Performance comparison of FFH and MCFH spread-spectrum systems withoptimum diversity combining in frequency-selective Rayleigh fadingchannels

The performance of frequency-hopping spread-spectrum systems employing noncoherent reception and transmission diversity is analyzed for frequency-selective Rayleigh fading channels. Two different types of transmission diversity systems, a fast frequency-hopping (FFH) system and a multicarrier frequency-hopping (MCFH) system, are investigated. In order to combine received signals from transmit diversity channels, the optimum diversity combining rule based on the maximum-likelihood criterion is developed. Probability of error equations are derived, and utilized to evaluate the performance of the two systems. The MCFH systems are found to outperform FFH systems when the channel delay spread is severe, while FFH systems are superior to MCFH systems when a channel varies rapidly. Furthermore, it is found that performance enhancement due to an increase of diversity order is more significant for MCFH systems than for FFH systems in frequency-selective fading channels. The effect of frequency-selective fading is also investigated in determining optimum frequency deviations of binary frequency-shift keying signals     

Performance analysis of an FFH/BFSK linear-combining receiveragainst multitone jamming

A computationally efficient bit-error rate (BER) expression for a fast frequency-hopping binary frequency-shift-keying (FFH/BFSK) spread-spectrum system is derived based on Taylor-series expansion of the central differences. The FFH system employs a soft-decision linear-combining receiver against the worst-case band multitone jamming (MTJ) and additive white Gaussian noise. The analytical results are shown to match closely with the BER results based on simulation. This approach allows us to efficiently analyze the performance of the linear-combining receiver with higher diversity levels, which is otherwise mathematically intractable     

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     

Channel capacity per user in a power and rate adaptive hybrid DS/FFH‐CDMA cellular system over Rayleigh fading channels

The theoretically achievable average channel capacity (in the Shannon sense) per user of a hybrid cellular direct sequence/fast frequency hopping code‐division multiple‐access (DS/FFH‐CDMA) system, operating in a Rayleigh fading environment, was examined. The analysis covers the downlink transmission and leads to the derivation of a novel expression between the average channel capacity available to each system's user under simultaneous optimal power and rate adaptation and the system's parameters, providing an optimistic upper bound, useful for practical modulation and coding schemes. The final derived closed‐form expression can be useful for the design of the DS/FFH‐CDMA system because it provides a theoretical tool for the initial quantitative analysis. Finally, avoiding the application of complex theoretical algorithm or lengthy simulation, we theoretically derived numerical results to illustrate the presented analysis. Copyright © 2011 John Wiley & Sons, Ltd.     

SINR analysis of FFH/OFDM over frequency selective Rayleigh fading channel

Fast frequency hopping/orthogonal frequency division multiplexing (FFH/OFDM) has been previously proposed to achieve frequency diversity over frequency selective channels. However, the performances of the FFH/OFDM scheme have been usually calculated using simulations over empirical channel models in earlier works. The main aim of this paper is to theoretically expose the diversity of the FFH/OFDM signal over statistical models, specifically Rayleigh distributed, for frequency selective fading channels. In order to achieve this aim, we first derive the decision variables and the signal‐to‐interference noise ratios of the FFH/OFDM signal at the output of minimum mean square error and zero forcing receivers. For various levels of quadrature amplitude modulation used in FFH/OFDM, the performances are calculated and validated via simulations. The results show that FFH/OFDM in case of zero forcing equalization does not provide any diversity gain even over a frequency selective channel. However, in case of minimum mean square error equalization, it brings significant diversity gain at high signal‐to‐noise ratio (SNR) values with the rise of number of sub‐carriers. Moreover, the FFH/OFDM with four quadrature amplitude modulation scheme provides better performance than that of the conventional OFDM even at low SNR values, as well as a significant diversity gain at high SNR values. Copyright © 2016 John Wiley & Sons, Ltd.     

