Performance of four-dimensional digital communication system infading channels

The authors derive a formula for the bit-error probability (BEP) of a four-dimensional signal and coherent but simple detector in fading channels with Rician or Nakagami probability density function for the received signal envelope. They compute the BEP in both cases and show its dependence on the energy-to-noise ratio per bit, E_b/N_o and channel parameters, K and m, respectively     

Performance analysis of an FFH/BFSK receiver with product-combining in a fading channel under multitone interference

The bit-error probability (BEP) is evaluated for a fast frequency-hopping binary frequency-shift-keying (FFH/BFSK) spread-spectrum communication system over Rician fading channels in the presence of worst-case multitone jamming (MTJ) and additive white Gaussian noise (AWGN). A diversity reception scheme of product-combining is applied at the receiver. Two types of MTJ models, namely n=1-band MTJ and independent MTJ, are considered in this letter. To obtain the final decision statistics, the closed-form or a single finite integral expressions of cumulative distribution functions (CDFs) of the ratio of two square-law detectors' outputs per hop are derived. According to the numerical results, it is shown, unlike the known knowledge for the AWGN channel, that independent MTJ is more harmful than n=1-band MTJ for the product-combining receivers (L/spl ges/2) in fading channels.     

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     

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.     

Comments on "Envelope Detector Performance for a Partially Coherent-Fading Sinewave in Noise"

The basic premise in a recent paper that the matchedfilter square-law envelope detector is generally appropriate for fastfading as well as slow-fading incoherent channels is questioned. Its inappropriateness for a fast-fading incoherent Gaussian channel is demonstrated by evaluation of probability of error for this receiver and for the optimum receiver. As a result, modifications to some of the conclusions drawn regarding attainable performance gain with increasing observation time are proposed. In addition, it is pointed out that the performance predictor adopted, viz., deflection, exhibits anomalous behavior (for at least some incoherent fading channels), thereby rendering the other conclusions questionable.     

Error probability analysis of multicarrier direct sequence code division multiple access system under imperfect channel estimation and jamming in a Rayleigh fading channel

The performance of a multicarrier direct sequence code division multiple access (MC-DS-CDMA) system in fading environment has been extensively analysed in the literatures. The analysis that is available in the literatures did not take into account the impact of jamming and channel estimation errors on the performance of the system. In this study, closed-form expressions of the average bit error probability (BEP) of the MC-DS-CDMA system with channel estimation errors in the presence of partial band, broadband and multitone jamming are derived in a Rayleigh fading channel. The analysis shows that the magnitude of the normalised correlation between the actual and the estimated complex fading channel gain, A, greatly affects the performance of the MC-DS-CDMA system. For large signal-to-noise ratio, the average BEP with A=1 and without multiple access interference (MAI) tends to zero. When A?1, the BEP of the system exhibits an error floor even without MAI. This error floor increases as the number of users increases. It is also shown that increasing the number of the system subcarriers enhances the system performance against jamming.     

Multitone jamming rejection of FFH/BFSK spread-spectrum system overfading channels

Analytical expressions for bit-error probability are derived for a fast frequency-hopping binary frequency-shift keying (FFH/BFSK) spread-spectrum communication system over a fading channel with worst-case band multitone jamming (MTJ) and additive white Gaussian noise (AWGN). An FFH system employing either a linear-combining receiver or a clipper receiver is investigated. The desired signal and MTJ are assumed to undergo independent fading, and our analysis, validated with simulation results, shows that the performance of the system is slightly improved as the severity of the MTJ fading is increased. The clipper receiver is found to be superior to the linear-combining receiver when the jamming power is strong. The worst-case MTJ is shown to be more harmful than the corresponding worst-case partial-band noise jamming over a fading channel with AWGN     

Error probabilities of an FFH/BFSK self-normalizing receiver in aRician fading channel with multitone jamming

