Sample timing selection and frequency offset correction for U.S. digital cellular mobile receivers

A Time Division Multiple Access (TDMA) radio system achieves synchronization by performing a two-step synchronization. A simplified frame/slot synchronization is followed by a symbol synchronization of higher accuracy. This symbol timing is passed to a frequency offset unit which determines the amount of frequency drift between the transmitter and receiver and compensates for the frequency drift. This results in improved receiver performance for the TDMA digital radio system.

CROSS-REFERENCE TO RELATED APPLICATIONS 
This application is related to the following U.S. patent applications 
assigned to the present assignee: H. Lester et al. Ser. No. 07/754,471 and 
continuation-in-part application Ser. No. 08/095,367 filed Jul. 20, 1993 
"Automatic Simulcast Alignment"; and R. Toy, et al. U.S. Pat. No. 
5,177,740 issued Jan. 5, 1993 "Frame/Slot Synchronization for U.S. Digital 
Cellular TDMA Radio Telephone System". 
BACKGROUND OF THE INVENTION 
1. Field of the Invention 
This invention relates generally to a telecommunication method and 
apparatus and, in particular, to method and apparatus for achieving sample 
timing selection and frequency offset correction in conjunction with 
transmitting digital information in a Time Division Multiple Access (TDMA) 
cellular radio telephone system. 
2. Description of Prior Art 
Mobile radio involves communication via transmission of radio frequency 
signal between a mobile unit in a vehicle and a base station, or between 
mobile units. Time division multiple access (TDMA) digital mobile radio 
systems are described in the aforementioned "Frame/Slot Synchronization 
for U.S. Digital Cellular TDMA Radio Telephone Systems" by R. L. Toy and 
S. Chennakeshu, and "A. Bit Synchronization and Timing Sensitivity Viterbi 
Equalizers for Narrowband TDMA Digital Mobile Radio Systems", A. Baier, G. 
Heinrich, and U. Wellens, IEEE Vehicular Technology Conference, 
(Philadelphia), pp. 377-384, 1988. The communicating units must determine 
the beginning and end of signals intended for them, known as frame/slot 
synchronization. The complexity and accuracy of the frame/slot 
synchronization depend upon the number of points at which the signal is 
sampled. More samples per transmitted symbol implies greater accuracy at 
the expense of a higher complexity. 
In order to keep the complexity reasonable for a practical implementation, 
fewer samples per symbol are employed for establishing frame/slot 
synchronization. The reduced number of samples, however, results in 
reduced accuracy with which frame/slot synchronization can be established. 
The resulting inaccuracy degrades receiver performance. Thus a more 
accurate sample timing scheme is required. 
The transmitted signal may be reflected from physical and natural 
obstructions causing echoes which are received with the original 
transmission and is commonly known as multipath propagation. Multipath 
propagation further reduces receiver performance. 
An additional problem with these systems is that the frequency of a local 
oscillator in the mobile station is likely to differ from that of the base 
station, and vice versa. The resulting frequency offset introduces a phase 
shift which causes the transmitted symbols to appear to be phase rotated 
at the receiver, thereby causing an ambiguity in the detection process. 
This severely degrades the performance of the receiver. In order to 
counteract this degradation in performance, it is necessary to estimate 
this frequency offset and apply a suitable correction to the received 
symbols. 
Currently there is a need for a TDMA digital radio system which accurately 
selects sample timing for synchronization and corrects frequency offset in 
the presence of multipath propagation. 
OBJECTS OF THE INVENTION 
It is an object of the invention to provide a simplified method and 
apparatus, relative to the prior art, for achieving symbol synchronization 
in time division multiple access (TDMA) radio systems in the presence of 
multipath propagation. 
It is another object of the invention to provide a method and apparatus for 
achieving and maintaining symbol synchronization in the U.S. digital 
cellular radio system and that corrects frequency offsets between a 
transmitter and a receiver even in the presence of multipath propagation. 
SUMMARY OF THE INVENTION 
A digital communication system comprises a transmitter for transmitting 
reference symbols and data symbols in a radio signal, and a receiver for 
decoding the signal. In the receiver, a transmit oscillator governs the 
frequency of the transmitted digital radio signal. An analog-to-digital 
(A/D) converter samples the transmitted radio signal to provide a 
plurality of received reference sample sets r.sub.pre.sup.(k) (n) 
corresponding to transmitted reference symbols and a plurality of data 
sample sets r.sub.sp.sup.(k) (n) corresponding to transmitted data 
symbols. 
