Abstract:
A frequency offset estimation is generated without explicitly generating a channel estimation for a frequency selective fading communication channel. This is realized by recognizing that, in the absence of additive noise, the channel output at a time n depends only on the last previous predetermined number, L, of data symbols, and that a “state” is a sequence of the last L symbols. Specifically, in a receiver, a received signal is mixed with a locally generated frequency corresponding to a frequency offset to generate a mixed signal. A calculation is made on the mixed signal in which channel outputs of the same state are combined and accumulated. Then, a summation is made over all possible states of the combined and accumulated channel outputs to yield a so-called metric calculation value for that mixed signal. The metric calculation is then repeated for a plurality of different locally generated frequencies corresponding on a one-to-one basis with a plurality of frequency offsets. The frequency offset corresponding to the largest metric calculation value is selected as the desired frequency offset estimate. In one embodiment of the invention, a representation of a frequency offset estimation value is obtained by employing an open loop arrangement. In another embodiment of the invention, a frequency offset estimation value is generated by employing an closed loop arrangement.

Description:
TECHNICAL FIELD 
     This invention relates to communication systems and, more particularly, to burst communication systems. 
     BACKGROUND OF THE INVENTION 
     Communication channels, and particularly, wireless communication channels, are subject to channel impairments such as multipath propagation, i.e., spread, and fading, in addition, to additive noise. Carrier frequency offset that typically occurs because of transmitter and receiver oscillator mismatch in such systems is further compounded by Doppler shifts in mobile communication systems. Rapid frequency acquisition and tracking are crucial for accurate decoding of the information being received. 
     In receivers, frequency lock loops have typically been used to generate a carrier frequency offset estimate, which, in turn, is used to compensate a locally generated carrier frequency. However, in a burst communication system, e.g., a time division multiple-access (TDMA) system, in a fading environment, it may be required to used a so-called open loop offset frequency estimator based on a data burst preamble in order to avoid so-called “hang-up” effects. A frequency offset estimate may be required to be generated at the start of each burst before decoding the information. Rapid acquisition of the carrier frequency and, consequently, rapid generation of the carrier frequency offset, is required in burst communication systems because of the small number of training symbols available in the burst preamble. Additional known frequency acquisition techniques based on phase locked loops tend to have acquisition times longer than the duration of a burst. While there are open loop techniques for fast frequency or phase estimation, these estimation techniques generate estimates having a large variance in the presence of strong multipath spread. Adaptive equalizers, typically used in a multipath environment, are capable of adequately tracking small frequency offsets. However, with a large initial frequency offset the adaptive equalizer is incapable of tracking the frequency offset satisfactorily. Consequently, it is necessary to estimate the frequency offset and perform frequency correction before equalization. 
     A specific technique that has been proposed to generate frequency offset estimates is the so-called maximum likelihood estimation technique. This technique compensates for the phase changes caused in a received signal because of data modulation and generates an average over a number of symbols to remove the effect of noise. However, the maximum likelihood estimation technique fails in an environment including multipath spread because the received signal, due to data modulation, depends on more than one data symbol and, therefore, cannot be compensated by merely generating the conjugate of the training sequence, namely, x(n)*. 
     Additionally, it is known that frequency offset estimation in a frequency selective fading channel can be obtained jointly with the channel estimation. However, adaptive equalizer coefficients that are used for canceling intersymbol interference are often obtained directly without generating an explicit channel estimation. Consequently, joint frequency offset estimation and channel estimation for such systems results in additional complexity that is not necessary. 
     SUMMARY OF THE INVENTION 
     These and other problems and limitations of prior known frequency offset estimation arrangements and techniques are addressed by generating a frequency offset estimation without explicitly generating a channel estimation for a frequency selective fading communication channel. This is realized by recognizing that, in the absence of additive noise, the channel output at a time n depends only on the last previous predetermined number, L, of data symbols, and that a “state” is a sequence of the last L symbols. 
