Symbol-rate timing recovery comprising the optimum signal-to-noiseratio in a digital subscriber loop

The paper investigates a symbol-rate timing recovery algorithm that is based on the correlation between an error from the decision feedback equalizer and the arriving signal samples. The mean-square error due to uncancelled precursor intersymbol interference is applied as a criterion to choose optimal timing instants. Various signal and error combinations may be used to approximate its minimum as a function of the steady-state location of the sampling instants. The timing function is selected on the premise that the estimated correlation function passes through zero only once, at the desired sampling phase. We propose a semianalytical framework for analyzing the relationship among the timing estimate variance, the acceptable noise level, and the dead-zone thresholds. It allows us to achieve a compromise between, on the one hand, the ability to track and compensate for frequency drift and for changes in the transmission media, and on the other hand, immunity against unnecessary phase corrections. The performance of the postulated timing function is examined by means of simulations     

On quantization,truncation and jitter errors in the sampling theorem and its generalizations

Any band-limited signal f(t) can, according to the sampling theorem, be exactly reconstructed from its sampled values. If the signal is not necessarily band-limited, an alternative model states that it can be approximately reconstructed from its samples. Such signals can also be approximated by generalized sampling sums which can be interpreted as discretized convolution integrals of Fejér's type. In all three cases the physically realized signal is often only roughly equal to f(t) due to errors caused e.g. by the sampling mechanism.In this paper the following types of errors are treated: (1) round-off error arising when quantized sampled values are used, (2) truncation error, arising when a truncated sum is used for representation, (3) time jitter error, a result of sampling at instants slightly different from the sample values. All proofs employ deterministic methods.     

Energy Optimization of Band-Limited Nyquist Signals in the Time Domain

This paper presents a theoretical consideration of the optimal design of band-limited Nyquist-type signal shapes for data transmission, which maximizes its energy in a given time interval and which generates no intersymbol interference at the periodic sampling instants. A method based on a completely analytical approach is given for design of such signals. The optimal signal is a solution of an inhomogeneous linear integral equation of Fredholm type. A technique for solving this equation is given. The computation is straightforward and involves the determination of eigenvalues and eigenfunctions of a positive definite and symmetric kernel in terms of prolate spheroidal wave functions. The constraint for intersymbol interference is shown to be easily included into the problem. Finally, some numerical examples are given and the performance of the optimal signal shapes is compared to that resulting from the use of the "raised-cosine" type of signals. It is also concluded that especially for small values of rolloff factor, the optimal signals, thus obtained, are almost maximally immune to small timing offsets at the sampling instants.     

Componentwise coherence function of correlated periodically nonstationary random processes

In this paper we consider a novel componentwise coherence function, which is determined by the cross-spectral densities of stationary components of periodically nonstationary random processes i.e. stationary correlated random processes, which modulate their carrier harmonics. The properties of the introduced coherence function are specified for the amplitude- and phase-modulated signals. Its graphical frequency dependencies have been obtained for the specified signal parameters. The advantages of componentwise coherence function in comparison with previously suggested integral coherence function are shown. We present the method for the selection of stationary modulating components, which is based on the frequency shift and low-pass filtration. The properties of selected components for the cases of amplitude- and phase-modulated processes are analyzed.     

Functionally Weighted Lagrange Interpolation of Band-Limited Signals From Nonuniform Samples

A modification of the conventional Lagrange interpolator is proposed in this paper, that allows one to approximate a band-limited signal from its own nonuniform samples with high accuracy. The modification consists in applying the Lagrange method to the signal, but pre-multiplied by a fixed function, and then solving for the desired signal value. Its efficiency lies in the fact that the fixed function is independent of the sampling instants. It is shown in this paper that the function can be selected so that the interpolation error decreases exponentially with the number of samples, for the case in which the sampling instants have a maximum deviation from a uniform grid. This paper includes a low-complexity recursive implementation of the method. Its accuracy is validated in the numerical examples by comparison with several interpolators in the literature, and by deriving upper and lower bounds for its maximum error.     

A Class of Phase Detector Characteristics for Symbol Synchronizers Yielding Unbiased Estimates

Most practical synchronizers operating on a PAM waveform corrupted by additive noise can be analyzed by means of the theory of the phase-locked loop (PLL). In this paper, we present a class of synchronizers for which the equivalent phase detector characteristic is such that the timing instants generated by the voltage controlled clock (VCC) are unbiased with respect to the ideal sampling instants to be used in the data reconstruction path. As a consequence of this, the VCC output signal can directly activate the sampler in the data reconstruction path, without being properly delayed for bias compensation.     

