Method and apparatus for signal burst classification

A burst classifier is useful in a digital communication system transmitting a signal burst of a plurality of different burst types. The burst classifier includes a plurality of filters associated with the plurality of different burst types, respectively. Each filter generates correlation data based on the signal burst and a respective plurality of reference signals offset by a plurality of time offsets. The respective pluralities of reference signals are indicative of a corresponding burst type of the plurality of different burst types. A comparator then analyzes quantities based on the correlation data from each filter to determine the burst type of the signal burst.

BACKGROUND OF THE INVENTION
 1. Field of the Invention
 The invention relates generally to digital communication systems and, more
 particularly, to systems utilizing reference symbols to assist in the
 demodulation of transmitted information.
 2. Description of the Related Art
 Digital communication systems typically utilize bandwidth-efficient
 modulation schemes to maintain high bit rates for a number of user
 channels. Such systems transmit bursts of information symbols that may
 include both reference symbols and data symbols. The reference symbols are
 known by a receiver to assist in the demodulation of the data symbols.
 Some signal bursts are designed to provide control information only. For
 instance, FACCH (fast access control channel), SDCCH (stand-alone
 dedicated control channel), and SACCH (slow associated control channel)
 bursts provide messaging information for upper layer protocols. These and
 other types of signal bursts are to be distinguished from data bursts that
 carry voice and/or other data information, such as TCH (normal traffic
 channel) and RACH (random access channel) bursts. In order to benefit from
 these different types of bursts, the receiving portion of the
 communication system must be capable of distinguishing between burst
 types. Past systems have classified incoming bursts by devoting a portion
 of a preamble segment to identification data.
 In order to demodulate the identification data (and the rest of the data
 contained in the signal burst), the clock in the receiver must be
 synchronized with the clock in the transmitter and, further, the
 oscillator in the receiver must be aligned with the actual frequency of
 the carrier signal. With certain modulation schemes (e.g., QPSK), the
 receiver is capable of deriving timing and frequency information from the
 information symbols themselves subsequent to removing the modulation.
 These conveniences are not available with modulation schemes such as GMSK
 (Gaussian Minimum Shift Keying), in which modulated information is
 transmitted over a plurality of bit periods, inasmuch as no single
 non-linearity exists for modulation removal. However, such memory-inducing
 modulation schemes provide several advantages, not the least of which is
 the constant envelope of the transmitted signal. This advantage is
 particularly useful for satellite communication systems, inasmuch as
 cheaper Class C amplifiers may be used in both the satellites and the
 receivers.
 In past systems utilizing memory-inducing modulation schemes, the preamble
 segment of each signal burst also included portions for estimating the
 timing and frequency of the signal burst. For the timing variable, a first
 portion provided reference symbols having considerable variation such that
 the transmitted signal has high frequency components. A second portion
 provided symbols all set to "1" to obtain high resolution for the
 frequency variable. However, evaluation of these portions of the preamble
 became an undesirable prerequisite to burst type classification. Moreover,
 allocating separate bits to timing and frequency estimation as well as
 burst type classification has limited the data throughput of such systems.
 SUMMARY OF THE INVENTION
 The present invention is useful in a digital communication system
 transmitting a signal burst of a plurality of different burst types.
 According to one aspect of the present invention, a burst classifier
 includes a plurality of filters associated with the plurality of different
 burst types, respectively. Each filter generates correlation data based on
 the signal burst and a respective plurality of reference signals offset by
 a plurality of time offsets. The respective pluralities of reference
 signals are indicative of a corresponding burst type of the plurality of
 different burst types. The burst classifier further includes a comparator
 that analyzes quantities based on the correlation data from each filter to
 determine the burst type of the signal burst.
 According to another aspect of the present invention, a method of
 classifying a signal burst as one of a plurality of burst types
 transmitted in a digital communication system includes the step of
 calculating correlation data based on the signal burst and a respective
 plurality of reference signals offset by a plurality of time offsets. The
 respective pluralities of reference signals are indicative of a
 corresponding burst type of the plurality of different burst types. The
 inventive method further includes the step of comparing quantities based
 on the correlation data to determine the burst type of the signal burst.
 According to yet another aspect of the present invention, a method is
 useful for classifying a signal burst modulated by a modulation scheme
 that induces memory therein as one of a plurality of burst types
 transmitted in a digital communication system. The inventive method
 includes the step of comparing the signal burst with a respective
 plurality of reference signals to generate comparison data not reflecting
 the memory induced by the modulation scheme. The respective pluralities of
 reference signals are indicative of a corresponding burst type of the
 plurality of different burst types. The inventive method further includes
 the step of combining the comparison data non-coherently over a plurality
 of reference segments distributed within the signal burst to generate
 combined comparison data for each of a plurality of time offsets and for
 each burst type. The inventive method still further includes the step of
 removing uncertainty associated with a timing offset of the signal burst
 by generating a maximum comparison value for each burst type from the
 combined comparison data for the plurality of time offsets. Lastly, the
 inventive method includes the step of determining the burst type of the
 signal burst from the maximum comparison values.

DETAILED DESCRIPTION OF THE INVENTION
 The present invention provides an apparatus and method for classifying
 incoming bursts having reference symbols. To this end, the different burst
 types include distinguishable reference symbols distributed throughout the
 burst. The present invention provides a technique for classifying the
 burst without knowledge of the noise and signal levels, or the timing,
 carrier phase, frequency, or channel fading conditions.
