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.     

基于Monte Carlo模型的FFH/BFSK合并技术研究

分析了FFH/BFSK接收机的两种合并方式:平方律线性合并和具有自适应增益控制(AGC)的平方律非线性合并;在部分频带噪声干扰下,使用Monte Carlo模型对这两种合并方式进行仿真得到误码率曲线,仿真结果与理论误码率吻合,并得出结论:在热噪声功率受限的情况下,使用AGC合并能有效的抑制部分频带噪声干扰.     

Error-correcting codes and nonlinear diversity combining againstworst case partial-band noise jamming of frequency-hopping MFSK systems

Error probability analyses are performed for a coded M-ary frequency-shift keying system (MFSK) using L hops per M-ary word frequency-hopping spread-spectrum waveforms transmitted over a partial-band Gaussian noise jamming channel. The bit error probabilities are obtained for a square-law adaptive gain control receiver with forward-error-control coding under conditions of worst-case partial-band noise jamming. Both thermal noise and jamming noise are included in the analyses. Performance curves are obtained for both block codes and convolutional codes with both binary and M-ary channel modulations. The results show that thermal noise cannot be neglected in the analysis if correct determinations of the optimum order of diversity and the worst-case jamming fraction are to be obtained. It is shown that the combination of nonlinear combining, M -ary modulation, and forward-error-control coding is effective against worst-case partial-band noise jamming     

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.     

The Analyses of Uncoded Performances for Certain ECCM Receiver Design Strategies for Multihops/Symbol FH/MFSK Waveforms

Frequency-hopping (FH)M-ary FSK (MFSK) spread-spectrum modulation is an effective choice for an electronic counter-countermeasures (ECCM) system. When the power efficient MFSK (M > 2) baseband orthogonal waveform is transmitted withL-fold diversity under constrained symbol energy, the resultant multiple (L) hops/symbol FH/ MFSK becomes a most viable low probability of intercept (LPI) waveform. In this paper, analyses are presented for the uncoded performance of such a waveform for two types of square-law nonlinear combining soft-decision receiver strategies under the assumption of worst-case partial-band noise jamming (countermeasures). 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. The primary focus is on exact analytical results and, as such, the system's thermal noise is not neglected in the analyses. Numerical results of the error rates are graphically displayed as a function of signal-to-jamming power ratio withLandMas parameters under assumed values of signal-to-noise ratio. It is shown that. a diversity gain for error-rate improvement is realized for the nonlinear diversity combining receiver strategies. No attempt is made in this paper to compare the diversity performance to any error-control coding schemes.     

Diversity combining in FH/BFSK systems to combat partial bandjamming

A combiner for a frequency-hopped binary frequency-shift keyed (FH/BFSK) system, called the product-combining receiver (PCR), is introduced. The performance of the PCR is evaluated for the cases of an on/off partial-band noise with optimum-jamming fraction, and worst-case, partial-band tone jamming. The performance of PCR is shown to be comparable to that of the clipper receiver. The effect of diversity combining, along with convolutional coding and ratio-threshold technique, is analyzed. Whereas the clipper requires the knowledge of signal-to-noise ratio for threshold adjustments, the PCR does not require this knowledge for this operation     

短波差分跳频系统抗部分频带干扰性能分析

对接收端采用非相干平方律能量检测器及维特比译码器的短波差分跳频通信系统,在无衰落信道和频率非选择性慢衰落信道下抗部分频带干扰的性能进行了理论分析.若信道存在衰落,则假设每跳所经历的衰落过程是相互独立的,且服从瑞利分布.部分频带干扰被模拟为加性高斯噪声,分析中考虑了背景热噪声.结果表明:差分跳频相邻两跳频率之间的相关性为系统提供了良好的抗部分频带干扰的能力.若忽略背景热噪声,则当信干比为20dB时,在无衰落信道下最坏情况比特误码率可达10-5,而在频率非选择性瑞利慢衰落信道下最坏情况比特误码率可达10-3.     

Partial-band jammer suppression in FFH spread-spectrum system usingFFT

This paper presents the performance evaluation of partial-band jammer suppression using fast Fourier transform (FFT) as an alternative in a fast frequency-hopped spread-spectrum (FFH/SS) communication system. The FFH/SS system employs a clipper to restrict the effect of a partial-band jammer before diversity combining. No additional side information of the jammer is required, and the analytical expression for the bit error rate (BER) is derived. It is shown that the performance of the FFT-based clipper receiver is better than that of the square-law linear combining receiver and comparable to that of the square-law clipper receiver     

Limiter-differential detection of a frequency-hopped CPFSKdiversity system in partial-band jamming

The error probability achieved by a differential detector with a bandpass limiter preceding the receiver is analyzed for a slow-frequency-hopped CPFSK diversity waveform transmitted over a partial-band noise jamming channel, and is compared to the system's performance without the bandpass limiter. The system's thermal noise is not neglected in the analysis. In principle, each bit is repeated on L different hops, and for the FH/CPFSK system analyzed, these repetitions are combined to yield a soft decision. The main result is that a diversity gain for error rate improvement in worst-case partial-band jamming is realized with the detector preceded by a limiter, but not without the limiter. This is shown by considering the error probability for L=2 in comparison with that for L=1     

