Self-Recovering Equalization and Carrier Tracking in Two-Dimensional Data Communication Systems

Conventional equalization and carrier recovery algorithms for minimizing mean-square error in digital communication systems generally require an initial training period during which a known data sequence is transmitted and properly synchronized at the receiver. This paper solves the general problem of adaptive channel equalization without resorting to a known training sequence or to conditions of limited distortion. The criterion for equalizer adaptation is the minimization of a new class of nonconvex cost functions which are shown to characterize intersymbol interference independently of carrier phase and of the data symbol constellation used in the transmission system. Equalizer convergence does not require carrier recovery, so that carrier phase tracking can be carried out at the equalizer output in a decision-directed mode. The convergence properties of the self-recovering algorithms are analyzed mathematically and confirmed by computer simulation.     

Performance evaluation and implementation of convolution coded OFDM modem in wireless underwater acoustic communication

High‐data transmission rate and reliable communication in underwater acoustic channel is challenging because of limited bandwidth, multipath propagation, and Doppler shift, which results in poor bit error performance. Under this constraint, this paper explains the simulation results of underwater wireless acoustic data transmission system by using quadrature phase shift keying modulation with convolution encoder at the transmitter and proposed Viterbi decoder at the receiver. The decoder algorithm in comparison with MATLAB inbuilt function shows asserting improved results. This paper evaluates the performance of convolution coded orthogonal frequency division multiplexing modem, which is studied over typical underwater channel through an extensive computer simulation and a semirealistic experimentation. The performance of convolution coded orthogonal frequency division multiplexing system is measured in time domain plots, bit error rate curves, and number of bit errors per frame over additive white Gaussian noise and Rayleigh channel conditions.     

The theory of functionals of stochastic backscattered fields

The theory of wave scattering by anisotropic statistically rough surfaces, which is an important part of statistical radiophysics, is considered. A new analytic method is developed and generalized for solving problems of radar imaging. The method involves analytic determination of the functionals of stochastic backscattered fields and can be applied to solve a wide class of physical problems with allowance for the finite width of an antenna’s pattern. The unified approach based on this method is used to analyze the generalized frequency response of a scattering radio channel, a generalized correlator of scattered fields, spatial correlation functions of stochastic backscattered fields, frequency coherence functions of stochastic backscattered fields, the coherence band of a spatial-temporal scattering radar channel, the kernel of the generalized uncertainty function, and the measure of noise immunity characterizing radar probing of the Earth’s surface or extended targets. The introduced frequency coherence functions are applied for thorough and consistent study of techniques for measuring the characteristics of a rough surface, aircraft altitude, and distortions observed when radar signals are scattered by statistically rough, including fractal, surfaces. To exemplify urgent applications, radiophysical synthesis of detailed digital reference radar terrain maps and microwave radar images that was proposed earlier is considered and improved with the use of the theory of fractals.     

Multiuser detection in a horizontal underwater acoustic channelusing array observations

We present a multisensor, multiuser receiver that is capable of operating in an underwater acoustic channel with severe multipath. For each active user, the receiver consists of a multi-input, single-output array processing filter followed by a single-channel adaptive equalizer. The array processing filter is chosen to maximize an averaged performance metric which measures reduction in the interference from multiple asynchronous cochannel users and the reduction in intersymbol interference caused by time spreading of the transmitted signal. The single-channel adaptive equalizer that follows the array processing filter eliminates the remaining intersymbol interference prior to hard symbol decisions. The division of labor between the array processing filter and single-channel equalizer reduces receiver complexity by allowing the array processing filter weights to be based on the fixed deterministic channel component and the single-channel equalizer to be based on the stochastic channel component. Receiver performance is demonstrated using data obtained from two shallow-water acoustic channels where two cochannel users are transmitting in shallow water at 18 and 30 nautical miles from the receiver array     

Convex cost functions in blind equalization

Existing blind adaptive equalizers that use nonconvex cost functions and stochastic gradient descent suffer from lack of global convergence to an equalizer setup that removes sufficient ISI when an FIR equalizer is used. The authors impose convexity on the cost function and anchoring of the equalizer away from the all-zero setup. They establish that there exists a globally convergent blind equalization strategy for 1D pulse amplitude modulation (PAM) systems with bounded input data (discrete or continuous) even when the equalizer is truncated. The resulting cost function is a constrained l₁ norm of the joint impulse response of the channel and the equalizer. The results apply to arbitrary linear channels (provided there are no unit circle zeros) and apply regardless of the initial ISI (that is whether the eye is initially open or closed). They also show a globally convergent stochastic gradient scheme based on an implementable approximation of the l₁ cost function     

Adaptive equalization of CPM signals transmitted over fast Rayleighflat-fading channels