符号速率相关的带通采样速率选取及其仿真

带通采样速率选取是软件无线电技术的关键问题之一。分析了常用带通采样速率选取方法的不足：采样速率一般不是符号速率的整数倍,后续基带数字信号处理需要进行复杂的小数内插或抽取算法运算,实现相当困难且运算量很大。为解决这一问题,提出了一种实用的与符号速率相关的带通采样速率选取方法,在满足带通采样定理基础上,附加频谱间隔最大条件选取符号速率整数倍的采样速率,最后通过软件仿真验证了符号速率相关的带通采样速率选取方法的正确性和可行性。     

A Subsampling Quadrature Σ∆ Modulator Based on Distributed Resonators for Use in Radio Receiver

The receiver architecture proposed in this brief seizes the subsampling properties of continuous-time sigma-delta (SigmaDelta) modulators based on distributed resonators to construct a quadrature receiver. The proposed architecture is based on a low-pass SigmaDelta modulator that subsamples an intermediate frequency signal around the sampling frequency and does not require quadrature mixers. Instead, the quadrature mixing is replaced by suitably choosing the sampling instants inside the loop. Two practical circuit implementations are proposed. The first one uses separate circuitry for the I and Q paths. The second architecture introduces an innovative way to produce the I and Q outputs that is immune to path mismatch due to the sharing of all the analog circuitry for both paths. The proposed modulator may be feasible for the typical IF frequencies used in cellular base stations.     

FFT processing of randomly sampled harmonic signals

The influence of random instabilities in the sampling instants on spectral estimation by the fast Fourier transform (FFT) of harmonic, stochastic processes is considered. The degradation due to the deviation from a uniform sampling is presented by explicit formulas. This degradation, a decrease of the desired signal and an increase of the sidelobe noise, is expressed in terms of the characteristic function of the jitter's distribution     

Discrete-time spectral estimation of continuous-parameter processes -- A new consistent estimate

This paper presents a new estimation scheme for the spectral density function of a stationary time series from observations taken at discrete instants of time. The sampling instants are determined by a Poisson point process on the positive real line. Under weak smoothness conditions on the spectral density, asymptotic expressions for the bias and Variance are derived, and it is shown that the estimate is mean-square consistent for all positive values of the average sampling rate. The new estimate compares favorably with the classical continuous-time spectral estimates.     

Demodulation of PM Signal in the Presence of White Gaussian Noise

The maximum likelihood estimates of all the parameters of a PM signal, when the baseband signal is a harmonic process and the PM signal observed is contaminated by an independent Gaussian white noise, are derived. The sampling distribution of the maximum likelihood estimates of the parameters and the demodulated signal are also investigated. Alternative estimates for the carrier frequency and the modulating frequency, together with their sampling properties, are also studied. The methods are illustrated with two examples and in each case the demodulated signal is compared to the true baseband signal. Some comments about the performance of the demodulated signals are also included.     

基于FPGA的BPSK信号载频估计单元设计与实现

根据BPSK调制信号调制机理和平方倍频法原理,在FPGA平台上设计实现了BPSK调制信号载波频率估计单元。利用ModelSim仿真环境对载频估计功能进行仿真,验证了平方倍频法对BPSK信号进行载波信号估计的有效性。仿真表明基于FPGA的BPSK信号载频估计单元,有较高的估计精度,且实现原理简单,有一定的实际应用价值。     

平稳随机过程非均匀采样信号的数字谱研究

目前的随机信号分析多是基于作等时间间隔采样以描述信号特征,而实际应用中往往不能避免采样的非均匀性;传统的谱分析方法必然产生原理误差。本文引入平稳随机点过程的知识,建立了广义平稳随机信号的非均匀采样序列模型,推导了其数字频谱的一般公式,分析了具有典型分布函数的随机采样情况。     

A new interpolation theorem with application to pulse transmission

An interpolation theorem is determined for the case when there are a finite number of arbitrarily placed sampling instants and the interpolation function is the output of a known filter. They are also the interpolation functions with the specified properties that have minimum energy. The theorem is used to determine the input to a communications channel given a finite number of samples of its output. This provides a generalization of matched filters and a perspective on the benefits of fractionally spaced equalization. The theorem is also used to construct masks of a family of pulses that are specified by the range of pulse voltages at a finite number of sampling instants. The theory determines how the pulse masks thus constructed is transformed when the pulse family is transmitted through a filter such as a length of transmission line     

Model-Based Multichannel Compressive Sampling with Ultra-Low Sampling Rate

The emerging compressive sampling (CS) theory makes processing ultra-wide-band (UWB) signal at a low sampling rate possible if the underlying signal has a sparse representation in a certain basis. The feasibility of model based compressive sampling for ultra-wide-band (UWB) signal is investigated. In this paper, a multichannel compressive sampling architecture is developed to capture UWB signal at a rate much lower than Nyquist rate. The proposed framework considers sub-Nyquist sampling stream of delayed and weighted versions of a known signal with finite support in time domain. A basis function is constructed to realize sparse signal representation. To reduce the hardware cost, a segmented architecture is suggested. In addition, a joint signal recovery algorithm is presented. Experimental results indicate that, with this system, a UWB signal sampled at about 4% of Nyquist rate still can be recovered with overwhelming probability.     