Multitone jamming rejection of FFH/BFSK linear-combining receiverover Rayleigh-fading channels

A computationally efficient BER expression for an FFH/BFSK linear-combining receiver against multitone jamming and AWGN over Rayleigh-fading channels is derived based on a Taylor series expansion. The analytical expression, validated by simulation results, allows us to efficiently analyse the system performance with higher diversity levels, which is otherwise mathematically intractable     

On the optimum processing gain for a hybrid DS/FFH‐CDMA cellular system over Rayleigh fading channels

The optimization between the processing gain and the theoretically achievable average channel capacity per user (in the Shannon sense) of a constant total system's allocated bandwidth hybrid direct sequence/fast frequency hopping code‐division multiple‐access (DS/FFH‐CDMA) cellular system, when operating in a Rayleigh fading environment, is presented. Then, the spectral efficiency, expressed in (bits/s/Hz), is estimated in terms of the achievable average channel capacity per user, during the operation over a broadcast cellular time‐varying link, and leads to a simple theoretical novel‐closed‐form expression for the optimal processing gain value based on the maximization of the achieved spectral efficiency. The final expression derived can be useful for the practical design of a DS/FFH‐CDMA cellular system and for an initial quantitative analysis since it relates to the optimal processing gain applied and all system's parameters. Finally, numerical results are presented to illustrate and prove the validity of the presented analysis. Copyright © 2011 John Wiley & Sons, Ltd.     

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     

Performance analysis of an FFH/BFSK product-combining receiverunder multitone jamming

The performance of a fast frequency-hopped binary frequency-shift keying (FFH/BFSK) spread-spectrum (SS) communication system is studied in this paper. The FFH system employs a product-combining receiver against the worst case multitone jamming (MTJ) and additive white Gaussian noise (AWGN). The compact characteristic functions of the natural logarithm of the product-combiner outputs are obtained based on the Taylor series expansion. The characteristic functions are then used to derive the bit error rate (BER) expressions that are applicable to higher diversity levels. Our analysis, validated by the simulation results, shows that the band MTJ is generally more harmful than the corresponding independent MTJ. The BER performance of the product-combining receiver is shown to possess good MTJ rejection capability compared to that of the soft-decision linear-combining receiver, especially under both moderate and strong MTJ power conditions     

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     

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。     

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.     

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     

Spectral efficiency for a hybrid DS/FH code-divisionmultiple-access system in cellular mobile radio

The spectral efficiency of a hybrid cellular direct-sequence/frequency hopping code-division muItiple-access (DS/FH-CDMA) system operating in a Rayleigh-fading environment is examined. In this work, spectral efficiency is evaluated in terms of the theoretically achievable channel capacity (in the Shannon sense) per user, on the condition that this is estimated in an average sense. The analysis covers the downlink assuming a static model of operation and a direct-sequence/slow-frequency hopping (DS/SFH) as well as a direct-sequence/fast-frequency hopping (DS/FFH) scheme. As it is shown, the spectral efficiency of cellular DS/FFH-CDMA operating in a Rayleigh-fading environment is greater than that of broad-band DS- and DS/SFH-CDMA systems operating under normalized conditions. This is justified by the combination of path-diversity reception as achieved by conventional coherent RAKE receivers and the frequency diversity that is inherently present in FFH transmission     

MFSK/FFH系统多用户能力分析与仿真

MFSK/FFH系统特指采用快速跳频（FFH）技术和多进制频移键控（MFSK）非相干解调技术的系统,主要研究MFSK/FFH通信系统的多用户能力,并把它与差分跳频技术DFH的组网能力进行对比分析。通过分析MFSK/FFH通信系统的性能,给出了MFSK/FFH通信系统和差分跳频系统的比特差错率公式,为了公平对比MFSK/FFH网络和差分跳频网的组网能力,采用多用户频带利用率这个参数,理论和仿真表明,采用特定的检测方法,MFSK/FFH系统的多用户能力比差分跳频系统的好。     