A synchronizer estimates channel impulse response (CIR) coefficients 
c.sub.i from the received reference samples and a set of stored reference 
symbols and creates a set of estimated reference symbols r.sup.(k) (n) 
which are compared to received reference samples r.sub.pre.sup.(k) (n). 
Based upon the comparison, a sample timing is selected which minimizes the 
difference. A frequency offset means receives the estimated reference 
samples r.sup.(k) (n) and received reference samples r.sub.pre.sup.(k) (n) 
to determine frequency drift between the transmitter oscillator and the 
receiver oscillator. This frequency drift estimate is used to correct a 
data sample set corresponding to a best sample timing by a frequency 
correction means. A decoder decodes the corrected data sample set into 
digital information which is then utilized by an output device.

DETAILED DESCRIPTION OF THE INVENTION 
FIG. 1 is a block diagram of the present invention showing a transmitter 20 
and a receiver 120. Digital information desired to be transmitted is 
provided to a block assembly unit 8. The digital information may be 
digitized speech data from an operator speaking into a handset 2 to create 
an analog voltage signal that is sampled by an analog to digital (A/D) 
converter 4 and analyzed by a vocoder 6 to provide coded speech data to a 
block assembly unit 8. Block assembly unit 8 combines coded speech data, 
reference symbols s(n) from a symbol storage unit 7, and other required 
data in a standardized format into a slot of data which is later 
interleaved with other data slots to be employed in a time division 
multiple access (TDMA) system. 
Encoder 10 of FIG. 1 encodes the slot of data in a desired manner and 
passes the encoded data to a mapper 12 which maps several bits to a symbol 
of a predetermined symbol constellation. Mapped symbols are provided to a 
digital to analog (D/A) converter 14 which converts the mapped samples to 
an analog signal at a rate governed by a transmit clock 16 and reference 
oscillator 17. The analog signal is then filtered by bandpass filter 18 
and passed to a radio frequency (RF) amplifier 22 which creates an RF 
signal transmitted through antenna 24. 
The transmitted signal is sensed by a receiving antenna 124, passed to an 
RF preamplifier 122 and heterodyned by a down converter 118 to provide an 
intermediate frequency (IF) signal. An A/D converter 114 in the receiver 
samples the IF signal at a rate determined by a receive clock 116 and 
reference oscillator 117, resulting in a plurality of received reference 
samples r.sub.sp.sup.(k) (n) (n=1,2, . . . N.sub.p), where N.sub.p is the 
number of symbols in the reference symbol set) and data samples 
r.sub.sp.sup.(k) (j) (j=1,2, . . . N.sub.d,) where N.sub.d is the number 
of data symbols) corresponding to samples of reference symbols and data 
symbols, respectively. A/D converter 114 samples at a rate to provide a 
plurality of samples for each symbol, each acquired at a different sample 
timing k measured from the beginning of a symbol period. Samples obtained 
at a given sample timing offset k for all symbol periods comprise a sample 
set. The samples are provided to a synchronization unit 50, coupled to a 
reference symbol storage unit shown as ROM 88, adapted for retaining 
predetermined reference symbols being the same as: 
1) the symbols of preamble 166 or Coded digital Verification Color Code 
(CDVCC) data 176 shown in FIG. 2 and described on p. 85-86 of Jan. '91 
EIA/TIA "Interim Standard--Cellular System, Dual Mode Mobile Station--Base 
Station Compatibility Standard" Publication IS-54-A by the Electronics 
Industries Assoc., Engineering Dept., and 
2) reference symbols combined with data symbols by block assembly unit 8 of 
FIG. 1. 
Synchronization unit 50 analyzes and compares each of the received 
reference sample sets it receives from A/D converter 114 to that of ROM 88 
and determines a sample timing k=b corresponding to a best match. Data 
samples r.sub.sp.sup.(b) (j) corresponding to the best sampling timing b 
are passed to frequency correction unit 90. Synchronization unit 50 also 
estimates preamble data r.sup.(k) (n) derived from reference symbols s(n) 
of ROM 88 as they would appear after being transmitted and received by 
receiver 120, and provides received reference samples r.sub.pre.sup.(b) 
(n) to a frequency offset unit 70. Frequency offset unit 70 then 
determines a frequency offset .DELTA..phi. which represents the phase 
drift between transmit oscillator 17 and receive oscillator 117. 