ML-based follower jamming rejection in slow FH/MFSK systems with an antenna array

The jamming robustness of frequency hopping (FH) systems with M-ary frequency shift keying (MFSK) modulation may be potentially neutralized by a follower partial-band jammer. In this paper, a maximum likelihood (ML)-based algorithm that uses a two-element array is proposed for joint follower jamming rejection and symbol detection in slow FH/MFSK systems over quasi-static flat Rayleigh fading channels. The algorithm is derived by treating both the received jamming components and the unknown data symbols as deterministic quantities to be jointly estimated in an integrated ML operation. In addition, an approximate expression for the symbol error rate (SER) of the proposed scheme is derived when BFSK signaling is employed in a jamming dominant scenario. Analytical and simulated results show that the proposed approach is able to remove jamming and outperform the conventional and sample matrix inversion (SMI)-based beam-formers in the presence of a follower partial-band jammer.     

Effects of fading and partial-band noise jamming on a fast FH/BFSKacquisition receiver with noise-normalization combination

We present the performance analysis of a fast frequency-hopped (FH) binary orthogonal frequency-shift keying acquisition receiver for communication against adverse environments. The receiver employs noncoherent, noise-normalized, matched-filtered (MF) correlation detection for rapid acquisition in the search mode. Our analysis includes four types of communication environments, namely additive white Gaussian noise (AWGN) channel, AWGN channel with partial-band noise jamming, fading channels, and fading channels with partial-band noise jamming. The considered fading channels include Nakagami-m, Rician, and Rayleigh amplitude models. Based on Beaulieu's (see ibid., vol.38, no.9, p.1463, 1990) convergent series approach, efficient analytical formulas are developed for performance evaluation. Example performance results for various environments are presented in terms of two acquisition probabilities, namely the detection probability and the false alarm probability of the noise-normalized MF detector. It is analytically shown that with a short MF correlation length and with a sufficiently large ratio of signal power to noise power the fast FH diversity combining yields noticeable performance improvement for environments with strong fading. When the MF correlation is lengthened, this improvement tends to fade away and the diversity combining results in performance loss     

Performance of FFH/BFSK product combining receiver over aRician-fading channel with partial-band jamming

A theoretical performance evaluation for an FFH/BFSK spread spectrum product combining receiver over a Rician-fading channel in the presence of partial-band jamming and AWGN is presented. The BER of this receiver is better than that of a linear combining receiver for a strong direct signal, and improvement is significant when diversity is increased     

Coherent Detection of Frequency-Hopped Quadrature Modulations in the Presence of Jamming--Part I: QPSK and QASK Modulations

This paper examines the performance of coherent QPSK and QASK systems combined with FH or FH/PN spread spectrum techniques in the presence of partial-band multitone or noise jamming. The worst-case jammer and worst-case performance are determined as functions of the signal-to-background noise ratio (SNR) and signal-to-jammer power ratio (SJR). Asymptotic results for high SNR are shown to have a linear dependence between the jammer's optimal power allocation and the system error probability performance.     

动态频谱抗干扰系统在部分频带干扰下的性能

为了评估动态频谱抗干扰新体制在抗干扰通信中的性能,采用理论分析与仿真相结合的方法,研究了动态频谱抗干扰系统在部分频带干扰下的信道容量及比特误码率,并将其与常规跳频系统在部分频带干扰下的信道容量及比特误码率进行了比较.结果表明:在很宽的部分频带干扰因子取值范围内,动态频谱抗干扰系统的信道容量均大于常规跳频系统的信道容量,...     

Rejection of partial-band noise jamming with FFH/BFSK productcombining receiver over Nakagami-fading channel

The bit error rate performance of a noncoherent fast frequency-hopping binary frequency shift keying system equipped with a product combining receiver is evaluated in the presence of partial-band noise jamming and additive white Gaussian noise over a Nakagami-faded channel. Using the derived output characteristic function, numerical results are generated for different fading conditions     

Partial-band jamming rejection of FFH/BFSK with product combiningreceiver over a Rayleigh-fading channel

An exact closed-form expression of the characteristic function is derived for a fast frequency-hopping (FFH) binary orthogonal frequency-shift-keying (FSK) spread-spectrum (SS) communication system. The FFH system employs a product combining receiver over a Rayleigh-fading channel with partial-band jamming and additive white Gaussian noise (AWGN). The derived characteristic function is then used to obtain a compact bit error rate (BER) expression for different diversity levels. Our study shows that there exists an optimum diversity level under certain channel conditions     

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.     

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.     

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     

Multitone jamming of FH/BFSK in Rician channels

A new bit error rate (BER) expression for a noncoherent frequency-hopped binary-frequency-shift-keying (FH/BFSK) receiver in Rician channels, subjected to independent multitone and wideband noise interference, is derived. Unlike previously published analyzes, we combine the signal and jammer multipath components, the additive white Gaussian noise (AWGN), and other wideband interference as a single Gaussian process. This method leads to a BER expression which consists of only a single rather than a triple integral requiring numerical computation. We also present a new derivation of the probability density function (PDF) of the ratio of two Rician random variables, used in a previously published approximate BER analysis