Error-rate evaluation of linear equalization and decision feedbackequalization with error propagation

We propose applying an approximate Fourier series to evaluate efficiently the bit-error-rate (BER) performance of finite-length linear equalization (LE) and decision feedback equalization (DFE). By extending the Fourier series, we enable BER calculations for quadrature phase-shift keying (QPSK) transmission on complex channels with in-phase and crosstalk intersymbol interference (ISI). The BER calculation is based on determining the residual ISI samples and background Gaussian noise variance at the equalizer output for static channels or for realizations of quasi-static fading channels. A simple bound on the series error magnitude in terms of the Fourier series parameters ensures the required accuracy and precision. Improved state transition probability estimates are derived and verified by simulation for an approximate Markov model of the DFE error propagation for the case in which residual ISI exists even when the previous decisions stored in the feedback filter (FBF) are correct. We demonstrate the ease and widespread applicability of our approach by producing results which elucidate a variety of equalization tradeoffs. Our analysis includes symbol-spaced and fractionally spaced minimum mean-square error (MMSE)-LE, zero-forcing (ZF)-LE, and MMSE-DFE (with and without error propagation) on static ISI channels and multipath channels with quasi-static Rayleigh fading; a comparison between suboptimum and optimum receiver filtering in conjunction with equalization; and an assessment of the accuracy of some widely used equalization BER approximations and bounds     

Upper bounds to the error probability of decision feedbackequalization

The exact computation of the symbol error probability of systems using decision feedback equalization is difficult due to the propagation of errors. New upper bounds to the error probability of decision feedback equalization, which take error propagation into account, are developed. The derivations of the bounds assume a causal channel response, independent data symbols, and independent noise samples. The bounds are valid for any noise process that has a symmetric and unimodal probability density function. In some cases, the new bounds are significantly tighter than a well-known upper bound of D.L. Duttweiler et al. (1974)     

Improved bounds for error recovery times of decision feedbackequalization

New upper and lower bounds on the mean recovery time of decision feedback equalization (DFE) are derived. The recovery time is defined as the time it takes the decision feedback equalizer (DFEQ) to reach the error-free state after an error has corrupted an error-free DFEQ. The derivations of the bounds assume a causal channel response, independent data symbols, and independent noise samples. The bounds are found to be tighter, especially at large SNR, than previous bounds in a numerical example     

The effect of decision delay in finite-length decision feedbackequalization

In this correspondence we derive the finite-length, minimum mean-squared error decision feedback equalizer (MMSE-DFE). We include decision delay as an explicit parameter. Our derivation yields an algebraic interpretation of the effect of decision delay on DFE performance (measured by mean-squared error). It also allows the fast computation of the MMSE-DFE for several different values of both decision delay and the number of feedback taps. Our approach is especially useful for short filter lengths, when the decision delay can significantly affect DFE performance     

Mitigating error propagation effects in a decision feedbackequalizer

We present an approximate analysis approach to the computation of the probability of error and mean burst error length for a decision feedback equalizer (DFE) that takes into account feedback of decision errors. The method uses a reduced-state Markov model of the feedback process and is applicable to linear modulation formats. We use this technique to analyze a DFE design that mitigates the effects of feedback error by incorporating a soft decision device into the feedback path and a norm constraint on the feedback filter weights. We apply the DFE design and analysis approach to a dispersive multipath propagation environment     

Performance of narrowband CPM systems withlimiter-discriminator-integrator detection and decision feedbackequalization in mobile radio channels

A completely analytical approach is presented to achieve error probability analysis of limiter-discriminator-integrator (LDI) detection of binary continuous-phase modulation in a land mobile radio channel characterized by Rayleigh fading and Doppler effects. Optimum choice of the postdetection integration time is carried out when varying both system parameters and propagation characteristics, namely the Doppler shift. The improvements obtainable by means of decision feedback equalization (DFE) are also considered, in the presence of error propagation. The algorithm allows a very general analysis, which can be applied both to a partial and a full response modulation pulse, with narrowband IF filter and multipath propagation. This leads to the optimization of various system parameters, such as filter bandwidth, the modulation index, and the postdetection integration time, whatever the choice of the modulation pulse     

Digital error correction technique for binary decision successive approximation ADCs

A digital error correction technique with negligible hardware overhead is proposed for binary successive approximation ADCs. A redundant decision phase is inserted between the normal SAR operations, and the coarse decision error caused by incomplete DAC settling is corrected by a digital code addition. The relaxed DAC settling requirement for coarse decision increases the conversion speed.     

