of a method or algorithm described in connection with the embodiments disclosed herein may be embodied directly in hardware, in a software module executed by a processor, or in a combination of the two. A software module may reside in RAM memory, flash memory, ROM memory, EPROM memory, EEPROM memory, registers, hard disk, a removable disk, a CD-ROM, or any other form of storage medium known in the art. An exemplary storage medium is coupled to the processor such the processor can read information from, and write information to, the storage medium. In the alternative, the storage medium may be integral to the processor. The processor and the storage medium may reside in an ASIC. The ASIC may reside in a user terminal. In the alternative, the processor and the storage medium may reside as discrete components in a user terminal.  
     [0078] The previous description of the disclosed embodiments is provided to enable any person skilled in the art to make or use the present invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the generic principles defined herein may be applied to other embodiments without departing from the spirit or scope of the invention. Thus, the present invention is not intended to be limited to the embodiments shown herein but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.