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.     

Error Performance of FH Wireless LANs in DS and Tone Interference

In this paper the bit error probability of the SFH/MFSK system in presence ofwideband and tone interference in a fading environment is evaluated.Simultaneous license-free operation of tone-like applications, FrequencyHopping (FH), and Direct Sequence (DS) based LAN clusters is assumed to be theprime interference facing the subject FH wireless LAN (of the IEEE 802.11standard). The wideband DS interference is considered to have asinc²() shape Power Spectral Density (PSD) centered at the middleof FH signal band and tone interferers are assumed to be spread over the wholeFH band of the intended signal. Assumptions of slow non-selective fading alongwith slow hopping justify a quasi-static treatment. Results shows that the FHsystem is more sensitive to tone interference and fading and less sensitiveto wideband interference variations. The paper sheds light on the performanceof wireless LAN operation in the unlicensed free band where many other LANsmay exist.     

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.     

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.     

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.     

短波FH/OFDM通信系统抗跟踪式干扰性能分析

对于短波多载波跳频通信系统,跟踪式干扰是一种有效的干扰模式。分析了正交频分复用( OFDM)部分子信道干扰与符号误码率的关系,通过仿真获得了最佳跟踪干扰的部分时间参数,结合OFDM频谱结构与干扰频谱关系,推导了高斯信道条件下部分频带干扰和多音干扰时系统误码率,分析了短波FH/OFDM通信系统抗跟踪式干扰的误码率性能,仿真结果表明：跟踪干扰时间窗口对误码率的影响与部分频带干扰因子和信干比有关;在部分频带干扰与部分时间干扰之间,存在等效的干扰效果区域;多音干扰因子越大,系统所受影响越大,跟踪干扰时间窗口对误码率的影响与多音干扰因子和信干比有关,针对OFDM符号的多音干扰影响要远大于部分频带干扰的影响;跳频与OFDM技术的结合、提高载波跳速、减小跟踪式干扰对OFDM符号的影响,也是消除多音干扰的重要手段。     

Performance of FH/BFSK with generalized fading in worst casepartial-band Gaussian interference

For frequency-hopped (noncoherent) binary frequency shift keying (FH/BFSK) on a worst-case partial-band Gaussian interference channel, the bit error probability results are well known for the extreme cases where the signal is either nonfading or Rayleigh fading. In this work, the region between these extremes is filled in by considering the general Nakagami-m fading model. The worst-case partial-band Gaussian interference results are given by a one-parameter family which for m→∞ gives the Viterbi-Jacobs nonfading result, and for m=1 gives the Rayleigh fading result. In the latter case, a broadband interference strategy is optimal. Thus, the Nakagami- m results provide a smooth one-parameter bridge between the Viterbi-Jacobs channel and the Rayleigh fading channel. The results show that the worst-case interference fraction ρ increases as the fading variance increases, up to Rayleigh fading. Any fading less severe than Rayleigh, however slight the departure from Rayleigh, requires a partial-band strategy for sufficiently large E_b/N_I     

Capacity of FH wireless multi-hop networks

In this article, the capacity of wireless multi-hop networks with the frequency hopping (FH) technique is derived. Different from the previous work based on non- spread spectrum (SS) system, this study is based on frequency hopping spread spectrum (FHSS) and the retransmission mechanism. The analysis results show that the normalized transport capacity decreases as 1/(Mλ) , when the total available frequency band is divided into M sub-bands for frequency hopping and the nodes are randomly distributed in space according to a Poisson point process with intensity λ . In this work, the best transmission range per hop to get the maximum capacity is also derived. Besides, the results summarize how the capacity of FH wireless multihop networks is affected by the outage probability, target signal to interference plus noise ratio (SINR) and other system parameters.     

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     

混合DS－SFH扩频多址室内无线数字通信性能分析

本文讨论了ＤＳ－ＳＦＨ扩频多址室内无线通信系统在瑞利多径衰落信道中的平均差错概率和多址容量。基于多径干扰、多址干扰和信道噪声的机理分析，推导了计算平均差错概率的有效近似公式。理论分析和数值模拟指出：混合系统的ＤＳ部分具有良好的多址容量并提供抗来自指定用户的多径干扰能力，混合系统的ＦＨ部分则具有抗来自非指定用户的多址和多径干扰能力。     

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     

Multiple-access capability of frequency-hopped spread-spectrumrevisited: an analysis of the effect of unequal power levels

A method for the evaluation of the probability of error of uncoded asynchronous frequency-hopped spread-spectrum multiple-access communications is presented. For systems with binary FSK modulation this method provides an accurate approximation and a tight upper bound to the bit error probability; for systems with M-ary FSK modulation, it provides tight upper bounds to the symbol error probability. The method enables the computationally efficient averaging of the error probability with respect to the delays, phase angles, and data streams of the different users. It relies on the integration of the product of the characteristic function of the envelope of the branch of the BFSK demodulator, which carries the desired signal, and of the derivative of the characteristic function of the envelope of the other branch. For sufficient frequency separation between the BFSK tones, the method can achieve any desirable accuracy. Moreover, the computational effort required for its evaluation grows linearly with the number of interfering users. In the M-ary case, tight upper bounds based on the union bound and the results of the binary case are derived. The method allows the effect of unequal power levels on other-user interference in FH/SSMA systems to be quantified accurately for the first time. The results indicate that the FH/SSMA systems suffer from the near-far problem, although less seriously than direct-sequence SSMA systems     

Spectral-estimation-based acquisition for frequency-hoppingspread-spectrum communications in a nonfading or Rayleigh-fading channel

