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ABSTRACT: Spread-spectrum techniques such as frequency hopping (FH) have been used to reduce the vulnerability of satellite communications to jamming. In such a system, error correcting (EC) codes play an essential role. Thus a knowledge of the performance of various EC codes is necessary in order to choose an EC code and related system parameters in the design of an anti-jam system, this paper examines the performance of various types of error correcting codes under worst case partial band noise jamming and worst case multitone jamming using fast frequency-hopped, non-coherent M-ary frequency-shift keying (NCMFSK) with optimum diversity. A comprehensive study including convolutional codes, binary and non-binary block codes and concatenated codes has been conducted. This paper presents bit error rate (BER) performances of various error correcting codes. New candidate codes with superior anti-jam performance are identified.
International Journal of Satellite Communications 12/2006; 7(3):115 - 128.
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ABSTRACT: In this paper, the error performance of on-off frequency-shift keying (OOFSK) over fading channels is analyzed. A closed-form expression for the probability of error is obtained as a function of the instantaneous signal-to-noise ratio (SNR) when OOFSK signals are received over a coherent Rician fading channel. It is shown in simulation results that error performance improves especially at low SNR values as the duty cycle decreases. The error performance is also studied when the channel is assumed to be unknown at both the transmitter and receiver. For this case, the optimum detection rule is identified and analytical expressions for the probability of error are obtained. Similarly, it is concluded that probability of error decreases if one operates with lower duty cycle.
Information Sciences and Systems, 2006 40th Annual Conference on; 04/2006
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ABSTRACT: Maximum-likelihood diversity combining is investigated for an
FFH/MFSK spread spectrum system in partial-band noise (PBN). The
structure of maximum-likelihood diversity reception in PBN plus white
Gaussian noise is derived. It is shown that signal-to-noise ratio and
the noise variance at each hop have to be known to implement this
optimum diversity combiner. Several suboptimum diversity combining
schemes are also considered. The performance of the optimum combining
scheme is evaluated. It is shown that adaptive gain control diversity
combining actually achieves the optimum performance when interference is
not very weak
IEEE Transactions on Communications 01/1999; · 1.68 Impact Factor
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ABSTRACT: We derive a closed-form expression for the power spectral density
of amplitude/phase-shift keyed bit sequences randomized through
self-synchronizing scrambling when the source sequence is a stationary
sequence of statistically independent bits. In addition to the
dependence on the symbol pulse shape, duration, and the signal space
values with which symbols are represented, we show that the power
spectral density is dependent only on the probability of logic ones in
the source bit stream, the period of the impulse response of the
scrambling shift register, and the number of logic ones in this period.
Our results confirm that optimum randomization results with use of
primitive scrambling polynomials and poorest randomization occurs with
“two-tap” polynomials of the form x<sup>D</sup>+1
IEEE Transactions on Information Theory 08/1998; · 3.01 Impact Factor
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ABSTRACT: The authors develop a practical method of evaluating the power
spectral density of guided scrambling line-coded sequences. Analysis of
block-coded signals is reviewed, and it is shown that it is impractical
to analyse continuous guided scrambling coded sequences with expressions
presented elsewhere in the literature. Alternative expressions for
sequence autocorrelation are derived which depend on the relationship of
several code parameters. Two relationships are considered in detail, and
it is shown how expressions derived in these instances can be applied to
other guided scrambling codes. Using these expressions, the spectral
characteristics of several continuous guided scrambling codes are
evaluated. These spectra demonstrate the important result that variation
in the average statistics of the coded sequences with varying
source-stream statistics decreases as the degree of the scrambling
polynomial increases
IEE Proceedings - Communications 05/1997; · 0.32 Impact Factor
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ABSTRACT: We derive several properties of guided scrambling (GS) encoders
and the sequences they generate. We first highlight symmetrical aspects
of the GS encoding mechanisms proposed to date, and then show that the