     Specifically, in a receiver, a received signal is mixed with a locally generated frequency corresponding to a frequency offset to generate a mixed signal. A calculation is made on the mixed signal in which channel outputs of the same state are combined and accumulated. Then, a summation is made over all possible states of the combined and accumulated channel outputs to yield a so-called metric calculation value for that mixed signal. The metric calculation is then repeated for a plurality of different locally generated frequencies corresponding on a one-to-one basis with a plurality of frequency offsets. The frequency offset corresponding to the largest metric calculation value is selected as the desired frequency offset estimate. 
     In one embodiment of the invention, a representation of a frequency offset estimation value is obtained by employing an open loop arrangement. More specifically, the frequency offset estimation value is obtained by generating simultaneously a plurality of metric calculation values over a corresponding plurality of predetermined frequency values. This is realized by mixing an input signal with each of the plurality of predetermined frequency values to generate a corresponding plurality of mixed signals and, then, obtaining a separate metric calculation over each the mixed signals. The maximum metric calculation value is selected and the frequency offset estimate is the frequency that corresponds to the selected metric calculation value. 
     In another embodiment of the invention, a frequency offset estimation value is generated by employing a closed loop arrangement. The received signal is mixed with a frequency offset estimation value and employed in a metric calculation to yield an error signal. A filtered version of the error signal is used to control, in one example, a numerically controlled oscillator to generate the frequency offset estimation value. The metric calculation is made at both a positive step frequency from a frequency offset value and at a negative step frequency from the frequency offset value. The resulting metric calculation values are algebraically subtracted and filtered to yield the error signal. 
    
    
     BRIEF DESCRIPTION OF THE DRAWING 
     FIG. 1 shows, in simplified block diagram form, details of an open loop frequency offset estimator including an embodiment of the invention; 
     FIG. 2 is a flow chart illustrating the steps in the metric calculation process employed in the embodiments shown in FIGS. 1 and 3; and 
     FIG. 3 shows, in simplified block diagram form, details of a closed loop frequency offset estimator including an embodiment of the invention. 
    
    
     DETAILED DESCRIPTION 
     A. Theoretical Discussion 
     1. Background 
     Consider a burst communication system having a preamble including N training symbols {x(n)}) n=0   N−1 . The training symbols are assumed to be chosen at random from a binary signaling alphabet. We first consider an additive white complex Gaussian noise (AWGN) channel and, then, consider a frequency selective Ricean fading channel. Let f 0  be the frequency offset at a receiver. In the absence of any intersymbol interference a received signal r(n) is given by 
     
       
           r ( n )= x ( n )e j2πf     0     n   +w ( n )  (1) 
       
     
     where w(n) is the additive white complex Gaussian noise. The log-likelihood is given by          Λ        (     f   0     )       =     -       ∑     n   =   0       N   -   1                     r        (   n   )       -       x        (   n   )                   j2π                   f   0        n     =   φ                2                                
     and, hence, the maximum likelihood estimate {circumflex over (f)} 0   ML  is given by                        f   ^     0   ML     =     arg                     min       f   ^     0              min   φ            ∑     n   =   0       N   -   1                     r        (   n   )       -       x        (   n   )                   j2π                     f   ^     0        n     +   jφ                2                         =     arg                     max       f     ^               0              max   φ          2                   Re        (       ∑     n   =   0       N   -   1              r        (   n   )              x        (   n   )       *                   -   j2π                       f   ^     0        n     -   jφ           )                             =     arg                     max       f   ^     0                   ∑     n   =   0       N   -   1              r        (   n   )              x        (   n   )       *                 -   j2π                       f   ^     0        n                      ,                 (   2   )                                
     where * is the conjugate. The above noted maximum likelihood estimator is consistent. The optimization involved in equation (2) can be implemented approximately by searching over a discrete set of frequency values:              f   ^     0   ML     ≈     arg                     max     {             f   ^     0     |       f   ^     0       =     k                 Δ                 f       ,     k   =     -   p       ,   ⋯              ,     0      ⋯                 p       }                   ∑     n   =   0       N   -   1              r        (   n   )              x        (   n   )       *                 -   j                   2      π                     f   ^     0        n                      ,                          
     where Δf is the bin size that determines the resolution of the estimate and [−pΔf, pΔf] is the range of possible frequency offsets. A tree search process is known for the efficient implementation of the above maximization. 
