Conventional DPSK systems are adversely affected by transmitter/receiver frequency offsets due to frequency reference errors and Doppler shifts. Two DPSK modem concepts are presented which avoid the long frequency acquisition process of conventional DPSK. One technique involves a modified demodulator for conventional DPSK signals, while the other involves making minor changes to both the modulator and demodulator. Simulation results are provided showing performance relative to conventional DPSK

Dutta, S.

Nicholas, D. C.

English

NASA Technical Reports Server

N9 2- 24 1'7 5
Frequency-Offset Insensitive Digital
Modem Techniques
S. Dutta and D. C. Nicholas
Mobile Communication Satellite System
Rockwell International Corporation
400 Collins Road, NE
Cedar Rapids, Iowa 52498
ABSTRACT
Conventional DPSK systems are
adversely affected by transmitter/receiver
frequency offsets due to frequency reference
errors and Doppler shifts. We present two
DPSK modem concepts which avoid the
long frequency acquisition process of con-
ventional DPSK. One technique involves a
modified demodulator for conventional
DPSK signals, while the other involves
making minor modifications to both the
modulator and demodulator. Simulation
results are provided showing performances
relative to conventional DPSK.
INTRODUCTION
The desire for small low-gain antennas in
mobile satellite systems results in power
budgets permitting only relatively low data
rates (e.g. 600 bps). Low data rates at the
high cartier frequencies of satellite systems
(e.g. 1.5 GHz) make DPSK demodulators
very susceptible to frequency errors, which
may be a significant fraction of the data rate.
While in many applications the carrier can
be frequency located and tracked with a
phase-locked loop, for some applications,
such as burst demodulation, the lock-on
time is excessive.
We review first the "gold standard" - fully
coherent demodulation. We then discuss
conventional differential demodulation,
which is often preferred because of the diffi-
culty of establishing a sufficiently "clean"
local phase reference with noisy input sig-
nals. For differential detection, we point out
the important distinction between predetec-
tion and postdetection matched filtering
(MF). It is shown that while predetection
MF is required for optimum performance,
postdetection MF can ease the frequency
acquisition problem.
Two new modem techniques, both
derived from DPSK, are suggested. The first
utilizes conventional differential modula-
tion and a new split delay line (SDL) tech-
nique to recover the signal, independent of
carrier offset. The second (DDPSK) utilizes
double differential modulation and then
recovers data with a double differential
demodulator using either pre- or postdetec-
tion MF.
These techniques are examined for the
case of binary phase shift keying (BPSK)
using a square symbol shape. This case is
important in satellite applications, which
tend to be power limited rather than
bandwidth limited.
Conventional Binary Modem Techniques
Phase shift keyed (PSK) modulation and
coherent demodulation constitute the most
power efficient data transmission technique.
In BPSK modulation, the transmitted car-
tier is shifted in phase by 0 or 7r radians,
depending on the transmitted data. Demod-
ulation is accomplished at the receiver by
multiplication with a regenerated, phase-
International Mobile Satellite Conference, Ottawa, 1990
633
https://ntrs.nasa.gov/search.jsp?R=19920014932 2020-03-17T12:27:56+00:00Z
locked carrier followed by baseband MF.
For square modulation, the MF is an inte-
grate and dump device. Figure 1 shows a
block diagram of a BPSK demodulator.
BPF
-I Oeclslon
Integrate i Device
& Dump I
Matched Filter For
Square Modulation I
L Envel°pe I
Data
Out
Fig. 1. Coherent BPSK demodulator
The bit error rate (BER) for BPSK in
additive white gaussian noise (AWGN),
using ideal coherent detection, is given by
BERBPsK = 0.5erfc(Eb/No) (1)
Coherent demodulation requires three
levels of parameter acquisition -- carrier
frequency, carrier phase and data clock.
DPSK modems require only carrier fre-
quency and data clock acquisition.
In DPSK modulation, the reference phase
for any transmitted symbol is the previous
