On the probability distribution of differential phase perturbed bytone interference and Gaussian noise

This paper presents a novel method for determination of the general probability distribution of a received differential phase corrupted by both continuous tone jamming and Gaussian noise. An alternative and yet simple expression is derived for this general probability distribution. As an example of its application, we analyze the error performance of a general uncoded SFH/DPSK system under partial-band multitone jamming     

Performance of fast frequency hopped noncoherent MESK witha fixed hop rate under worst case jamming

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     

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.     

Probability distribution of DPSK in tone interference andapplications to SFH/DPSK

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     

Performance study of a maximum-likelihood receiver for FFH/BFSKsystems with multitone jamming

We derive the optimum structure of a maximum-likelihood (ML) receiver for a fast frequency-hopped binary frequency-shift-keying (FFH/BFSK) spread-spectrum (SS) communication system operating in the presence of multitone jamming (MTJ) and additive white Gaussian noise (AWGN). It is shown that the side information of noise variance, signal tone amplitude, and multiple interfering tone amplitude at each hop, as well as the computation of nonlinear modified Bessel function are required to implement the optimum ML receiver. We have also derived and analyzed two suboptimum receivers-namely, the ML-I and ML-II receivers-for large and small signal-to-noise ratio (SNR), respectively. Performance comparisons among various receivers show that the ML receiver gives the best performance, while the ML-I and ML-II receivers also outperform the other existing methods under both high and low SNR conditions     

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.     

Antijam Performance of Fast Frequency-Hopped M-ary NCFSK--An Overview

The antijam performance ofM-ary noncoherent FSK with fast frequency hopping (one or more hops per symbol) is studied. A summary of terminology, definitions, and an overview of the literature is given. A general analysis method based upon circularly symmetric signal theory is presented. It provides a means for exact analysis of performance forM-ary operation with any combination of signal tone distribution (frequency bins contiguously or noncontiguously spaced), jamming distribution, jamming form (partial-band noise or multitone), and receiver system noise. Some previous results are derived as subcases of the general theory. A simple robust diversity combining technique of transmitting a symbol onLhops followed by a majority vote decision is found to provide significant performance improvements. This improvement is comparable to that obtained by most error-correction coding methods. Illustrative calculations of performance were chosen to indicate trends rather than to be exhaustive. Performance is usually presented as probability of bit error versus fraction of the band jammed to emphasize worst-case operation.     

Design and analysis of a fast frequency-hopped DBPSK communicationsystem. I. Error performance in AWGN plus partial-band noisejamming

The purpose of the paper is to present the design and performance analysis of a fast frequency-hopped (FFH) spread spectrum communication system employing differential binary phase-shifted-keying (DBPSK) modulation and differentially coherent demodulation. The receiver utilizes a hop time tracking loop to “lock” the hop clock. The authors present an analysis of the average bit error probability of the overall system when it is operating in additive white Gaussian noise plus partial-band noise jamming. The effect of channel phase distortion is also studied     

噪声跟踪干扰检测算法性能分析

基于认知无线电中协作频谱感知的思想,提出了一种跳频通信中噪声跟踪干扰的检测算法。首先采用能量检测算法,研究了干扰条件下单跳信号的检测性能。在此基础上,应用“k out of n”准则,在决策融合模块实现对噪声跟踪干扰的检测,推导了AWGN信道下噪声跟踪干扰的检测性能。理论分析和仿真结果表明,随着信干噪比的逐渐减小,对于单跳信号和噪声跟踪干扰的检测概率均逐渐增大;而在相同信干噪比情况下,噪声跟踪干扰的检测概率较单跳信号的检测概率得到了提高。      

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     

Performance of asynchronous slow frequency-hop multiple-accessnetworks with MFSK modulation

The performance of asynchronous slow frequency-hop spread-spectrum multiple-access networks where each user transmits L, M-ary symbols per hop using M-ary frequency-shift keying (FSK) modulation with noncoherent demodulation is investigated. Expressions for the decision variables are derived for a given multiple FSK (MFSK) symbol within a hop hit by K' interfering users under additive white Gaussian noise and Rayleigh fading channel models. For the special case when M=2, an accurate analytic approximation for the average error probability is derived as a function of L and K' and semianalytic Monte Carlo simulations are performed to estimate the probability of error for M larger than 2. The results are used to investigate the dependence of the average symbol error probability on L and M. Finally, the effect of enforcing phase transition between the MFSK symbols within a hop is investigated     

Symbol error probability evaluation for PSK modulation schemes in generalized non‐Gaussian noise channels

The average symbol error probability (ASEP) performance over the faded radio frequency (RF) link when the noise is additive in nature and has generalized Laplacian distribution is evaluated in this paper. The additive white generalized Laplacian noise (AWGLN) distribution can model different impulsive and non‐Gaussian noise environments often encountered in practice and provides a robust alternative to Gaussian distribution. A new expression for evaluating the exact symbol error probability over a multilevel M‐ary PSK‐modulated AWGLN channel is derived. Based on the obtained expression, the ASEP for the single‐hop RF link that models the shadowing and fading conditions over the RF channel by a generalized –K (GK) distribution is derived. Further, the error performance of a decode‐and‐forward relayed and GK‐distributed two‐hop RF link is discussed, and the results are validated through numerical plots.     

