Coding for Frequency-Hopped Spread-Spectrum Communication with Partial-Band Interference--Part I: Capacity and Cutoff Rate

The performance of optimal codes on frequency-hopped channels with partial-band interference is investigated. The performance measures considered are channel capacity and cutoff rate. Worst-case partial-band Gaussian noise interference is assumed with the interference independent of the transmitted signal. The capacity and cutoff rate are calculated as a function of the signal-to-noise ratio. We consider soft decision receivers and hard decision receivers with and without side information. Optimal code rates are found for each of the above cases. The required signal-to-noise ratio for reliable communication when codes are used is determined as a function of the code rate.     

Clipped diversity combining for channels with partial-bandinterference. II. Ratio-statistic combining

For pt.I see ibid., vol.COM-3, no.12, p.1320 (1987). Ratio-statistic combining is proposed for mitigating partial-band interference in systems with diversity transmission and frequency-hop signaling. Systems with noncoherent demodulation and binary orthogonal signaling are covered. The partial-band interference is Gaussian, and Gaussian quiescent noise is included in the analysis to account for wideband noise sources. The exact probability of error is found for a receiver using ratio-statistic combining, and this is compared to the exact error probabilities for receivers with optimum combining with perfect side information, clipped-linear combining, the ratio-threshold test with majority-logic decoding, and self-normalization diversity combining. Numerical results are also given for a frequency-hop system which uses ratio-statistic combining for channels with Rayleigh fading and partial-band interference. It is determined that ratio-statistic combining is an excellent diversity combining scheme for systems with partial-band interference and fading     

Clipped Diversity Combining for Channels with Partial-Band Interference--Part I: Clipped-Linear Combining

Clipped-linear diversity combining is analyzed for receivers without side information. Communication systems with noncoherent demodulation, binary andM-ary orthogonal signaling, and diversity transmission are considered. The main source of interference is additive Gaussian partial-band interference, but a nonzero quiescent noise level is also included in the analysis to account for wide-band noise sources. Some of the results apply to general (non-Gaussian) interference. The numerical results demonstrate that clipped-linear combining can perform well in terms of both narrow-band interference rejection capability and maximum signal-to-interference ratio requirement. A practical disadvantage of clipped-linear combining is that it relies on measurements of the signal output voltage.     

Bayesian methods for erasure insertion in frequency-hopcommunication systems with partial-band interference

The erasure of unreliable symbols improves the performance of most types of error-control coding if a good method is used to decide which symbols should be erased. Bayesian decision theory is employed to obtain such a method for use in frequency-hop communications with Reed-Solomon coding and errors-and-erasures decoding. The performance of frequency-hop communications with Bayesian erasure insertion is analyzed for channels with both partial-band and wideband Gaussian noise. The Bayesian technique is compared with Viterbi's ratio-threshold test, and these are compared to receivers that do not erase and use errors-only decoding. Comparisons are also made with receivers that erase all the symbols that are affected by the partial-band interference. When interference is strong, large coding gains result from the Bayesian method, and error probabilities are reduced by several orders of magnitude     

Erasure insertion in frequency-hop communications with fading andpartial-band interference

The use of block coding and errors-and-erasures decoding can enhance performance substantially in frequency-hop communication systems, provided that a good scheme is employed to determine which symbols to erase. In this paper, methods for determining erasures derived from Bayesian decision theory are applied to the mitigation of fading and partial-band interference. The performance of receivers using the Bayesian technique is compared with that of receivers that make erasure decisions using Viterbi's (1982) ratio-threshold test. The performance of hard-decision demodulation and the theoretical performance of receivers with access to perfect side information are also compared. It is found that the Bayesian receiver provides the best performance, and that error probabilities for the Bayesian receiver are lower than those for hard-decision demodulation by as much as six orders of magnitude     

Probability of Error Analyses of a BFSK Frequency-Hopping System with Diversity Under Partial-Band Jamming Interference--Part II: Performance of Square-Law Nonlinear Combining Soft Decision Receivers