 Referring to FIG. 1, a digital communication system 20 includes a receiver
 22 and an antenna 24 for receiving a signal transmitted from another
 portion (not shown) of the digital communication system 20. The received
 signal is down-converted by a down-converter 25 and then filtered by a
 front end filter 26, which may be a pass band filter for removing any
 out-of-band frequencies and re-developing the baseband signal. The
 received baseband signal (hereinafter referred to for simplicity as "the
 received signal") is then provided to a demodulator 28 and a burst
 analyzer 30. In order to demodulate the received signal accurately, the
 demodulator 28 receives on lines 32, 34, and 35 a timing synchronization
 signal t.sub.SYNCH, a frequency offset signal f.sub.OFFSET, and a burst
 classification signal, respectively, each of which is generated by the
 burst analyzer 30 as set forth hereinbelow. The demodulator 28 includes a
 clock (not shown) and an oscillator (not shown) that utilize the timing
 and frequency signals, respectively, to accurately demodulate the received
 signal. The demodulator 28 may include multiple demodulator components
 (not shown) for each burst type. The burst classification signal is
 utilized by the demodulator 28 to determine which component is appropriate
 for demodulating the received signal. However, different burst types may
 be modulated according to the same modulation scheme and, therefore, may
 utilize the same demodulator component. The timing synchronization signal
 and the frequency offset signal are also provided to a channel fade
 estimator 36, which is also coupled to the front end filter 26 for
 provision of the received signal. As is known to those skilled in the art,
 the channel fade estimator 36 tracks the channel complex gain resulting
 from channel fading, and provides that information to the demodulator for
 compensation.
 The digital communication system 20 may, for example, transmit a
 time-division multiplexed access (TDMA) signal for accommodating a number
 of users. TDMA and other systems known to those skilled in the art may
 transmit a plurality of different types of signal bursts to provide
 control information as well as voice, data, or other information. For
 instance, prior to transmission of any voice information, a typical TDMA
 system may transmit a random access channel (RACH) burst that provides the
 receiving portion of the digital communication system 20 with rough
 estimates (i.e., ranges) of the timing and frequency of the subsequent
 signal bursts. In general, however, it will be appreciated that a variety
 of techniques for providing rough estimates of both timing and frequency
 are known to those skilled in the art. Accordingly, the method and
 apparatus of the present invention should not be limited to digital
 communication systems utilizing a particular multiplexing scheme.
 The digital communication system 20 may comprise a mobile satellite
 communication system. However, the present invention is more generally
 applicable to any communication system in which multiple types of signal
 bursts are transmitted. The invention is particularly applicable to those
 wireless communication systems in which the timing and frequency of the
 signal burst are unknown at the receiving portion of the system 20, such
 as those systems transmitting a constant envelope signal (or a signal with
 memory).
 In general, the digital communication system 20 may utilize a variety of
 different bandwidth-efficient modulation schemes. The present invention is
 particularly useful with the modulation scheme specified by a typical
 mobile satellite communication system, which transmits a Gaussian Minimum
 Shift Keyed (GMSK) signal burst, s(t), defined in complex form as:
EQU s(t)=Re{s.sub.GMSK (t-.epsilon.T)e.sup.j(2.pi..DELTA.ft+.theta..sup..sub.c
 .sup.) }
 where .epsilon. represents the timing offset introduced during transmission
 (normalized by the symbol period T), .DELTA.f is the carrier frequency
 drift introduced by the channel, and .theta..sub.c is the initial carrier
 phase. The values .epsilon. and .DELTA.f may be derived from the
 respective signals t.sub.SYNCH and f.sub.OFFSET. The received signal s(t)
 may have a 3 dB bandwidth B normalized by a symbol period T (i.e., the
 bandwidth-symbol period product BT) of 0.3. It shall be understood,
 however, that the effectiveness of the present invention is not limited to
 any particular normalized bandwidth, or any particular channel condition
 or noise level. For the sake of simplicity only, additive white Gaussian
 noise (AWGN) has been assumed s(t)+AWGN shall be referred to as r(t) and,
 thus, the GMSK signal may be set forth as:
 ##EQU1##
 for nT.ltoreq.t.ltoreq.(n+1)T, which corresponds to an nth time interval
 with a duration of one symbol (i.e., bit) period, and where S represents
 the signal strength or amplitude. The data {.alpha..sub.i ; i=0, . . . ,
 (N-1)} comprises a differentially encoded version of an independent and
 identically distributed binary stream generated at rate T.sup.-1. A phase
 pulse q(t) comprises the integral of a modulation pulse g(t), which, in
 turn, is a Gaussian function convolved with a rectangular pulse. The phase
 pulse q(t) reaches a final value in a time LT, where L is representative
 of the memory induced by the GMSK modulation, i.e., the amount to which
 the modulation distributes a bit over several symbol periods.
 The modulating pulse g(t) for the GMSK signal s.sub.GMSK (t) may be
 expressed as:
 ##EQU2##
 where Q(x) is a Gaussian probability integral as follows:
 ##EQU3##
 The phase value .theta..sub.n represents the accumulation of all of the
 bits that have reached a final value during the nth time interval [nT,
 (n+1)T], or
 ##EQU4##
 From the above, it is clear that, in this particular modulation scheme, the
 phase value .theta..sub.n may take on one of four different values:
 ##EQU5##
 Referring now to FIG. 2, the received signal comprises a signal burst 40
 having a plurality of segments. The signal burst 40 may comprise, for
 example, a traffic channel burst, and, therefore, include information
 segments 42 that primarily carry information (i.e., data) bits rather than
 bits utilized primarily for control purposes. The information segments 42
 are separated by a plurality of reference segments 44, each of which
 carries reference bits utilized by the apparatus and method of the present
 invention to estimate timing, frequency, and burst type. In accordance
 with the present invention, the reference segments 44 are distributed
 throughout the signal burst 40. The signal burst 40 may also include other
 segments (not shown) that provide, for instance, control information.
 The reference segments 44 may, but need not, be distributed uniformally
 across the signal burst 40 as shown. As distributed, however, each
 reference segment 44 comprises a unique word (UW) that may be the same as,
 or different from, the other unique words in the signal burst 40. The data
 in each unique word, of course, must be predetermined (i.e., known by the
 receiving portion of the digital communication system 20) to enable
 recognition thereof.