Acquisition of frequency-hopping spread-spectrum (FH/SS) signals based on autoregressive spectral estimation is addressed for nonfading and Rayleigh-fading channels. The hopped frequency is synthesized using a linear feedback shift register (LFSR). The most significant bit (MSB) of the frequency estimate is loaded into the LFSR. A new acquisition logic is devised for the acquisition scheme that employs the autoregressive spectral-estimation acquisition technique (ASEAT). To characterize the statistical distributions of the frequency estimation error, the truncated Gaussian and uniform distributions are considered. The probability of the MSB error and the mean acquisition time of the acquisition logic are derived. For the ASEAT with the acquisition logic, the acquisition scheme that uses multiple antennas is also addressed. Numerical results for the probability of the MSB error and the corresponding mean acquisition time are illustrated for the performance evaluation of both cases     

Lower Bounds on Error Probability in the Presence of Large Intersymbol Interference

A lower bound on the symbol error probability achieved by any estimator of a digital pulse-amplitude-modulated sequence in the presence of white Gaussian noise and intersymbol interference is presented. The bound reduces to the well-known single-pulse error probability bound when intersymbol interference is small, but is tighter when interference is large. For example, on the singlepole (RC) channel, the effective signal-to-noise ratio for any estimator is shown to decrease by at least 3 dB for every doubling in pulse rate T^-1asT rightarrow 0and, on the double-pole channel, by at least 9 dB, thus disproving a recent conjecture [2] on the performance of nonlinear receivers.     

Performance of RS coded M-ary modulation with and without symbol overlapping

In this paper, we present analytical bit error probability results for M-ary modulation concatenated with Reed Solomon (RS) codes. The analysis of bit error probability is nontrivial as the number of bits per symbol for the RS codes may not be an integer multiple of the number of bits per symbol for a modulation symbol. We propose a Markov chain technique which allows analytical evaluation of the bit error probability for such cases. The performance of RS coding with coherent biorthogonal, coherent/non-coherent orthogonal modulation over an additive white Gaussian noise (AWGN) channel is evaluated. Simulation of the bit error probability of RS code concatenated with a Nordstrom Robinson (NR) code as an inner code is performed and compared with the case of biorthogonal modulation. From the results, we notice that a stronger inner code gives better bit error probability. In addition, the throughput of the coded system with biorthogonal modulation over an AWGN channel is discussed. For a Rayleigh flat fading and block fading channel, we analyze the bit error probability of RS codes concatenated with biorthogonal modulation. From the result, we notice that a stronger outer code gives a better bit error probability for the case of Rayleigh flat fading channel.     

Worst-case error probability of a spread-spectrum system inenergy-limited interference

We consider a communication channel corrupted by thermal noise and by an unknown and arbitrary interference of bounded energy. For this channel, we derive a simple upper bound to the worst-case error probability suffered by a direct sequence (DS) communication system with error-correction coding, pseudorandom interleaving, and a correlation receiver. This bound is exponentially tight as the block length of the error correcting code becomes large. Numerical examples are given that illustrate the dependence of the bound on the choice of error correcting code, the type of interleaving used, and the relative energy of the Gaussian noise and arbitrary interference     

Co-Channel Interference of Spread Spectrum Systems in a Multiple User Environment

This paper considers the mutual interference problem of several users employing the same spread spectrum technique in selected multiple user environments. The spread spectrum techniques consist of pseudo noise (PN), time division multiple access/PN, synchronous and asynchronous frequency hopping (FH). The environment consists of a desired transmitter-receiver pair located in an area where there areMinterfering users distributed in accordance with a specified probability density function. Both coherent phase-shift-keyed-and noncoherent frequency-shift-keyed modulations are considered. The general relationship between the probability of bit error of PN and FH systems is derived which is independent of the signal modulation and distribution of users. The degradation of the communication system performance (average probability of bit error) of the desired link as a function of the total number of interfering users within the considered area is investigated. The analysis shows that the mutual interference problem is less severe with users employing synchronous FH than with the other spread spectrum techniques. The comparison between asynchronous FH and PN is highly dependent on the relative location of interferers to the desired link and the time duty factor of the hopping.     

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     

Coherent detection of M-ary phase-shift keying in thesatellite mobile channel with tone calibration

A formula is derived for the error probability of M-ary phase-shift keying (PSK) in the satellite mobile channel when the signal is accompanied by a pilot tone which is used in the receiver for coherent detection of the signal. The author computes the error probability as a function of the signal-to-noise ratio, the ratio of powers in the specular and diffused signal component, the ratio of bandwidth in the pilot tone and signal extraction filters, and the numbers of symbols, i.e. M, while optimizing the ratio of powers in the pilot tone and signal. He computes results when the diffused component is not delayed with respect to the specular component, as well as for the opposite case, i.e. when the symbol in the diffused component is independent of the symbol in the main component     

A dual-tone reference digital demodulator for mobile digitalcommunication

A demodulator applicable to the dual-pilot tone modulation technique is presented. Examination of orthogonal and ISI (intersymbol interference) free pulse shapes leads to the novel demodulator structure. This demodulator is advantageous because the processing is strictly linear, the pilot channel and data channel ideally do not interfere or create self-noise, no differential encoding is required since no phase ambiguity is created with the pilot tone processing, and near ideal bit error probability performance is achieved. This demodulator offers an alternative to the transmitted tone-in-band and the pilot symbol assisted modulation techniques. The author considers π/4-QPSK modulation with 33% excess bandwidth in the isotropic time-varying fading channel as a design example