Parametric Waveform Design Using Discrete Prolate Spheroidal Sequences for Enhanced Detection of Extended Targets

For numerous applications in the field of signal processing, it is desired to design a compact window that can simultaneously concentrate maximum energy in finite time interval and frequency band. Although zero‐order discrete prolate spheroidal sequence (DPSS) meets this requirement, it is of infinite support. Limiting this sequence to finite support no longer guarantees the optimality property. This study aims at designing a discrete finite length window that can maximise the energy simultaneously in narrow time interval and frequency band. A multi‐objective optimisation approach is adopted to obtain the upper bound of maximum achievable time and frequency domain energy concentrations for finite length sequences. The optimal sequence thus obtained is termed as the optimal window with finite support (OWFS), and its various associated properties are discussed. It is shown analytically that as the support of OWFS approaches infinity, it converges to zero‐order DPSS. In order to illustrate its optimality, the compactness of the proposed OWFS is compared with those of various window functions. Extending the proposed OWFS, this study also discusses the formulation and associated properties of the zero‐order periodic DPSS. Further, the closed form expression for the upper bound of achievable time and frequency domain energy concentrations is also derived.

The discrete prolate spheroidal sequences are optimum waveforms in many communication and signal processing applications because they comprise the most spectral efficient set of orthogonal sequences possible. Generation of the sequences has proven to be difficult in the past due to the absence of a closed form solution. A new method of easily generating any single discrete prolate spheroidal sequence, including sequences of very long length, is presented. Also shown are some example sequences generated using the algorithm presented.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

The plasma sheath has a serious impact on the propagation of electromagnetic waves, resulting in the radio blackout problem in aerospace communications. Existing studies have shown that the coherence time of the plasma sheath channel can be as low as 0.1µs, which is smaller than the symbol period in aerospace telemetry communications. However, the traditional symbol detection method based on correlation filters only uses the orthogonality of transmission symbols, without considering the channel variation within one symbol period. In this paper, a new symbol detection scheme is proposed under the high-dynamic plasma sheath channel. Firstly, the discrete prolate spheroidal sequences are used to expand the dynamic channel. Then, based on an analysis of the log-likelihood ratio, a linear combination detection scheme is proposed, which has a simple form and is suitable for symbol detection under the plasma sheath channel. In particular, we show that the performance of communication systems under the plasma sheath channel can be improved by spreading the signal dimension. Finally, simulation results are carried out based on the shock tube experimental data, showing that the proposed detection scheme has better performance compared with the correlation-based detection method.

Basis expansion model for tracking and equalizing rapidly varying multimode fiber channels

Background and Aim: The study objective was to assess chaotic global metrics in malnourished children following power spectral manipulations. Methods: We evaluated the complexity of heart rate (HR) variability (HRV) in malnourished subjects via six power spectra (Welch, multi-taper method (MTM), Burg, covariance, Yule-Walker, and periodogram) and then, when adjusted by the MTM parameters, for further refinement. Seventy children were split equally (controls &amp; malnourished) and the HR was monitored for 20 min; 1000 RR-intervals were attained for HRV analysis. Results: The results stipulate that CFP1 (chaotic forward parameter) and CFP3 are the best metrics to distinguish the two groups. The most appropriate power spectra were Welch, MTM, and Yule-Walker. Results indicate that CFP3 calculated using MTM power spectra is the best combination to discriminate between the two groups. Yet, if the RR intervals are set to 400, discrete prolate spheroidal sequences (DPSS) to 3, and Thomson’s nonlinear combination to ‘adaptive’, a greater level of significance can be achieved (Cohen’s ds = -1.57). This significantly outperforms that under default conditions (Glass’s ∆ Delta = -1.06, and Cohen’s ds = -0.95). Conclusion: Malnourished children have a lower response to chaotic global metrics than the control group. CFP3 with the aforementioned settings is the best combination to discriminate between these groups on the basis of RR intervals. It has the greatest significance by Cohen’s ds. Our data suggest impaired autonomic function in malnourished children, which may have consequences for cardiovascular risks.

In active sonar, the reverberation plus target time series can be modeled as the joint convolution of the signal with the channel and scatterer impulse responses. Especially in shallow water, the channel response cannot be adequately modeled as propagation over discrete paths. A maximum likelihood type approach is proposed for estimating the arrival times of signals which have propagated via a continuum of paths, i.e., temporally spread channels. The channel spreading is included in the model by using a discrete prolate spheroidal sequence (DPSS) to represent the channel impulse response of given duration, but unknown shape. Thus the unknown parameters are the arrival times and the scale factors of the DPSS expansion. The parameters are estimated using an iterative methodology which decomposes the original data into its constituent components and then estimates the parameters of the individual components through a sequence of one-dimensional searches. Experimental data and computer simulation examples indicate that the method performs well.

A new constrained optimization method for all-pole digital filter design is presented. The design philosophy employed minimizes a function of the area between the ideal low-pass filter response in the passband and the actual filter response subject to a quadratic constraint which ensures filter realizability. It is shown that unique solutions are obtained which are related to eigenvectors of a Toeplitz matrix whose elements form a scaled discrete prolate spheroidal wave sequence (DPSS). It is therefore possible to exploit the properties of DPSS and discrete prolate spheroidal wave functions (DPSWF's) to reduce the filter design effort. The ratio of passband energy to total energy over the entire filter bandwidth is optimal for these designs.

