Squared envelope-based SNR estimation

Two novel squared envelope (SQE)-based and nondata-aided (NDA) signal-to-noise ratio (SNR) estimators over slow fading channel are proposed, which are robust to carrier offsets and can be applied to both nonconstant modulus (NCM) and constant modulus (CM) constellations. First, the moment-based first-and-second moments (M1M2) estimator is proposed because of its simple computation. The NDA approach has some difficulties when it is applied to NCM constellations, mainly due to self-noise introduced by the variability in the amplitude of transmitted symbols. Therefore, an expectation-maximization (EM) estimator, to solve the problem, instead of using the maximum-likelihood estimation, which is too complex for practical implementation, is proposed. For comparison purposes, the normalized Cramér–Rao lower bound is numerically evaluated as the performance benchmark for those estimators. Simulation results have verified that the two novel SQE and NDA SNR estimators are better at estimating the corresponding SNR range for different constellations. Besides, two hybrid schemes combining M1M2 with EM estimators are suggested to reduce deficiencies caused by these methods when they are employed independently to estimate the SNR.     

Channel estimation for time-hopping pulse position modulation ultra-wideband communication systems

Ultra-wideband (UWB) communication systems are used in indoor environments with dense multi-path characteristics. Therefore channel estimation has an important role in the receiver of these systems. A new approach for data-aided (DA) and non-data-aided (NDA) channel estimation is proposed, which is called the pulse compression (PC) method. This method is useful for UWB systems employing time-hopping pulse position modulation. The PC method requires only some basic operations such as sampling, overlap-add and finite impulse response filtering. The PC method, in both DA and NDA scenarios, in spite of its low complexity, outperforms the maximum-likelihood (ML) method in channel parameters estimation. The bit error rate (BER) of the DA method, in single-user scenario, performs as well as the ML method, and in multi-user scenario, in the worst case, there is only 0.5 dB loss compared with the ML method. In the case of NDA scenario, the proposed method outperforms the NDA-ML method, that is, in the single-user scenario about 4 dB gain at the BER of 1023 is observed. In multi-user scenario, it outperforms significantly the NDA-ML method, and its performance loss in comparison with the perfect channel knowledge scenario is about 3 dB at the BER of 1023.     

数字采样测量噪声误差的估计和分析

针对高频数字采样中的附加噪声和时间抖动误差估计问题，给出了高频数字采样测量噪声误差的最大似然估计方法。在获得了相应的数学模型后，对最小二乘估计和最大似然估计方法进行了比较。仿真结果表明，对于此类误差最大似然估计比最小二乘估计有效性更好。另外最大似然估计的一个优点是用于不确定度计算的克拉美一罗下限值更易于获得。     

Parameter Estimation Employing a Dual-Channel Sine-Wave Model Under a Gaussian Assumption

The CramÉr–Rao bound (CRB) is a lower bound on the error variance of any estimator. For a Gaussian scenario, the CRB is derived for a seven-parameter, dual-channel sine-wave model, which is a model relevant to applications such as impedance measurements and the estimation of particle size and velocity by laser anemometry. Four different parameterizations were considered: the common quadrature/in-phase and amplitude–phase models and two relative amplitude–phase models. The CRB indicated the achievable error variance of an unbiased estimator as a function of the signal-to-noise ratio (SNR), the number of samples, and noise power. A nonlinear least squares fit of the signal model to the collected data was employed. The problem at hand is separable and can be solved by a 1-D search followed by a linear least squares fit of the remaining parameters. The performance of the method was investigated with the aid of a simulation study, and the outcome was compared with that of the corresponding CRB and with a recently proposed seven-parameter fit. For high SNRs, the performance of the proposed method is close to optimal with an error variance close to the predictions made by the CRB.      

