Abstract:
An effective receiver is achieved for situations where the receiver is mobile, and may be traveling at relatively high speed, and where the receiver&#39;s internal demodulation oscillator causes a frequency offset, with processing that shares a common algorithm for both frequency offset and channel characteristics estimations. Specifically, the commonly employed algorithm, such as the LMS algorithm, computes an estimate of the frequency offset, and that very same algorithm is also used to estimate the channel characteristics. When the LMS algorithm is used, a frequency offset estimate can be derived from signals derived in the course of executing the LMS algorithm. A frequency compensation factor is then developed and applied to the incoming signal to create a signal that that not have an appreciable frequency offset. That signal is then applied to a process that also employs the LMS algorithm, in combination with a detection algorithm, such as, for example, the Viterbi algorithm, to recover from the incoming signal the information signals that had been encoded into the incoming signals.

Description:
BACKGROUND OF THE INVENTION 
     This invention relates to signal detection and, more particularly, to channel tracking techniques in mobile receivers adapted to receive phase-modulated signals. 
     One well-known technique for transmitting information to mobile receivers is to convert the signal to digital symbols, to map those symbols onto a two-dimensional space, to modulate a carrier with the mapped symbols, and to transmit the modulated carrier to the receiver. The modulation of a symbol mapped onto a two-dimensional space (having x and y coordinates) takes place by amplitude-modulating the x component of the symbol by a carrier signal, amplitude-modulating the y component of the symbol by the carrier signal shifted by 90 degrees, and adding the two modulation products. In some applications the mapping is restricted to a circle, and that, effectively, results in phase modulation of the carrier. 
     A mobile unit receives signals that are corrupted by inter-symbol interference (ISI) as well as by thermal noise, and the challenge is to detect the so-distorted symbols. The ISI is a non-stationary process when the mobile unit is moving. That is, the characteristics of the channel are based on the location of the mobile unit relative to the transmitter, and when that location changes, the channel characteristics change. Prior art systems allow for adapting a receiver&#39;s response to the channel characteristics, but this adapting requires processing, and the processing requires time. As long as the channel characteristics change slowly, there is no problem. When the channel characteristics change rapidly, such as when the mobile unit changes its location rapidly (e.g. the mobile unit is in a car, or a plane), the currently-used adapting processes are able to keep up with the changes under ideal conditions. 
     The challenge to track the changing channel characteristics is compounded by the fact that the mobile unit has no information about the precise time when symbols are applied to the transmitter&#39;s modulator, and therefore does not know precisely when to sample the received signal. Furthermore, although the receiver nominally knows what the transmitter&#39;s carrier frequency is, the actual carrier frequency may be off and, in any event, the receiver&#39;s local frequency may be off from its specified value because of normal manufacturing tolerance issues, temperature variations, etc. 
     When the receiver&#39;s local oscillator is not equal to the transmitter&#39;s oscillator, an offset in frequency is said to exist. When there is no offset in frequency, the received signal is sampled, converted to digital form, and applied to a detection algorithm. The detection algorithm must remove the ISI introduced by the channel and must also compensate for the changing characteristics of the channel due to the movements of the mobile unit (e.g., in a car moving at 60 miles per hour, the channel characteristics change fairly rapidly). One technique that accomplishes channel tracking is the Least-Mean-Squared (LMS) algorithm. The LMS algorithm, however, is not thought of as being able to handle changing channel characteristics when there is a significant frequency offset. 
     When the receiver&#39;s frequency does have a significant offset, conventional differential detectors can be used to estimate the frequency offset and to compensate therefor. Differential detectors are described, for example, by Proakis in “Digital Communication,” McGraw Hill, 1989, Chapter 4.2.6. However, differential detectors fail when the channel characteristics change rapidly. 
     To overcome the problem of both a frequency offset and a rapidly changing channel, practitioners have included a training word in the symbol sequence, and once the training word is detected and its position is ascertained, the frequency offset can be extracted. An algorithm for accomplishing this, which is quite complex, is presented, for example, by Bahai and Sarraf in “A Frequency Offset Estimation for Nonstationary Channels,”  Proc. of ICASSP  97, pp. 3897-3900, April, 1997. 
     A simpler solution would obviously be advantageous. 
     SUMMARY 
     A simpler solution is, indeed, available where, in accord with the principles disclosed herein, a given algorithm, such as the LMS algorithm, computes an estimate of the frequency offset, and that very same algorithm is also used to estimate the channel characteristics. When the LMS algorithm is used, a frequency offset estimate can be derived from signals derived in the course of executing algorithm. A frequency compensation factor is then developed and applied to the incoming signal to create a signal that does not have an appreciable frequency offset. That signal is then applied to a process that also employs the LMS algorithm, in combination with a detection algorithm, such as, for example, the Viterbi algorithm, to recover from the incoming signal the information signals that had been encoded into the incoming signals. In addition to carrying out the disclosed process during training intervals, the process can be carried out during normal transmission of data. 
     Thus, in at least one embodiment of this invention, a fairly simple algorithm is employed to estimate the frequency offset. Moreover the algorithm employed for estimating channel characteristics is the very same as the algorithm employed to compensate for frequency offsets. This simplifies the receiver&#39;s construction and reduces its cost. 
    