 For the purposes of explanation only, the signal burst 40 is shown to
 include a total of six unique words distributed over a signal burst having
 240 symbols or bits. In accordance with one embodiment of the present
 invention, these six unique words may each comprise the four bits {-1, -1,
 1, -1}, the set of which provides sufficient data variation to enable
 accurate timing estimation. As shown in FIG. 2, after the first
 information segment 42, which occupies symbol positions 1T-17T, the first
 unique word UW.sub.1 is located at time interval 18T-21T. The locations of
 the other unique words, normalized by the symbol period T, are also set
 forth in FIG. 2. With each reference segment 44 taking up four bits, the
 non-terminal (i.e., internal) information segments 42 comprise 40T
 segments.
 In the digital communication system 20 described above, each unique word is
 provided to the burst analyzer 30 in the form of a reference signal
 modulated, for example, according to the memory-inducing GMSK modulation
 scheme. The modulated reference signal is, therefore, determined at least
 partially by the in information bits in an adjacent information segment 42
 to an extent determined by the normalized bandwidth. With BT=0.3, a
 reasonable approximation for L is 3, meaning that the three nearest bits
 to any bit in the unique word will affect the shape of the reference
 signal at that bit position. Thus, for example, with four bits in each
 unique word and L=3, it can be shown that the burst analyzer 30 must
 accommodate a total of eight different reference signal waveforms.
 However, it shall be understood that additional reference waveforms may be
 necessary in the event that the unique words in the signal burst 40 are
 not identical.
 FIGS. 3 and 4 illustrate examples of various reference waveforms that may
 result from the GMSK modulation (with BT=0.3) of the first unique word
 UW.sub.1 (-1,-1,1, -1) located in the time interval (18T, 21T). As is
 known to those skilled in the art, in a typical GMSK-modulated signal,
 even numbered bits are transmitted by the in-phase component, while odd
 numbered bits are transmitted by the quadrature component. Accordingly,
 FIG. 3 shows an eye pattern of the in-phase component of the reference
 waveform versus time (normalized by T), while FIG. 4 shows an eye pattern
 of the quadrature component. In the embodiment of the present invention
 utilizing the reference waveforms of FIGS. 3 and 4, the in-phase and
 quadrature components combine to provide a possibility of eight complex
 reference waveforms. Reference waveforms, as used hereinbelow, are to be
 understood to comprise complex waveforms and, thus, both the in-phase and
 quadrature components.
 With continued reference to FIGS. 3 and 4, the least-varying portion of
 each reference waveform shown is located in the time interval (20T, 24T)
 for the in-phase component and in the time interval (19T, 23T) for the
 quadrature component. This approximate two-bit delay may be viewed as
 being introduced by the Gaussian filtering introduced by the modulation
 and may be accounted for appropriately by the receiving portion of the
 system 20, as is well known to those skilled in the art.
 In view of the eye patterns of FIGS. 3 and 4, the burst analyzer 30 may
 compare the received signal with a plurality of possible reference
 waveforms (e.g., eight) to determine the timing, frequency, and burst type
 information. This comparison occurs during an observation interval
 corresponding with the locations of the least-varying portions of the
 received signal. The burst analyzer 30 may, however, compare the received
 signal with fewer reference waveforms at the expense of performance
 degradation. As will be explained further hereinbelow, a reference
 waveform (i.e., one used by the burst analyzer 30) may be designed to
 constitute an average of two or more of the possible reference waveforms
 shown in FIGS. 3 and 4. Thus, in principle, the burst analyzer 30 may
 compare the received signal with as few as only one reference waveform,
 which would constitute an average of all of the eight possible reference
 waveforms, or as many as necessary to achieve a certain performance level.
 The observation interval of the burst analyzer 30 need not correspond with
 the number of bits in a unique word. For example, it can be shown that, if
 the comparison performed by the burst analyzer 30 is extended to a five
 bit interval, the burst analyzer 30 may then compare the received signal
 against sixteen is different reference waveforms (once again, with L=3).
 Such an extension improves the performance of the present invention
 without having to devote additional bits to the reference segments 44,
 thereby maintaining the same data throughput rate. As set forth above,
 however, the number of reference waveforms compared to the received signal
 may be reduced by averaging two or more of the sixteen reference waveforms
 to reduce computation times and/or system complexity. Eye patterns similar
 to those shown in FIGS. 3 and 4 may be used to decide which reference
 waveforms should be averaged.
 The determination of the timing and frequency of the signal burst will now
 be described in connection with FIG. 5, which shows the burst analyzer 30
 in greater detail. Heavier (wider) lines indicate transmission of signals
 representative of complex values, while more narrow lines indicate
 transmission of signals representative of real values. The received signal
 r(t) is provided to a matched filter bank 50 comprising a plurality of
 matched filters 52 (FIG. 6). The number of matched filters 52 corresponds
 with the number of reference waveforms N that are to be compared with the
 received signal. The number of reference waveforms N, in turn, corresponds
 with the size of the set of differentially encoded data {.alpha..sub.i ;
 i=0, . . . , N-1)}, which may be denoted by .alpha.. As shown in FIG. 6,
 if M defines the number of symbol or bit periods in an observation (or
 correlation) interval, then the received signal may be compared with a
 total 2.sup.M-1 reference signals (with L=3). The length of the
 observation interval may correspond with the number of bits in each unique
 word or, alternatively, to increase accuracy, the observation interval
 length M may be increased such that the number of symbol or bit periods
 therein is greater than a number of bits in each unique word. However, in
 the event that possible reference signals are averaged as set forth above,
 then the number of reference waveforms N utilized for comparison and,
 hence, the number of matched filters 52, is some number less than
 2.sup.M-1.