existence of discrete components in the power spectrum of the
pulse-amplitude-modulated encoded sequence can be predicted from the
weight of the scrambling polynomial. We also show that with equiprobable
source words, the block or continuous nature of the code has no effect
on the statistics of the encoded sequence. We conclude by demonstrating
how these properties simplify evaluation of the spectral characteristics
of GS coded sequences
IEEE Transactions on Information Theory 02/1997; · 3.01 Impact Factor
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ABSTRACT: Guided scrambling (GS) is a line coding technique developed
specifically for high bit rate fiber optic transmission systems. This
paper continues the development of GS coding by introducing more
scrambling polynomials that can be used with this technique. First, a
method is presented for constructing polynomials which can be used with
balanced encoding. Then it is shown that these polynomials can be used
as bases for large families of polynomials, an expansion whose
usefulness is demonstrated with the presentation of power spectra for
several code configurations. These results indicate that polynomials can
be selected from these families to exercise control over average as well
as worst-case statistics of the encoded bit stream, a property not
available with any other single efficient, balanced line coding
technique developed to date. Criteria for polynomial selection are
given, and polynomials are recommended for several GS code
configurations
IEEE Journal on Selected Areas in Communications 05/1995; · 3.41 Impact Factor
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ABSTRACT: Maximum-likelihood diversity combining for an FFH/MFSK spread
spectrum system on a partial-band noise (PBN) interference channel is
investigated. The structure of maximum-likelihood diversity reception on
a PBN channel with additive white Gaussian noise (AWGN) is derived. It
is shown that signal-to-noise ratio and the noise variance at each hop
have to be known to implement this optimum diversity combining. The
performance of the maximum-likelihood combining can be used as a
standard in judging the performance of other suboptimum, but more
practical diversity combining schemes. The performance of the optimum
combining scheme is evaluated. It is shown that the performance
difference between some of the known diversity combining schemes, which
do not require channel information to operate, and the optimum scheme is
not small when the diversity order is low
Military Communications Conference, 1993. MILCOM '93. Conference record. 'Communications on the Move'., IEEE; 11/1993
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ABSTRACT: Line codes are used in digital communication systems to control
the characteristics of transmitted symbol sequences. Recently, an
efficient and easily implemented family of codes called guided
scrambling (GS) codes has been introduced. Previous work indicated that
continuous GS (CGS) codes can be configured to generate encoded
sequences with statistics nearly independent from those of the source
bit stream, a property not available with any other efficient line code
technique developed to date. This paper presents analysis of the
spectral characteristics of these codes which confirms this conjecture.
The principle of guided scrambling is reviewed. Then, by showing that
the scrambling polynomials currently recommended for GS codes can be
regarded as base polynomials for large families of polynomials, expanded
sets of scrambling polynomials are proposed. Evaluation of the power
spectral density of CGS codes which use scrambling polynomials from
these expanded sets is then considered, under the condition only that
the input bit stream is stationary. Expressions which limit required
computation to practical limits are developed, and results for several
code configurations are given. Here it is demonstrated that when
scrambling polynomials of high degree are used, the characteristics of
the transmitted symbol sequence become nearly independent of the source
bit stream statistics
Electrical and Computer Engineering, 1993. Canadian Conference on; 10/1993
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ABSTRACT: The coded performance of a slow-frequency hopped differential PSK (SFH/DPSK) system in the presence of both tone jamming and additive white Gaussian noise (AWGN) is studied. The error correlation due to DPSK demodulation and the effect of tone jamming is considered when evaluating the block and decoded error probabilities. The decoded error probabilities in some special cases are computed. The effect of interleaving on system performance is addressed under various conditions. A nearly optimum code rate for a Reed-Solomon code is determined for systems employing interleaving techniques. The effect of partial-band tone jamming is demonstrated.< >
Communications, Speech and Vision, IEE Proceedings I 09/1993;