Bit error probability for coherent M-ary PSK systems

A simple technique for evaluating the bit-error probability of coherent M-ary phase-shift keying (PSK) with any bit-mapping is proposed. Closed-form expressions are given in terms of error functions for half- and quadrant-plane probabilities in the decision space, avoiding the numerical evaluation of complicated integrals that occurs in the direct method. Bit error probability expressions for M-ary PSK with Gray, natural binary, and folded binary bit-mappings are derived     

A review of error propagation analysis in systems

Error propagation analysis in reliable systems has been studied widely. Unlike classical sensitivity analysis which investigates the range of system performance, the distribution function of system performance studies error propagation analysis. Thus, error propagation analysis is essentially a statistical analysis.This paper reviews and classifies current research articles in error propagation. An overview is presented of error propagation applied to various systems and models. A standard analysis procedure is also given. Finally, several conclusions are drawn. It is recommended that i) basic research on error propagation be carried out, ii) an efficient (least cost) method be developed to analyze large-size problems, and iii) human error be included in the system modeling. It is our opinion that error propagation analysis be treated as part of decision-making procedures in system analysis.Error propagation analysis is extremely important for expensive or rare-event systems. This report can benefit those who analyze these systems.     

M-ary symbol error outage over Nakagami-m fading channels in shadowing environments

This letter addresses the problem of finding a tractable expression for the symbol error outage (SEO) in flat Nakagami-m fading and shadowing channels. We deal with M-ary phase shift keying (M-PSK) and quadrature amplitude modulation (M-QAM) which extends our previous results on BPSK signaling. We propose a new tight approximation of the symbol error probability (SEP) holding for M-PSK and M-QAM signals which is accurate over all signal to noise ratios (SNRs) of interest. We derive a new generic expression for the inverse SEP which facilitates the derivation of a tight approximation of the SEO in a lognormal shadowing environment.     

Application of convolutional error correcting codes in ultrawideband M-ary PPM signaling

The interference issues related to ultrawideband (UWB) radio pose tight restrictions on the maximum data rate of UWB radio telecommunication systems. A possible solution is to reduce the required signal to interference ratio (SIR) that gives satisfactory performance to the UWB system. In this letter, we propose coded M-ary UWB radio communication systems. Two classes of convolutional codes, namely, low-rate superorthogonal codes and high-rate punctured codes are considered for this purpose. Simulation results on the bit error rate of the proposed system indicates that the system is capable to work in lower SIR's and therefore supports higher data transmission rates in a real interference environment compared to the previously proposed UWB communication systems.     

Bit error rate analysis of M-ary DPSK in frequency selective Ricianfading

A simple, exact expression for the probability distribution of differential phase noise is derived for calculating the average bit error rate (BER) of M-ary DPSK in frequency selective Rician fading. The irreducible BER due to multipath delay spread is evaluated for M=2-16 assuming a double-spike delay profile of the Rayleigh faded diffused component and a spectrally raised cosine Nyquist filter response     

A multi coding technique to reduce transition activity in VLSI circuits

Advances in VLSI technology have enabled the implementation of complex digital circuits in a single chip, reducing system size and power consumption. In deep submicron low power CMOS VLSI design, the main cause of energy dissipation is charging and discharging of internal node capacitances due to transition activity. Transition activity is one of the major factors that also affect the dynamic power dissipation. This paper proposes power reduction analyzed through algorithm and logic circuit levels. In algorithm level the key aspect of reducing power dissipation is by minimizing transition activity and is achieved by introducing a data coding technique. So a novel multi coding technique is introduced to improve the efficiency of transition activity up to 52.3% on the bus lines, which will automatically reduce the dynamic power dissipation. In addition, 1 bit full adders are introduced in the Hamming distance estimator block, which reduces the device count. This coding method is implemented using Verilog HDL. The overall performance is analyzed by using Modelsim and Xilinx Tools. In total 38.2% power saving capability is achieved compared to other existing methods.     