 Each matched filter 52 has an impulse response h(t,.alpha..sub.i) that
 corresponds with a particular reference waveform to be compared with the
 received signal. The set of impulse responses corresponding with the set
 of differentially encoded data may be expressed as:
 ##EQU6##
 Thus, the burst analyzer 30 compares the received signal with each
 reference waveform by convolving the received signal with the impulse
 response h(t,.alpha..sub.i) associated with each reference waveform over
 the observation interval. The convolution results in a correlation value
 Z.sup.(l).sub.M-1 (.epsilon..vertline..alpha..sub.i), where l identifies
 the particular unique word or reference segment 44 and .epsilon.
 represents the time offset from the symbol period T.
 Referring now to both FIGS. 5 and 6, the matched filter bank 50 also
 includes a plurality of samplers 54 respectively coupled to each matched
 filter 52. Each sampler 54 samples the output of its corresponding matched
 filter 52 at a rate equal to T.sup.-1 at every (n.sub.l +M+.epsilon.)T,
 such that the convolution operation may be expressed as:
EQU Z.sub.M-1.sup.(l) (.epsilon..vertline..alpha.)=r+L
 (t)*h(t;.alpha.).vertline..sub.t=(n.sub..sub.l .sub.+M+.epsilon.)T
 where n.sub.l identifies the location of the l-th unique word or reference
 segment 44. For example, for the first unique word UW.sub.1 shown in FIG.
 2, n.sub.l is equal to 18. In this manner, the matched filter bank 50
 calculates the convolution of the received signal at UW.sub.1 (e.g., from
 18T to 21 T, for M=4) with the impulse response associated with a
 particular reference waveform. As a result of the sampling, a set of the
 correlation values Z(.epsilon..vertline..alpha.) are generated for each
 reference waveform (as defined by .alpha..sub.i) and each time offset
 .epsilon.. The above-described correlation calculations are then performed
 for each reference segment 44, such that
 Z(.epsilon..vertline..alpha..sub.i) is identified as Z.sup.(l)
 (.epsilon..vertline..alpha..sub.i) in FIGS. 5 and 6 for completeness.
 The sets of correlation values Z(.epsilon..vertline..alpha..sub.i) are
 provided to a plurality of absolute value (or magnitude) generators 58
 (FIG. 5) to remove the overall effect of any shift in carrier phase and,
 therefore, to prepare for the non-coherent combining of the correlation
 data. Once the magnitude of each of the correlation values has been
 determined, a maximum correlation value is determined for each reference
 segment 44 and time offset e by a maximum correlation value determinator
 60. For example, for a burst analyzer 30 handling three reference
 waveforms, the maximum correlation value for the first unique word
 (UW.sub.1) and time offset .epsilon..sub.1 would be expressed as:
EQU Z.sup.(1).sub.max (.epsilon..sub.1)=MAX[.vertline.Z.sup.(1)
 (.epsilon..sub.1,.alpha..sub.1).vertline., .vertline.Z.sup.(1)
 (.epsilon..sub.1,.alpha..sub.2).vertline., .vertline.Z.sup.(1)
 (.epsilon..sub.1,.alpha..sub.3).vertline.]
 The maximum correlation values are stored in a buffer or memory (not shown)
 as necessary for each time offset and each reference segment 44. Such
 buffers or memories may be utilized throughout the calculation of the time
 and frequency offsets and the burst type classification and, therefore,
 will not be referenced further hereinbelow. It shall be noted that a
 "maximum correlation value" as used hereinbelow will refer to a
 correlation value with a maximum magnitude.
 As a result of the above-described processing of the correlation data, the
 correlation data has been modified in preparation for non-coherently
 combining the correlation data for the entirety of the signal burst 40.
 Next, the maximum correlation values are provided to a summer or
 accumulator 62, which sums or otherwise combines the maximum correlation
 values Z.sup.(l).sub.max across the reference segments 44. For the
 embodiment associated with the signal burst 40 of FIG. 2, the output of
 the summer 62 may be expressed as the total maximum correlation for a
 certain time offset .epsilon..sub.i :
EQU Z.sub.TOTALmax (.epsilon..sub.i)=Z.sup.(1).sub.max
 (.epsilon..sub.i)+Z.sup.(2).sub.max (.epsilon..sub.i)+ . . .
 +Z.sup.(6).sub.max (.epsilon..sub.i)
 Because the phase of the received signal is not known a priori, it should
 be noted that the summer 62 non-coherently combines the correlation
 statistics over the plurality of unique words or reference segments 44 by
 summing the magnitudes of the maximum correlation values. This
 non-coherent combination is also useful in the event that the channel is
 unknown. It should also be noted that the argument corresponding to the
 differentially encoded data a is no longer a factor, inasmuch as the
 correlation data associated with a particular reference waveform having
 the maximum correlation has already been elected.
 Upon determination of each Z.sub.TOTALmax (.epsilon..sub.i) for each time
 offset, the timing offset .epsilon. at which the total maximum correlation
 value Z.sub.TOTALmax (.epsilon..sub.i) is a maximum is determined by an
 inverse maximum value determinator 64. The timing offset .epsilon. is then
 represented by the t.sub.SYNCH signal and provided via the line 32 to the
 demodulator 28 for synchronizing the clock in the demodulator 28 with the
 signal burst.
 The accuracy of the time offset estimation is based on how finely each
 symbol period T is analyzed (in other words, the granularity of the
 normalized time offset .epsilon.), which, in turn, is determined by the
 sampling rate. For example, a sampling rate resulting in eight samples per
 symbol period, without more, would limit the resolution of the burst
 analyzer 30 to a maximum uncertainty of .+-.T/16. However, the resolution
 may be improved by interpolating the results between the samples.
 More generally, the above-described technique for determining the timing
 offset .epsilon. in accordance with the present invention may be expressed
 as:
 ##EQU7##
 where M represents the length of the observation interval. This general
 representation provides a simple, robust technique for determining the
 timing offset for a signal burst. This technique can be further justified
 through the statistical analysis set forth below.