     Now consider a frequency selective block fading channel. Assume that the channel is changing sufficiently slowly that it is essentially static over the duration of the data burst and, in particular, during the preamble interval that is used for open loop frequency estimation. Let the symbol spaced channel impulse response be given by {h(k)} k=0   L−1 . Then, the received sampled signal is given by                r        (   n   )       =         (       ∑     k   =   0       L   -   1              x        (     n   -   k     )            h        (   k   )                   -   j2π                   Δ                 fk           )               j2π                   f   0        n         +     w        (   n   )                 (   3   )                                
     For the Ricean fading frequency selective channel the direct path gain h(0) is Ricean distributed while the multipath gains h(k), l≦k≦L are Rayleigh distributed. The maximum likelihood estimator is not optimal in the presence of multipath spread. It can be shown that the maximum likelihood estimator performance at high signal-to-noise ratios (SNR) is seriously affected by intersymbol interference (ISI). At high SNRs, noise is no longer the limiting factor in the frequency estimation. 
     The maximum likelihood estimator in the presence of multipath spread can also be derived. The channel impulse response {h(k)} is unknown at the receiver. The log likelihood Λ(f 0 ,h) is given by                Λ        (       f     0   ,          h     )       =     -       ∑     n   =   0       N   -   1                     r        (   n   )       -       (       ∑     k   =   0       L   -   1              x        (     n   -   k     )            h        (   k   )                   -   j2π                     f   0        k           )               j2π                   f   0        n                2                 (   4   )                                
     The maximum likelihood estimate of the carrier frequency offset is obtained by jointly maximizing the likelihood function over f 0  and h:                  f   ^     0   ML     =     arg                     max     f   0              max   h          Λ        (       f   0     ,   h     )                         =     arg                     min     f   0              min   h            ∑     n   =   0       N   -   1                     r        (   n   )       -       (       ∑     k   =   0       L   -   1              x        (     n   -   k     )            h        (   k   )                   -   j2π                     f   0        k           )               j2π                   f   0        n                2                                          
     However, the complexity of the maximum likelihood estimation prevents it from being used in practical systems. 
     2. Inventive Frequency Estimators 
     I have discovered a new carrier frequency offset estimator, namely, a maximum state-based accumulation (MSA) estimator. Motivation for the MSA estimator comes from an understanding of the maximum likelihood (ML) estimator in the absence of multipath spread. From equation (2) above, it is easy to see that the ML estimator compensates for the in phase changes in the received signal due to data modulation and averages over N symbols to remove the effect of noise. The ML estimator fails in a multipath spread scenario because the received signal phase due to data modulation depends on more than one data symbol and cannot be compensated for by merely multiplying by the conjugate of the training sequence, namely, x(n)*. 
     While the channel impulse response is not known, it is known that the channel output at time n depends only on the past L data symbols. The training sequence can be associated with the state at each time n based on the past L data symbols. I define the state s(n) at time n to be s(n)=[x(n),x(n−1), . . . , x(n−L+1)]. Then, assuming that the channel impulse response is of length L and that the training sequence is binary valued, there are N s =2 L  possible states. The received signal at time n depends only on the state s(n) (and not on n) and is given by                r        (   n   )       =         (       ∑     k   =   0       L   -   1              x        (     n   -   k     )            h        (   k   )                   -   j2π                     f   0        k           )               j2π                   f   0        n         +     w        (   n   )                       =           h   ~     ′          s        (   n   )                 j2π                   f   0        n         +     w        (   n   )           ,                                
     where {tilde over (h)}(k)=h(k)e −j2πf     0     k . Hence, it follows that                E        (           r        (   n   )                   -   j2π                     f   0        n         |     s        (   n   )         =   u     )       =                    h   ~     ′        u                 =                           h   ~     ′        u                    jθ        (   u   )                                        
     for every state u and where E is the expectation. Note that the right side of the above equation is independent of the offset frequency f 0 . Hence,            ∑   u               E        [           r        (   n   )                   -   j2π                     f   0        n         |     s        (   n   )         =   u     ]              =       ∑   u                     h   ~     ′        u          .                              