Synchronization unit 50 also selects data samples r.sub.sp.sup.(b) (j) 
corresponding to the best sample timing b (as defined hereinafter) and 
provides these to a frequency correction unit 90. Frequency correction 
unit 90 employs frequency offset .DELTA..phi. and data samples 
r.sub.sp.sup.(b) (j) to compensate for the frequency offset, creating 
adjusted data samples r.sub.sp.sup.(b,.DELTA..phi.) (j) and provide them 
to a decoder 110. Decoder 110 decodes the adjusted data samples into 
digital information to be utilized by an output device. The output device 
in this embodiment is a vocoder 106 which synthesizes digital speech 
waveforms. A D/A converter 104 converts the digital speech waveforms into 
analog speech at handset 102. The output device may be any device which 
may make use of digital information. 
FIG. 2 shows a typical slot of data 144 (slot 2) which comprises a preamble 
166, a slow associated control channel (SACCH) data block 168, the encoded 
data 174 and 178 (which may be encoded speech data), a coded digital 
verification color code (CDVCC) block of data 176 and a reserved block of 
data 179. Three slots together comprise a frame 140. This frame/slot 
structure has been described on pp. 533-537 in "Digital Cellular Systems 
for North America", ROC. GLOBECOM by C.E. W. Sundberg and N. Seshadri, ", 
PP. 533-537. 
Sample Timing Selection 
At the mobile station receiver, the data is received and sampled using 
N.sub.s samples per symbol. To reduce complexity, frame/slot 
synchronization is computed with fewer samples per symbol, such as 
N.sub.s1. Because of the lower sampling rate, the accuracy of the 
synchronization is reduced to .+-.(N.sub.s /N.sub.s1) samples from the 
true synchronization point t.sub.0. This is adequate for frame/slot 
synchronization, but the inaccuracy degrades the performance of the 
receiver. Thus, more accurate sample timing selection leads to higher 
receiver performance. 
For a general Time Division Multiple Access (TDMA) system, the sample 
timing selection should be chosen as close to an optimum sampling point as 
possible to optimize the performance of the receiver. The optimum sampling 
point is selected from one of the possible points sampled at time t.sub.k. 
##EQU1## 
where k is the sampling point with k=0, .+-.1, .+-.2 . . . ,.+-.[N.sub.s 
N.sub.s1 ], 
T.sub.s is the symbol period, 
t.sub.0 is the sample location obtained by a coarse frame/slot 
synchronization, 
N.sub.8 is the number of samples per symbol. 
FIG. 3 is an illustration of a method of sampling the IF signal received by 
A/D converter 114, shown in FIG. 1, which is compatible with the present 
invention. A/D Converter 114 samples the IF signal at a rate several times 
higher than the symbol rate with a sampling period of T.sub.s /N.sub.s. In 
the preferred embodiment, N.sub.s equals 8 samples per symbol numbered 
from -4 to 4 with the sample labeled 0 being a coarse sample timing at 
time t.sub.0. 
Ultimately, the best sample timing b within each symbol should be chosen to 
minimize the calculated error between a set of received reference samples 
r.sub.pre/.sup.(k) (n) which may be samples of preamble symbols 166, 181 
in successive slots such as slots 2 and 3 of FIG. 2, and a set of 
estimated reference samples r.sup.(k) (n) calculated from stored reference 
symbols s(n). This may be stated as: 
##EQU2## 
where N.sub.p is the number of symbols in the preamble, 
k is the sample index, and 
r.sub.pre.sup.(k) (n) is the sample of nth symbol of preamble corresponding 
to sampling instant k. 
The estimated reference samples r.sup.(k) (n) are an estimate of stored 
reference symbols s(n) as they would appear if transmitted through the 
channel. The estimated reference samples r.sup.(k) (n) are calculated by: 
##EQU3## 
where L is the duration of the (finite) channel impulse response (CIR), 
corresponding to the multipath channel; 
c.sub.i.sup.(k) are the coefficients, each being a complex number 
signifying the estimated gain for the i.sup.th reflected radio path 
corresponding to the k.sup.th sampling instant in each symbol over the 
preamble, and 
s(n) represents the n.sup.th reference symbol of the preamble. 