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ABSTRACT: An error-correction scheme for an M -ary symmetric channel
( M SC) characterized by a large error probability
p <sub>e</sub> is considered. The value of
p <sub>e</sub> can be near, but smaller than, 1-1/ M ,
for which the channel capacity is zero, such as may occur in a jamming
environment. The coding scheme consists of an outer convolutional code
and an inner repetition code of length m that is used for each
convolutional code symbol. At the receiving end, the m inner
code symbols are used to form a soft-decision metric, which is passed to
a soft-decision decoder for the convolutional code. The effect of finite
quantization and methods to generate binary metrics for M >2
are investigated. Monte Carlo simulation results are presented. For the
binary symmetric channel (BSC), it is shown that the overall code rate
is larger than 0.6 R <sub>0</sub>, where R <sub>0</sub>
is the cutoff rate of the channel. New union bounds on the bit error
probability for systems with a binary convolutional code on 4-ary and
8-ary orthogonal channels are presented. For a BSC and a large
m , a method is presented for BER approximation based on the
central limit theorem
IEEE Transactions on Communications 07/1993; · 1.68 Impact Factor
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ABSTRACT: In direct sequence (DS) spread-spectrum systems, correlation techniques are used to extract information from the received signal. The various correlation procedures used in established DS systems offer a tradeoff between acquisition time, correlator complexity, and system performance. The paper introduces a new spread-spectrum technique which employs an easily implemented spreading/despreading mechanism that despreads the received signal immediately upon its reception. The data signal is spread through modulo-2 division using shift register techniques and despread through multiplication using a delay-and-multiply circuit. Since the sequence transmitted is a quotient, the technique is called transmitted-quotient direct sequence (TQ-DS). Preliminary performance results indicate that the cost of zero-acquisition time and low complexity is a significant degradation in system bit error rate (BER) performance relative to that of established spread-spectrum systems
Wireless Communications, 1992. Conference Proceedings., 1992 IEEE International Conference on Selected Topics in; 07/1992
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ABSTRACT: A diversity combining scheme using the Viterbi ratio-threshold
technique is discussed. The performance of the ratio-threshold diversity
combiner in fast frequency hop spread spectrum systems with
M -ary frequency shift keying modulation (FFH/MFSK) in partial
band noise interference and background thermal noise is analyzed. Exact
bit error probabilities are computed by using an average computation
model. The relationship between the system performance and the system
parameters, such as the ratio-threshold, the diversity order, and the
thermal noise level, is illustrated. The performance of the combining
scheme under worst case interference is compared with that of soft
linear combining with perfect side information. One merit of this
combiner is that its output can be directly fed to a soft-decision
forward error correction decoder
Communications, 1992. ICC '92, Conference record, SUPERCOMM/ICC '92, Discovering a New World of Communications., IEEE International Conference on; 07/1992
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ABSTRACT: The performance of fast frequency hopped spread spectrum systems with
M-ary frequency shift keying and error correction coding under jamming
conditions are analyzed. Ratio threshold diversity combining is used.
The decoding scheme is error erasure decoding with metrics generated by
the diversity combiner. The bit error probability of the system is
computed and improvements offered by error correction coding are shown.
The performance of several error correction codes is compared under
different channel conditions. The notion of an arbitrarily varying
channel (AVC) is discussed, including capacities of AVC's and a discrete
memoryless channel, and two Gaussian AVC models are described. Coded
performance of a slow frequency hopped differential phase shift keying
(DPSK) system in presence of both additive white Gaussian noise and tone
jamming is studied. The error correlation due to DPSK demodulation and
the effect of tone jamming are considered in evaluating the block and
decoded error probabilities. The effect of interleaving on system
performance is addressed. A nearly optimum code rate for a length 255
Reed-Solomon code is derived for systems employing interleaving.
Finally, a parallel approach to the design of universal receivers for
unknown and time-varying channels is applied to DPSK systems in the
presence of noise and tone interference.
NASA STI/Recon Technical Report N. 03/1992; 94:24697.