In this paper, error probability analyses are performed for a binary frequency-shift-keying (BFSK) system employingLhop/bit frequency-hopping (FH) spread-spectrum waveforms transmitted over a partial-band Gaussian noise jamming channel. The performance results for two types of square-law nonlinear combining soft decision receivers under worst-case partial-band jamming are presented. The receivers employ, prior to combining, nonlinear weighting strategies of 1) adaptive gain control and 2) soft limiting (clipping) of the detector output of each channel of the dehopped waveform. Both thermal noise and jamming are included in the analyses. It is shown in the paper that a diversity gain for error rate improvement is realizable for nonlinear combining receivers provided that the noncoherent combining loss is less dominant than the jamming power reduction realized by the weighting strategy. Performance comparisons between linear and nonlinear combining receivers are presented.     

Performance of a fast frequency-hopped noncoherent MFSK receiverwith nonideal adaptive gain control

An error probability analysis is performed for an orthogonal noncoherent M-ary frequency-shift keying (MFSK) communication system employing fast frequency-hopped (FFH) spread spectrum with diversity. The signal is assumed to be transmitted through a frequency-nonselective slowly fading channel with partial-band noise interference. The partial-band interference is modeled as a Gaussian process. Both the information signal and the partial-band noise interference signal are assumed to be affected by channel fading; it is assumed that the two fading processes are independent and that channel fading need not necessarily affect the information signal and the interference signal in the same way. Each diversity reception is assumed to fade independently according to a Rician process. Adaptive gain control is employed to minimize partial-band interference effects, and the effect of inaccurate noise measurement on the ability of the adaptive gain control receiver to reject partial-band interference is examined. The effect of thermal noise is included in the analysis     

Performance of Reed-Solomon Coded Frequency-Hop Spread-Spectrum Communications in Partial-Band Interference

This paper is concerned with the performance of a Communications system which utilizes frequency-hop spread spectrum, diversity transmission, Reed-Solomon coding, and parallel error-correction and erasure-correction decoding. Both binary signaling andM-ary orthogonal signaling are considered. The goals are twofold. First, it is desirable to provide good performance in partial-band Gaussian noise interference by use of coding and diversity with an efficient error-correction algorithm. Second, it is necessary to totally neutralize narrow-band interference (regardless of the power level or statistical distribution of the interference) in order to have an effective spread-spectrum system. Through an analysis of the effects of partial-band interference on a frequency-hop spread-spectrum system with diversity, it is shown that the use of ReedSolomon coding with a parallel errors and erasures decoding algorithm accomplishes these goals. The paper also investigates the accuracy of the Chernoff bound as an approximation to the true performance of a frequency-hop spreadspectrum communication system with diversity; side information,M-ary orthogonal signaling, and Reed-Solomon coding. The performance results presented in the paper are based on analysis and computer evaluation. Approximate results based on the Chernoff bound are also given. It is shown that the Chernoff bound forM-ary orthogonal signaling gives a very poor approximation for many cases of interest. This is largely due to the looseness of the union bound.     

Performance of fast frequency-hopped MFSK receivers with linear andself-normalization combining in a Rician fading channel withpartial-band interference

An error probability analysis is performed for both self-normalized and conventional M-ary orthogonal frequency-shift-keying (MFSK) noncoherent receivers using fast frequency-hopped (FFH) spread-spectrum waveforms transmitted over a Rician fading channel with partial-band interference. The self-normalization receiver uses a nonlinear combination procedure to minimize performance degradation due to partial-band interference. The performance of the conventional receiver is significantly degraded by worst-case partial-band interference regardless of the modulation order or number of hops per data symbol used, while the self-normalization receiver can provide a significant immunity to worst-case partial-band interference for many channel conditions when diversity is used, provided the signal-to-thermal-noise ratio is large enough to minimize degradation due to nonlinear combining losses. The improvement afforded by higher modulation orders is dependent on channel conditions     

Antijam performance of FFH/BFSK with noise-normalization combining in a Nakagami-m fading channel with partial-band interference

The bit error rate (BER) performance of a noncoherent fast frequency-hopped binary orthogonal frequency-shift-keying (FFH/BFSK) spread spectrum noise-normalization combining receiver is evaluated in the presence of partial-band interference (PBI) and additive white Gaussian noise (AWGN) over independent frequency-nonselective slowly Nakagami-m fading channels. It is shown from the analytical results, and verified by simulation, that a higher diversity level greatly improves the worst-case performance of the noise-normalization receivers over Rayleigh or more severe fading channels, while a lower diversity level is preferred for less severe fading channels. In the former case, a full band strategy is optimal for the interferer and a partial-band strategy is more disruptive in the latter case.     

