Performance of blind and group-blind multiuser detectors

In blind (or group-blind) linear multiuser detection, the detector is estimated from the received signals, with the prior knowledge of only the signature waveform of the desired user (or the signature waveforms of some but not all users). The performance of a number of such estimated linear detectors, including the direct-matrix-inversion (DMI) blind linear minimum mean square error (MMSE) detector, the subspace blind linear MMSE detector, and the form-I and form-II group-blind linear hybrid detectors, are analyzed. Asymptotic limit theorems for each of the estimates of these detectors (when the signal sample size is large) are established, based on which approximate expressions for the average output signal-to-interference-plus-noise ratios (SINRs) and bit-error rates (BERs) are given. To gain insights on these analytical results, the performance of these detectors in an equicorrelated code-division multiple-acces (CDMA) system is compared. Examples are provided to demonstrate the excellent match between the theory developed here and the simulation results     

Time-scale detection of microemboli in flowing blood with Dopplerultrasound

Small formed elements and gas bubbles in flowing blood, called microemboli, can be detected using Doppler ultrasound. In this application, a pulsed constant-frequency ultrasound signal insonates a volume of blood in the middle cerebral artery, and microemboli moving through its sample volume produce a Doppler-shifted transient reflection. Current detection methods include searching for these transients in a short-time Fourier transform (STFT) of the reflected signal. However, since the embolus transit time through the Doppler sample volume is inversely proportional to the embolus velocity (Doppler-shift frequency), a matched-filter detector should in principle use a wavelet transform, rather than a short-time Fourier transform, for optimal results. Closer examination of the Doppler shift signals usually shows a chirping behavior apparently due to acceleration or deceleration of the emboli during their transit through the Doppler sample volume. These variations imply that a linear wavelet detector is not optimal. We apply linear and quadratic time-frequency and time-scale detectors to a set of noise-corrupted embolus data. Our results show improvements of about 1 dB using the time-scale detectors versus an STFT-based detector signifying that embolus detection is best approached as a time-scale problem. A time-scale-chirp detector is also applied and is found to have the overall best performance by about 0.5-0.7 dB while coming fairly close (about 0.75 dB) to a theoretical upper bound.     

基于小波变换域估计的瞬态信号检测

在未知瞬态信号检测中，一般采用广义似然比检测，然而广义似然比检测不能有效利用瞬态信号的固有特性，检测性能不是很好。文中在介绍瞬态信号和噪声的小波变换特性基础上，提出了基于小波变换域估计的检测方法，最后给出了几种检测器的工作特性比较。     

Detection of non-Gaussian signals using integrated polyspectrum

We consider the problem of detecting an unknown, random, stationary, non-Gaussian signal in Gaussian noise of unknown correlation structure. The same framework applies if one desires to determine whether the given random signal is non-Gaussian. The most commonly used method for detection of random signals is the so-called energy detector, which cannot distinguish between Gaussian and non-Gaussian signals and requires the knowledge of the noise power. Recently, the use of bispectrum and/or trispectrum of the signal has been suggested for detection of non-Gaussian signals. The higher order spectra-based detectors do not require the knowledge of the noise statistics if the noise is Gaussian. In this paper, we suggest the use of an integrated polyspectrum (bispectrum of trispectrum) to improve computational efficiency of the detectors based on polyspectrum and to possibly further enhance their detection performance. We investigate conditions under which use of the integrated polyspectrum is appropriate. The detector structure is derived, acid its performance is evaluated via simulations and comparisons with several other existing approaches     

Asymptotic analysis of blind multiuser detection with blind channel estimation

The analytical performance of the subspace-based blind linear minimum mean-square error (MMSE) multiuser detection algorithm in general multipath multi-antenna code-division multiple-access (CDMA) systems is investigated. In blind multiuser detection, the linear MMSE detector of a given user is estimated from the received signals, based on the knowledge of only the spreading sequence of that user. Typically, the channel of that user must be estimated first, based on the orthogonality between the signal and noise subspaces. An asymptotic limit theorem for the estimate of the blind linear detector (when the received signal sample size is large) is obtained, based on which approximate expressions of the average output signal-to-inference plus noise ratios (SINRs) and bit error rates (BERs) for both binary phase-shift keying (BPSK) and quaternary phase-shift keying (QPSK) modulations are given. Corresponding results for group-blind multiuser detectors are also obtained. Examples are provided to demonstrate the excellent match between the theory developed in this paper and the simulation results.     