Bayesian and least squares approaches to ultrasonic scatterer size image formation

Scatterer size images can be used to describe renal microstructure and function in vivo. Such information may facilitate early detection of disease processes. When high range resolution is required, however, it is necessary to analyze short data segments. Periodogram-based maximum likelihood (ML) techniques for scatterer size estimation are limited in these situations by noise and range-gate artifacts. Moreover, when the input signal-to-noise ratio (SNR) of the echo signal is small, performance is further degraded. If accurate prior information about the approximate properties of the object is available, it can be incorporated into the solution to improve the estimates by reducing the number of possible solutions. In this paper, use of prior knowledge in scatterer size image formation is investigated. A maximum a posteriori (MAP) estimator, based on a random-object model, and an iterative constrained least squares (CLS) estimator, based on a deterministic-object model, are designed. Their performances and that of a Wiener filter are compared with the ML technique as a function of gate duration and SNR.     

Frequency division transmission imaging and synthetic aperture reconstruction

In synthetic transmit aperture imaging only a few transducer elements are used in every transmission, which limits the signal-to-noise ratio (SNR). The penetration depth can be increased by using all transmitters in every transmission. In this paper, a method for exciting all transmitters in every transmission and separating them at the receiver is proposed. The coding is done by designing narrow-band linearly frequency modulated signals, which are approximately disjointed in the frequency domain and assigning one waveform to each transmitter. By designing a filterbank consisting of the matched filters corresponding to the excitation waveforms, the different transmitters can be decoded at the receiver. The matched filter of a specific waveform will allow information only from this waveform to pass through, thereby separating it from the other waveforms. This means that all transmitters can be used in every transmission, and the information from the different transmitters can be separated instantaneously. Compared to traditional synthetic transmit aperture (STA) imaging, in which the different transmitters are excited sequentially, more energy is transmitted in every transmission, and a better signal-to-noise-ratio is attained. The method has been tested in simulation, in which the resolution and contrast was compared to a standard synthetic transmit aperture system with a single sinusoid excitation. The resolution and contrast was comparable for the two systems. The method also has been tested using the experimental ultrasound scanner RASMUS. The resolution was evaluated using a string phantom. The method was compared to a conventional STA using both sinusoidal excitation and linear frequency modulated (FM) signals as excitation. The system using the FM signals and the frequency division approach yielded the same performance concerning both axial (of approximately equal to 3 wavelengths) and lateral resolution (of approximately equal to 4.5 wavelengths). A SNR measurement showed an increase in SNR of 6.5 dB compared to the system using the conventional STA method and FM signal excitation.     

Maximum‐likelihood localization of closely‐spaced sources by MLSUM algorithm

Abstract

In this paper, we present a new scheme called the maximum log‐likelihood sum (MLSUM) algorithm to simultaneously determine the number of closely‐spaced sources and their locations by uniform linear sensor arrays. Based on the principle of the maximum likelihood (ML) estimator and a newly proposed orthogonal‐projection decomposition technique, the multivariate log‐likelihood maximization problem is transformed into a multistage one‐dimensional log‐likelihood‐sum maximization problem. The global‐optimum solution of the approximated ML localization is obtained by simply maximizing the single one‐dimensional log‐likelihood function. This algorithm is applicable to coherent sources as well as incoherent sources. The computer simulations show that the MLSUM algorithm is much superior to the MUSIC when the element SNR is low and/or the number of snapshots is small.     

The combined effect of signal decorrelation and random noise on the variance of time delay estimation