     On the other hand for {circumflex over (f)}≠f 0 ,                  ∑       n   :     s        (   n   )         =   u            E        [           r        (   n   )                   -   j2π                       f   ^     0        n         |     s        (   n   )         =   u     ]         =                    h   ~     ′        u          ∑         n   :   s9n     )     =   u                   j2π        (       f   0     -       f   ^     0       )          n                       ≈              0                                
     for a sufficiently long training sequence {s(n)}. 
     Then, the following frequency offset estimator is defined                    f   ^     0   MSA          =   Δ          arg                     max     f   0              ∑     s   =   S                   ∑       n   =   0     ,       n   :     s        (   n   )         =   s         N   -   1              r        (   n   )                   -   j2π                     f   0        n                        ,           (   5   )                                
     where S is the set of all possible training sequences of L symbols. For binary training sequences |S|=2 L . 
     The optimization of the frequency offset estimator of equation (5) can be implemented approximately by determining the maximum {circumflex over (f)} 0   MSA  over a discrete set of frequency bins. 
     The frequency offset estimator of equation (5) is an open loop arrangement that requires the simultaneous computation of the frequency discrimination function at several values of the frequency. The frequency offset estimate is then ascertained by a maximum selection process. 
     A closed loop arrangement is also proposed that requires less computational effort than the open loop arrangement. 
     A necessary condition for the maximum in equation (5) to be achieved is that the derivative of the objective function be zero. This suggests that the following error signal can be employed to adjust the frequency of an oscillator in generating a carrier signal at the desired frequency:                      e        (       f   ^     0     )       =                  ∂     M        (       f   ^     0     )           ∂       f   ^     0                       ≈                    M        (         f   ^     0     +     Δ                 f       )       -     M        (         f   ^     0     -     Δ                 f       )           2      Δ                 f         ,                 (   6   )                                
     where M({circumflex over (f)}) is defined to be the objective function in equation (5), namely,            M        (     f   ^     )       =       ∑     s   =   0         2   L     -   1                   ∑       n   =   0     ,       n   :     s        (   n   )         =   s         N   -   1              r        (   n   )                   -   j2π                     f   0        n                    ,                          
     and Δf is some fixed step size. 
     B. Embodiments of MSA Frequency Estimators 
     FIG. 1 shows, in simplified block diagram form, details of an open loop MSA frequency offset estimator  100 . A received data signal r(n) is supplied to input  101  of a receiver and, therein, to one input of each of mixing units  102 - 1  through  102 -N, e.g., multipliers. In this example, numerically controlled oscillators (NCOs)  103 - 1  through  103 -N are employed to generate a corresponding plurality of N discrete frequencies, namely, e −j2πf     1     n  through e −j2πf     N     n  respectively, which frequencies are supplied to a second input of the corresponding ones of mixing units  102 - 1  through  102 -N, respectively. It should be noted any number of other types of oscillators may equally employed to generate the desired frequencies. The generated discrete frequencies are mixed with the received signal in mixers  102 - 1  through  102 -N to yield r(n)e −j2πf     1     n  through r(n)e −j2πf     N     n , respectively, which are supplied on a one-to-one basis to metric calculation units  104 - 1  through  104 -N, respectively. Each of metric calculation units  104 - 1  through  104 -N makes a metric calculation as shown in FIG.  2  and described below to generate metric calculation values M f     1    through M f     N   , at corresponding frequencies f 1  through f N , respectively. Metric calculation values M f     1    through M f     N    are supplied to find maximum unit  105 , where the maximum one of metric calculation values M f     1   , through M f     N   , is selected and, then the frequency offset estimate f 0  corresponds to the frequency over which the selected metric calculation was made. Thus, as seen a plurality of N discrete metric calculation values M f     1    through M f     N    are generated simultaneously and the frequency f 1  through f N  of the metric calculation having the maximum amplitude value is selected as the desired frequency offset estimate f 0 . 