Linear frequency-modulated signal detection using Radon-ambiguitytransform

A novel time-frequency technique for linear frequency modulated (LFM) signal detection is proposed. The design of the proposed detectors is based on the Radon transform of the modulus square or the envelope amplitude of the ambiguity function (AF) of the signal. A practical assumption is made that the chirp rate is the only parameter of interest. Since the AF of LFM signals will pass through the origin of the ambiguity plane, the line integral of the Radon transform is performed over all lines passing through the origin of the ambiguity plane. The proposed detectors yield maxima over chirp rates of the LFM signals. This reduces the two-dimensional (2-D) problem of the conventional Wigner-Ville distribution (WVD) based detection or the Radon-Wigner transform (RWT) based detector to a one-dimensional (1-D) problem and consequently reduces the computation load and keeps the feature of “built-in” filtering. Related issues such as the finite-length effect, the resolution, and the effect of noise are studied. The result is a tool for LFM detection, as well as the time-varying filtering and adaptive kernel design for multicomponent LFM signals     

Near-optimum detection in synchronous code-division multiple-accesssystems

Communication networks using code division multiple access (CDMA) include applications where several packets of information are transmitted synchronously and simultaneously over a common channel. Consideration is given to the problem of simultaneously demodulating every packet from such a transmission. A nonlinear detection scheme based on a linear complexity multistage multiple-access interference rejection algorithm is studied. A class of linear detectors is considered as constituting the first stage for the multistage detector. A bit-error probability comparison of the linear and multistage detectors is undertaken. It is shown that the multistage detectors are capable of achieving considerable improvements over the linear detectors, particularly in near-far situations, i.e., in the demodulation of weak signals in the presence of strong interfering signals. This problem has been of primary concern for currently operational CDMA systems     

Channel knowledge and optimal performance for two-wave Rayleighfading channels

The optimal detector structures and error probability performances for the two-wave Rayleigh fading channel with known delay are compared for different levels of channel knowledge. A number of different detectors are examined, for equal energy signals having equal complex autocorrelation magnitudes. Envelope orthogonal frequency-shift keying and variants of chirp signals are considered, so that the complex cross correlation of the signals is unconstrained. The performance of the optimal detector, when the fading in neither wave is tracked, is obtained. Two other, suboptimal, quadratic detectors are also considered for this case. Optimal detection, when the fading in only one of the waves is tracked, while a statistical knowledge of the other wave is available, is examined. The optimal performance that can be achieved by a time-varying matched-filter detector that makes use of complete knowledge of the channel fading in both waves is also determined. These detectors, for all the different levels of channel information considered, are studied in a unified framework, the probability of error being expressed as the probability that a quadratic form in Gaussian random variables is less than zero. It is found that the power gain that can be derived from partial or complete tracking is small. All these detectors exhibit a diversity-like effect for all nonzero values of the delay and for most values of the signal parameters. Signals with larger dispersion factors, such as chirp signals and variants, perform well on the channel, enhancing the diversity effect, even at small delays     

The linear prediction of deterministic signals

A method is presented for linear estimations of functionals of deterministic signals containing additive noise. The method is based on statistical decision theory and assumes discrete observations. In general terms a deterministic signal, with the noise subtracted, is a member of a class of functions with no probability distribution over the members of the class. In this paper the class is restricted to real one-dimensional functions parametrized by a real vector. The linear minimax estimate of the function to be estimated is proposed and the problem of computing it shown to be equivalent to a quadratic programming problem which can be solved exactly when the class of true signals is finite and sometimes when the class is infinite. In the latter case the problem can be solved approximately, subject to some mild restrictions on the signal. The exact algebraic solution is given for prediction of linear signals for up to three observations and is compared with the solution based on Wiener's theory.     

Performance bounds for linear MMSE receivers in CDMA systems with partial channel knowledge

In code division multiple access (CDMA) systems employing linear adaptive receivers, the detector is typically estimated directly from the received signals, based on some partial knowledge about the system, e.g., signature waveforms of one or several users. We derive the Cramer-Rao lower bounds on the covariances of the estimated linear detectors, under three different assumptions on the mechanism for estimating the detectors, namely, a) finite-alphabet-based (FA) blind detectors, b) constant-modulus-based (CM) blind detectors, and c) second-order-moments-based (SO) blind detectors. These bounds translate into the upper bounds on the achievable signal-to-interference-plus-noise ratio (SINR) by the corresponding adaptive receivers. The results are asymptotic in nature, either for high signal-to-noise ratio (SNR) or for large signal sample size. The effects of unknown multipath channels on these performance bounds are also addressed. Numerical results indicate that while the existing subspace blind or group-blind detectors perform close to the SINR bound for the SO detectors, the SINR bounds for the FA and CM detectors are significantly higher, which suggests potential avenues for developing more powerful adaptive detectors by exploiting more structural information from the system.     