Rejection of frequency sweeping signal in DS spread spectrumsystems using complex adaptive filters

It is already known that the performance of narrowband interference adaptive filtering in DS spread spectrum systems is additionally degraded in the presence of a frequency hopped jamming signal compared to the case with CW interference. Even so, the adaptive filter can be rather efficient because during the hopping interval, while the jamming signal parameters are constant, the filter adjusts its weights; and if the hopping rate is not too high, there are time periods when the interfering signal is suppressed. In order to have a better insight into the performance of these systems, we analyze the DS spread spectrum receiver behavior, when the jamming signal frequency is continuously changing (chirp signal). We find that this is a reasonable step for a jammer that is trying to be more efficient. In such a case, a two-sided filter structure shows worse overall performance than a prediction error structure. As the jamming frequency sweeping rate or bandwidth is increased, the system performance is degraded. The analysis provides an insight into how much the system performance will be degraded as a function of the interfering (frequency sweeping) signal parameters     

Frequency-hopped spread-spectrum transmission with band-efficientmodulations and simplified noncoherent sequence estimation

Frequency-hopped spread-spectrum transmission using band-efficient modulations that are phase-continuous during each hop, is presented. A range of system parameters is considered, including signaling spectrum, reception, system complexity, and performance in the presence of noise and jamming. The particular cases where the hopped modulation is minimum-shift-keying (MSK), duobinary minimum-shift-keying (DMSK), or tamed-FM (TFM), are studied in detail. Results are presented for various modulation indexes, rectangular and raised cosine pulse shapings, and a range of hop interval lengths. Sequence estimation on a hop-by-hop basis is considered. The noncoherent likelihood sequence receiver must keep all possible paths, and so the computation and complexity becomes large for system transmitting many bits per hop. Therefore, a simplified noncoherent Viterbi-like sequence estimation algorithm with reduced complexity is introduced. System performance has been evaluated in Gaussian noise, partial-band jamming and multiple-tone jamming, using bounds and a system simulation. The compact nature of the hopped spectrum, when a number of bits are transmitted per hop, offers greater spectrum utilization and the prospect of improved performance in the presence of multiple-tone jamming or interference     

Performance of FH/QPR signals under frequency selective fading andpartial band tone jamming

The probability of bit error is evaluated for a communication system using frequency hopping for jamming rejection and quadrature partial-response signaling for baseband modulation. The environment in which the system is operating is modeled as severe partial-band tone jamming under frequency-selective fading affecting both the signal and the jammer. Error-correction coding is used to improve the performance of the system     

Performance Analysis of a Two‐Hop Fixed‐Gain MIMO Multiuser Relay Network with End‐to‐End Antenna Selection

This letter analyzes the performance of a two‐hop MIMO multiuser relay network with a fixed gain amplify‐and‐forward protocol and antenna selection at the transmitter and receiver. A new expression for the cumulative distribution function of the highest instantaneous end‐to‐end signal‐to‐noise ratio is derived. Based on the above result, closed‐form expressions for outage probability and bit error rate are presented. Also, the diversity order of the system is determined. Finally, computer simulations are compared to the analytical results, and insights and observations are provided.     

对GPS接收机的一种新宽带压制干扰样式分析

针对单频连续波干扰极易通过频域滤波加以抑制,而宽带连续阻塞式干扰又存在干扰效率低下的问题,提出脉冲连续波这种新的宽带梳状拦阻式干扰样式。根据C/A码、P(Y)码和M码信号功率谱特点分别设置脉冲连续波的干扰频率覆盖范围。以码跟踪误差作为干扰效果评估指标,对不同干扰环境下采用窄带非相干延迟锁定环的GPS接收机码跟踪性能进行仿真分析。仿真结果表明:脉冲连续波干扰对不同伪随机噪声码(PRN)编号和副载波调制相位下的C/A码和M码信号影响是不同的,在相同干信比(JSR)条件下,脉冲连续波的干扰效果要优于宽带高斯噪声和匹配谱干扰。     

Error rate and outage of dual‐hop DF relay system with selection combining over Rice fading

Performance of dual‐hop decode‐and‐forward relay system with selection‐combining receiver is analyzed over Rice fading channels. The following closed‐form expressions of performance metrics are derived: moment generating function for selection‐combining receiver output signal‐to‐noise ratio, exact average bit error rate of noncoherent modulations, approximate average symbol error rate for coherent modulations, and outage probability. We also obtain simple asymptotic expressions for moment generating function, exact average bit error rate, average symbol error rate, and outage probability, which are useful to characterize the diversity order and the coding gain. The optimal power allocation analysis suggests that the optimal power allocation factor is independent of total signal‐to‐noise ratio and source‐to‐destination link fading parameters. The accuracy of the obtained analytical expressions are supported by computer simulation results.     

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.     

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.