The value of k that minimizes Eq. (2) is the optimum or best sample timing 
b. Thus, the set of samples r.sup.(b) (n) corresponding to the best sample 
timing b are decoded in the receiver. The samples at other sample timings 
are discarded. 
Eq. (3) requires that the CIR coefficients be calculated before determining 
the estimated reference symbols r.sup.(b) (n) and performing the sample 
timing selection. 
For the U.S. digital cellular system, the preamble is 14 symbols long, and 
the multipath channel is characterized by a two-ray channel model with the 
two rays being separated by a maximum of 1 symbol as described on p. 20-21 
of the March 1991 draft of EIA/TIA "Cellular System, Recommended Minimum 
Performance Standards for 800 MHz Dual-Mode Mobile Stations" Publication 
TIA TR45.3, Project No. 2216 by the Electronics Industries Assoc., 
Engineering Dept.. Also, assuming that N.sub.s =8 samples per symbol, and 
N.sub.s1 =2 samples per symbol, then, there are nine possible sampling 
points according to Eq. (1). 
In this case, the equations (2) and (3) become 
##EQU4## 
and 
EQU r.sup.(k) (n)=c.sub.i.sup.(k) s(n)+c.sub.2.sup.(k) s(n-1), (5) 
respectively. 
CIR Coefficient Estimation 
An estimate of the CIR coefficients is required for computing the estimated 
received signal in Eq. (3). 
As described above, the preamble has length N.sub.p, and the CIR has length 
L. To simplify the expressions, equation (3) may be expressed in matrix 
form as the following matrices: 
##EQU5## 
where S is the (N.sub.p -L+1).times.L matrix of known symbols, C.sup.(k) 
is the L-vector of channel coefficients, and R.sup.(k) is the vector of 
received samples of length N.sub.p -L+1. 
Equation (3) then becomes the matrix equation 
EQU SC.sup.(k) =R.sup.(k) (9) 
This is an over-determined set of N.sub.p -L+1 equations in the L unknowns, 
C.sup.(k). To obtain a solution, a least-squares technique is performed, 
resulting in: 
EQU C.sup.(k) =MR.sup.(k) (10) 
EQU where 
EQU M=[S.sup.H S].sup.-1 S.sup.H (11) 
S.sup.H denotes the Hermitian transpose (conjugate transpose) of S. Since S 
is known a priori, M can be computed beforehand without the need for 
received symbols. 
For the U.S. digital cellular system, Eqs. (10) and (11) cannot be directly 
applied since each symbol is differentially encoded (i.e. transmitted as a 
difference in phase from a previously transmitted symbol). Thus, for the 
preamble, the fourteen differential phase angles given by the set 
{.DELTA..PHI..sub.1, .DELTA..PHI..sub.2, . . . , .DELTA..PHI..sub.14 } are 
known, but the actual transmitted symbols are not. However, if an 
arbitrary starting symbol s(0) is assumed, the remaining preamble symbols 
may be determined by: s(n)=s(n-1)e.sup.j.DELTA..PHI.n If s(0) is the 
actual starting symbol, then: 
EQU s(0)=e.sup.j.pi.l/2 s(0),l=0,1,2,3 (12) 
Applying this assumption to Eqs. (10) and (11), then: 
##EQU6## 
Thus, the CIR estimate is rotated by a factor of e.sup.-j.pi.l/2 from the 
true CIR values. However, when we form the estimated received signal, 
R.sup.(k), it is correct. 
##EQU7## 
The only effect of the above factor e.sup.-j.pi.l/2 will be that the 
decoded symbols will have a constant phase shift of .pi.l/2. Differential 
decoders, such as those used in U.S. digital cellular radio systems to 
demodulate .pi./4-shifted Differentially Quadrature Phase Shift Keying 
(DQPSK) signals, only measure the phase differences between a transmitted 
phase angle and a previously transmitted phase angle, and not the actual 
phases. Therefore, the differential decoder will remove the effect of this 
constant phase shift. 
