Method and apparatus for obtaining initial carrier and symbol phase estimates for use in synchronizing transmitting data

A method and apparatus for determining initial carrier and symbol phase estimates in a burst mode digital communication system are described. In-phase and quadrature sample of a BPSK preamble are sampled to obtain correlation values. Next, sum and differences of the correlation values are obtained. Then the initial carrier phase estimate (THETAHAT) and the initial symbol phase estimate (TAUHAT) are obtained through application of an algorithm. The apparatus that implements the method consists of adders, inverters, arc tangent look-up tables and divide by 2 logic units.

BACKGROUND OF THE INVENTION 
1. Field of Invention 
This invention relates to burst mode digital communication systems where 
data transmission is preceded by an alternating binary phase shift keying 
(BPSK) preamble for rapid acquisition of carrier and symbol 
synchronization. The preamble is sampled and the set of samples obtained 
are processed to provide carrier and symbol phase estimates. 
2. Description of Related Art 
One of the techniques used in burst mode digital communication systems is 
time division multiple access (TDMA). This technique allows multiple users 
to share a single communication channel. Each user is assigned a time slot 
in which to transmit data. The time slot is measured from a frame marker 
which repeats at a fixed period. The time slot can be variable in length 
and can be preassigned or assigned as needed on demand. 
To control and configure a TDMA system, a time interval called a is frame 
is defined. A frame is divided into time slots, and a burst consists of an 
integer number of slots. Bursts typically consist of a preamble, a unique 
word and random symbol data (message portion). 
A receiver uses the preamble to synchronize its processor with the time and 
frequency of the signal it is receiving. A preamble consists of a signal 
interval for carrier and symbol-timing recovery and a unique word for 
burst synchronization and other symbols. 
In order to establish communications, carrier and symbol synchronization 
must take place. A digitally implemented BPSK demodulator, a portion of 
which is shown in FIG. 1, performs these functions. The basic functions of 
the different elements are as follows. 
A sampling interpolator unit 1 calculates output sample components, X and 
Y, twice per symbol at the instants defined by the timing reference from 
the symbol synchronizer. In some implementations, the interpolator is 
removed and the analog-to-digital converter sampling times are defined by 
the timing reference. 
A coherent demodulator unit 3 provides soft decision sample values to a 
decoder that follows. 
A system timing unit 5 controls the timing of the carrier and symbol 
acquisition and synchronization functions. 
A carrier and symbol acquisition unit 2 generates initial carrier and phase 
estimates that are input into a carrier synchronizer unit 4 and symbol 
synchronizer unit 6, respectively. 
A carrier synchronization unit 4 generates a reference carrier with a phase 
closely matching that of the data signal. It provides the estimates of 
carrier frequency and phase which are necessary for coherent demodulation. 
A symbol synchronizer unit 6 provides the timing reference required for 
sampling at the correct intervals so that bit decisions can be made on the 
data symbols. Further information on burst demodulators is contained in an 
article by S. A. Rhodes and S. I. Sayegh entitled, "Digital On-board 
Demodulator for Reception of an Up-link Group of TDMA/QPSK Channels," 
Proceedings of ICDSC8, Guadalupe, F.W.I., April 1989, which is 
incorporated herein by reference. 
The present invention is related to the carrier and symbol acquisition 
functions. 
TDMA system timing prior to signal acquisition is assumed to be available 
with an accuracy of a few symbol intervals. This timing is used to gate 
the acquisition and tracking modes for carrier and symbol synchronization. 
Complex time domain samples, Z=X+jY, are used to represent the quadrature 
components of a received signal, after demodulation, with a carrier 
reference of approximately the correct frequency, but an arbitrary phase 
angle. Quadrature samples of the desired channel are input to a sample 
interpolator at a rate of approximately three complex samples per symbol. 
Another input to the sample interpolator feeds back the estimated symbol 
timing from the symbol synchronizer. 
In-phase and quadrature samples of the BPSK preamble are sampled at the 
rate of N.sub.S complex (in-phase and quadrature) samples per symbol, 
where N.sub.S is typically (but not necessarily) equal to 2 samples per 
symbol. 