Adaptive detection of statistical signals in noise

This paper deals with the forms and properties of a detector operating in an environment in which little statistical information about either the signal or noise field is or can be available. An adaptive detector based on the theory of nonparametric statistics has been designed for this purpose. The detector uses amplitude samples taken from two distinct receivers, only one of which may contain signals from a target. The detector maintains a constant false alarm rate despite any nonstationarity of the noise. The theory of nonparametric statistics suggests that the data from the two sources be ranked in order of amplitude, that a linear weighting (a correlator) be applied to the ranking, and the result be applied to a threshold. In this study, we have considered an adaptive detector of this form. The adaptation mechanism selects the weight (correlating) function on the basis of the past observed data. This class of adaptive detectors is shown to have excellent performance in terms of signal detectability for signals of adequate strength. However, for a given detector design, signals weaker than a certain critical threshold cannot be detected regardless of the amount of data available. Thus, in contrast to the kind of signal suppression effect which characterizes conventional passive detection schemes, the adaptive detector has a sharp minimum detectable signal threshold.     

Linear Differentially Coherent Multiuser Detection for Multipath Channels

By combining multipath processing, differential signal detection, and multiuser detection techniques, we develop a class of near-far resistant linear detectors for differentially coherent multipath signals. We derive and establish performance relationships among the following detectors: an optimally near-far resistant detector, a suboptimum detector which does not require knowledge of the signal coordinates, and a minimum mean square error (MMSE) detector which achieves near-optimum asymptotic efficiency. We present an adaptive multiuser detector which converges to the MMSE detector without training sequences and which requires less information than the conventional single user rake receiver.     

Fractional Fourier transform of the Gaussian and fractional domain signal support

The fractional Fourier transform (FrFT) provides an important extension to conventional Fourier theory for the analysis and synthesis of linear chirp signals. It is a parameterised transform which can be used to provide extremely compact representations. The representation is maximally compressed when the transform parameter, /spl alpha/, is matched to the chirp rate of the input signal. Existing proofs are extended to demonstrate that the fractional Fourier transform of the Gaussian function also has Gaussian support. Furthermore, expressions are developed which allow calculation of the spread of the signal representation for a Gaussian windowed linear chirp signal in any fractional domain. Both continuous and discrete cases are considered. The fractional domains exhibiting minimum and maximum support for a given signal define the limit on joint time-frequency resolution available under the FrFT. This is equated with a restatement of the uncertainty principle for linear chirp signals and the fractional Fourier domains. The calculated values for the fractional domain support are tested empirically through comparison with the discrete transform output for a synthetic signal with known parameters. It is shown that the same expressions are appropriate for predicting the support of the ordinary Fourier transform of a Gaussian windowed linear chirp signal.     

Wavelet transform-based QRS complex detector

In this paper, we describe a QRS complex detector based on the dyadic wavelet transform (Dy WT) which is robust to time-varying QRS complex morphology and to noise. We design a spline wavelet that is suitable for QRS detection. The scales of this wavelet are chosen based on the spectral characteristics of the electrocardiogram (ECG) signal. We illustrate the performance of the Dy WT-based QRS detector by considering problematic ECG signals from the American Heart Association (AHA) data base. Seventy hours of data was considered. We also compare the performance of Dy WT-based QRS detector with detectors based on Okada, Hamilton-Tompkins, and multiplication of the backward difference algorithms. From the comparison, results we observed that although no one algorithm exhibited superior performance in all situations, the Dy WT-based detector compared well with the standard techniques. For multiform premature ventricular contractions, bigeminy, and couplets tapes, the Dy WT-based detector exhibited excellent performance.     

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.     