 In general, the correlation data generated by the matched filter bank 50
 provides a method of accurately estimating the timing offset because the
 optimal method of estimating the timing offset can be approximated via the
 convolution process described above. More particularly, the optimal
 solution is the timing offset that maximizes the likelihood-ratio function
 averaged over the random phase of the received signal. The
 likelihood-ratio function essentially compares the received signal with
 the known reference waveforms as a function of the timing offset. The
 likelihood of the received signal during the l-th unique word or reference
 segment 44 having four bits, conditional on knowing the timing offset and
 the carrier phase, may be expressed as:
 ##EQU8##
 where:
 ##EQU9##
 where C is a term independent of the received signal and r(t) is the
 baseband complex envelope of the received signal. Typically, the phase
 change due to the frequency term over a unique word interval is small
 enough that it can be safely absorbed into the initial carrier phase,
 modifying .theta..sub.c into .psi..sub.c. Averaging over the unknown
 carrier phase, for which we express the quantity Z.sub.3.sup.(l)
 (.epsilon..vertline..alpha.) in complex form as:
EQU Z.sub.3.sup.(l) (.epsilon..vertline..alpha.)=.vertline.Z.sub.3.sup.(l)
 (.epsilon..vertline..alpha.).vertline.exp(j&lt;Z.sub.3)
 the resultant averaged likelihood ratio function becomes:
 ##EQU10##
 where I.sub.0 (x) is the zeroth-order modified Bessel function of the first
 kind. Because the random phase is modeled to be uniformly distributed, the
 determination of the timing offset will be independent of the carrier
 phase.
 To account for the unknown data bits which contribute to the shape of the
 reference waveform, the averaged likelihood ratio function is further
 averaged (over the eight possible reference waveforms), yielding:
 ##EQU11##
 Because the noise is independent for different unique word intervals, the
 statistics may be non-coherently combined by multiplying the individual
 likelihood ratio functions. The optimal solution for the timing offset is,
 accordingly, the time offset that maximizes the following likelihood
 function (or its logarithmic version):
 ##EQU12##
 An embodiment implementing the optimal solution as set forth immediately
 above would be much more complex than the embodiment set forth above in
 connection with FIGS. 5 and 6. However, the added complexity would not
 necessarily provide improved performance, as shown hereinbelow.
 The optimal maximum-likelihood expression may be simplified to avoid having
 to evaluate non-linearities and remove the reliance on the signal and
 noise levels. Such simplifications are desirable in most mobile satellite
 communication systems, for instance, because shadowing and fading can
 considerably vary the gain of the received signal burst. More
 particularly, certain series approximations may be made, namely, that the
 average of the different I.sub.0 (x) terms will be dominated by the term
 with the largest argument and that ln(I.sub.0 (x)).apprxeq.x for large x.
 Such approximations lead to the following simplifications, which remove
 any dependence on the signal amplitude or strength S, the noise N.sub.0,
 or the non-linearity introduced by the Bessel function I.sub.0 :
 ##EQU13##
 As explained above, for performance enhancement, the correlation interval
 for the matched filter 50 may be extended beyond the number of bits in a
 reference segment 44. The averaging operation, however, accounts for
 inter-symbol interference effect caused by the random information bits
 adjacent the reference segment 44. Thus, as set forth above, the more
 general expression that extends the correlation interval to M bits and
 non-coherently combines statistics from the different unique words may be
 expressed as:
 ##EQU14##
 where N is the number of unique words or reference segments 44. As
 described above, the quantity Z.sup.(l).sub.M-1
 (.epsilon..vertline..alpha.) may also be expressed as the convolution of
 the received signal r(t) with a set of filters each having impulse
 responses matched to the reference waveforms.
 With reference again to FIG. 5, the determination of the frequency offset
 for the signal burst will now be described. Generally, the frequency
 offset determination is based on both the current time offset .epsilon.
 (determined as set forth above) and the correlation data utilized to
 generate it. However, before describing the technique for arriving at such
 a determination, it can be shown that the output of the matched filter
 bank 50 is a function of the incoming frequency f.sub.a. For example, for
 an AWGN (additive white Gaussian noise) channel, the correlation value
 Z.sup.(l).sub.3 for the l-th unique word is a Gaussian random variable
 because the matched filter bank 50 comprises a linear operator that
 preserves the Gaussian characteristics of the received signal. In other
 words, the correlation value may be expressed as a summation of signal and
 noise portions:
EQU Z.sub.3.sup.(l) =Z.sub.3,s.sup.(l) +Z.sub.3,n.sup.(l)
 The noise portion of the correlation value has a mean of zero and a
 variance that may be shown to be 2N.sub.0 (4T). It shall be further noted
 that the noise portions across different reference segments 44 are
 un-correlated and, therefore, independent, or
 ##EQU15##
 Once the correct timing offset .epsilon. has been determined the correct
 matched filtering operation may be selected for each unique word in the
 signal burst. The correct matched filter 52 will, in turn, remove the
 effect of the GMSK modulation, leaving the signal part of the selected
 correlation values dependent only on the frequency and phase shifts
 introduced by the channel. In other words, the signal part of the selected
 correlation values may be expressed as a continuous wave:
 ##EQU16##
 where sin c(x)=sin(.pi.x)/.pi.x. By properly rearranging terms, the signal
 part of the correlation value may be expressed as a single-tone (i.e., a
 continuous wave) of which we have six samples separated equally by 40T:
EQU Z.sub.3,s.sup.(l) =b.sub.0 e.sup.j(2.pi.f.sup..sub.a
 .sup.(l-1)40T+.theta..sup..sub.0 .sup.) ; l=1,2, . . . ,6
 where the amplitude and phase are defined as:
EQU b.sub.0 =2S+L 4T sin c(4f.sub.a T)
EQU and
EQU .theta..sub.0 =.theta..sub.a +2.pi.f.sub.a (20T)
 Typically, the incoming frequency falls within a range such that 4f.sub.a
 T&lt;&lt;1 and, thus, the amplitude may be approximated as:
EQU b.sub.0.apprxeq.2S+L 4T
 which is independent of the incoming frequency f.sub.a.