symbol. Demodulation may be accom-
plished by differential detection, which is
correlation detection using the previous
symbol as the reference. A choice exists in
DPSK of performing MF before or after dif-
ferential detection. Predetection MF is
superior because detection is a nonlinear
process. As a result filtering after detection
always yields greater noise power than filter-
ing before detection. Figure 2 shows the
block diagram of optimum DPSK, using
predetection MF. Postdetection MF would
involve moving the integrate and dump
device to immediately after the detector. In
the latter case, the noise bandwidth at the
detector input would be established by the
IF filter.
Matched Decls_on
Filter (Sq Mad ) DevK:e
Real I ÷ O eomp4ex
Complex_e_exd Sample
* = Complex Conlugate
Fig. 2. Optimum DPSK demodulator
(predetection MF)
The bit error rate (BER) for optimum
DPSK is given by:
BERDPsK = 0.5exp(-Eb/No) (2)
The analytical expression for the BER of
DPSK using postdetection MF has not been
derived and does not appear to be available
in the open literature. However, simulation
results showing the degradation incurred by
postdetection MF are presented in Figures
5, 7 for a IF-bandwidth/data-rate ratio of 8.
As mentioned above, DPSK does require
carrier frequency acquisition. In land
mobile applications, the Doppler shift due
to vehicle motion can be of the order of 100
Hz, while typical data rates are 600-1200
bps. Thus, even without transmitter/
receiver frequency drift, Doppler shift can
be a significant source of frequency error.
Both pre- and postdetection MF DPSK
suffer performance degradations due to fre-
quency offset. However, the susceptibilities
are different. In the case of postdetection
MF, with a relatively wide IF bandwidth,
the error will only be due to the carrier
phase error, _o_.r, where Aw: frequency off-
set in radians and _-:symbol period. On the
contrary, predetection MF suffers both due
to the carrier phase error as well as a reduc-
tion in the MF's peak output amplitude.
The latter is referred to as correlation loss
and has a sin (Aw._-/2)/(Aw.r/2) dependence
on Aw. = It is clear that, for frequency offsets
less than 25% of the data rate, the correla-
tion loss is a much weaker function of Aw
than the carrier phase error. Therefore, the
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degradations of pre- and postdetection MF
DPSK are similar for small frequency off-
sets, but predetection MF suffers greater
degradation for large offsets.
NEW MODEM PROPOSALS
Basic Concept
We now present two modifications of
conventional DPSK that considerably
reduce the sensitivity to frequency offsets.
Both techniques use a common overall
demodulation philosophy - double differen-
tial detection - although they were devel-
oped independently. The basic concept of
double differential detection is that a time-
invariant carrier phase error, as defined
above, may be cancelled by two cascaded
differential detections involving three equi-
distant points in time. One application of
the above concept is termed the Split Delay
Line (SDL) demodulator, and applies
double differential detection to a conven-
tional DPSK waveform; hence it can be
retrofitted to existing DPSK transmission
systems. The other technique, Double Dif-
ferential Phase Shift Keying (DDPSK),
involves modifications to both the modula-
tor and the demodulator of conventional
DPSK. The advantage of DDPSK over SDL
is greater power efficiency, although both
techniques are less efficient than DPSK in
the absence of frequency offsets. Both SDL
and DDPSK can be used with pre- and
postdetection MF. The details of the two
techniques are given below.
Split Delay Line Demodulation
The following discussion of postdetection
MF DPSK and SDL DPSK utilizes the arc
tangent and manipulates only the angle.
Both approaches are shown in Figure 3.
The input signal is:
z(t) = x(t) + jy(t), where
x(t) = cos(,_t+ _(t));
y(t) = sin(wt + ¢(t));
4_(t) = 0, 7r ; and
r = the bit period.
Delay Delay
..___.'°_%%_....
From Bit Sync
Tracker
Fig. 3. DPSK and split delay line
demodulator (postdetection
MF)
In DPSK, we extract the angle using the
arc tangent function and, using a single
delay line of length r, form the difference:
