Evaluation of error probabilities in the presence of timing errors and fading

Using the approximate Fourier series technique we obtain expressions for the probability of error for bandlimited BPSK signalling in the presence of timing errors and fading. The derived results can be used to compute the error probabilities to any desired accuracy for Nakagami-m and Weibull fading channels. The effect of timing error on the performance of the raised cosine pulse has been evaluated for several fading parameters. We also compare the performance of some useful Nyquist pulses known     

Performance of chaos-based asynchronous DS-CDMA with different pulse shapes

A general framework to assess the joint effect of pulse shaping and spreading sequence statistics on asynchronous DS-CDMA is developed. With this, the effect of three possible pulse shapes (rectangle, band-limited rectangle, and square-root raised-cosine) associated with three possible spreading sequences (i.i.d., chaos-based, and optimum) is analyzed. Improvements up to 16% in users capacity are shown over traditional systems.     

On the ultimate limits of chaos-based asynchronous DS-CDMA-I: basic definitions and results

The ultimate limits of chaos-based asynchronous direct-sequence code-division multiple access systems are investigated using the concept of capacity taken from information theory. To this aim, we model the spreading at the transmitter and the sampling of the incoming signal at the receiver with a unique linear multi-input multi-output transfer function. We then assume the existence of a coding/decoding pair that is able to transmit information through this channel with a vanishing error probability. The capacity of the system is then identified with the maximum rate at which such an errorless link may operate. The capacity is a random quantity depending on the spreading sequences and, due to the asynchronism, on the users relative delays and phases. We then compare different spreading strategies [classical m and Gold codes, independent identically distributed (i.i.d.) and chaos-based codes] in terms of expected performance as well as of the probability that one method outperforms another. To ease further analytical investigations that should cope with expectations of logarithms, we measure capacity not only in bits per use but also in codewords per use. Some formal results along with extensive numerical evidence show that this does not alter the performance ranking. Such a ranking shows that chaos-based spreading always outperforms i.i.d. spreading and those trying to mimic it. This aligns with and complements what was already known about the ability of chaos-based techniques of minimizing multiple access interference.     

Analysis and optimization of DS-CDMA systems with time-limited partial response chip waveforms

Conventional direct sequence code division multiple access systems (DS-CDMA) using offset quadrature phase shift key (OQPSK) usually employ a strictly bandlimited partial response square-root raised cosine pulse as the chip waveform. They have the disadvantage of large envelope fluctuation that will incur performance degradation due to the intermodulation and bandwidth enlargement caused by post nonlinear processing. To improve the performance of DS-CDMA systems, the chip waveform and receiver should be properly selected. This paper presents a systematic performance analysis of a matched filter receiver and zero-forcing filter (ZF) receiver for DS-CDMA using a time-limited partial response chip waveform. Nevertheless the systematic performance analysis is applicable to bandlimited chip pulse as well. For the zero-forcing filters, we propose to select the frequency responses that satisfy the first Nyquist criterion. With this class of filters, we can choose the roll-off factor to minimize the total power of multiple access interference and noise power. The zero-forcing filter with proper choice of roll-off factor, referred to as optimum ZF, yields a performance better than the matched filter counterpart. The bit error rate (BER) performance of the optimum ZF with superposed quadrature amplitude modulation signal as the time pulse waveform is evaluated. It is shown that the optimum ZF provides better BER performance than conventional OQPSK and minimum shift keying, and its envelope uniformity is much better than that of OQPSK.     

Interference in DS-CDMA systems with exponentially vanishingautocorrelations: chaos-based spreading is optimal

A novel estimation of the minimum achievable interference in direct sequence-code division multiple access (DS-CDMA) systems is introduced, which holds when spreading sequences with exponentially vanishing autocorrelation are employed. This can be applied to many of the recently proposed improvements to classical maximum-length or Gold sequences, such as chaos-based spreading. Asymptotic, infinite-bandwidth results are also provided, clarifying the maximum attainable gain. Empirical evidence shows that this theoretical maximum is achieved by some chaos-based sequences which are therefore optimal     

UWB pulse design using constraint convex sets method

In this paper, we propose a constrained convex sets–based method for designing ultra‐wideband (UWB) pulse. The UWB pulses designed using earlier proposed methods either do not fit well in UWB spectral mask or require extra processing circuitry for pulses to fit in the UWB spectral mask. The proposed constraint sets–based method is flexible and optimum for the UWB mask. The pulse designed by the proposed method is Federal Communication Commission compliant and has an autocorrelation function similar to the Gaussian pulse. The bit error rate performance of time hopping binary phase shift keying using the proposed method and some of the existing methods such as Norman and Lee pulses and sixth derivative Gaussian pulse is analyzed in additive white Gaussian noise and Saleh‐Valenzuela channels. Pulse designed using the proposed method outperforms existing pulse design, and the same is verified through simulations. The proposed algorithm is flexible and can also be used to mitigate narrow band interference, multiband UWB pulse generation and any other Federal Communication Commission (or other regulatory body) compliant spectrum mask by modifying the parameter of the proposed constraint set(s).     