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ABSTRACT: The authors consider frequency-hopped spread-spectrum
multiple-access communications using M -ary modulation and
error-correction coding. The major concerns are multiple-access
interference and the network capacity in terms of the number of users
that can transmit simultaneously for a given level of codeword error
probability. Block coding is studied in detail. The authors first
consider the use of Q -ary Reed-Solomon (RS) codes in
combination with M -ary modulation with mismatched alphabets so
that Q > M . It is shown that the network capacity is
drastically reduced in comparison with the system with matched
alphabets. As a remedy, the use of matched M -ary BCH codes is
proposed as an alternative to mismatched RS codes. It is shown that when
the number of users in the system is large, a BCH code outperforms an RS
code with a comparable code rate and decoding complexity. The authors
consider the use of a robust technique for generation of reliable side
information based on a radio-threshold test. They analyze its
performance in conjunction with MFSK and error-erasure correction
decoding. It is shown that this nonideal ratio-threshold method can
increase the network capacity in comparison with the system with perfect
side information
IEEE Journal on Selected Areas in Communications 03/1992; · 3.41 Impact Factor
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ABSTRACT: A nonlinear diversity combining scheme using the Viterbi
radio-threshold technique is discussed. The performances of the
radio-threshold diversity combiner in fast frequency-hop spread-spectrum
systems with M -ary frequency shift keying modulation (FFH/MFSK)
under band multitone jamming without and with additive white Gaussian
noise are analyzed. The exact bit error probabilities are computed by
using an average computation model. The performances under band
multitone jamming and under partial-band noise jamming are compared. For
binary FSK modulation, the performances under the two types of jamming
are almost the same, but for 8-ary FSK modulation, tone jamming is more
effective against communications. The structure of the combiner is very
simple. Another merit of this combiner is that its output can be
directly fed to a soft-decision FEC decoder
Military Communications Conference, 1991. MILCOM '91, Conference Record, 'Military Communications in a Changing World'., IEEE; 12/1991
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ABSTRACT: Results of a study into the performance of slow frequency hopping
M -ary differential phase shift keying (MDPSK) signaling in the
presence of both tone jamming and Gaussian noise are presented. Previous
work has been extended by considering larger signal sets and skewed
differential phases with unequal decision regions. Probability
distributions are used instead of calculating a set of probabilities
over symmetrical decision regions. This allows the optimization of the
decision regions in tone jamming from the equal regions used in Gaussian
noise environments. The error performance when a frequency offsets
exists between the jamming tone and MDPSK carrier is also considered
Military Communications Conference, 1991. MILCOM '91, Conference Record, 'Military Communications in a Changing World'., IEEE; 12/1991
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ABSTRACT: The performance of fast-frequency-hopped M -ary
frequency-shift keying with a fixed hop rate is evaluated, utilizing the
Chernoff union bound method. The performance criterion used is a
throughput measure i.e., an information rate sustained by a system for a
given bit error rate, normalized by the hop rate. Both uncoded and coded
systems are considered. It is shown using the cutoff rate argument that
coding can provide a few dB gain in throughput. This is confirmed by the
performance evaluation of various convolutional and block codes. Both
partial-band noise jamming and multitone jamming with one tone per M
-ary band are considered. Jamming parameters are assumed to be the
worst case against the coding channel. Determination of the optimum
M is also addressed
IEEE Transactions on Communications 11/1990; · 1.68 Impact Factor
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ABSTRACT: The probability distribution of the received DPSK (differential
phase-shift keying) signal under tone jamming is studied. The results
should facilitate the analysis of the SFH/DPSK (slow frequency-hopped
DPSK) system. The results given are more general than those previously
published, in several aspects. First, the differential phase of the
transmitted DPSK signal can assume any value. Second, probability
distributions are derived instead of a set of probabilities calculated
over certain symmetrical regions. This allows analyzing performance for
arbitrary selected decision regions as well as determining optimum
decision regions for demodulating the DPSK signal. Third, the joint
probability distribution of both the magnitude and differential phase of
the jammed DPSK signal is given. This can be used in the analysis where
both tone jamming and Gaussian noise are considered. These results are
used to analyze the error probability performance of a general uncoded
SFH/DPSK signal under worst-case tone jamming and Gaussian noise
IEEE Journal on Selected Areas in Communications 07/1990; · 3.41 Impact Factor
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ABSTRACT: The authors evaluate the throughput performance of FFH/MFSK (fast frequency hopping/ M -ary frequency-shift keying) with a fixed hop rate for both uncoded and coded systems. The performance criterion used is a throughput measure, that is information rate sustained by a system for a given bit-error rate normalized by the hop rate. It is shown that the performance can be greatly improved through the use of coding. As with a fixed data rate, multitone jamming is more effective for M >2, and partial-band-noise jamming for M =2. However, the optimum M is a monotonic increasing function of E <sub>h</sub>/ J <sub>O</sub>. This affects the choice of a code if it is related to M , such as a dual- K code. The best convolutional codes are the rate 1/2 Trumpis code, the semiorthogonal code for K =3, and the dual- K codes. The best block codes are the (255,221) RS code, the (255,207) BCH code, and the (63,53) RS code, in that order. As with a fixed data rate, the best convolutional codes perform better than the best block codes
Military Communications Conference, 1989. MILCOM '89. Conference Record. Bridging the Gap. Interoperability, Survivability, Security., 1989 IEEE; 11/1989