Parallel acquisition of multicarrier direct-sequence spread-spectrum signals in fading and partial-band interference

The frequency diversity of multicarrier direct-sequence signaling can potentially offer robust performance in frequency-selective channels. The paper focuses on the acquisition of multicarrier signals in channels containing fading and partial-band interference. The maximum-likelihood decision rule for parallel acquisition in frequency-selective fading and partial-band interference is derived. Several simpler, near-optimal decision rules are also discussed. The performance of these decision rules is compared to that of equal-gain combining for multicarrier acquisition. Results show that the decision rules designed specifically for partial-band interference give significantly better performance. Methods of acquisition with a limited number of correlators are also discussed. Finally, the potential benefits of estimating the signal strength on each subcarrier prior to acquisition are examined.     

Diversity and coding for FH/MFSK systems with fading and jamming.II. Selective diversity

For pt.1 see ibid., vol.COM-35, p.1329-41 (1987). A performance evaluation is presented for selective diversity with feedback for frequency-hopping M-ary frequency-shift-keyed systems operating over Rayleigh faded channels in the presence of partial-band noise and partial-band tone jamming. The behavior of uncoded and coded systems is studied. For coded systems, the performance is evaluated for hard-decision receivers without channel state information and soft-decision receivers with perfect jammer state information. The results demonstrate that the performance of uncoded FH/MFSK with selective diversity is unacceptable. However, this diversity technique can offer definite improvements for coded FH/MFSK systems. Specifically, the effectiveness of selective diversity signaling depends on the provision of a feedback channel between the transmitter and receiver to provide the transmitter with the fading gains of the independently faded channels. To obtain an improvement from the selective diversity signaling scheme described here, there must be multiple independently faded channels between the transmitter and receiver. If not, the performance of the selective diversity signaling scheme will be identical to the performance of FH/MFSK without diversity     

Strategies for FH/MFSK Signaling with Diversity in Worst-Case Partial-Band Noise

Optimum diversity and worst-case partial-band noise jamming conditions have been derived for noncoherent energy detection of frequency-hopped (FH)M-ary frequency-shift keyed (MFSK) signals using a soft-chip decision suboptimum linear combining metric with perfect jamming-state side information. However, the assumption implicit in previous publications is that the error rate is first maximized over the jammer's partial-band duty factor for arbitrary diversity, and the result is then minimized over the amount of diversity. This paper shows that if the order of optimization is reversed, different conditions and performance are produced; that is, the previous solution is not a saddlepoint. This introduces some game-theoretic considerations for the communicator and the jammer, the risks and advantages of which are explored.     

Carbon Copying Onto Dirty Paper

A generalization of the problem of writing on dirty paper is considered in which one transmitter sends a common message to multiple receivers. Each receiver experiences on its link an additive interference (in addition to the additive noise), which is known noncausally to the transmitter but not to any of the receivers. Applications range from wireless multiple-antenna multicasting to robust dirty paper coding. We develop results for memoryless channels in Gaussian and binary special cases. In most cases, we observe that the availability of side information at the transmitter increases capacity relative to systems without such side information, and that the lack of side information at the receivers decreases capacity relative to systems with such side information. For the noiseless binary case, we establish the capacity when there are two receivers. When there are many receivers, we show that the transmitter side information provides a vanishingly small benefit. When the interference is large and independent across the users, we show that time sharing is optimal. For the Gaussian case, we present a coding scheme and establish its optimality in the high signal-to-interference-plus-noise limit when there are two receivers. When the interference power is large and independent across all the receivers, we show that time-sharing is again optimal. Connections to the problem of robust dirty paper coding are also discussed     

