Bit Error Rate Evaluation for Spread-Spectrum Multiple-Access Systems

A unified method for approximating and bounding the average bit error probability for spread-spectrum multiple-access communication systems is presented. Various forms of direct-sequence spreadspectrum modulation are considered including binary phase-shift keying, quadriphase-shift keying, and minimum-shift keying. The analysis of the multiple-access interference makes use of a number of moments sufficent to evaluate the error probability with a high degree of accuracy. A computationally efficient algorithm for computing the moments is also given. The subsequent transformation from the moments to the average bit error probability is carried out by means of Gauss-type numerical integration formulas. It is shown that the same approach can be exploited for evaluating two classes of upper and lower bounds on the bit error rate. Finally, some results and comparisons are reported.     

Evaluating the error probability in lightwave systems withchromatic dispersion, arbitrary pulse shape and pre- and postdetectionfiltering

A novel approach to analytically evaluate the bit error probability in optically preamplified direct-detection systems is presented, which can take into account the effects of pulse shaping, chirping, filtering at the transmitter and the receiver, both pre- and postdetection, chromatic dispersion, and ASE noise. The method is computationally very fast in that the saddle point integration method for solving the resulting line integral of a particular moment generating function is adopted. A closed-form approximation for the bit error probability is also provided, which is within 0.01 dB from the exact numerical results     

Atmospheric Optical CDMA Communication Systems via Optical Orthogonal Codes

We propose and consider using a class of multiple-access sequences, namely, optical orthogonal codes (OOCs) in atmospheric optical code-division multiple-access systems. We obtain analytical solutions to the error probability for various channel models using positive-intrinsic-negative diode and avalanche photodiode photodetectors. In our analysis, the effects of atmospheric turbulence, ambient light, thermal noise, and multiuser interference are considered, in the context of a semiclassical photon-counting approach. The performance of the systems taking advantage of space diversity and error-correcting codes are also evaluated. Two common and widely used optical modulations, on–off keying and pulse-position modulation, are considered. Receiver structures based on correlator and chip level are used for OOC detection. Unlike the traditional chip-level receiver, here a generalized form of chip-level structure with two threshold levels is considered. Upper and lower bounds on the error probability for the above-chip-level receiver structure is obtained. From our analytical results, we can deduce that the chip-level receiver outperforms a simple correlator in the absence or weak atmospheric fading; however, in a strong fading environment, the simple correlator outperforms the chip-level receiver.     

Near-optimum quantization for signal detection

A heuristic approach to design quantizers for signal detection is presented. Quantizer parameters are obtained that minimize a tight upper bound on the probability of error. This approach is applied to the design of distributed detection systems. Numerical examples are presented to illustrate its near-optimum performance     

Error Rates for Fading NCFSK Signals in an Additive Mixture of Impulsive and Gaussian Noise

The effects of slow and nonselective signal fading on the performance of multilevel noucoherent FSK (NCFSK) systems in an additive mixture of Gaussian and highly impulsive noise are analyzed. For binary systems the bit error rate is derived; forM-ary NCFSK systems upper and lower bounds of the character error probability are obtained. The analysis is performed considering the maximum likelihood receiver for additive white Gaussian noise.     

Performance and Optimization of Switched Diversity Systems for the Detection of Signals with Rayleigh Fading

The performance and optimization of switched diversity systems are considered. First, the one-dimensional distribution and probability density functions of the envelope of the received signal are obtained for three different switching strategies. This information is used to obtain the average probability of bit error for the case of non-coherent detection of binary FSK signals with Rayleigh fading envelopes and additive white Gaussian noise. The optimization of two of these switching strategies is then considered, and it is shown that by proper selection of switching thresholds, the average probability of bit error during detection can be minimized. It is also shown that these optimized switching strategies yield a significant improvement in performance over non-diversity systems and can approach the performance of more complex receivers such as maximal ratio combining. Computer simulations of switched diversity systems using a practical field model are used to verify the analysis.     

Direct-sequence codes based blind synchronization algorithm for UWB systems

A new blind (non-data-aided) synchronization algorithm based on direct-sequence (DS) codes is proposed for ultra-wideband (UWB) systems. The proposed approach fully exploits prior knowledge of DS codes and bypasses channel estimation. The real-time acquisition is achieved using integrating-and-dumping (I&D) operation and DS codes matching filter. Because of pseudo randomicity and periodicity of DS codes, both the speed and the accuracy of synchronization are improved significantly. A lower bound on the acquisition probability of the proposed approach is also derived. Simulations confirm performance improvement of the proposed algorithm relative to existing alternatives in terms of acquisition probability, normalized mean square error (NMSE), and bit error rate (BER).     

Performance of Multilevel Baseband Digital Systems in a Nonlinear Environment

A good deal of effort has been spent, in the past few years, to devise numerical algorithms for evaluating the performance of digital communication systems over noisy linear channels, i.e., in the presence of intersymbol interference and noise. In this concise paper we present a method for computing the error probability of multilevel baseband digital modulation systems when the channel is nonlinear with memory. The algorithm is based on a Volterra series expansion of the nonlinearity; with this model, we show that the moments of the disturbance can be computed recursively, and the same techniques in use for linear channels can be applied for evaluating the error probability. This approach can be generalized to consider noise entering the nonlinear channel. The computing algorithms are described in detail, and a complete example is worked out.     