A new algorithm for adapting the coefficients of an equalizer for continuous phase modulated data signals in a flat-fading environment is presented. The cost function to optimize is based on the maximum likelihood sequence estimation index for such signals and channel conditions. It is shown that this equalizer algorithm, called the maximum likelihood equalizer, involves the iterative computation of one of the eigenvectors of a matrix. An implementation is proposed, which combines iterative estimation procedures for QR decomposition, matrix eigenvalue tracking and channel prediction error. Simulation results are presented that demonstrate the ability of the algorithm to equalize the channel filtering effects in a fast fading environment, without requiring phase coherent carrier recovery     

Decision feedback equalization of the indoor radio channel

The measured multipath profiles from five different indoor areas are used for the performance analysis of a binary phase shift keying (BPSK) modem with a decision feedback equalizer (DFE). The performance from the measured multipath profiles is compared with the performance predictions based on a computer simulated channel model. Both average probability of error and probability of outage are calculated for a DFE with three fractionally spaced forward and three feedback taps. An equivalent delay power spectrum function, determined from the ensemble of the measured channel impulse responses, is defined. Using this function, analytical lower bounds on the average probability of error and the probability of outage of the BPSK/DFE modem with an infinite number of feedback taps and three forward taps are determined and compared with the results based on measured data and the computer generated channel impulse responses     

Diagnostics of the scattering function of a stochastic narrowband shortwave radio channel

The technique for determining the scattering function of stochastic narrowband shortwave channels during ionospheric sounding by linear frequency-modulated signals is presented. The instrumental resolutions of measurements of time delay and Doppler frequency are estimated for a perfect channel. The system developed for determining the scattering function of ionospheric shortwave channels is considered. The results of its investigation with the use of the middle-latitude communications link 5.5 × 10⁶ m long are discussed.     

Improving bit-error-rate performance of the free-space optical communications system with channel estimation based on radiative transfer theory

In order to improve the performance of terrestrial free-space optical communication systems in adverse visibility conditions, we present a method for estimation of the atmospheric channel impulse response function which governs the optical intensity propagation. This method reduces run-time computational demands and system complexity in comparison to our previously proposed dual-wavelength channel estimation technique. We consider propagation of optical wavelengths in fog, where the droplet diameters are close to the wavelength and thus scattering and absorption effects are significant. A method for rapid calculation of a channel response function based on estimating the effective optical depth of the channel and curve-fitting is described. The channel response estimate can then be used to design a receiver-side equalizer (minimum meansquared error linear equalizer) to correct the signal distortion due to propagation through the dispersive channel. The channel estimates are based on parametric curve-fitting functions which have been developed using the modified-vector radiative transfer theory to model the channel response. The optimal fit parameters are found using particle-swarm optimization to minimize the simulated bit-error rate of the received signal.     

Adaptive equalization of indoor radio channels for 156-Mb/s,QPSK data transmission

Indoor radio communication in the 20–60 GHz band using TDMA with differentially encoded QPSK is consideed. A burst-type transmission, based on a basic time slot consisting of a preamble for synchronization and equalizer training and of an information data section, is adopted. We employ fractionally spaced decision feedback equalization and give the relevant analytical and simulated performance results in terms of Doppler frequency. An upper limit is determined for the channel variations which can be tracked by the equalizer. Performance results are obtained for equalization with and without carrier phase recovery. Calculated and simulated probability of error show that error propagation degrades the performance by about 6 dB at a bit error rate of 10^–3 for a channel without any diversity. However, the effect of past decision errors is negligible for dual diversity. Numerical stability, required accuracy, and hardware complexity are also discussed.     

Digital Transmission Performance on Fading Dispersive Diversity Channels

The reception and detection of a single digit under known channel conditions are investigated. The probability of error for an optimum one-shot receiver instantaneously matched to the channel state is averaged over an ensemble of dispersive diversity channels. The average probability of error as a function of energy to noise ratio is found to be solely dependent on the ratio of rms dispersion width to data symbol width. For these dispersive channels an implicit diversity effect is qualitatively explained in terms of eigenvalues that depend on the ensemble statistic. The one-shot receiver performance provides a bound for practical receivers. In a comparison with a decision feedback equalizer, it is shown that on moderately dispersive channels the equalizer nearly achieves optimum one-shot performance. Since an adaptive version of this equalizer exists, this means data transmission on slowly fading channels is possible at rates above the natural rate suggested by the channel dispersion spread without bandwidth expansion and with small intersymbol interference penalty. The use of one-shot receiver performance curves can also be used as estimates of equalizer performance in situations where computation of the latter is impractical.     