We derive the analytical bit-error rate (BER) expressions for a fast frequency-hopped binary frequency-shift keying self-normalizing receiver over a fading channel with the worst-case band multitone jamming (MTJ) and additive white Gaussian noise (AWGN). The desired signal and MTJ are assumed to undergo independent Rician fading and our analyses, validated with simulation results, show that the system performance is not sensitive to different types of MTJ fading conditions. The self-normalizing receiver is found to be superior to the linear-combining receiver when the signal amplitude does not experience severe fading, while the converse is true under Rayleigh fading signal conditions. Under a Rician fading channel and AWGN conditions, the worst-case MTJ and the worst-case partial-band noise jamming are shown to have similar effects on the BER performance of the self-normalizing receiver with diversity     

Envelope-aided Viterbi receivers for GMSK signals with limiter-discriminator detection

Continuous phase modulation schemes, such as Gaussian minimum-shift keying (GMSK), are frequently used with limiter-discriminator (LD) detectors. This paper studies how the side information derived from the signal envelope can enhance the performance of a Viterbi algorithm (VA)-based receiver operating on the LD output of a GMSK scheme. By considering the joint probability density function of envelope and frequency, different approximations yield different novel metrics for VA, using the three-variables envelope and its derivative, and frequency error in different combinations. Simulation results confirm that such envelope-aided VA gives significant performance gains, and that envelope information complements the frequency information output by the LD detector in frequency-selective fading channels.     

Analytical study of FFH systems with square-law diversity combiningin the presence of multitone interference

An analytical study of the performance of fast frequency-hopped (FFH), M-ary orthogonal frequency-shift keyed noncoherent modulation with linear combining of square-law envelopes in the presence of multitone interference is presented. The multiple equal-power interference tones are assumed to correspond to some of the possible FFH/M-ary orthogonal signaling tones. It is also assumed that the channel fading characteristics of the signal and interference tones are independent. We evaluate the effect of the channel fading on the system's performance as a function of various parameters, such as the number of hops per symbol, the signal power to multitone interference power ratio, and the number of interference tones. Our numerical results indicate that by use of square-law time diversity combining, a large number of hops per symbol make the bit-error probability of the system more sensitive to the fading of multitone interference. Finally, the analysis has been proven valid by simulation     

Antijamming performance of space-frequency coding in partial-band noise

Space-frequency coded (SFC) orthogonal frequency-division multiple access (OFDMA) system is considered under partial band noise jamming (PBNJ). Analytical expressions for the bit error probability (BEP) are derived for OFDMA with and without SFC in a frequency-selective fading environment. It is shown that SFC increases the resistance of OFDMA against PBNJ and reduces the BEP considerably.     

FFH/BFSK选择分集合并接收机在部分频带干扰Nakagami-m信道下的性能分析

快速跳频通信系统选择分集合并接收机可以有效减轻干扰及衰落对系统带来的性能损伤。该文给出了快速跳频BFSK系统在部分频带干扰下的选择分集合并接收机模型,并对该接收机在同时存在部分频带干扰以及加性高斯白噪声的非频率选择性Nakagami-m衰落信道下的性能进行了推导,给出了误码率的闭合表达式。最后进行了仿真验证,仿真结果与理论分析结果完全一致。分析表明：具有高分集度的选择分集合并接收机受干扰影响较小;在干扰功率较大时,其性能要好于其它几种分集合并接收机;在一定的信道条件下,存在一个最佳分集度。最后针对选择分集合并接收机在弱干扰信号下的性能不足,提出相应的改进措施。     

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     

M-ary NCFSK with S+N selection combining in Rician fading

The performances of general M-ary and binary orthogonal noncoherent frequency-shift keying signal-plus-noise (S+N) receiver structures in slow, flat Rician fading channels are examined. The fading on the diversity branches is assumed to be independent, but not necessarily identically distributed. For each receiver, a symbol-error probability expression is derived as a single integral with finite integration limits. Extensive Monte Carlo simulation results are presented to validate the analytical expressions. The results indicate that, unlike previously published results, the performance of S+N selection combining (SC) is not always superior to that of classical SC in fading and is dependent on the value of the signal-to-noise ratio (SNR), the modulation order, the diversity order, the multipath intensity profile, and the fading parameter. It is further shown that increasing the number of diversity branches in a S+N SC receiver does not necessarily decrease the probability of error if the system is operating in the low-SNR region. The performances of S+N SC schemes are also compared with the performances of equal-gain combining and square-law combining receivers.     