多进制正交扩频技术在矿井下的应用

针对传统的通信方式无法适用于矿井下的复杂环境,采用多进制正交扩频技术实现矿井下通信。通过对多进制正交扩频系统性能的仿真和分析,多进制正交扩频通信系统具有抗干扰能力强、传输距离远和自适应性强等优点,具有广泛的应用性,适应于矿井下进行通信。     

Cancellation technique to reduce intercarrier interference in OFDM

Orthogonal frequency division multiplexing (OFDM) systems are sensitive to frequency errors, which cause intercarrier interference among subcarriers. A new cancellation method to reduce the effects of frequency offset errors is presented. The main feature is to map each data symbol a_k which is to be transmitted onto a pair of non-adjacent subcarriers, with weightings +1 and -1, rather than to a single subcarrier. The carrier-to-interference ratio gain of the proposed method over normal OFDM varies between 10 to 30 dB. This method also offers a frequency diversity effect in a multipath fading channel     

On the error probability of binary and M-ary signals in Nakagami-m fading channels

In this letter, we present new closed-form formulas for the exact average symbol-error rate (SER) of binary and M-ary signals over Nakagami-m fading channels with arbitrary fading index m. Using the well-known moment generating function-based analysis approach, we express the average SER in terms of the higher transcendental functions such as the Gauss hypergeometric function, Appell hypergeometric function, or Lauricella function. The results are generally applicable to arbitrary real-valued m. Furthermore, with the aid of reduction formulas of hypergeometric functions, we show previously published results for Rayleigh fading (m=1) as special cases of our expressions.     

一种新的研究捷联惯导系统误差传播特性的方法

针对飞行器纯惯性导航条件下自控终点散布的计算问题,提出了一种新的定量分析研究捷联惯导系统误差传播特性的方法。把初始对准的三个误差角看作系统状态初值,引起的导航误差传播为零输入响应,把机体系中三个陀螺常值漂移和三个加速度零偏看作系统输入,引起的导航误差传播为零状态响应。采用单一变量法,通过导航仿真,逐个研究九个因素引起的误差传播特性,并进行多项式拟合,分别得到各个变量引起的导航误差的解析表达式。根据叠加性原理,得到九种因素共同作用下导航误差随时间变化的解析表达式。仿真表明,此方法切实可行,通过解析表达式求得的位置误差和姿态误差具有较高的精度,与实际值相比,位置估计误差为0.2″(3σ),姿态估计误差为0.2″(3σ),此方法对于导航误差具有一定的预测能力。     

Channels leading to rapid error recovery for decision feedbackequalizers

The authors define the DFE (decision feedback equalizer) system of interest and their finite-error-recovery-time problem. They present their basic result, which establishes that whenever the channel satisfies a simple frequency-domain constraint, the error recovery time of an ideal DFE is always finite. They also include four applications of this theorem, including analysis of a real channel. Convergence rates and explicit bounds, given an exponential overbound on the channel impulse response, are presented. Results of greater practical interest, where the authors relax most of the major idealized assumptions, are also given. The authors present the result for M-ary data and relate the error recovery time bound back to the binary case. A formula for the error probability, given a high signal-to-noise-ratio channel, is provided     

A novel fast approach for estimating error propagation in decisionfeedback detectors

The study of error-burst statistics is important for all detection systems, and more so for the decision feedback class. In data storage applications, many detection systems use decision feedback in one form or another. Fixed-delay tree search with decision feedback (FDTS/DF) and decision feedback equalization (DFE) are the direct forms, whereas the partial response detectors such as the reduced state sequence estimator (RSSE) and noise predictive maximum likelihood (NPML) detectors are the other forms. Although DF reduces the system complexity, it is inevitably linked with error propagation (EP), which can be quantified using error-burst statistics. Analytical evaluation of these statistics is difficult, if not impossible, because of the complexity of the problem. Hence, the usual practice is to use computer simulations. However, the computational time in traditional bit-by-bit simulations can be prohibitive at meaningful signal-to-noise ratios. In this paper, we propose a novel approach for fast estimation of error-burst statistics in FDTS/DF detectors, which is also applicable to other detection systems. In this approach, error events are initiated more frequently than natural by artificially injecting noise samples. These noise samples are generated using a transformation that results in significant reduction in computational complexity. Simulation studies show that the EP performance obtained by the proposed method matches closely with those obtained by bit-by-bit simulations, while saving as much as 99% of simulation time     

Channel error propagation in adaptive tv coders

DPCM coders with adaptive predictors are used and compared with nonadaptive DPCM coders for processing composite color television signals. The transmission error propagation for different predictors both adaptive and fixed is investigated. Propagation of transmission noise is dependent on the type of prediction and on the location of noise, i.e., whether in a uniform region or in an active region. By introducing leak in predictor output and/or predictor function, it is shown that error propagation can be significantly reduced. The leaky predictors not only attenuate and/or terminate the channel error propagation but also improve the predictor performance based on quantitative evaluation such as peak value and mean-square-error. In order to protect the high picture quality from error propagation, an error-correcting code is needed.