 In summary for the embodiment described above, the matched filter bank 50
 transforms a GMSK signal burst having six unique words into a set of six
 samples of a continuous wave spanning the 240 bit signal burst. Those
 samples are taken uniformly at a rate of (40T).sup.-1 Hz:
 ##EQU17##
 It shall be noted that the uniform distribution of the unique words over
 the signal burst is not necessary for determination of the frequency (or
 the timing) of the signal burst 40. Moreover, the exact locations of the
 unique words within the signal burst are also not crucial, as the burst
 analyzer 30 will be aware of the general locations of the unique words.
 However, the distributed nature of the unique words does provide more
 meaningful sample data.
 As shown in FIG. 5, the correlation values generated by the matched filter
 bank 50 are provided to a discrete-time Fourier transformer 70, which may
 implement a Fast Fourier Transform (FFT) algorithm. The Fourier
 transformer 70 is coupled to each of the matched filters 52 and then
 elects particular correlation values depending on the current timing
 offset .epsilon. and the maximum correlation values provided on lines 72
 and 74, respectively. Knowing that the correlation data from the matched
 filter bank 50 (for the correct timing offset and correct reference
 waveform) provides a plurality of samples of a continuous wave, the
 frequency of that wave can be determined from the frequency domain
 distribution generated from the Fourier transform operation. The frequency
 domain distribution is provided to an absolute value or magnitude
 generator 76, which, in turn, may provide the magnitude of the frequency
 domain distribution to a memory (not shown). That same memory may also be
 utilized by the Fourier transformer 70 to analyze the correlation data.
 The memory may collect data representative of the frequency domain
 distribution of the correlation data for a predetermined time period, and
 then an inverse maximum value determinator 78 analyzes the data to
 determine the frequency f.sub.a at which the magnitude of the frequency
 domain distribution is a maximum. To this end, the inverse maximum value
 determinator 78 generates a signal equal to, or representative of, the
 f.sub.OFFSET signal on the line 34.
 The above-described technique for determining the actual frequency f.sub.a
 of the incoming signal burst may be further justified via statistical
 analysis based on the optimal likelihood-ratio function. The likelihood
 function at the output of the matched filter bank 50 may be written as:
 ##EQU18##
 where C is a term independent of the received signal. Because the phase of
 the received signal is unknown, the likelihood must be averaged over the
 random phase, for which we express the quantity Z.sup.(l).sub.3 in complex
 form as set forth above. The resultant averaged likelihood-ratio function
 becomes:
 ##EQU19##
 The estimate of the frequency under the unknown phase condition is the
 value at which the likelihood is maximized:
 ##EQU20##
 A closer look at the likelihood function to be maximized reveals that it is
 the magnitude of the discrete-time Fourier transform (DFT) evaluated at
 the frequencies to be tested. The DFT may be expressed as:
 ##EQU21##
 where the discrete-time points are sampled at a rate B (Hz). While the
 frequency determination is not limited to the manner in which the DFT is
 implemented, well-known procedures for performing a fast fourier transform
 (FFT) are computationally efficient. Such procedures may be advantageous
 for extending the observation interval to M bits (as set forth above in
 connection with the timing offset determination), such that the carrier
 frequency estimate becomes:
 ##EQU22##
 where the correlation values Z are selected from the set of correlation
 values based on the signals on the lines 72 and 74. As was the case in
 connection with the timing offset determination, performance has been
 shown to improve with M larger than four (the number of bits in an unique
 word). With reference now to FIGS. 7 and 8, the performance of the burst
 analyzer 30 for joint determination of timing and frequency offsets is
 shown in terms of estimation error. The amount of error is presented as
 the standard deviation of the estimation error as a function of the signal
 energy per bit to noise power spectral density E.sub.b /N.sub.0 of the
 received waveform. For the purposes of evaluation only, the timing
 uncertainty was set to .+-.14 microseconds and the frequency was set to
 .+-.200 Hz.
 FIG. 7 shows the timing synchronization performance when using four- and
 five-bit correlation intervals. The five-bit correlation interval
 embodiment provides about 1.5 dB of gain in required input signal to noise
 ratio (SNR) over the four-bit embodiment (for a fixed amount of estimation
 error). Thus, the extension of the correlation interval provides
 significant performance improvements. Further, bandwidth-efficient systems
 that can only assign a small number of reference bits will benefit greatly
 from that particular embodiment. Despite these improvements, it shall be
 noted that the burst analyzer 30 is not limited to embodiments that extend
 the correlation interval beyond what has been assigned as reference
 information, and certainly not to an embodiment utilizing a four- or
 five-bit correlation interval.
 As shown hereinabove, the performance of the burst analyzer 30 for the
 frequency offset determination depends on the accuracy of the timing
 synchronization. As shown in FIG. 8, performance of the burst analyzer 30
 with the timing uncertainty set to .+-.14 microseconds is quite comparable
 to the theoretical lower bound of a continuous wave (i.e., perfect timing
 conditions). The ideal situation may be expressed as a function of E.sub.b
 /N.sub.0 as follows:
 ##EQU23##
 where N_bits is the number of bits in the signal burst. The performance
 data shown in FIG. 8 evaluated a 240 bit signal burst embodiment, with
 four-bit unique words and a four-bit correlation interval. Improvements
 may be obtained by increasing the correlation interval.
 As shown in FIGS. 7 and 8 and set forth above, the burst analyzer 30
 provides accurate determinations of both the timing and frequency of a
 signal burst in a feed forward manner (i.e., no feedback necessary).
 However, in certain applications requiring even greater accuracy, the
 estimation error may be further improved by providing a closed loop system
 incorporating the burst analyzer 30, a memory (not shown), and a processor
 (not shown) for providing tracking over different signal bursts.