Denoting the carrier phase by .theta..sub.R, and the clock phase by 
T.sub.R, and noting that the received filtered alternating preamble is 
sinusoidal, the following expressions may be written: 
EQU X.sub.n =cos(.theta..sub.R)*cos(.pi.R.sub.s nT+T.sub.R) 
EQU Y.sub.n =sin(.theta.R)*cos(.pi.R.sub.s nT+T.sub.R) 
where X.sub.n is the in-phase sample, Y.sub.n is the quadrature sample, 
R.sub.s is the symbol rate, and T the sampling interval. 
These samples are correlated with samples from a sine and a cosine waveform 
that have the same period as the alternating BPSK preamble, namely with 
sin(.pi.R.sub.s nT) and cos(.pi.R.sub.s nT). 
Correlating the in-phase received samples with a sine and a cosine waveform 
produce odd and even in-phase sample correlations X.sub.o (odd) and 
X.sub.E (even), respectively, as shown below. Similarly, correlating the 
quadrature received samples with a sine and a cosine waveform produce odd 
and even quadrature sample correlations Y.sub.O (odd) and Y.sub.E (even), 
respectively, as shown below: 
EQU X.sub.o =-cos(.theta..sub.R)*sin(T.sub.R) 
EQU X.sub.E =cos(.theta..sub.R)*cos(T.sub.R) 
EQU Y.sub.o =-sin(.theta..sub.R)*sin(T.sub.R) 
EQU Y.sub.E =sin(.theta..sub.R)*cos(T.sub.R) 
These correlations result in four correlations values X.sub.O, X.sub.E, 
Y.sub.O, and Y.sub.E. In the absence of a significant frequency offset, 
these four values are sufficient to derive the desired initial carrier and 
symbol phase estimates. 
Two algorithms are readily available for processing the preamble samples. 
However, the first algorithm is overly sensitive to any amplitude slope 
that may be present over a non-equalized communication channel. The second 
algorithm is not sensitive to amplitude slope, however, it requires more 
hardware than the present invention to implement. 
The purpose of the invention is to provide a method and apparatus for 
obtaining initial carrier and symbol phase estimates that can be easily 
implemented with a minimal amount of hardware. This is accomplished by 
deriving the maximum likelihood algorithms and mapping them into an easily 
implementable set of equations. The actual hardware implementation is 
described in the detailed description section. 
All of algorithms discussed here (the existing two and the subject of the 
invention) use the four correlation values X.sub.O, X.sub.E, Y.sub.O, and 
Y.sub.E to derive the desired initial carrier and symbol phase estimates. 
The differences among the three algorithms lie in how the four values are 
processed. 
Once obtained, these initial carrier and clock phase estimates initialize 
the synchronizers at the end of the preamble. These initialization values 
represent memory inherent in the accumulators for the phase-locked loops 
that are used in the tracking mode of synchronization. 
In existing algorithm 1, the initial carrier phase estimate (THETAHAT) and 
initial symbol phase estimate (TAUHAT) are obtained as follows: 
##EQU1## 
The main problem with this algorithm is that in the presence of an 
amplitude slope over the communications channel, the estimates obtained by 
the algorithm may be grossly inaccurate. FIG. 2 illustrates this fact by 
showing how the estimated value of the angle (THETAHAT or TAUHAT) is 
significantly different from the actual value (.theta..sub.R or T.sub.R), 
if an amplitude slope of a few dBs is present on the link. 
In existing algorithm 2, the initial carrier and symbol phase estimates are 
obtained by the following expressions: 
EQU ANUM=2((X.sub.o *Y.sub.o)+(X.sub.E *Y.sub.E)) 
EQU ADEN=(X.sub.E *X.sub.E)-(Y.sub.E *Y.sub.E)+(X.sub.O *X.sub.O)-(Y.sub.o 
*Y.sub.O) 
EQU THETAHAT=0.5arctan(ANUM/ADEN) 
EQU BNUM=-2((X.sub.O *X.sub.E)+(Y.sub.o *Y.sub.E)) 
EQU BDEN=(X.sub.E *X.sub.E)+(Y.sub.E *Y.sub.E)-(*X.sub.O *X.sub.O)-(Y.sub.O 
*Y.sub.O) 
EQU TAUHAT=0.5arctan(BNUM/BDEN) 
Implementation of this algorithm results in more accurate estimates, 
however, it requires more hardware than algorithm 1, making it 
unattractive for applications requiring a compact implementation. 