Extraction of decision level for envelope-detected amplitude-shift keying

The optimum decision level for envelope-detected on/off amplitude-shift keying (ASK) in Gaussian noise is a complex function of the signal/noise ratio. A practical method is described which allows the decision threshold to be automatically extracted from the values at the decision instants of the binary levels.     

Sampling, data transmission, and the Nyquist rate

The sampling theorem for bandlimited signals of finite energy can be interpreted in two ways, associated with the names of Nyquist and Shannon. 1) Every signal of finite energy and bandwidth W Hz may be completely recovered, in a simple way, from a knowledge of its samples taken at the rate of 2W per second (Nyquist rate). Moreover, the recovery is stable, in the sense that a small error in reading sample values produces only a correspondingly small error in the recovered signal. 2) Every square-summable sequence of numbers may be transmitted at the rate of 2W per second over an ideal channel of bandwidth W Hz, by being represented as the samples of an easily constructed band-limited signal of finite energy. The practical importance of these results, together with the restrictions implicit in the sampling theorem, make it natural to ask whether the above rates cannot be improved, by passing to differently chosen sampling instants, or to bandpass or multiband (rather than bandlimited) signals, or to more elaborate computations. In this paper we draw a distinction between reconstructing a signal from its samples, and doing so in a stable way, and we argue that only stable sampling is meaningful in practice. We then prove that: 1) stable sampling cannot be performed at a rate lower than the Nyquist, 2) data cannot be transmitted as samples at a rate higher than the Nyquist, regardless of the location of sampling instants, the nature of the set of frequencies which the signals occupy, or the method of construction. These conclusions apply not merely to finite-energy, but also to bounded, signals.     

The equivalence theorem for the vectors of nonstationary electromagnetic field intensities in a conducting medium

An integral representation is obtained in the time domain for the vectors of the intensities of the nonstationary electromagnetic field in a homogeneous isotropic conducting medium. It is shown that, at any instant, the field at an arbitrary point in a closed volume is expressed through an integral over the surface bounding this volume and an integral over the volume. The derived formulas for the integrand functions contain the field intensities, external currents and charges and the time derivatives of these quantities at instants preceding the observation instant.     

Spectrum Conservation and Characteristics of Single-Sideband Phase Modulation

Phase modulation with an analytic signal, which is a Gaussian random process, is examined in order to determine the amount of spectrum conservation that may be achieved by using single-sideband phase modulation (SSB-PM) rather than conventional phase modulation (PM). The autocorrelation function is derived and found to be an analytic signal in terms of the autocorrelation function of the actual modulating signal and its Hilbert transform. When the modulating signal strength is very low, the sideband spectral distribution is the same as that of the actual modulating signal or single-sideband amplitude modulation. As the modulating signal mean-square value is increased, the sideband spectrum broadens and approaches a Gaussian shape. The average power output of an SSB-PM system increases exponentially with input modulating signal strength, while the carrier power remains constant. For the same modulating signal mean-square value, a greater fraction of power is in the one sideband of an SSB-PM system than in the two sidebands of conventional PM. Single-sideband phase or frequency modulation always effectuates spectrum conservation in the continuum when it is compared with conventional phase or frequency modulation on the basis of equal relative sideband power. A Fourier transform computer program is used to generate SSB-PM spectral distributions with varying modulating signal mean-square values, when the modulating signal spectrum is a low-pass rectangular spectrum, a narrowband pass spectrum, and the shape of an average voice spectrum. These examples illustrate the power series formulation of the output spectrum as well as the theoretical analysis of bandwidth.     

基于数字匹配滤波器与多径合并的CDMA码跟踪环

PN码跟踪环是DS-CDMA蜂窝移动通信系统的关键技术。本文针对第三代(3G)移动通信系统，着眼于对下行公共导频信道的充分利用，提出了一种基于数字匹配滤波器(DMF)和多径误差合并的全数字式码跟踪环。导频信道的DMF输出，一方面可用于信道估计与多径搜索，另一方面用于提取码定时误差，二者结合可以进行码定时误差的多径RAKE合并。理论推导与仿真结果表明，该跟踪环性能良好，具有较高的实用价值。