A comparison of system performance using two different chip pulsesin multiple-chip-rate DS/CDMA systems

This paper describes a comparison of system performance using two different chip waveforms of spreading sequences in multiple-chip-rate (MCR) direct-sequence (DS)/code-division multiple-access (CDMA) systems. The chip pulses used in this study are closely related to the characteristics of output filter employed at transmitter. In general, the chip waveform is an important factor to determine the link performance. The raised cosine chip pulse with a roll-off factor of α will be adopted for IMT-2000 systems in order to reduce both the intersymbol effect and the spectral width of the modulated signal. However, due to the complexity of obtaining quantitative results on the performance of MCR-DS/CDMA systems, rectangular chip pulses are mainly utilized in performance analysis. Therefore, it is necessary to investigate the effect of the chip pulses used, i.e., a rectangular and a raised cosine chip pulses on system performance in order to evaluate MCR-DS/CDMA systems accurately. Thus, the effect of the chip pulses used on the performance in MCR-DS/CDMA systems is investigated in terms of the system capacity and blocking probability. It is shown that the system using a raised cosine chip pulse (i.e., RC system) supports at least 80% more capacity and 57% more traffic than that using a rectangular chip pulse (i.e., R system)     

Artificial Bee Colony and Tabu Search Enhanced TTCM Assisted MMSE Multi-User Detectors for Rank Deficient SDMA-OFDM System

In this paper, we present a generalized accurate methodology to predict the bit error rate performance for non-coherent chaos-based communication systems. The Gaussian approximation approach, which is widely used to compute the performance of such systems, leads to inaccurate results, especially with respect to low spreading factors. Our new approach based on the chaos bit energy distribution gives accurate results even for low spreading factors. The system is studied and simulated under an additive white Gaussian noise, Rice and Rayleigh channels. Finally, we compare our approach to the Gaussian approximation approach. Computer simulations shows a high accuracy for our method, especially for small spreading factors.     

An improved Gaussian approximation for probability of bit-erroranalysis of asynchronous bandlimited DS-CDMA systems with BPSK spreading

This paper analyzes probability of bit-error (P_e) performance of asynchronous bandlimited direct-sequence code-division multiple-access systems with binary phase-shift keying spreading. The two present methods of P_e analysis under bandwidth-efficient pulse shaping: the often-cited standard Gaussian approximation and the characteristic function (CF) method suffer from either a low accuracy in regions of low P_e (< 10^-3) or a prohibitively large computational complexity. The paper presents an alternate method of P_e analysis with moderate computational complexity and high accuracy based on a key observation. A sequence of chip decision statistics (whose sum yields a bit statistic) forms a stationary, m-dependent sequence when conditioned on the chip delay and phase offset of each interfering signal. This observation permits the generalization of the improved Gaussian approximation previously derived for the rectangular pulse and the derivation of a numerically efficient approximation based on the CF method. Numerical examples of systems using the square-root raised-cosine and IS-95 pulses illustrate THE P _e performance, user capacity and the accuracy of the proposed method     

非正弦波通信时域正交椭圆球面波脉冲设计方法

针对非正弦波信号的频带传输问题,同时为了有效提高非正弦波通信系统的频带利用率及功率利用率,提出了时域正交椭圆球面波脉冲集设计方法。通过参数设置、频段划分、求解方程、Schmidt正交化等步骤设计时域正交椭圆球面波脉冲集,调整脉冲参数实现脉冲集信号的频谱搬移与频谱控制,脉冲集信号为频谱特性可控的带限信号。仿真结果表明:时域正交椭圆球面波脉冲集具有较好的能量聚集性,利用该脉冲集实现多路信息并行传输时,在保证系统具有较好的功率利用率前提下,系统的频带利用率可快速接近奈奎斯特速率。     