Maximum-likelihood diversity combining in partial-band noise

Maximum-likelihood diversity combining is investigated for an FFH/MFSK spread spectrum system in partial-band noise (PBN). The structure of maximum-likelihood diversity reception in PBN plus white Gaussian noise is derived. It is shown that signal-to-noise ratio and the noise variance at each hop have to be known to implement this optimum diversity combiner. Several suboptimum diversity combining schemes are also considered. The performance of the optimum combining scheme is evaluated. It is shown that adaptive gain control diversity combining actually achieves the optimum performance when interference is not very weak     

Capacity analysis of M-SC receivers over TWDP fading channels

An expression for the probability distribution function (PDF) of the signal-to-noise ratio of a selection combining receiver in two-wave with diffuse power fading channel is derived. Using this PDF expression, the capacity for the different adaptive transmission techniques employing selection combining (SC) are obtained. The study presents the effects of the ratio of total dominant signal power to the scattered signal power on the system capacity. The change in the capacity of the system with the diversity order for a SC receiver in the fading channel is also presented.     

Capacity of synchronous coded DS SFH and FFH spread-spectrummultiple-access for wireless local communications

The performance of synchronous spread-spectrum multiple-access (SSMA) communications based on direct-sequence (DS), slow frequency-hopped (SFH), and fast frequency-hopped (FFH) systems for wireless local communications of micro-cellular personal communications is analyzed. Using an indoor multipath fading channel model with clusters of arriving rays, we investigate multiuser DS systems with RAKE and diversity reception by selection combining (SC), multiuser SFH systems with equal-gain (EG) diversity reception, and multiuser FFH systems with correlated EG and self-normalization (SN) combining techniques. Reed-Solomon codes are considered to further improve the system performance. Given a fixed available bandwidth with narrow band interference (NBI), capacities and packet error rates are determined under various system configurations. Total capacities of hybrid frequency-division multiple-access (FDMA)/SSMA (DS and SFH) systems are compared with those of wide-band SSMA systems. For high data rate communications, wide-band DS-SSMA systems have larger capacities than hybrid FDMA/DS-SSMA systems. For low data rate communications, a capacity comparison between wide-band DS-SSMA and hybrid FDMA/DS-SSMA systems depends on fading statistics. Hybrid FDMA/SFH-SSMA systems have larger capacities than wide-band DS-SSMA systems, FFH-SSMA systems could not provide satisfactory performance due to correlation among hopping bands     

Nakagami-m衰落信道下固定增益中继系统性能分析

 在Nakagami-m衰落信道下,分析了两跳固定增益放大转发中继通信系统的性能.首先采用基于概率密度函数(PDF)的性能分析法推导了无协作分集时系统的中断概率和平均误符号率(ASER)的闭合表达式,然后采用基于矩生成函数(MGF)的方法推导了有协作分集时系统的中断概率和ASER表达式以及接收信噪比的n阶矩的闭合表达式.仿真结果显示,所推导的闭合表达式与数值仿真结果吻合良好,协作分集和较大的m值可提升系统性能,中继前后两跳的信道质量对系统性能的影响并不相同.     

Another look at the BER performance of FFH/BFSK with productcombining over partial-band jammed Rayleigh-fading channels

Product combining (PC) is a well-known diversity technique that effectively combat the effect of partial-band jamming (PBJ) affecting fast-frequency hopping/frequency-shift-keying (FFH/FSK) systems. We present two approaches for the average bit error rate (BER) evaluation of FFH/FSK systems with PC over Rayleigh channels subject to PBJ. We first rely on the fact that the decision statistic at the output of PC receivers can be viewed as a product of F-variates to obtain the average BER in the form of a rapidly converging infinite series, which can be readily evaluated numerically for cases of practical interest. We then rely on the theory of H function random variables to present a second approach for the average BER evaluation of PC over partial-band jammed Rayleigh-fading channels. The final closed-form formula is expressed in terms of the Meijer's G function, which can be easily evaluated using common mathematical software for small values of the diversity order. Based on this result, we also develop another infinite series representation for the average BER. Numerical experiments show that the latter series representation offers a speed-up factor in evaluating the average BER for high values of the diversity order. The mathematical formalism is illustrated by numerical examples showing the effect of various parameters on the performance of the system