Since s(0) is implicitly employed, the following additional equation may 
inserted from Eq. (9): 
##EQU8## 
This additional equation helps to improve the accuracy of the CIR estimate, 
especially over the short CDVCC words. 
The U.S. digital cellular system typically assumes a two-ray ray model for 
the channel. Hence, L=2, and Eq. (9) becomes: 
##EQU9## 
where the additional Eq. (17) is employed. For the CDVCC, which consists 
of six symbols, the equations become: 
##EQU10## 
where s(n) is now the reference symbol from the CDVCC word. The CIR 
estimated is obtained from equation 10. 
In FIG. 4, a more detailed block diagram of synchronization unit 50 of FIG. 
1 is shown using N.sub.s samples per symbol for each of the reference 
symbols (i.e., preamble, but in some embodiments over several preambles 
and other reference features), and each of the data symbols (174, 178 of 
FIG. 2) are stored in a buffer 52. A frame synchronization unit 54 
provides a coarse sample timing b. 
A channel estimator 56 receives stored reference symbols s(n) from ROM 88 
and received reference samples from buffer 52 and determines channel 
impulse response (CIR) coefficients c.sub.i which are provided to a 
reference symbol estimator 58. The coarse symbol timing b from frame 
synchronization unit 54 is also provided to reference symbol estimator 58 
which determines estimated reference samples r.sup.(k) (n) and passes them 
to a timing selection unit 62. Timing selection unit 62 compares a 
received reference sample r.sub.pre.sup.(k) (n) from buffer 52 to the 
corresponding estimated reference sample r.sup.(k) (n) from reference 
symbol estimator 58. Timing selection unit 62 repeats this process for all 
symbols in the preamble and determines a deviation of received reference 
samples r.sub.pre.sup.(k) (n) from the estimated reference samples 
r.sup.(k) (n) according to Eq. (2). This deviation is determined for a 
given sample timing k. This process is then repeated for all other values 
of k in a predetermined window spanning the symbol timing centered at 
coarse sample timing b. In the preferred embodiment, the sample timing k 
will vary from four samples before coarse symbol timing b to four samples 
after the coarse symbol timing. The sample timing corresponding to the 
least deviation between the estimated reference samples r.sup.(k) (n) and 
the actual received samples r.sub.pre.sup.(k) (n) is used as the best 
sample timing b. 
The received reference samples r.sub.pre.sup.(b) (n) and the estimated 
reference samples r.sup.(b) (n) corresponding to best sample timing index 
b are passed from timing selection unit 62 to frequency offset unit 70 of 
FIG. 1. Sample timing index b is passed to a data selection unit 64 which 
selects received data samples r.sub.sp.sup.(b) (n) for decoding from 
buffer 52 and passes them to frequency correction unit 90 of FIG. 1. 
Frequency Offset Correction 
Let .phi..sub.o (n) be the received signal phase at time n when no 
frequency offset is present. When a frequency offset of f.sub.0 Hz is 
present, the received signal phase has an additional phase component that 
causes each successive symbol to be rotated an additional 
.DELTA..phi.=2.tau.f.sub.o T.sub.s radians per symbol, where T.sub.s is 
the symbol period. Let .phi.(n) be the received signal phase with 
frequency offset. Then .phi.(n)=.phi..sub.o 
(n)+n.DELTA..phi.+.DELTA..phi..sub.o is a constant frequency offset due to 
the unknown phase relationship between the transmit oscillator 17 and the 
receive oscillator 117 of FIG. 1. This offset cannot be ignored because it 
appears in the estimates of the channel impulse response that are required 
for synchronization. 
The goal is to estimate .DELTA..phi. so that the appropriate frequency 
correction may be applied to remove the effects of the frequency offset. 