 The above-described burst analyzer 30 is the subject of a co-pending
 application filed concurrently herewith and entitled "Method and Apparatus
 for Joint Timing Synchronization and Frequency Offset Estimation." The
 burst classification method and apparatus of the present invention may be
 advantageously utilized in a digital communication system incorporating
 the burst analyzer 30 and, thus, has been described in connection
 therewith. However, it shall be understood that application of the present
 invention is not limited to use with the burst analyzer 30 of the digital
 communication system 20 described above.
 Generally, the method and apparatus of the present invention provides a
 mechanism for classifying incoming signal bursts in digital communication
 systems that assign reference symbols. Burst type classification according
 to the present invention is performed non-coherently and, accordingly,
 does not require knowledge of the timing of the burst, the carrier phase,
 or the carrier frequency offset. Furthermore, compensation for unknown
 channel conditions is not necessary.
 With reference now to FIG. 9, the received signal is also provided to a
 burst classifier 90 in accordance with the present invention. The burst
 classifier 90 may be incorporated into the burst analyzer 30 of FIG. 1,
 but alternatively may constitute a stand-alone component of the receiving
 portion of the digital communication system 20. The burst classifier 90
 includes multiple matched filter banks 92, each of which is coupled to the
 front end filter 26 (FIG. 1) to be provided with the received signal. In
 accordance with one embodiment of the present invention, the matched
 filter bank 50 (FIG. 5) of the burst analyzer 30 constitutes one of the
 matched filter banks 92. As will be evident from the description to
 follow, the processing according to one embodiment of the present
 invention for burst type classification overlaps to great extent with the
 above-described processing necessary for timing and frequency estimation.
 Regardless of whether such efficiencies are realized, each matched filter
 bank 92 processes the received signal in the same manner as set forth in
 FIG. 6 and described above.
 In the embodiment shown in FIG. 9, two matched filter banks 92 are provided
 for two different unique words, UW.sub.0 and UW.sub.1, respectively. In
 general, a corresponding matched filter bank 92 is provided for each
 possible burst type. In this manner, each burst type may have one or more
 distinct unique words assigned thereto for identification purposes and are
 assumed to be different for different burst types. For example, the unique
 word (-1, -1, 1, -1) of the TCH burst 40 of FIG. 2 may constitute
 UW.sub.0, while UW.sub.1 signifies a FACCH or other burst type. Thus, in
 the embodiment shown in FIG. 9, UW.sub.0 and UW.sub.1 are not to be
 confused with different unique words in a single signal burst, but rather
 each constitutes a unique word assigned to identify a particular burst
 type.
 As set forth in connection with FIG. 6, each matched filter bank 92
 comprises a plurality of filters matched to the possible reference
 waveforms representative of the unique words, along with averages thereof,
 if desired. If more than one unique word has been associated with a
 particular burst type such that the burst includes different unique words
 in the reference segments 44 thereof, the plurality of filters must also
 accommodate the reference waveforms associated therewith.
 The filters of each matched filter bank 92 compare the received signal with
 each of the reference waveforms thereof over an observation or correlation
 interval in the manner described above in connection with the burst
 analyzer 30. The observation interval may be extended beyond that which is
 assigned as reference bits, thereby increasing the number of reference
 waveforms from, for example, eight to sixteen (unless suitable averaging
 is utilized to reduce complexity). Improvements in burst classification
 similar to those exhibited in connection with the timing and frequency
 determinations would result from such an extension.
 For each reference waveform to be tested, the respective filter of the
 matched filter bank 92 has an impulse response h(t,.alpha..sub.i) that
 corresponds with the reference waveform. The impulse response is based on
 the differentially encoded data of the unique word as set forth above in
 connection with the matched filters 52 of the burst analyzer 30 and,
 therefore, will not be further explained here.
 In summary, the matched filter banks 92 of the burst classifier 90 compare
 the received signal with each reference waveform (offset by a plurality of
 time offsets) associated with each possible burst type, respectively, by
 convolving the received signal with each respective impulse response over
 the observation interval. The convolution results in correlation data
 represented by the same type of correlation values Z.sup.(l).sub.M-1
 (.epsilon..vertline..alpha..sub.i) generated in connection with the burst
 analyzer 30. It shall be noted that the discrete correlation values are
 generated by a plurality of samplers (see FIG. 6 and the corresponding
 description) coupled to each filter in each matched filter bank 92.
 With continued reference to FIG. 9, the correlation data for each matched
 filter bank 92 is provided to a plurality of absolute value (or magnitude)
 generators 94. Of course, the magnitude generators 94 may be "shared" by
 the matched filter banks 92 to avoid unnecessary system complexity through
 suitable programming. Once the magnitude of each correlation value has
 been generated, a maximum correlation value Z.sup.(l).sub.max
 (.epsilon..sub.i) is determined for each reference segment 44 (see FIG. 2)
 and time offset .epsilon. by a maximum correlation value determinator 96.
 Once again, the burst classifier 96 may include a plurality of such
 determinators 96, each being dedicated to a particular matched filter bank
 92 or, alternatively, include a single, shared software routine, for
 example, that is accessed when necessary for each set of correlation
 values.
 As further explained above in connection with the burst analyzer 30, the
 correlation data associated with each possible burst type has been
 modified in preparation for non-coherently combining the correlation data
 for the entirety of the signal burst. Accordingly, the maximum correlation
 values are provided to a summer or accumulator 98, which sums or otherwise
 combines the maximum correlation values across the reference segments of
 the signal burst to generate a total maximum correlation Z.sub.TOTALmax
 (.epsilon..sub.i) for each respective time offset.
 Instead of finding the time offset at which the output of the summer 98 is
 a maximum, which would result in a timing offset value for the signal
 burst as set forth above, the burst classifier 90 includes a maximum value
 determinator 100 that finds the maximum Z.sub.TOTALmax (.epsilon..sub.i)
 across all possible time offsets. The processing resulting in this
 collective maximum correlation for each burst type has, thus, removed the
 uncertainty associated with the unknown timing variable. These collective
 maximum correlations for all of the burst types are then supplied to a
 comparator 102 that elects the burst type having the most correlation with
 the received signal. Alternatively, the comparator 102 may be implemented
 as an inverse maximum operator over the hypothesis index.