Volterra series approach for optimizing fiber-optic communicationssystem designs

A new methodology for designing long-haul fiber-optic communication systems is presented. We derive the overall Volterra series transfer function of the system including linear dispersion, fiber nonlinearities, amplified spontaneous emission (ASE) noise from the fiber amplifiers, and the square-law nature of the direct detection (DD) system. Since analytical expressions for the probability of error are difficult to derive for the complex systems being used, we derive analytical expressions for an upper bound on probability of error for integrate-and-threshold detection at the receiver. Using this bound as a performance criterion, we determine the optimal dispersion parameters of each fiber segment required to minimize the effects of linear dispersion, fiber nonlinearities and ASE noise from the amplifiers. We study the dependence of optimal dispersion parameters on the average power levels in the fiber by varying the peak input power levels and the amplifier gains. Analytical expressions give us the freedom to choose system parameters in a practical manner, while providing optimum system performance. Using a simple system as an example, we demonstrate the power of the Volterra series approach to design optimal optical communication systems. The analysis and the design procedure presented in this work can be extended to the design of more complex wavelength division multiplexed (WDM) systems     

Random geometric series and intersymbol interference

An interesting and long-standing problem in probability theory is surveyed, and its applications to analyzing the effects of intersymbol interference in digital transmission systems are discussed. Old and new results are presented which enable one to obtain analytical forms for the probability density function of the intersymbol interference in special eases. The probability of error is then computed and compared with some popular upper bounds.     

Error Probability Performance of M-ary CPSK Systems With Intersymbol Interference

We derive upper and lower bounds on the probability of error ofM-ary CPSK systems subject to intersymbol interference and additive Gaussian noise. The bounds are expressed in terms of the error probability obtained with a finite pulse train and some parameters associated with the residual pulse train. Methods are given to compute the probability of error with a finite number of interference terms and it is shown that the difference between the upper and the lower bounds is a monotone decreasing function of the number of pulses in the finite pulse train. The applicability of the method to compute the probability of error with any desired degree of accuracy is illustrated by examples for quaternary and octonary systems.     

最大比合并接收系统在n-Rayleigh信道下的性能分析

在n-Rayleigh信道下,研究了MRC(Maximal Ratio Combining)合并接收系统的平均码字错误率(ASEP)性能。基于矩生成函数(MGF)的方法,推导了MRC接收系统在n-Rayleigh衰落信道上采用M进制相移键控(MPSK),M进制正交幅度调制(MQAM)和M进制脉冲幅度调制(MPAM)等几种M进制数字调制方式的ASEP的计算式。然后在不同条件下,仿真了系统的ASEP性能,仿真值与理论值相一致,理论分析的正确性得到了证明。分析结果表明:分集支路数和衰弱因子对系统的ASEP性能有重要影响。     

Further results on the bit error probabilities of MDPSK over thenonselective Rayleigh fading channel with diversity reception

This paper presents a fundamental approach for deriving the bit error probability of BDPSK and QDPSK over the nonselective Rayleigh fading channel for a receiver with an arbitrary IF filter, and for a fading process with an arbitrary Doppler spectrum with arbitrary Doppler bandwidth. The results generalize those published earlier which were restricted to matched filter reception and to a fading process with a small Doppler bandwidth compared to the symbol rate. This allows the error probability to be studied in the presence of varying degrees of ISI due to the bandlimitation of the received signal by the IF filter, and in the presence of fading fluctuations of various rates. The analytical approach presented is simple, and yet powerful in that it can handle the case of diversity reception. This is a great advantage over the alternative approach of using the distribution of the differential phase of the received signal over a symbol interval. The bit error probability results apply to both conventional BDPSK and QDPSK, as well as π/2-2DPSK and π/4-4DPSK, and allow the irreducible bit error probability as well as the SNR at which this irreducible value sets in to be studied as a function of the Doppler bandwidth and IF filter bandwidth. The computed results are applicable to the design of digital cellular mobile communication systems     

Performance bounds for turbo-coded multiple antenna systems

We derive performance bounds for turbo-coded systems with transmit and receive antenna diversity. The bounds are derived by limiting the conditional union bound before averaging over the fading process. It is demonstrated that this approach provides a tight upper bound on the error probability of the turbo-coded multiple antenna systems. We also describe a method for deriving the weight-enumerating function of turbo-coded multiple antenna systems in order to take into account the presence of transmit and receive antenna diversity. Examples of the bounds are presented to illustrate their usefulness.     