Soft decision direct-sequence DPSK receivers

Several soft-decision receiver structures are proposed for coded direct-sequence differential-phase-shift-keyed (DPSK) spread spectrum systems operating over pulse-jammed channels. The performance of the maximum-likelihood soft-decision receivers and a number of suboptimal soft decision receivers is considered. Soft-decision receivers require channel side information for satisfactory performance in the presence of pulse jamming. Two techniques are investigated for generating channel side information to mitigate the effects of pulse jamming     

Probability of Error Analyses of a BFSK Frequency-Hopping System with Diversity Under Partial-Band Jamming Interference--Part I: Performance of Square-Law Linear Combining Soft Decision Receiver

In this paper, error probability analyses are performed for a binary frequency-shift-keying (BFSK) system employingLhop/bit frequency-hopping (FH) spread-spectrum waveforms transmitted over a partial-band Gaussian noise jamming channel. The error probabilities for theLhop/bit BFSK/FH systems are obtained as the performance measure of the square-law linear combining soft decision receiver under the assumption of the worst-case partial-band jamming. The receiver in our analysis assumes no knowledge of jamming state (side information). Both exact and approximate (multiple bound-parameter Chernoff bound) solutions are obtained under two separate assumptions: with and without the system's thermal noise in the analyses. Numerical results of the error rates are graphically displayed as a function of signal-to-jamming power ratio withLand signal-to-noise ratio as parameters. All of our results, exact and approximate, indicated that the higher number of hops per bit produced higher error probabilities as a result of increased combining losses when the square-law linear combining soft decision receiver is employed in demodulating the multihop-per-bit waveform.     

Adaptive-rate coding for frequency-hop communications over Rayleighfading channels

Because of the variability of the channels in frequency-hop wireless systems and networks, the performance of error-control coding can be improved by adapting the rate of the code to the channel conditions. In this paper, adaptive-rate error-control coding is investigated for slow frequency-hop communications with Reed-Solomon coding. Two methods are investigated that use decoder side information as a means for selecting the code rate. These methods are based on counts of errors and erasures, which are provided by the demodulator and the decoder. The performance of the adaptive-rate coding system is evaluated for channels with Rayleigh fading, partial-band interference, and thermal noise     

Maximum-likelihood diversity combining in partial-band noise

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     

Probability of Error Analyses of a BFSK Frequency-Hopping System with Diversity Under Partial-Band Jamming Interference--Part III: Performance of a Square-Law Self-Normalizing Soft Decision Receiver

Linear and nonlinear diversity combining receivers for multihops-per-bit FH/BFSK waveforms in the partial-band noise jamming environment were studied in Parts I and II. It was shown that nonlinear combining receivers (Part II) can achieve a diversity gain for error rate improvement, while the linear combining receiver (Part I) cannot. The two types of nonlinear combining receivers treated in Part II required knowledge of system operational parameters for their optimum performance, such as measured noise power and the signal energy level at the receiver. In this paper, a self-normalizlng nonlinear combining receiver is shown to achieve a diversity gain without knowledge of signal or jamming levels, unlike the nonlinear schemes studied previously. The worst-case error probability performance of the self-normalizing receiver is obtained with and without system thermal noise. The numerical results are compared to those for the receivers studied earlier.     

Diversity and Coding for FH/MFSK Systems with Fading and Jamming--Part I: Multichannel Diversity

The performance of diversity and/or coding is evaluated for FH/MFSK signaling over Rayleigh fading channels in the presence of jamming. The effects of partial-band tone and partial-band noise jamming on uncoded and coded systems are considered. The results indicate that FH/MFSK signaling with diversity provides satisfactory performance for jammed fading channels. For coded FH/MFSK signaling over fading channels, noise jamming may be more effective than tone jamming. The amount of improvement resulting from the use of diversity in conjunction with coding depends upon many factors, including the nature of the channel, the degree of channel state information available at the decoder, the type of decoding, and the modulation alphabet size.