Estimation via Phase Adjustment Loops 
Frequency offset estimation can be performed using phase adjustment loops 
(s). Frequency offset unit 70 of FIG. 1, which acts as a , is 
illustrated in a more detailed block diagram in FIG. 5. The received 
reference samples r.sub.pre.sup.(b) (n) and estimated reference samples 
r.sup.(b) (n) corresponding to the best sample timing index b are provided 
to phase computation units 72a and 72b to produce phases .phi.(n) and 
.psi.(n) which are provided to summer 74. The difference in phase 
.DELTA..theta..sub.n produced by a summer 74 and a feedback signal 
.epsilon.(n-1) are provided to a summer circuit 76. The output signal d(n) 
of summer 76 is multiplied by factors .alpha. and .beta. in gain units 78a 
and 78b, respectively to adjust the signal's gain. The gain adjusted 
samples from gain unit 78a are provided to a summer 80a along with 
feedback signal .epsilon.(n-1) and a signal .omega.(n) to create the 
signal .epsilon.(n) which is delayed in a delay unit 82a to produce the 
feedback signal .epsilon.(n-1). The output signal of gain unit 78b is 
provided to a summer 80(b) to determine the difference between this signal 
and the feedback signal .omega.(n-1) of a delay unit 82b. The output 
signal .omega.(n) produced by summer 80b is passed to an averager circuit 
84 to determine a signal .DELTA..phi. which is an estimate of the phase 
adjustment for the phase difference between transmit oscillator 17 and 
receive oscillator 117 of FIG. 1. Frequency correction unit 90 of FIGS. 1 
and 5 employed in the preferred embodiment of the present invention may be 
described by: 
##EQU11## 
where .psi.(n), .phi.(n)=the phase angles of the complex received 
reference samples r.sub.pre.sup.(k) (n) and the estimated reference 
samples r.sup.(k) (n), respectively, 
.alpha.(n),.beta.(n) filter coefficients, which can be time varying, 
c.sub.i =channel coefficients, 
L=length of channel impulse response, and 
s(n)=reference symbols. 
For proper operation, the must be designed with appropriate 
coefficients. If the channel coefficients, c.sub.i are assumed to be known 
exactly, if there are no other components in the intersymbol interference, 
and if there is no noise, then .phi.(n)-.psi.(n) must contain only the 
frequency offset component. It can be shown that for a frequency offset of 
.DELTA..phi. radians per symbol, .omega.(n).fwdarw..DELTA..phi. as 
n.fwdarw..infin.. Thus, .omega.(n) is an estimate of the frequency offset. 
In practice, noise is present, the channel coefficients are not known 
precisely, and n cannot grow indefinitely. However, for the U.S. digital 
cellular system, since the preamble symbols s(n) are known, the CIR 
coefficients c.sub.i can be estimated over the preamble, and the preamble 
is sufficiently long to obtain an estimate of the frequency offset 
.DELTA..phi.. 
Let the preamble contain N.sub.p symbols. While .omega.(N.sub.p) can be 
used as the estimated frequency offset, .omega.(N.sub.p) tends to be 
rather noisy. To combat the noise, .omega.(n) is averaged by an averager 
84 of FIG. 5 over the last few symbols of the preamble to produce the 
frequency offset per symbol, .DELTA..phi.: 
##EQU12## 
Therefore in a first embodiment, .omega.(n) is averaged by averager 84 and 
passed to a phase logic circuit 86 which simply sets a frequency 
correction to the frequency offset .DELTA..phi.. Although the sum shown 
here employs N.sub.p -N.sub.1 +1 symbols, where N.sub.1 -1 is the number 
of symbols skipped at the beginning of the reference symbol set, the 
number of symbols employed may vary. N.sub.1 -1 symbols are skipped to 
allow the phase locked loop to stabilize. More symbols (smaller N.sub.1), 
reduces the effect of noise but introduces more frequency offset 
estimation error because .omega.(n) ramps up from zero to .DELTA..phi.. 
Fewer symbols (larger N.sub.1) reduces the frequency offset estimation 
error due to the ramping up of .omega.(n), but results in noisy estimates. 
A reasonable tradeoff, depending on the length of the preamble, is to use 
the last half of the preamble for averaging .omega.(n). 
Due to channel impairments, this estimate can sometimes produce widely 
varying values, which is contrary to the constant frequency offset that 
would be expected. Thus, an averaging filter is employed to further 
improve the estimates. Let .DELTA..phi.(m) be the estimated frequency 
offset for slot m, and let .DELTA..phi..sub.s (m) be the smoothed 
frequency offset. Then 
EQU .DELTA..phi..sub.s (m)=.DELTA..phi..sub.s 
(m-1)+s(m)[.DELTA..phi.(m)-.DELTA..phi..sub.s (m-1) (25) 
where s(m) is a weighting coefficient determined by 
s(m)=max(s.sub.0,.lambda..sup.m), where s(m) is the larger of s.sub.0 
being a constant representing a minimum threshold value, and .lambda. 