SUMMARY OF THE INVENTION 
The method of the present invention develops initial carrier and symbol 
phase estimates by first obtaining the sum and differences of the 
correlation values. Then the initial carrier phase estimate (THETAHAT) and 
the initial symbol phase estimate (TAUHAT) are obtained, as shown below. 
EQU ANUM=Y.sub.E -X.sub.O 
EQU ADEN=X.sub.E +Y.sub.O 
EQU SUMANG=arctan(ANUM/ADEN) 
EQU BNUM=Y.sub.E +X.sub.O 
EQU BDEN=X.sub.E -Y.sub.O 
EQU DIFANG=arctan(BNUM/BDEN) 
EQU THETAHAT=0.5(SUMANG+DIFANG) 
EQU TAUHAT=0.5(SUMANG-DIFANG) 
The apparatus of the present invention consists of adders, inverters, arc 
tangent look-up tables and divide by 2 logic units.

DETAILED DESCRIPTION OF THE INVENTION 
The present invention combines the accuracy and robustness of algorithm 2, 
with the simple implementation of algorithm 1. This is done by using a 
method that obtains sum and difference values of the correlation values 
and then determining the initial carrier and symbol phase estimates. Refer 
to FIG. 3. 
The first step involves sampling in-phase and quadrature samples of a BPSK 
preamble at a rate of N.sub.S samples per symbol, wherein N.sub.X is an 
integer greater than 1 (step 100). Next, odd and even sets of correlation 
values X.sub.O, X.sub.E, Y.sub.O and Y.sub.E are obtained (step 110). 
After that, a sum of a carrier and symbol phase estimate are determined 
(step 120), wherein: 
EQU ANUM=Y.sub.E -X.sub.O 
EQU ADEN=X.sub.E +Y.sub.O 
EQU SUMANG=arctan(ANUM/ADEN) 
After the summed value has been obtained, a difference value of a carrier 
and symbol phase estimate is obtained (step 130), wherein 
EQU BNUM=Y.sub.E +X.sub.O 
EQU BDEN=X.sub.E -Y.sub.O 
EQU DIFANG=arctan(BNUM/BDEN) 
The initial carrier phase error estimate THETAHAT is then determined as 
follows (step 140): 
##EQU2## 
The initial symbol phase error estimate TAUHAT is then determined as 
follows (step 150): 
##EQU3## 
Next, an apparatus that implements the carrier and symbol acquisition unit 
will be described with reference to FIG. 4. The apparatus consists of 
adders 9-12 and 16-17, inverters 7, 8 and 15, arc tangent look-up tables 
13 and 14 and divide by 2 logic units 18 and 19. 
The first step in obtaining the initial phase estimates is to generate sum 
and difference values. The sum value is obtained by inputing correlation 
values X.sub.O, X.sub.E, Y.sub.O, and Y.sub.E into adders 9 and 10 and 
inverter 7 as shown in FIG. 4. Arc tangent look-up table 13 then receives 
the outputs from adders 9 and 10, ANUM and ADEN, respectively, and outputs 
the sum value. 
Next, the difference value is obtained by inputing correlation values 
X.sub.O, X.sub.E, Y.sub.O, and Y.sub.E into adders 11 and 12 and inverter 
8 as shown in FIG. 4. Arc tangent look-up table 14 then receives the 
outputs from adders 11 and 12, BNUM and BDEN, respectively, and outputs 
the difference value. Note that the order in which the sum and difference 
values are obtained is not important to the invention. 
The initial carrier phase estimate is obtained by inputing the sum and 
difference values into adder 16 and dividing the output of adder 16 by 2 
in divide by 2 unit 18. 
The initial symbol phase estimate is obtained by inputing the sum and 
difference values into adder 17 and inverter 15 as shown in FIG. 4 and 
dividing the output of adder 17 by 2 in divide by 2 unit 19. 
While the above is a description of the invention in its preferred 
embodiment, various modifications and equivalents may be employed. 
Therefore, the above description and illustration should not be taken as 
limiting the scope of the invention which is defined by the claims.