Dt + _(t)] - D(t - r) + e(t - r)]
= _(t) - e(t - _) + _
We then require that the original modula-
tor choose wr = 2_rn, where n is an integer.
Then
cos D(t) - ,(t - T) + _T]= +1,
which is the desired signal. However, as wr
approaches 90 degrees, the useful output is
reduced to zero.
In satellite systems we do not have suffi-
cient control of w, as received with Doppler
shift and tuning errors, to guarantee that wr
will be close to 2_-n. This results in a carrier
phase error, which is overcome in the SDL
approach as shown in Figure 3, which
instead forms:
D(t) = cos[wt+_(t)
- 2[w(t-r/2) + 4,(t-r/2)]
+ _(t-_) + _(t-_)]
= cos [4_(t) - 24_(t-r/2) + 4_(t-r)]
= ±1, the desired signal.
(3)
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635
To show the last step,we observethat the
argument of the cosine is [4_(t)- 4_(t-r)] dur-
ing the first half of the symbol and -[4_(t) -
4_(t-r)] over latter half. Since the cosine is
the same in both cases, we obtain the
desired signal.
For both DPSK and SDL, the cosine out-
put is passed through an integrate and dump
MF (for square envelope) that performs
integration over the full symbol. Adequate
symbol synchronization is assumed. The
output of the MF is sampled for bit deci-
sions at the end of the integration period.
Table 1. BPSK, DPSK and DDPSK
modulation/demodulation
Predetection MF for SDL is similar to
that for DPSK (c.f. Figure 2) with the excep-
tion that four half-symbol predetection inte-
grations (#1, 2, 3 and 4) are performed over
two adjacent symbols. Then, SDL process-
ing (equation (3)) is perlbrmed using MF
outputs (#1, 2, 3) or (#2, 3, 4). Approxi-
mately 1-dB of additional performance
improvment may be realized by equal-gain
combining the two SDL outputs; this was
implemented in the simulation model for
predetection MF SDL.
The SDL receive processing expressed by
equation (3) is equivalent to two cascaded
levels of differential detection involving sig-
nals A(t), B(t) and C(t) in Figure 3. The first
involves A(t),B(t) and B(t),C(t) , while
the second differential detection involves
the outputs of the first.
Double Differential Phase Shift Keying
In DDPSK, the data is encoded not on the
first difference of the phase between two
adjacent symbols (as in DPSK), but on the
second difference of the phase involving
three adjacent symbols. This concept is
illustrated in Table 1. It is noteworthy that
the rows for BPSK, DPSK 1st Difference,
and DDPSK 2nd Difference contain identi-
cal entries. This implies identical data out-
puts from the respective demodulators.
Figure 4 shows a block diagram of the
DDPSK demodulator using postdetection
MF. Note that the MF follows the first dif-
ferential detector. The input to the second
differential detector is a complex sample at
the symbol rate. Hence, the additional com-
putation load over DPSK demodulation is
minimal.
Complex
BaseOand
r_elVed signal
x(t) + ly(t)
DeC_slon
Integrator Real Dev,ce
Complex }=art
Sample
__ Demod
v Data
From Bit Sync
Tracker
* = Complex Conjugate
Fig. 4. Double differential PSK (DDPSK)
demodulator (postdetection MF)
To implement the predetection MF ver-
sion of DDPSK demodulation, one simply
moves the integrate and dump device to a
position prior to the first differential detec-
tor. The input to the first differential detec-
tor is then a complex sample at the symbol
rate. Although accurate frequency acquisi-
tion is not required in DDPSK, symbol syn-
chronization is required, as in any other
data modem. DDPSK symbol synchroniza-
tion is no more difficult than that of DPSK.
Hence, similar techniques may be used.
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International Mobile Satellite Conference, Ottawa, 1990
MONTE CARLO SIMULATIONS
Monte Carlo, discrete time simulations
were performed to examine the BER per-
formances of the SDL and DDPSK modems
relative to conventional DPSK. Results
were obtained with both pre- and postdetec-
tion MF, and both with and without fre-
quency offset.
Results
The results are shown in Figures 5-8. The
following abbreviations are used for the dif-
ferent modem curves:
A: Theoretical coherent BPSK (no fre-
quency offset).
B: Theoretical DPSK (no frequency
offset).
C: Simulated DPSK (frequency offset