基于Kalman滤波的水声混合双向迭代信道均衡算法

水声信道均衡中基于信道估计的均衡方法理论上具有更优的均衡性能,但较高的计算复杂度限制了算法的实际应用。针对这一问题,该文首先基于Kalman滤波和Turbo均衡提出一种迭代Kalman均衡器,实现了基于软符号的迭代信道估计与迭代Kalman均衡,且复杂度较常规方法降低约1个数量级。其次,针对单一均衡算法和单一方向Turbo均衡器存在的误差传递现象,设计了基于迭代Kalman均衡器与改进成比例归一化LMS (IPNLMS)自适应均衡器相结合的混合双向Turbo均衡器,提高了自适应均衡器的收敛速度和均衡性能,并通过双向均衡结构带来的增益改善了符号估计误差传递的现象。理论分析与仿真实验验证了该文算法的有效性。     

A channel subspace post-filtering approach to adaptive least-squares estimation

A major challenge while communicating in dynamic channels, such as the underwater acoustic channel, is the large amount of time-varying inter-symbol interference (ISI) due to multipath. In many realistic channels, the fluctuations between different taps of the sampled channel impulse response are correlated. Traditional least-squares algorithms used for adapting channel equalizers do not exploit this correlation structure. A channel subspace post-filtering algorithm is presented that treats the least-squares channel estimate as a noisy time series and exploits the channel correlation structure to reduce the channel estimation error. The improvement in performance of the post-filtered channel estimator is predicted theoretically and demonstrated using both simulation and experimental data. Experimental data is also used to demonstrate the improvement in performance of a channel estimate-based decision feedback equalizer that uses this post-filtered channel estimate to determine the equalizer coefficients.     

一种快速收敛的水声信道分数间隔盲均衡算法

为了加快常数模盲均衡算法(CMA)的收敛速度并降低剩余均方误差,提出了一种快速收敛的分数间隔常数模算法。新算法采用T/2分数间隔均衡器,针对水声通信中常用的BPSK信号,设计了一个新的误差函数,取代常数模算法中的误差函数。最后,采用浅海水声信道进行了仿真,结果表明,新算法性能稳定;收敛速度高于常数模算法和分数间隔常数模算法;剩余均方误差与分数间隔常数模算法处于同一水平。     

Performance analysis of Godard-based blind channel identification

We analyze a blind channel impulse response identification scheme based on the cross correlation of blind symbol estimates with the received signal. The symbol estimates specified are those minimizing the Godard (1980) (or constant modulus) criterion, for which mean-squared symbol estimation error bounds have been derived. We derive upper bounds for the average squared parameter estimation error (ASPE) of the blind identification scheme that depend on the mean-squared error of the Wiener equalizer, the kurtoses of the desired and interfering sources, and the channel impulse response. The effects of finite data length and stochastic gradient equalizer design on ASPE are also investigated. All results are derived in a general multiuser vector-channel context     

Performances asymptotiques des égaliseurs fractionnés

The analytical method for deriving the mean square error at the output of a linear fractional tap-spacing equalizer with an infinite number of taps is presented. The mean square error is expressed as a function of the spectral characteristics of the transmission channel, and for equalizer tap-spacings which are a rational part of the system symbol period. Moreover, for particular tap-spacing values, the equalizer equivalent structure is detailed. This method is applied to a particular case related to radiolink transmission system. It is shown that the mean square error sensitivity to the timing phase, though important for synchronous equalizers, is a fast decaying function of the fractional tap-spacing.     

稀疏水声信道判决反馈盲均衡算法研究

针对高速水声通信中信道的稀疏特性,提出了一种基于常数模准则的稀疏水声信道判决反馈盲均衡算法。该算法将改进的常数模算法与一种变化的判决反馈均衡器结构(部分反馈均衡器)有机结合,利用水声信道的稀疏特性,不但很好地实现了稀疏水声信道的盲均衡,而且简化了计算,易于算法的硬件实现。用典型稀疏水声信道进行了计算机仿真。结果表明,该算法性能稳定,计算量小,稳态均方误差低,整体性能与基于自适应LMS的稀疏迭代算法接近。该研究为高速水声通信中稀疏信道的均衡提供了一种可实现的方法。     

一种用于多径衰落水声信道的盲均衡算法研究

信道均衡是现今高速水声通信系统中克服码间干扰一项关键技术,如何提高均衡器的性能是目前研究的热点课题。针对水声信道的时变多普勒特性,在分析信道模型及盲均衡器结构特点的基础上,提出了一种时域解相关的变步长恒模算法,并对算法进行了仿真及试验分析。结果表明改进算法能够有效克服实际水声通信中的码间干扰效应,具有更快的收敛速度和更小的剩余误差,提高了浅海水声通信的有效性和可靠性,具有广阔的工程应用前景。     

一种水声信道自适应均衡算法研究

由声波传播的多途效应所引起的码间干扰及信号衰落,使得水下数据传输的速率和可靠性都大大降低。针对多途干扰严重的水声信道,将一种基于最小均方误差算法的信道自适应均衡器应用于水声信号处理中。对该均衡器的基本理论及其结构进行了归纳,结合水声多途信道的基本特点,建立了仿真模型,重点分析了步长参数、信噪比等对算法收敛速度和稳态误差等方面性能的影响,为实现高质量的水下信息传递提供技术支持。