Compression of biomedical signals with mother wavelet optimization and best-basis wavelet packet selection

We propose a novel scheme for signal compression based on the discrete wavelet packet transform (DWPT) decompositon. The mother wavelet and the basis of wavelet packets were optimized and the wavelet coefficients were encoded with a modified version of the embedded zerotree algorithm. This signal dependant compression scheme was designed by a two-step process. The first (internal optimization) was the best basis selection that was performed for a given mother wavelet. For this purpose, three additive cost functions were applied and compared. The second (external optimization) was the selection of the mother wavelet based on the minimal distortion of the decoded signal given a fixed compression ratio. The mother wavelet was parameterized in the multiresolution analysis framework by the scaling filter, which is sufficient to define the entire decomposition in the orthogonal case. The method was tested on two sets of ten electromyographic (EMG) and ten electrocardiographic (ECG) signals that were compressed with compression ratios in the range of 50%-90%. For 90% compression ratio of EMG (ECG) signals, the percent residual difference after compression decreased from (mean +/- SD) 48.6 +/- 9.9% (21.5 +/- 8.4%) with discrete wavelet transform (DWT) using the wavelet leading to poorest performance to 28.4 +/- 3.0% (6.7 +/- 1.9%) with DWPT, with optimal basis selection and wavelet optimization. In conclusion, best basis selection and optimization of the mother wavelet through parameterization led to substantial improvement of performance in signal compression with respect to DWT and randon selection of the mother wavelet. The method provides an adaptive approach for optimal signal representation for compression and can thus be applied to any type of biomedical signal.     

Maximum likelihood estimation of signals in autoregressive noise

Time series modeling as the sum of a deterministic signal and an autoregressive (AR) process is studied. Maximum likelihood estimation of the signal amplitudes and AR parameters is seen to result in a nonlinear estimation problem. However, it is shown that for a given class of signals, the use of a parameter transformation can reduce the problem to a linear least squares one. For unknown signal parameters, in addition to the signal amplitudes, the maximization can be reduced to one over the additional signal parameters. The general class of signals for which such parameter transformations are applicable, thereby reducing estimator complexity drastically, is derived. This class includes sinusoids as well as polynomials and polynomial-times-exponential signals. The ideas are based on the theory of invariant subspaces for linear operators. The results form a powerful modeling tool in signal plus noise problems and therefore find application in a large variety of statistical signal processing problems. The authors briefly discuss some applications such as spectral analysis, broadband/transient detection using line array data, and fundamental frequency estimation for periodic signals     

Optimal Detection of Hard-Limited Data Signals in Different Noise Environments

A number of digital techniques for detecting binary antipodal signals are based on examining the polarities of the received signal samples and ignoring their amplitudes. The structure of the optimum detector for the hard-limited samples is derived, and its performance is compared to those of some commonly used schemes in impulsive as well as Gaussian noise environments. The optimum receiver forM-ary signaling based on received signal samples quantized to an arbitrary number of levels is obtained and compared to other detectors.     

All-purpose and plug-in power-law detectors for transient signals

A power-law statistic operating on discrete Fourier transform (DFT) data has emerged as a basis for a remarkably robust detector of transient signals having unknown structure, location, and strength. We offer a number of improvements to Nuttall's (1994) original power-law detector. Specifically, the power-law detector requires that its data be prenormalized and spectrally white; a constant false-alarm rate (CFAR) and self-whitening version is developed and analyzed. Further, it is noted that transient signals tend to be contiguous both in the temporal and frequency sense, and consequently, new power-law detectors in the frequency and the wavelet domains are given. The resulting detectors offer exceptional performance and are extremely easy to implement. There are no parameters to tune. They may be considered “plug-in” solutions to the transient detection problem and are “all-purpose” in that they make minimal assumptions on the structure of the transient signal, save of some degree of agglomeration of energy in time and/or frequency     

A Wideband Wavelet Based Estimator Correlator and its Properties

Maximum likelihood detectors of narrowband, non-stationary random echos in Gaussian noise can be efficiently implemented in the time-frequency domain. When the transmitted signals have large time-bandwidth products, the natural implementation of estimators and detectors is in the time-scale or wavelet transform domain. This paper presents a wideband wavelet transform domain implementation of an estimator-correlator (EC) detector and details the components of this processor, including weighted wavelet transforms and cascaded scattering functions. Key properties associated with this wavelet based wideband EC are also presented. The theoretical developments of the processor are based on group theory which provides a unified approach to detector development for both narrowband and wideband processors. The group theoretic concepts provide a powerful analysis tool for complex signal processing problems.