     Advantages of the embodiment of the invention shown in FIG. 1 are that its implementation is less complex and its frequency offset estimation accuracy is improved over prior known frequency estimators, for example, the maximum likelihood frequency estimator described above. 
     FIG. 2 is a flow chart illustrating the steps in the metric calculation process employed in the embodiments shown in FIGS. 1 and 3. In FIG. 2, r(n) is the received signal, f 0  is the frequency offset at which the metric is calculated and M(i) is the metric corresponding to state “i”. Thus, the metric calculation process starts in step  201  by initializing M(i)=0 for all states. Then, step  202  causes the state at symbol n to be found (say, state i). Thereafter, step  203  updates M(i), namely, setting M(i)=M(i)+r(n)e −j2πf     0     n . This is the same as the inner summation in equation (5), namely          ∑       n   =   0     ,       n   :     s        (   n   )         =   s         N   -   1              r        (   n   )                     -   j2π                     f   0        n       .                              
     Step  204  tests to determine if all training symbols have been used. If the test result in step  204  control is supplied to step  205  and the training symbol is indexed, namely, it is set to n=n+1. Thereafter, control is returned to step  202  and steps  202  through  205  are iterated until step  204  yields a YES test result. Then, step  206  generates the desired metric at the particular frequency by summing all the |M(i)| for all states. This is the outer summation in equation (5), namely          ∑     s   =   0         2   L     -   1                     ∑       n   =   0     ,       n   :     s        (   n   )         =   s         N   -   1              r        (   n   )                   -   j2π                     f   0        n                .                            
     FIG. 3 shows, in simplified block diagram form, details of a closed loop frequency estimator  300  including an embodiment of the invention. A received signal r(n) is supplied via input  301  to one input of mixing unit  302 . A representation of a desired frequency offset estimate {circumflex over (f)} 0 =e −j2πf     0     n  is supplied to a second input of mixing unit  302 , where it is mixed with received signal r(n) to yield r(n)e −j2πf     0     n . In turn, r(n)e −j2π     0     n  is supplied to metric calculation unit  303 . Metric calculation  303  makes the same metric calculation as described above in relationship to FIG. 2, but does it twice, once for first frequency value ({circumflex over (f)} 0 +Δf) and once for second frequency value ({circumflex over (f)} 0 −Δf) to yield M({circumflex over (f)} 0 +Δf) and M({circumflex over (f)} 0 −Δf) respectively. As indicated above. Δf is a predetermined step frequency value. In turn, M({circumflex over (f)} 0 +Δf) and M({circumflex over (f)} 0 −Δf) are supplied to algebraic combining unit  304  where they are algebraically subtracted. The result of the subtraction is supplied to loop filter  305  which yields error signal e({circumflex over (f)} 0 ). Error signal e({circumflex over (f)} 0 ), in this example, is used to control numerically controlled oscillator (NCO)  306  to generate the desired frequency offset estimate {circumflex over (f)} 0 . The frequency offset estimate {circumflex over (f)} 0  is supplied as an output and to the second input of mixing unit  302 . Thus, the carrier signal having the desired frequency is generated in this embodiment of the invention in accordance with equation (6) described above. 
     As in the embodiment shown in FIG.  1  and described above, advantages of the embodiment of the invention shown in FIG. 3 are that its implementation is less complex and its acquisition time for acquiring the carrier frequency is shorter than prior known frequency estimators, for example, the maximum likelihood frequency estimator described above.