    
     BRIEF DESCRIPTION OF THE DRAWING 
     FIG. 1 illustrates some salient elements of a mobile receiver; 
     FIG. 2 presents a block diagram of a pre-processing module in accordance with the principles of this invention; 
     FIG. 3 depicts the processing within processor  231  in accordance with one tracking approach; and 
     FIG. 4 depicts the processing within processor  231  in accordance with another tracking approach. 
    
    
     DETAILED DESCRIPTION 
     FIG. 1 presents a block diagram of various elements of a receiving process, including channel  100  to which symbols modulated onto a carrier are applied. Channel  100  introduces additive noise, and the resulting signal is applied to demodulator  200 , which employs local oscillator  210 . The demodulated output is sampled and converted to digital form in block  220 , and the digital signal is applied to digital processor  230 . Processor  230  is shown to include a pre-processing module  231 , an LMS algorithm module  232 , a Viterbi algorithm module  233 , and a post-processing module  234 . During a training period processor  230  conventionally employs the LMS algorithm (module  232 ) to estimate the channel characteristics, and the derived information is employed by a symbol-detection algorithm during the data transmission period to recover the transmitted data. An example of a symbol-detection algorithm is the Viterbi algorithm, depicted in FIG. 1 by module  233 . 
     As also indicated above, the LMS algorithm cannot compensate for rapidly varying channel characteristics in the presence a frequency offset, without additional and fairly complex algorithms. See, for example, the method reported in the aforementioned Bahai et al paper. In accordance with the principles disclosed herein, however, a fairly simple algorithm is employed to estimate the frequency offset. Moreover the algorithm is the same as the algorithm employed for estimating channel. This simplifies the receiver&#39;s construction and reduces its cost. 
     The process carried out by the transmitter/receiver arrangement, in accord with the principles disclosed herein, is one where a training sequence that is known to the receiver is sent by the transmitter, and during that time the LMS algorithm evaluates an estimate of the frequency offset in the manner disclosed below. That is performed in processing module  231 . Thereafter, incoming signals (both data and training sequence signals) are compensated by the estimate of the frequency offset (also in processing module  231 ) and applied to modules  232  and  233 . FIG. 2 diagrammatically shows this by depicting module  231  in greater detail. It includes an LMS algorithm module  235  that interacts with processing module  236  to yield an estimate of the frequency offset. That signal is subtracted from the incoming signal in element  237  and applied to modules  232  and  233 . 
     The following develops the characteristics of signals employed to estimate the frequency offset by the use of the LMS algorithm. 
     The signal received by element  200  at time k, d(k), corresponds to the transmitted sequence of symbols (we assume for now that it is the training sequence), u k , that was first modulated by a carrier (resulting in u k e jωk ), then convolved with channel w o  to yield u k w o e jωk , and finally augmented with additive noise v′(k). When extracted from its carrier signal, i.e., demodulated, by element  210 , and when the receiver&#39;s local oscillator is offset from the carrier by frequency Ω, the received signal at time k is 
     
       
         d(k)=u k w o e jΩk +v(k).  (1) 
       