 In the embodiment of FIG. 9, only two possible burst types exist, each of
 which is represented by a single unique word (UW.sub.0 or UW.sub.1).
 However, it shall be understood that the comparator 102 may handle compare
 as many different inputs as necessary. In this manner, the burst
 classifier 90 may classify the incoming burst according to any number of
 different burst types transmitted in the digital communication system 20.
 A comparison of FIGS. 5 and 9 will yield that, with the exception of the
 maximum value determinator 100 and the comparator 102, the components of
 the burst analyzer 30 and the burst classifier 90 coincide to a great
 extent. As a result, the processing leading to timing and frequency
 determinations for a particular signal burst may be performed
 simultaneously with the burst type classification. Such dual processing
 will reduce processing time without adding extensive amounts of system
 complexity. Therefore, in some embodiments of the present invention, the
 timing and frequency offsets of a signal burst may be quickly and easily
 generated subsequent to burst type classification.
 As a further result of this overlap, the burst classifier 90 may be
 embodied as a portion of the burst analyzer 30 (or vice versa). However,
 the burst classifier 90, in general, may be implemented in any component
 of the receiving portion of the digital communication system 20 that is
 supplied with the received signal.
 The above-described method and apparatus for burst type classification may
 be justified via statistical analysis based on the likelihood-ratio
 function averaged over the unknown parameters (e.g., timing). For a two
 type case such as the one described above, the optimal classification rule
 may be expressed as a ratio of likelihood functions (averaged over the
 unknowns) wherein a particular burst type is declared whenever a threshold
 is exceeded, or
 ##EQU24##
 where &lt;.&gt;denotes the statistical average over the random variable, H.sub.i
 is the hypothesis that the burst is the i-th type, and P(H.sub.i) is the
 probability of occurrence of the i-th hypothesis. Because it can be
 assumed that the hypotheses are equally likely, the threshold may be set
 to unity. Other values of the threshold are possible.
 Based on knowing that the system 20 assigns different unique words for
 different burst types, the likelihood function for the received signal
 during the I-th unique word conditional on knowing the timing offset and
 the carrier phase under the i-th hypothesis may be expressed as:
 ##EQU25##
 where
 ##EQU26##
 and where C is a term independent of the transmitted signal and r(t) is the
 baseband complex envelope of the received waveform (i.e., the received
 signal).
 For non-coherent burst type classification (so that the technique does not
 require additional processing to estimate the carrier phase), the
 likelihood function is averaged over the random phase, for which we
 express the quantity Z.sup.(l).sub.M-1
 (.epsilon..vertline..alpha.;H.sub.i) in complex form as:
EQU Z.sub.3.sup.(l)
 (.epsilon..vertline..alpha.;H.sub.i)=.vertline.Z.sub.3.sup.(l)
 (.epsilon..vertline..alpha.;H.sub.i).vertline.exp(j&lt;Z.sub.3)
 The resultant averaged likelihood ratio becomes
 ##EQU27##
 where I.sub.0 (x) is the zeroth order Bessel function of the first kind.
 Because the random phase is modeled to be uniformly distributed, the
 performance of the present invention is independent of the carrier phase
 parameter.
 To account for the unknown data bits which contribute to the shape of the
 reference waveform, the averaged likelihood ratio function is further
 averaged (over the eight possible waveforms), yielding:
 ##EQU28##
 Because the noise is independent for different unique word intervals, the
 statistics may be non-coherently combined by multiplying the individual
 likelihood ratio functions. The optimal classification rule may then be
 expressed as
 ##EQU29##
 A simplified rule may then be derived using the same high SNR
 approximations set forth above in connection with the burst analyzer 30,
 thereby eliminating the non-linearities and removing any dependence on the
 signal amplitude. These approximations, together with a replacement of the
 averaging operation with the maximum operation, which is acceptable under
 high SNR conditions, are set forth below:
 ##EQU30##
 After some algebraic manipulations, the simplified classification rule (or
 its logarithmic version) for the two type case may be expressed as:
 ##EQU31##
 Once again, it shall be noted that the present invention is not limited to
 a system having only two types of signal bursts, inasmuch as the above
 principles may be extended to cover as many different burst types as
 necessary.
 The performance of the present invention may be evaluated in terms of the
 probability of making the correct decision, P(C), or
 ##EQU32##
 for equally likely hypotheses. Using computer simulations of the
 Monte-Carlo type, the burst classifier 90 of the present invention
 exhibited a probability of making incorrect decisions of merely 0.018%.
 The simulation was run for E.sub.b /N.sub.0 =2 dB and 50,000 bursts for
 high statistical reliability in an AWGN channel with the same induced
 timing and frequency uncertainties as utilized above in connection with
 the performance testing of the burst analyzer 30.
 The burst classifier 90 is not limited to application in an AWGN (additive
 white Gaussian noise) channel. The burst classifier 90 has exhibited a
 high degree of robustness in other environments frequently encountered in
 mobile satellite communications including, for example, Rician fading
 channels that are moderately or severely frequency-selective channels.
 The method and apparatus according to the present invention may also be
 implemented in a variety of ways. The steps of the inventive method may be
 carried out by a general purpose processor programmed with software
 routine(s) in accordance with the present invention. Alternatively, the
 general purpose processor may be replaced with a digital signal processor
 in the form of an ASIC or other specialized IC designed to perform the
 steps of the inventive method. It shall be understood that, regardless of
 the hardware utilized, the present invention may be implemented using any
 combination of hardware, software, and firmware.
 Numerous other modifications and alternative embodiments of the invention
 will be apparent to those skilled in the art in view of the foregoing
 description. Accordingly, this description is to be construed as
 illustrative only. The details of the structure and method may be varied
 substantially without departing from the spirit of the invention, and the
 exclusive use of all modifications which are within the scope of the
 appending claims is reserved.