A Methodology for Bit Error Rate Prediction in Chaos-based Communication Systems

This paper is devoted to the derivation of an exact analytical expression of the bit error rate for chaos-based DS-CDMA systems. For the studied transmission system, we suppose that synchronization is achieved perfectly, coherent reception is considered, and an Additive White Gaussian Noise channel (AWGN) is assumed. In the first part of the paper, performance of a mono-user system with different chaotic sequences is evaluated and compared in terms of the error probability. This comparison is realized thanks to the probability density function of the bit energy of a chaotic sequence. The bit error rate can be easily derived by numerical integration. In some particular cases, for certain chaotic sequences with known probability density function of bit energy, we propose an analytical expression of the bit error. In the second part of the paper, the performance of a chaos-based DS-CDMA system is evaluated in the multi-user case. A general conclusion is that probability density function of chaos bit energy, for a given spreading factor, can give a clear idea about how to choose a “good” chaotic sequence for improving the performance of the chaos-based CDMA system.     

On the ultimate limits of chaos-based asynchronous DS-CDMA-II: analytical results and asymptotics

The ultimate limits of chaos-based asynchronous direct-sequence code-division multiple access systems are investigated using the concept of capacity taken from information theory. To this aim, we model the spreading at the transmitter and the sampling of the incoming signal at the receiver with a unique linear multi-input multi-output transfer function depending on spreading sequences and on the users relative delays and phases. The capacity can be computed using a known formula and is a random quantity depending on the process generating the spreading codes and on the delays and phases that are random in asynchronous environments. In the companion paper, we show that chaos-based spreading is able to outperform classical spreading in most cases. We delve here into analytical investigations aimed at clarifying such phenomena and show that chaos-based spreading is actually able to reach the absolute maximum performance in the classical two-user case as well as when the number of users and the spreading factor grow to infinity. Under suitable conditions, and in complete analogy with what happens for suboptimal receivers dominated by multiple-access interference, maximum capacity is attained by spreading sequences whose auto-correlation profile is well approximated by an exponential trend with rate r-=-2+/spl radic/3.     

Coexistence of chaos-based and conventional digital communication systems of equal bit rate

Chaos-based communication systems represent a new category of spread-spectrum communication systems, whose working principle differs significantly from conventional direct-sequence and frequency-hopping spread-spectrum systems. However, like all other kinds of spread-spectrum systems, chaos-based systems are required to provide reasonable bit error performance in the presence of a narrow-band signal which can be generated from an intruder or a coexisting conventional communication system. In particular, the frequency band of this foreign narrow-band signal can fall within the bandwidth of the chaos-based system in question. Such a scenario may occur in normal practice when chaos-based systems are introduced while the conventional systems are still in operation. It is therefore important to examine the coexistence of chaos-based and conventional systems. The objective of this paper is to evaluate the performance of the chaos-based system when its bandwidth overlaps with that of a coexisting conventional system. In particular, the chaos-based systems under study are the coherent chaos shift keying (CSK) system and the noncoherent differential CSK (DCSK) system, whereas the conventional system used in the study employs the standard binary phase shift keying scheme. Also, both the chaos-based and conventional systems are assumed to have identical data rates. Analytical expressions for the bit-error rates are derived, permitting evaluation of performance for different noise levels, power ratios and spreading factors. Finally, results from computer simulations verify the analytical findings.     

PAM Pulse Generation Using Binary Transversal Filters

Modern narrow-band pulse-amplitude modulation (PAM) and pulse-code modulation (PCM) systems require the generation of precisely shaped pulses in order to avoid intersymbol interference. It is not a simple matter to design analog filters having pulse responses with the requisite carefully positioned zeros, and this has led researchers to study other approaches. It is shown that the use of a binary transversal filter (BTF) coupled with a simple low-pass filter can generate extremely good pulses with small bandwidths. A BTF consists of a digital shift register and weighting resistor network to construct a staircase approximation to the desired pulse. The attendant circuitry is very simple, such that a highquality pulse generator can be built and adjusted with remarkable ease. The problem of pulse design using BTF's is considered in some generality, and a computational procedure is developed for adjusting the weighting network in the BTF to generate optimum pulse shapes. This method is then applied to several practical cases, and the circuitry required to generate excellent pulses is discussed. Test results on an implementation of such a generator using only five taps are presented, revealing the inherent simplicity and quality of the approach.     

Precise error-rate analysis of bandwidth-efficient BPSK in Nakagami fading and cochannel interference

The bit-error rate (BER) of bandlimited binary phase-shift keying in a fading and cochannel interference (CCI) environment is derived for the case of perfect coherent detection. The fading-and-interference model assumed is general and of interest for microcellular system studies. The model allows both desired signal and interfering signals to experience arbitrary amounts of fading severity. A precise BER expression is derived using a characteristic function method. Using this accurate analytical result, the impact of the interfering users' fading severity on the desired user-error rate is examined. The BERs obtained under perfect coherent detection are also valid as lower performance bounds for practical realizable receivers where ideal coherent detection is difficult to implement. The error-rate performance of a novel bandwidth-efficient pulse shape is determined for the general fading and CCI environment. Analysis and numerical results show that the new pulse can provide better BER performance than the widely used raised-cosine pulse.     