Error performance of Uncoded Space Time Labelling Diversity in spatially correlated Nakagami‐q channels

Greater spectral efficiency has recently been achieved for Uncoded Space Time Labelling Diversity (USTLD) systems by increasing the number of antennas in the transmit antenna array. However, due to constrained physical space in hardware, the use of more antennas can lead to degradation in error performance due to correlation. Thus, this paper studies the effects of spatial correlation on the error performance of USTLD systems. The union bound approach, along with the Kronecker correlation model, is used to derive an analytical expression for the average bit error probability (ABEP) in the presence of Nakagami‐q fading. This expression is validated by the results of Monte Carlo simulations, which shows a tight fit in the high signal‐to‐noise ratio (SNR) region. The degradation in error performance due to transmit and receive antenna correlation is investigated independently. Results indicate that transmit antenna correlation in the USTLD systems investigated (3 × 3 8PSK, 2 × 4 16PSK, 2 × 4 16QAM, and 2 × 4 64QAM) causes a greater degradation in error performance than receive antenna correlation. It is also shown that 2 × 4 USTLD systems are more susceptible to correlation than comparable space‐time block coded systems for 8PSK, 16PSK, 16QAM, and 64QAM.     

Performance characterization of digital transmission systems withcochannel interference

This paper presents a general methodology for performance characterization of digital transmission systems in the presence of cochannel interference, as a function of the actual number of interferers (ranging from zero to infinity). The bit error probability in time-invariant channels and outage probability in time-varying quasi-stationary channels are discussed. More precisely, a general approach to an outage probability definition based on the concept of the outage domain is introduced. This allows the discussion of the relation to the other definitions which have appeared in the literature and the proposal of some new more accurate methods for the evaluation of outage probability. A suitable comparison between exact evaluation, the well-known Gaussian approximation, and the other new approaches proposed in this paper, is carried out to evaluate performance, bit error probability is suitably obtained for linearly modulated signals by adopting a semianalytical approach, and for nonlinear (e.g., continuous phase) modulation signals, by means of simulation. Finally, as an example, the different approaches to derive performance discussed in the paper have been applied to a linear microcellular scenario     

Novel signals for optimized timing synchronization in direct‐sequence spread‐spectrum communication systems

The paper presents design techniques for novel signaling waveforms to optimize timing synchronization in direct‐sequence spread‐spectrum communication systems. Both coarse code timing acquisition and fine delay‐locked loop tracking systems are considered, and their performance metrics are analyzed in terms of initial acquisition detection probability and residual tracking jitter, showing a strong dependency on signal waveform spectral characteristics. Bit error performance under imperfect synchronization is also assessed. A design methodology is formulated with a low complexity parametric optimization approach based on prolate spheroidal waveform expansions for the generation of signals that minimize the probability of acquisition miss and tracking error jitter subject to additional constraints on signal energy and phase transitions. Novel optimized waveforms are synthesized with different levels of effective root mean square bandwidth occupancy and compared with conventional pulses to illustrate their advantages. Performance trade‐offs are demonstrated between the acquisition and tracking systems, whereby signals with low effective bandwidth are found to have better acquisition capability at the expense of poorer tracking jitter, while the converse holds for signals with higher effective bandwidth. It is found that an effective root mean square bandwidth occupancy in the range of 40% to 50% of the chip rate can achieve a good compromise between the requirements of the 2 code timing synchronization phases. Numerical results are presented to quantify the relative merits of representative waveforms with respect to the different performance measures in terms of acquisition capability, tracking jitter, and bit error probability.     

Digital transmission through a land mobile satellite channel

An analytical derivation of the probability of bit error noncoherent frequency-shift keying (FSK) and coherent phase-shift keying (PSK) signals transmitted through a land-mobile satellite channel is described. The channel characteristics used in the analysis are based on a recently developed model which includes the combined effects of fading and shadowing. Analytical expressions for the probability of bit error of FSK and coherent phase-shift keying (CPSK) signals are obtained. The results show that large amounts of signal-to-noise ratio (SNR) are required to compensate for the combined effect of fading and shadowing. An analytical expression for the irreducible probability of bit error of a CPSK signal due to phase variations caused by fading and shadowing is derived. The results described should be useful in the design of land mobile satellite communication systems     

瑞利衰落信道MDPSK相位比较解调性能

本文提出一种适合于瑞利衰落信道多进制差分相移键控系统相位比较解调的性能分析方法，推导出符号错误率解析表示式，考虑了瑞利衰落、时间选择性衰落和高斯白噪声对体制性能的影响，并针对衰落功率谱为高斯型和矩形分别对二进制、四进制和八进制情形进行了数值计算。     

Performance ofM-ary PSK systems in Gaussian noise and intersymbol interference

A useful method is presented for the evaluation of the error probability ofM-ary phase-shift-keyed systems with Gaussian noise and intersymbol interference. By regarding a portion of the intersymbol interference as an equivalent Gaussian noise, this method suggests first calculating the probability of error caused by the combined effects of the Gaussian noise and the equivalent noise. Necessary correction terms are then added to the calculation to take into account the fact that the intersymbol interference is actually non-Gaussian. It is shown that with this method any desired accuracy can be theoretically achieved in the evaluation of the probability of error. This method has been programmed for numerical computations. Some examples are also given for illustrative purposes.