Design of binary bandlimited signals imbedded in colored Gaussian noise and intersymbol interference

This paper considers the design of binary bandlimited receiver signals as well as the design of the receiver filter for signal immunity to intersymbol interference and additive colored Gaussian noise. The design problem is treated in the frequency domain. The maximum probability of error is minimized by choosing signals with zero intersymbol interference. When transmission is below the Nyquist rate, bandlimited signals with gradual cutoff are designed. Other waveforms, with intersymbol interference but possessing no sequences of unbounded amplitude, are also investigated. Examples are given demonstrating the application of the theory.     

Expansion of likelihood ratio for signals in Gaussian noise

It is shown that the coefficients of the Taylor expansion of the likelihood ratio for random signals in Gaussian noise are proportional to the mean-square estimates of the successive powers of the signal evaluated at zero. A similar relationship holds for the expansion of the logarithm of the likelihood ratio.     

The equivalence- singularity problem for Gaussian signals in Gaussian noise (Corresp.)

The structural properties and sample path behavior of Gaussian signals which can and which cannot be perfectly detected in a given Gaussian noise are described.     

A general likelihood-ratio formula for random signals in Gaussian noise

It is shown that the likelihood ratio for the detection of a random, not necessarily Gaussian, signal in additive white Gaussian noise has the same form as that for a known signal in white Gaussian noise. The role of the known signal is played by the casual least-squares estimate of the signal from the observations. However, the "correlation" integral has to be interpreted in a special sense as an Itô stochastic integral. It will be shown that the formula includes all known explicit formulas for signals in white Gaussian noise. However, and more important, the formula suggests an "estimator-correlator" philosophy for engineering approximation of the optimum receiver. Some extensions of the above result are also discussed, e.g., additive finite-variance, not necessarily Gaussian, noise plus a white Gaussian noise component. Purely colored Gaussian noise can be treated if whitening filters can be specified. The analog implementation of Itô integrals is briefly discussed. The proofs of the formulas are based on the concept of an innovation process, which has been useful in certain related problems of linear and nonlinear least-squares estimation, and on the concept of covariance factorization.     

Time domain phase noise correction for OFDM signals

We introduce an algorithm for compensating for carrier phase noise in an OFDM communication system. Through the creation of a linearized parametric model for phase noise, we generate a least squares (LS) estimate of the transmitted symbol. Using digitized DVB-T RF signals created in a laboratory and a DVB-T compliant receiver model, simulation results are presented to evaluate the effectiveness of the algorithm in practical environments.     

超宽带信号在高斯噪声中传播性能的研究

超宽带无线通信技术使用微弱的、持续时间极短的脉冲进行短距离通信。超宽带信号具有极宽的射频带宽和较低的中心频率，这种特性可使短距无线通信利用较低的发射功率进行高速传输。根据信号的频谱及其在高斯噪声中的传播性能，研究超宽带信号的减少衰减余量特性，给出不同进制波形的PPM调制超宽带信号比特误码率仿真分析。     

Sparse fast Fourier transform for exactly sparse signals and signals with additive Gaussian noise

In recent years, the Fourier domain representation of sparse signals has been very attractive. Sparse fast Fourier transform (or sparse FFT) is a new technique which computes the Fourier transform in a compressed way, using only a subset of the input data. Sparse FFT computes the desired transform in sublinear time, which means in an amount of time that is smaller than the size of data. In big data problems and medical imaging to reduce the time that patient spends in MRI machine, FFT algorithm is not ‘fast’ enough anymore; therefore, the concept of sparse FFT is very important. Similar to compressed sensing, sparse FFT algorithm computes just the important components in the frequency domain in sublinear time. In this work, sparse FFT algorithm is studied and implemented on MATLAB and its performance is compared with Ann Arbor FFT. A filter is used to hash the frequencies in the n dimensional frequency-sparse signal into B bins, where \(B=n/16\). The filter is used for analyzing an important fraction of the whole signal, and therefore, instead of computing n point FFT, B point FFT is computed, and this results in a faster Fourier transform. The probability of success of the implemented algorithm is investigated for noiseless and noisy signals. It is deduced that as the sparsity increases, the probability of perfect transform also increases. If the performances of the algorithm in both cases are compared, it is clearly seen that the performances degrade when there is noise. Therefore, it can be concluded that the algorithm should be improved especially for noisy considerations. The solvability boundary for a constant probability of error is deducted and added to give insight for future studies.     

Nonsingular detection and likelihood ratio for random signals in white Gaussian noise

This paper is concerned with the mathematical aspect of a detection problem (a random signal in white Gaussian noise). Specifically, we obtain a sufficient condition for nonsingular detection and derive a likelihood-ratio expression in terms of least-mean-square estimates. The problem itself is old, and the likelihood-ratio expression is also well known. The contribution of this paper is a relatively elementary and self-contained derivation of the likelihood-ratio expression as well as the nonsingularity condition.     

Gaussian Cramer-Rao bound for direction estimation of noncircular signals in unknown noise fields

This paper focuses on the stochastic Cramer-Rao bound (CRB) on direction of arrival (DOA) estimation accuracy for noncircular Gaussian sources in the general case of an arbitrary unknown Gaussian noise field parameterized by a vector of unknowns. Explicit closed-form expressions of the stochastic CRB for DOA parameters alone are obtained directly from the Slepian-Bangs formula for general noncircular complex Gaussian distributions. As a special case, the CRB under the nonuniform white noise assumption is derived. Our expressions can be viewed as extensions of the well-known results by Stoica and Nehorai, Ottersten et al., Weiss and Friedlander, Pesavento and Gershman, and Gershman et al. Some properties of these CRBs are proved and finally, these bounds are numerically compared with the conventional CRBs under the circular complex Gaussian distribution for different unknown noise field models.     