as specified)
D: DDPSK (frequency offset as speci-
fied)
E: SDL (frequency offset as specified)
The curves A and B are shown in each
figure for reference.
In Figure 5, the simulation results for
DPSK are very close to the theoretical val-
ues, which provides a measure of assurance
for the validity of the simulation model.
Using BER=10 -3 as the reference, we note
that, in the absence of frequency offset,
DDPSK is approximately 3.5 dB and SDL 6
dB worse than DPSK. Figure 6 shows that,
in the presence of 100-Hz frequency offset
(which is 20% of the data rate) the perform-
ance of DPSK suffers extreme degradation,
whereas the degradations are 0.5 dB for
DDPSK and immeasureably small (at these
Eb/N 0 values) for SDL. At BER=10 -3, the
power efficiency of DPSK equals that of
DDPSK at a frequency offset of approxi-
mately 57 Hz, while it is equal to that of
SDL at 72-Hz offset.
The predetection MF results may be
explained as follows. For DPSK, the major
source of degradation at 20% of the data rate
is the carrier phase error, while the contribu-
tion of correlation loss is relatively quite
small. The SDL and DDPSK modems suf-
fer a small degradation because they are
insensitive to the carrier phase error but, for
the given offset value, are mildly sensitive
to the correlation loss.
The major observations from the results
for postdetection MF (Figures 7, 8) are as
follows. In the absence of frequency offset,
the degradation due to postdetection MF
(relative to predetection MF) is 2.2 dB for
DPSK, 0.7 dB for DDPSK and 2 dB for
SDL. The 100-Hz frequency offset produces
severe degradation in the case of DPSK.
However, there is no degradation for
DDPSK and SDL. The absolute frequency
insensitivity of SDL and DDPSK in the
postdetection MF case is due to the absence
of prefiltering of the input signals (in the
simulation), resulting in zero correlation
loss. In practice, some prefiltering will
always exist due to the bandpass IF stage,
which is necessary to limit the noise power.
It should be noted that the quantitative
results presented here for postdetection
integration are valid only for the specific
ratio of the input noise bandwidth (4 kHz)
to the noise bandwidth of the postdetection
integrator (500 Hz). A greater ratio between
the two will yield greater degradation of
postdetection MF relative to predetection
MF.
CONCLUSIONS
Two new modem proposals are presented
in this paper -- DDPSK and SDL. Both are
derivatives of binary DPSK but do not
share its performance sensitivity to fre-
quency offsets. Both techniques are less
power efficient than DPSK in the absence of
frequency offsets. However, in the presence
of frequency offsets greater than 12% of the
data rate, DPSK is worse than DDPSK,
while at 15% offset, the efficiency falls below
that of SDL.
international Mobile Satettfle Conference, Ottawa, _990
637
Both DDPSK and SDL can be used with
either pre- or postdetection MF. DDPSK is
fairly insensitive to the type of MF. This
means that DDPSK can be operated with a
wide IF bandwidth (e.g. 4-kHz for a 500-
baud data signal), with no post-IF frequency
acquisition. SDL offers similar frequency
insensitivity to DDPSK but is less power
efficient.
REFERENCES
Q Henry, J. C. IIl. Dec. 1970. DPSK
Versus FSK with Frequency Uncer-
tainty. IEEE Trans. Comm. Systems,
pp. 814-816.
BER
1.0
10_1 7"-"_,..
1o-_:"--_"__
- :\ -\-410 .3 "_ C
-5
104. 06.0 8.0 10.012.014.016.0
Eb/No (dB)
Fig. 5. Predetection matched filtering
(no frequency offset)
BER
1.0
10-1
lo-_""-"__
- \
10 -3 ,,.
% "\
10_4 \
\\ \
10 .5
4.0 6.0
E
_'_D _
,B'_'\
8.0 10.012.014.016.0
EJNo (dB)
Fig. 7. Postdetection matched filtering
(no frequency offset)
BER
1.0
10 -1 ____,----..-.,......,_ _C
10.3 -., -,.,,
, ,, -,_
10-4 ", ",,
A'","' B
\
-5
104.0 6.0 8.0 10.012.014.016.0
EJNo (dB)
Fig. 6. Predetection matched filtering
(100-Hz frequency offset)
BER
1.0 ,_,__.._ C
10-1 _ _.-.-....._
lO-2--. "_ _
"- "_ ,D
10 .3 "" ""
10 -4 \,"',
A\,", B
10-4.05 6.0 8.010.012.014.016.0
EJNo (dB)
Fig. 8. Postdetection matched filtering
(100-Hz frequency offset)
638
International Mobile Satellite Conference, Ottawa, 1990


Frequency-offset insensitive digital modem techniques

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