Performance analysis of a DS/CDMA system with noncoherent M-aryorthogonal modulation in Nakagami fading

The probability of error performance of a direct sequence code-division multiple-access (DS/CDMA) system employing noncoherent M-ary orthogonal signaling in a Nakagami multipath fading channel is analyzed. A RAKE receiver structure with square-law demodulation is used at the receiver. The multiple-access interference are modeled as Gaussian and expressions derived for the exact probability of error. The performance is also evaluated in terms of the number of users that can be supported by the system at a given probability of error. The effect of correlated fading on system performance is also investigated by considering two correlation models, which can be characterized by a single correlation coefficient ρ. In the first model, the correlation coefficient between any two diversity branches is constant. In the second model, it is assumed that the correlation coefficient between any two diversity branches decreases exponentially as the separation between them increases. For both models, it is found that the presence of correlation deteriorates system performance. The use of larger signal alphabets than binary modulation in conjunction with diversity reception provides a considerable performance improvement even in the presence of correlated fading     

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.     

Acquisition of Direct Sequence Signals with Modulation and Jamming

The effects of data modulation and/or narrow-band interference on the acquisition time of direct sequence (DS) systems are assessed when particular acquisition schemes are selected. Finally, the results of these analyses are used to propose receivers which mitigate the deleterious effects of the data or jamming. The analyses demonstrate that the I-Q detector, modified for a data modulated carrier, is superior to the correlator/square-law detector despite the latter's robustness to data. When the average pulsed jammer power is constrained, the analyses illustrate that the jammer's duty factor does not impact acquisition time when the pulse repetition frequency (PRF) is high; a duty factor of unity maximally degrades acquistion performance when the PRF is low. A proposed adaptive receiver provides considerable jamming protection; the acquistion performance of such a receiver bounds the performance of all adaptive acquistion receivers.     

Performance of wireless CDMA with M-ary orthogonal modulation andcell site antenna arrays

An antenna array-based base station receiver structure for wireless direct-sequence code-division multiple-access (DS/CDMA) with M-ary orthogonal modulation is proposed. The base station uses an antenna array beamformer-RAKE structure with noncoherent equal gain combining. The receiver consists of a “front end” beamsteering processor feeding a conventional noncoherent RAKE combiner. The performance of the proposed receiver with closed loop power control in multipath fading channels is evaluated. Expressions for the system uncoded bit-error probability (BEP) as a function of the number of users, number of antennas, and the angle spread are derived for different power control scenarios. The system capacity in terms of number of users that can be supported for a given uncoded BEP is also evaluated. Analysis results show a performance improvement in terms of the system capacity due to the use of antenna arrays and the associated signal processing at the base station. In particular, analysis results show an increase in system capacity that is proportional to the number of antennas. They also show an additional performance improvement due to space diversity gain provided by the array for nonzero angle spreads     

Direct-Sequence Spread-Spectrum Receiver for Communication on Frequency-Selective Fading Channels

The reception of direct-sequence spread-spectrum signals on frequency-selective fading communication channels is considered. The fading statistics are described using the wide-sense-stationary uncorrelated-scattering (WSSUS) channel model. It is shown that, under certain assumptions about this channel such as time-invariance over the duration of a data symbol, an orthogonal representation for the received distorted signal can be found. The optimum incoherent receiver can then be realized with reasonable complexity. The analysis shows that exploiting the inherent diversity of a frequency-selective channel can reduce the receiver error probability by several orders of magnitude. The optimum selective channel and the jamming susceptibility of the receiver are discussed.     

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.