     
     The time response of w o  is time-limited, and when quantized in time, i.e., sampled, the channel response w o  is represented by a vector of order M. Correspondingly, u k  is an M order vector containing the M latest symbols transmitted to the mobile receiver. The term v(k)=v′(k)e jΩk , and u k w o  is the dot product of the two component vectors. The first term of equation (1) can be also viewed as the dot product of transmitted symbols vector with a periodically changing channel vector, or as the dot product of the channel with a sequence u k  that includes a modulating offset frequency e jΩk . 
     The challenge, then, is to estimate the channel and to estimate the frequency offset. One known approach for estimating a channel that is not changing with time is to recursively derive an improved current estimate of the channel from the immediately previous estimate of the channel, combined with or modified by the newly arrived data. The following equation presents such an estimate at time k+1 based on information at time k, and is typically referred to as the LMS algorithm: 
     
       
         w k+1 =w k +μ(d(k)−u k w k )u k *.  (2) 
       
     
     In equation (2), W k  is the channel estimate at time k, u k  is the M order vector at the mobile receiver which, during training, is the k th  member of the training sequence. 
     The channel estimate at time k, w k  might differ from the actual channel response at that time, w o e jΩk , resulting in an error vector {tilde over (w)} k , i.e., 
     
       
         {tilde over (w)} k =w o e jΩk −w k   (3) 
       
     
     Combining equations (2) and (3) to express the error vector at time k+1 in terms of values at time k, and taking the expected value thereof yields 
     
       
         E[{tilde over (w)} k+1 ]=(I−μR)E[{tilde over (w)} k ]−w o e jΩk (1−e jΩ )  (4) 
       
     
     where the matrix R is the expectation of the outer dot product of vectors, u k * and u k ; i.e., 
     
       
         R=E[u k *u k ]. (5) 
       
     
     A solution of this recursive equation, in the form E[{tilde over (w)} k ]=ae jΩk , leads to 
     
       
         
           
             
               
                 
                   
                     
                       E 
                        
                       
                         [ 
                         
                           
                             w 
                             ~ 
                           
                           k 
                         
                         ] 
                       
                     
                     = 
                     
                       
                         
                           ( 
                           
                             I 
                             - 
                             
                               
                                 μ 
                                 
                                   1 
                                   - 
                                   
                                      
                                     
                                       j 
                                        
                                       
                                           
                                       
                                        
                                       Ω 
                                     
                                   
                                 
                               
                                
                               R 
                             
                           
                           ) 
                         
                         
                           - 
                           1 
                         
                       
                        
                       
                         w 
                         o 
                       
                        
                       
                          
                         
                           j 
                            
                           
                               
                           
                            
                           Ω 
                            
                           
                               
                           
                            
                           k 
                         
                       
                     
                   
                   , 
                 
               
               
                 
                   ( 
                   6 
                   ) 
                 
               
             
           
         
                 
         
             
         
      
     
     and to                E        [     w   k     ]       =       (     I   -       (     I   -       μ     1   -          j                 Ω              R       )       -   1         )          w   o                 j                 Ω                 k       .               (   7   )                                
     Combining two successive estimates of the channel in a dot product yields                  E        [     w   k   *     ]            E        [     w     k   +   1       ]         =     |     w   o          |   2                   1   -       1   -          j                 Ω           1   -   μ   -          j                 Ω                    -   1                   j                 Ω                                (   8   )                                
     and from equation (8), e jΩ  is derived by dividing the dot product of the two successive channel estimates by its magnitude. 
     FIG. 3 presents a block diagram that discloses, in conformance with the above analysis, the process carried out in processor modules  235  and  236 . In FIG. 3 the received sample, is applied to subtracter  301  where the dot product signal u k w k  is subtracted. The difference signal is applied to multiplier  302  where the signal is multiplied by the step size, μ, and thereafter to multiplier  304  where the signal is multiplied by the complex conjugate of the training sequence, u k *, derived from ROM  303 . The result is added to signal w k  in adder  306 , yielding the channel estimate at time k+1; i.e., w k+1 . The computed w k+1  is applied to a one-unit delay element  307 . At the time w k+1  is inserted into delay element  307 , the delay element outputs signal w k , and that signal is applied to adder  306  and to dot product multiplier  305 . The other input to dot product multiplier  305  is derived from ROM  303  which contains the training sequence. The product signal developed by multiplier  305  is u k w k , which is applied to subtracter  301 . This completes the elements that LMS algorithm includes. 
     To develop the frequency estimate in accordance with equation (8), the w k  and w k+1  signals at the output and input of delay element  307 , respectively, are applied to processing module  236  wherein they are combined in a dot product multiplier  306  and applied to processing module  309 . Module  309  divides its input signal by the signal&#39;s magnitude to obtain the phasor e −jΩ , and that phasor is rotated by the index k and applied to element  237  which multiplies the incoming signal by the frequency offset compensation factor e −jΩk . The output of multiplier  237  is applied to modules  232  and  233 . 
     A second, even simpler, process is given by evaluating an estimate of the angle of 
     