Transform coding of audio signals using perceptual noise criteria

A 4-b/sample transform coder is designed using a psychoacoustically derived noise-making threshold that is based on the short-term spectrum of the signal. The coder has been tested in a formal subjective test involving a wide selection of monophonic audio inputs. The signals used in the test were of 15-kHz bandwidth, sampled at 32 kHz. The bit rate of the resulting coder was 128 kb/s. The subjective test shows that the coded signal could not be distinguished from the original at that bit rate. Subsequent informal work suggests that a bit rate of 96 kb/s may maintain transparency for the set of inputs used in the test     

On the performance of ultra-wide-band signals in Gaussian noise anddense multipath

An ultra-wide-band (UWB) signal is characterized by a radiated spectrum with a very wide bandwidth around a relatively low center frequency. In this paper, we study the reduced fading margin property of UWB signals. To evaluate the fading margin, we compare the performance of UWB signals in an environment with only additive white Gaussian noise (AWGN) versus the performance of UWB signals in a dense multipath environment with AWGN. The assumption here is that the presence of multipath causes a small increase in the signal-to-noise ratio required to achieve reasonable levels of bit error rate. A numerical example confirms this assumption, more specifically, the example shows that to achieve a bit error rate equal to 10^-5, we require about 13.5 dB in the AWGN case and about 15 dB in the multipath case, resulting in a fading margin of just 1.5 dB. This small fading margin can be understood by the ability of the UWB signal to resolve the dense multipath     

Damped sinusoidal signals parameter estimation in frequency domain

Parameter estimation of noisy damped sinusoidal signals in the frequency domain is presented in this paper. The advantage of the frequency domain approach is having the spectral energy concentrated in frequency domain samples. However, the least squares criterion for frequency estimation using frequency domain samples is nonlinear. A low complexity three-sample estimation algorithm (TSEA) for solving the nonlinear problem is proposed. Using the TSEA for initialization, a frequency domain nonlinear least squares (FD-NLS) estimation algorithm is then proposed. In the case of white Gaussian noise, it yields maximum likelihood estimates, verified by simulation results. A time domain NLS (TD-NLS) estimation algorithm is also proposed for comparison.The Cramer-Rao lower bound (CRLB) of the frequency domain estimation algorithms is derived. The theoretical analysis shows that the FD-NLS can yield a near-optimal performance with few energy-concentrated samples. On the other hand, the TD-NLS does not have the energy concentration property and requires more time domain samples to perform satisfactory estimation. Simulation results verify that the frequency domain estimation algorithms provide better tradeoff between computational complexity and estimation accuracy than time domain algorithms.     

低信噪比情况下调频信号的瞬时频率估计

提出一种基于互Wigner-Ville分布(XWVD)的瞬时频率迭代估计方法.理论分析了该方法的收敛性,通过仿真比较了各种瞬时频率估计方法在噪声下的估计方差,证明此方法在低信噪比情况下对估计线性调频信号的瞬时频率有较好的效果.并采用加窗的方法改进了此算法,仿真结果证明,改进的方法对非线性调频信号的瞬时频率进行了有效估计.     

多波长光声信号的时域与频域比较

为了分析在不同激发波长下不同组织/目标光声信号的时域与频域特点和差异,根据光声信号产生的基本原理,采用光声信号时域和频域分析方法,设计了石墨仿体和离体组织等不同样品的多光谱光声实验。结果表明,样品的光声信号在时域与频域所展示的性能有很大的不同,不同样品的光声信号的声谱是不同的,且在不同激发波长下的声谱的峰值所对应的频率均相同,因而可以用于组织特性的描述、组分识别等用途。此研究有助于利用光声成像实现组织识别,并为进一步利用频谱分析方法研究多光谱光声成像奠定了基础。     

A further note on a general likelihood formula for random signals in Gaussian noise

A general likelihood ratio formula of the author's for the detection of signals in independent white Gaussian noise is extended to allow a "one-sided" dependence in which only the future white noise is required to be independent of past signal and noise. The assumption of Gaussian additive noise is also somewhat relaxed. The proof is based on some recent martingale theorems and on the concept of the innovations process.     

Estimation of randomly occurring stochastic signals in Gaussian noise (Corresp.)

This note applies the general likelihood ratio for the minimum-mean-square-error estimation of the signal when the presence of the signal at the receiver is uncertain during the entire observation interval.     

Information theoretic criteria for the determination of the numberof signals in spatially correlated noise

The problem of determining the number of signals in high-resolution array processing when the noise is spatially correlated (having an unknown covariance matrix) is examined. By considering a model in which two sensor arrays are well separated such that their noise outputs are uncorrelated, the authors develop a likelihood function whose maximum can be expressed in a very simple form involving the canonical correlation coefficients. This likelihood function and a choice of penalty functions constitute a number of new information theoretic criteria suitable for the determination of the number of signals in an unknown correlated noise environment. Furthermore, it is demonstrated that the new criteria are applicable in the case when only one sensor array is available