一种采用交织┐RS码纠错技术的自适应流星突发通信系统及性能分析

本文从便于实施的角度提出将一种交织－ＲＳ码纠错技术用于自适应流星突发（Ｍｅｔｅｏｒ－Ｂｕｒｓｔ）通信。为得到较佳的自适应纠错策略，将用最优化方法搜索出在给定条件下使分组成功译码概率达到最大时的最佳交织深度和最佳码长。从几种不同差错控制方案的比较来看，采用分段编码和交织技术能有效地改善ＭＢ通信系统的性能。本文还对数值结果进行分析并得出一些有用的结论     

Minimum-Bandwidth Optical Intensity Nyquist Pulses

The indoor diffuse wireless optical intensity channel is bandwidth-limited due to multipath distortion, and all transmitted signal amplitudes are constrained to be nonnegative. In order to control the impact of intersymbol interference (ISI) on this channel, pulse shaping is required. This paper derives the minimum bandwidth, ISI-free Nyquist pulse which satisfies the amplitude nonnegativity constraint. The minimum bandwidth required is twice that of conventional electrical channels. With the addition of excess bandwidth, the optimal bandlimited optical intensity pulse, in the sense of minimizing average optical power, is shown to be a squared double-jump pulse. Thus, a bandwidth versus optical power efficiency tradeoff in pulse design is quantified. The impact of timing jitter on the probability of symbol error for various excess bandwidths is quantified via simulation. Further, it is shown that there are no bandlimited root-Nyquist pulses satisfying the amplitude nonnegativity constraint. In fact, all practical optical intensity root-Nyquist pulses are shown to be necessarily time-limited to a single symbol interval     

Adaptive trellis-coded modulation for bandlimited meteor burstchannels

The throughput performances of three adaptive information rate techniques on the bandlimited meteor burst channel are investigated. Closed-form expressions for throughput are derived based on the channel model commonly used in the literature. The throughput performance is compared to the conventional fixed information rate modem and upper bounds on throughput improvement over the fixed rate modem are derived. It is shown that an adaptive technique that uses trellis-coded modulation (TCM) with three phase-shift keyed (PSK) signal sets can increase throughput over the conventional fixed rate modem by more than a factor of 3. Data from the US Air Force High Latitude Meteor-Scatter Test Bed confirm the superiority of the adaptive TCM technique. A practical implementation is suggested that uses a single rate 1/2 convolutional code for all three PSK signal sets. The use of this single code, versus the three best Ungerboeck codes, results in a throughput loss of less than 2%. An expression for the theoretical information capacity of the bandlimited meteor burst channel is derived     

The optimum transient radiation from an arbitrary antenna

Bounds on the optimum transient radiation from an arbitrary antenna enclosed by a spherical surface of specified size are presented. The optimization criterion is either maximization of the radiated electric field amplitude at a specified time and far-zone position, or maximization of the radiated energy density in a specified time interval for a particular far-zone position. The latter optimization results in the prolate spheroidal wave functions. In both cases, the total energy radiated by the antenna is constrained to be 1 J, and the antenna excitation is assumed to be bandlimited. The performance of the optimum arbitrary antenna is compared to that of optimized practical antennas, such as dipoles and arrays of dipoles. The effect of a sidelobe constraint is also studied.     

基于交叉相位调制的孤子脉冲压缩效应研究

在负色散区 ,基本孤子在光纤中传输时其波形与脉宽保持不变。提出一种在负色散区利用交叉相位调制效应压缩基本孤子脉冲的新方法。采用分步傅里叶方法对非线性耦合方程进行了数值计算与模拟。研究了不同抽运功率、不同抽运脉冲啁啾参数以及不同脉宽对基本孤子脉冲压缩的影响。发现基本孤子脉冲不仅能够被压缩 ,而且光纤存在最佳压缩长度。在抽运功率一定的条件下 ,选取负啁啾的抽运脉冲 ,可获得更高压缩比的压缩光脉冲。另外 ,不同的脉冲宽度对孤子脉冲的压缩产生较大的影响 ,一般情况下 ,选用较窄的抽运脉冲易于产生较短的压缩光脉冲