       
         d*(k)(u k w k ),  (11) 
       
     
     where d*(k)is the complex conjugate of the received signal. The expectation of d*(k)(u k w k ) is                  e        [         d   *          (   k   )            (       u   k          w   k       )       ]       =     |       w   o          u   k            |   2          (     1   -       1   -          j                 Ω           1   -   μ   -          j                 Ω             )         ,           (   12   )                                
     and, for small values of Ω and not too small values of μ, the angle of this expectation can be approximated by 
     
       
         Ω/μ  (13) 
       
     
     Once Ω is known, e jΩ  can be evaluated and multiplied by the index k to derive the offset frequency compensation factor, e −jΩk . This is illustrated in FIG. 4 where module  235  is identical to that of FIG. 3, but the output that is extracted from module  235  is the incoming signal, d(k), and the dot product signal u k w k  of multiplier  305 . These signals are applied to processing module  236  where the complex conjugate signal d*(k) is computed by processing module  311 . The output of module  236  is combined with u k w k  in processing module  312  to derive e −jΩk  (by multiplying the product of d*(k) and u k w k  by the step size, μ, and the index k, and finally, rotating the phasor e −j  by the result of the multiplication). 
     It should be understood that the processes disclosed above are the processes that are particularly relevant to the disclosed invention and that a receiver incorporating the principles disclosed herein will have other controls and processes that are not described herein. For example, the receiver would have a process for determining when the training sequence is being received. Such a process may reside within processing module  231 , or it may be in some other processing module that is not shown in FIG. 1 (because does not form a part of the advance in the art that is disclosed herein). 
     Also, the above-disclosed processes are described in connection with operations during training sequences, but that is not a limitation of this invention. Use of the training sequence in the above disclosure was deemed proper to make the algorithm clearer, because during the training sequence the receiver knows what to expect. However, it should be realized that the disclosed processes are equally valid for real data signal. Instead of using u k  and u k * signals from ROM  303 , one can use the signal developed by modules  233  and  234 . The reason that these non-training signals can be used is because most of the estimated signals are correct and are, therefore, as goos as the training symbols. In fact, there are many more estimated data signals than training signals and, therefore, using the real data symbols as well as the training symbols gives a more accurate estimate in a shorter time. 
     Lastly, the above-disclosed processes are generally shown to be carried out in processor  230 , and this processor may be part of a special purpose hardware implementation, or it may be realized with a conventional microprocessor operating under stored program control. The specific software that needs to be created is very straight forward given the functional description contained herein, and is, therefore, not described in further detail. Of course, a processor  230  that is implemented with special purpose integrated ICs will, more likely than not, attempt to take advantage of the fact that the frequency offset estimate and the channel characteristics estimates are carried out with the help of a given algorithm (in the case illustrated above, the LMS algorithm). That is, it is likely that a manufacturer would have an LMS IC, and use that IC once for frequency offset estimation, and another time for the channel characteristics estimation. Alternatively, a single IC can be designed that may be time-shared for both purposes. 
     It should be apparent that the foregoing disclosed the principles of this invention, and that various other embodiments are possible, as well as modifications to the presented illustrative embodiment, without departing from the spirit and scope of this invention.