Tissue motion and elasticity imaging techniques commonly use time delay estimation (TDE) for the assessment of tissue displacement. The performance of these techniques is limited because the signals are corrupted by various factors including electronic noise, quantization, and speckle decorrelation. Speckle decorrelation is caused by changes in the coherent interference among scatterers when the tissue moves relative to the ultrasound beam. In time delay estimation, the effect of noise is usually addressed through the signal-to-noise ratio (SNR) term. Decorrelation, often a significant source of error in medical ultrasound, is commonly described in terms of the correlation coefficient. A relationship between the correlation coefficient and the SNR was previously derived in the literature, for identical signals corrupted by uncorrelated random noise. In this paper, we derive the relationship between the peak of the correlation coefficient function and the SNR for two jointly stationary signals when a delay is present between the signals. Recently, an expression for the Cramer-Rao lower bound (CRLB) has been derived in the literature for partially decorrelated signals in terms of the SNR and the correlation coefficient. Since the applicability of the CRLB is determined not only by the SNR, but also by the correlation coefficient, it is important to unify the expression for the CRLB for partially correlated signals. In this paper, we derive an expression for the CRLB in term of an equivalent SNR converted from the correlation coefficient using an SNR-p relationship, and show this expression to be equivalent to the expression for CRLB. We also corroborate the validity of the SNR-p expression with a simulation. Using this formulation, correlation measurements can be converted to SNR to obtain a composite SNR. The use of this composite SNR in lieu of those in the CRLB expression in the literature allows the extension of the literature results to the solution of the common TDE problems that involve signal decorrelation.     

Multistage decoding for an internally coded fibre-optic time-hopping/optical code division multiple access communication system

A multistage decoder for the internally convolutionally coded fibre-optic time-hopping code division multiple access system recently introduced is considered. In this system, the decoder consists of several stages. The first stage is implemented using one of the single-user decoders introduced. The following stages are maximum likelihood (ML) decoders each of which use the decisions made by the previous stage. The performance of the proposed decoder is evaluated by a Monte Carlo simulation. Numerical results show that a multistage decoder with only two stages greatly outperforms the single-stage decoder with negligible increase in complexity. The authors also derive the Chernoff bound for the ML decoder with known interference, which is the ultimate performance of the multistage decoder.     

Use of modulated excitation signals in medical ultrasound. Part I: Basic concepts and expected benefits

This paper, the first from a series of three papers on the application of coded excitation signals in medical ultrasound, discusses the basic principles and ultrasound-related problems of pulse compression. The concepts of signal modulation and matched filtering are given, and a simple model of attenuation relates the matched filter response with the ambiguity function, known from radar. Based on this analysis and the properties of the ambiguity function, the selection of coded waveforms suitable for ultrasound imaging is discussed. It is shown that linear frequency modulation (FM) signals have the best and most robust features for ultrasound imaging. Other coded signals such as nonlinear FM and binary complementary Golay codes also have been considered and characterized in terms of signal-to-noise ratio (SNR) and sensitivity to frequency shifts. Using the simulation program Field II, it is found that in the case of linear FM signals, a SNR improvement of 12 to 18 dB can be expected for large imaging depths in attenuating media, without any depth-dependent filter compensation. In contrast, nonlinear FM modulation and binary codes are shown to give a SNR improvement of only 4 to 9 dB when processed with a matched filter. Other issues, such as depth-dependent matched filtering and use of filters other than the matched filter (inverse and Wiener filters) also are addressed.     

Space?frequency coded cooperation in OFDM multiple-access wireless networks

A cooperative space-frequency (SF) coded orthogonal frequency division multiplexing system is considered and its performance over quasi-static frequency-selective Rayleigh fading channels is evaluated. An expression for exact outage error probability is derived and its tight closed-form lower bound is presented. The tightness of the lower bound is demonstrated through Monte Carlo simulation. Asymptotic analysis indicates that the proposed protocol achieves full spatial and frequency diversities available in the cooperative communication system. The theoretical analysis of the proposed SF coded cooperation protocol is further confirmed by computer simulation using a previously introduced SF block code that is capable of achieving full spatial and frequency diversities.     

Use of modulated excitation signals in medical ultrasound. Part III: High frame rate imaging

This paper, the last from a series of three papers on the application of coded excitation signals in medical ultrasound, investigates the possibility of increasing the frame rate in ultrasound imaging by using modulated excitation signals. Linear array-coded imaging and sparse synthetic transmit aperture imaging are considered, and the trade-offs between frame rate, image quality, and SNR are discussed. It is shown that FM codes can be used to increase the frame rate by a factor of two without a degradation in image quality and by a factor of 5, if a slight decrease in image quality can be accepted. The use of synthetic transmit aperture imaging is also considered, and it is here shown that Hadamard spatial encoding in transmit with FM emission signals can be used to increase the frame rate by 12 to 25 times with either a slight or no reduction in signal-to-noise ratio and image quality. By using these techniques a complete ultrasound-phased array image can be created using only two emissions.     

