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.     

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.     

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.     

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 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.     

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     

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.     

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     

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     

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     

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     

Throughput analysis of a slotted frequency-hop multiple-accessnetwork

A link throughput analysis is presented for a slotted frequency-hop multiple-access (FHMA) packet radio network (PRN) operating in the presence of background noise, partial-band noise jamming, and partial-band tone jamming. The PRN consists of an arbitrary number of transceivers arranged in a paired-off topology. Forward error-correction coding is used for packet protection. M-ary FSK modulation is used with hard-decision decoding. Expressions are derived for the link throughput in terms of the channel cutoff rate and capacity. The dependency of the optimal processing gain, code rate, and jamming fraction on the population size, traffic intensity, bit energy to background noise ratio, and bit energy to jammer noise ratio is examined in detail. It is shown that a properly designed (optimized) PRN using random-access FHMA offers a significantly larger heavy-load throughput than a random-access frequency-division multiple-access PRN     

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,...     

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     

Coding for Frequency-Hopped Spread-Spectrum Communication with Partial-Band Interference--Part II: Coded Performance

The performance of codes in a frequency-hopped spreadspectrum communication system with partial-band interference is investigated. The performance measure considered is the decoded bit error probability. A simplified interference model and worst-case partial-band Gaussian noise interference model is considered with the interference noise statistically independent of the transmitted signal. We consider soft decision receivers with side information and hard decision receivers with and without side information.     

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     

Antijamming performance of a multicarrier direct-sequencespread-spectrum system

Uncoded antijamming capability of the multicarrier direct-sequence spread-spectrum system proposed by Kondo and Milstein (see ibid. vol.44, p.238-46, 1996 ) is analyzed. Joint pulse/partial-band noise jamming is considered with various subcarrier demodulator output combining schemes. We find that full-band pulse jamming maximizes the error probability for all cases considered. With Rayleigh fading and maximal-ratio combining, the multicarrier system achieves performance very close to that of the single-carrier system without fading even with a very small number of subcarriers     

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.     

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.