raised to a power m, where m is the slot index. .lambda. is a constant 
representing smoothing factor. Essentially, s(m) is an exponentially 
decreasing function which weights frequency offsets from recent preambles 
more than those obtained from subsequent preambles to a minimum amount 
determined by s.sub.0. Suggested values are s.sub.0 =0.05 and .lambda.=0.7 
which were determined to be a suitable tradeoff between the time to 
acquire the frequency offset and accurate tracking of the offset. To 
initialize the smoothing at m=0, .DELTA..phi..sub.s (0)=0 
.DELTA..phi..sub.s (-1)=0. 
In a second embodiment, phase logic circuit 86 sets a frequency correction 
to the smoothed frequency offset calculated from the estimated frequency 
offset .DELTA..phi.(m) for slot m calculated according to Eq. (24). 
Enhanced Frequency Offset Correction 
The development above assumed that only one estimate, .DELTA..phi..sub.1 is 
obtained from the first preamble. However, for the U.S. digital cellular 
system, another estimate on base-mobile transmission .DELTA..phi..sub.2 
may be obtained from the preamble of the adjoining slot. The use of this 
second preamble requires continuous transmission from the base station to 
the mobile unit. 
Phase logic circuit 86 receives the frequency offsets .DELTA..phi..sub.1 
and .DELTA..phi..sub.2 each determined by average 84 according to Eq. (24) 
and combines them into a single estimated frequency offset. 
In a third embodiment, phase logic circuit 86 combines the estimated 
frequency offsets according to: 
##EQU13## 
Phase logic circuit 86 then employs the single estimated frequency offset 
of Eq. (26) in Eq. (25) to result in a smoothed frequency offset passed on 
as the frequency correction. 
In a fourth embodiment, phase logic circuit 86 selects the the more 
reliable estimate of the frequency offset .DELTA..phi.(m) based on the 
slot containing more energy over the preamble. Specifically, let c.sub.i1 
and c.sub.i2 for i=0,1, . . . , L -1 be the channel coefficients from the 
preamble of the current slot and the preamble of the adjoining slot, 
respectively. 
Then the estimated frequency offset to be employed in Eq. (25) is: 
##EQU14## 
Eq. (27) selects the estimate corresponding to the reference samples with 
the greater received signal energy. As before, phase logic circuit 86 sets 
frequency correction to the smoothed frequency offset of Eq. (25) 
In a fifth and preferred embodiment, phase logic circuit 86 selects the 
frequency offset estimate that is closer to smoothed frequency offset. 
That is, 
##EQU15## 
In this case, the past history, contained in .DELTA..phi..sub.s, is used to 
select the estimate that is consistent with the past. The new frequency 
offset is used to produce a new smoothed frequency offset via equation 
(25). 
All of these techniques have been tested in conjunction with a Viterbi 
equalizer decoder using a two-tap channel model, L=2, for the U.S. digital 
cellular system. In this system, N.sub.p =14, so N.sub.1 =8 was selected 
in Eq. (24) for smoothing .omega.(n). The preferred technique is the 
approach expressed in equation (28). In tests with the Viterbi equalizer, 
this technique successfully removed the effect of the frequency offset so 
that performance was nearly identical to the case with no frequency 
offset. 
Extensions to the Method 
Sample timing selection is performed based upon reference symbols s(n) from 
preamble 166 of a TDMA slot as shown in FIG. 2. For U.S. digital cellular 
systems, additional information may be obtained from other portions of the 
TDMA slot such as the CDVCC 176 and the preamble 181 of the adjoining slot 
(slot 3 in this example), assuming continuous transmission from the base 
station to the mobile receiver. This can be used to improve the sample 
timing selection. Furthermore, different sample timing may be used for 
decoding different segments of the TDMA slot. For example, the second half 
of the slot can use the sample timing obtained from a subsequent adjoining 
preamble. The performance of the receiver should be improved by these 
techniques. 
While only certain preferred features of the invention have been 
illustrated and described herein, many modifications and changes will 
occur to those skilled in the art. It is, therefore, to be understood that 
the appended claims are intended to cover all such modifications and 
changes as fall within the true spirit of the invention.