Performance of blind channel estimation algorithms for space-frequency block coded multi-carrier code division multiple access systems

The problem of blind channel estimation for downlink space-frequency block coded multi-carrier code division multiple access (SFBC MC-CDMA) schemes is considered. For these schemes, the authors first develop a system model for complex modulated signals, which reduces the multichannel estimation problem to a single-input single-output problem. Then, they present an intuitive subspace-based channel estimation method along with the corresponding necessary and sufficient conditions under which the channel estimate is unique (within a complex scalar). Their studies highlight two interesting properties of SFBC MC-CDMA systems: (i) there is no antenna order ambiguity (also known as permutation ambiguity) even though only one spreading code is assigned to each user; (ii) channel identifiability is guaranteed, regardless of the channel zeros location. They also establish the unbiasedness of the channel estimates and derive closed-form expressions for the mean-square-error of the estimates as well as the corresponding Cramer-Rao bound (CRB). In the derivation of the CRB, they suggest a novel approach which assumes the knowledge of only the spreading code of desired user. This approach results in a tighter bound than the CRB derived based on the knowledge of all users' signatures.     

A new estimator for vector velocity estimation

A new estimator for determining the two-dimensional velocity vector using a pulsed ultrasound field is derived. The estimator uses a transversely modulated ultrasound field for probing the moving medium under investigation. A modified autocorrelation approach is used in the velocity estimation. The new estimator automatically compensates for the axial velocity when determining the transverse velocity. The estimation is optimized by using a lag different from one in the estimation process, and noise artifacts are reduced by averaging RF samples. Further, compensation for the axial velocity can be introduced, and the velocity estimation is done at a fixed depth in tissue to reduce the influence of a spatial velocity spread. Examples for different velocity vectors and field conditions are shown using both simple and more complex field simulations. A relative accuracy of 10.1% is obtained for the transverse velocity estimates for a parabolic velocity profile for flow transverse to the ultrasound beam and a SNR of 20 dB using 20 pulse-echo lines. The overall bias in the estimates was -4.3%     

A new wideband spread target maximum likelihood estimator for blood velocity estimation. I. Theory

The derivation and theoretical evaluation of new wideband maximum-likelihood strategies for the estimation of blood velocity using acoustic signals are presented. A model for the received signal from blood scatterers, using a train of short wideband pulses, is described. Evaluation of the autocorrelation of the signal based on this model shows that the magnitude, periodicity, and phase of the autocorrelation are affected by the mean scatterer velocity and the presence of a velocity spread target. New velocity estimators are then derived that exploit the effect of the scatterer velocity on both the signal delay and the shift in frequency. The wideband range spread estimator is derived using a statistical model of the target. Based on the point target assumption, a simpler wideband maximum-likelihood estimator is also obtained. These new estimation strategies are analyzed for their local and global performance. Evaluation of the Cramer-Rao bound shows that the bound on the estimator variance is reduced using these estimators, in comparison with narrowband strategies. In order to study global accuracy, the expected estimator output is evaluated, and it is determined that the width of the mainlobe is reduced. In addition, it is shown that the height of subsidiary velocity peaks is reduced through the use of these new estimators.     

Echography using correlation techniques: choice of coding signal

Theoretical studies made in the early 1980's suggest that ultrasonic imaging using correlation technique can overcome some of the drawbacks of classical pulse echography. Indeed by transmitting a continuous coded signal and then compressing it into a short, high resolution pulse at the receiver the total signal to noise ratio (SNR) is improved. The target location is determined by cross correlation of the emitted and the received signal. The band compression allows, by increasing SNR, the retrieval of echo signals buried in the receiver noise. Thus in medical-type echography, where the signal attenuation at fixed depth is proportional to the frequency, the SNR improvement allows the use of higher frequency signals and leads to improved resolution. We report here the results of comparative experimental studies of simple echo B type images as obtained by the classical pulse echo and correlation techniques. Because the optimisation of the coded signal plays a crucial role in the performance of the correlation technique we will also present a comparative study of the performances of the most common codes (m-sequences and complementary series). In particular we shall emphasise the following points: the relative importance of the central lobe as compared to the side lobes of the correlation function, which is directly related to the dynamic of the imaging system, the width of the correlation peak which is directly related to the axial resolution of the system, the facility of the realisation. The merit of B-mode images obtained with the coded signals will be discussed showing that as far as signal modulation is used the best results are obtained with periodic m-sequences     

New union bound on the error probability of bit-interleaved space-time codes with finite interleaver sizes

A new union bound on the bit error probability of bit-interleaved space?time (BI-ST) coded systems is derived. Unlike existing performance analysis tools for BI-ST systems, the new bound provides a general framework for analysing the performance of BI-ST systems employing finite interleaver sizes. The derivation is based on the uniform interleaving assumption of the coded sequence prior to transmission over multiple antennas. The new bound is a function of the distance spectrum of the code, the signal constellation used and the space?time (ST) mapping scheme. The bound is derived for a general BI-ST coded system and applied to two specific examples, namely, the BI space?time coded modulation and the BI space?time block codes. Results show that the analysis provides a close approximation to the BI-ST performance for a wide range of signal-to-noise ratios. The analysis can also accurately characterise the performance differences between different interleaver sizes, which is a breakthrough in the analysis of BI-ST coded systems.     

The discrete-time quadrature subsample estimation of delay

A high-resolution discrete-time delay estimator for determining the delay between two periodic signals is described. The technique is based upon the principles of analog quadrature detection and is relatively simple to implement digitally. Simulations in the presence of system noise show that the delay estimator does not exhibit any significant bias and outperforms other estimators in medium to high SNR situations     

Invariant activity detection of a constant magnitude signal with unknown parameters in white Gaussian noise

The authors propose invariant tests for the detection of a complex signal with unknown constant amplitude and unknown phase variation in additive white Gaussian noise (AWGN). The authors show that in this problem, the uniformly most powerful invariant (UMPI) detector does exist only if the number of samples N is two. For more than two samples N ges 3, the authors derive the most powerful invariant (MPI) detector in known signal-to-noise ratio (SNR) and use its performance as the upper bound benchmark for any invariant test. In addition, the authors derive the generalised likelihood ratio (GLR) detector and evaluate its performance against the MPI performance bound. This detector is very simple and represents the ratio of the L ₁-norm to the L ₂-norm of the data. Simulation results illustrate the close performances of the two detectors even at low SNRs, whereas in contrast to the MPI test the SNR is not required in the proposed GLR test. In order to understand why the knowledge of SNR is not so important in this detection problem, the authors also derive the GLR test for the case of known SNR. Interestingly, the resulting GLR detector (derived for the case of known SNR) turns out to be equivalent to the one derived for unknown SNR, i.e. a knowledge of the SNR is not used in any of the GLR tests. This reveals why the knowledge of the SNR is not so useful in this detection problem.     

Radiometric and signal-to-noise ratio properties of multiplex dispersive spectrometry

Recent theoretical investigations have shown important radiometric disadvantages of interferential multiplexing in Fourier transform spectrometry that apparently can be applied even to coded aperture spectrometers. We have reexamined the methods of noninterferential multiplexing in order to assess their signal-to-noise ratio (SNR) performance, relying on a theoretical modeling of the multiplexed signals. We are able to show that quite similar SNR and radiometric disadvantages affect multiplex dispersive spectrometry. The effect of noise on spectral estimations is discussed.