A novel approach is proposed for correlated multiple-input multiple-output (MIMO) channel estimation based on reduced-rank (RR) technique and partial channel state information (CSI). In contrast to previous proposals that used the channel correlation matrix (CCM) and its eigendecomposition, this paper shows that close linear minimum mean-square-error (LMMSE) performance can be achieved with the use of predefined bases derived from the knowledge of the maximum angular dispersion. A theoretical framework to synthesize a suitable set of bases is provided, from which discrete prolate spheroidal sequences (DPSSs) are identified as one of the appropriate predefined bases for spatial channel representation. The robustness of the proposed estimator allows changes in the propagation scenario to be managed according to the demands of realistic communications systems. The performance analysis of the channel estimator is shown and corroborated with simulation results.

In this paper, we provide a new approach in ultra Wideband (UWB) radars based on a Fourier series with time-varying coefficients resulting in a second-order cyclostationary characteristics for stationary (low-mobility) target and almost second-order cyclostationary characteristics in moving target scenario. We also provide a new method for blind detection based on detecting the presence of cyclostationarity. The new MMSE estimator is based on the unconditional orthonormal signal representation for almost cyclostationary characteristics, moreover, based on this estimation, a new method for detection of UWB radar signals in presence of (non)-Gaussian additive noise in stationary and moving target scenario is provided. We utilize the discrete prolate spheroidal sequences (DPSS) as the unconditional orthonormal signals. The purposed methods require no a priori information, except the pulse repetition interval, to detect signal of interest. Simulations for CFAR detectors are presented to compare the introduced new method with cyclostationary detector and the conventional UWB radar detectors called interleaved periodic correlation processing (IPCP).

The determination of the number of wideband signals impinging on a passive sensor array in the form of multiple groups (clusters), and the estimation of their directions of arrival is addressed. The idea of preprocessing by a set of orthogonal beamformers for dimensionality reduction is used to simplify wideband processing. The effectiveness of this approach is demonstrated with the use of discrete prolate spheroidal sequences (DPSSs) as the beamformers for linear uniform arrays. A weighting gain as an indicator of the improvement in the signal-to-noise ratio due to such preprocessing is introduced. Two versions of an algorithm that combines preprocessing/prefiltering and the coherent signal subspace method in the frequency domain are developed, and comparative performance evaluations are carried out. The relative effects of beamspace prefiltering on optimum and suboptimum estimators are explored. >

In this paper, a method for combining wideband and narrowband waveforms is proposed to improve target detection in shallow water environments. In this regard, a sonar waveform design suitable for target speed has been proposed too. The method uses a wideband frequency-modulated waveform for high range resolution in a reverberation environment and the Doppler-sensitive (DS) waveform to improve the detection of moving targets. The proposed combined waveform is mathematically modeled, and the Calculating of ambiguity function (AF) is performed. The AF and autocorrelation function (ACF) of the designed waveform indicate both DS and fair range resolution features simultaneously exist. So the initial range resolution for target detection is preserved. The Peak to Sidelobe level (PSL) ratio of the proposed waveform is at least 25 dB more than the previous state of the art waveforms. Calculating the Q-function criterion for the designed waveform reveals the superior reverberation suppression and detection performance with respect to the state of the art waveforms. After calculating the reverberation channel model, waveform echo, and detection of the target, the probability of detection (Pd) versus signal-to-reverberation ratio (SRR) was simulated by the Monte Carlo method. It was shown that the proposed waveform improved the probability of target detection by 20 dB, comparing to the base waveforms.

Radar Phase-Modulated Waveform Design for Extended Target Detection

A new scheme based on Kalman filtering to optimize the waveforms of an adaptive multi-antenna radar system for target impulse response (TIR) estimation is presented. This work aims to improve the performance of TIR estimation by making use of the temporal correlation between successive received signals, and minimize the mean square error (MSE) of TIR estimation. The waveform design approach is based upon constant learning from the target feature at the receiver. Under the multiple antennas scenario, a dynamic feedback loop control system is established to real-time monitor the change in the target features extracted form received signals. The transmitter adapts its transmitted waveform to suit the time-invariant environment. Finally, the simulation results show that, as compared with the waveform design method based on the MAP criterion, the proposed waveform design algorithm is able to improve the performance of TIR estimation for extended targets with multiple iterations, and has a relatively lower level of complexity.

The paper addresses adaptive detection of extended targets in Gaussian noise with unknown statistics. It is assumed that the radar can change the transmitted signal in azimuth. More precisely, it makes use of N N-dimensional signatures; the possible useful signal from each radar cell is a coherent pulse train while the disturbance is a Gaussian process, independent from cell to cell, but with the same (unknown) covariance matrix regardless of the illuminated one. Based on the above model, we propose an adaptive detector designed according to a two-step procedure. Its performance assessment and the comparison with a previously-proposed detector show that the proposed one can be a viable means to cope with uncertain scenarios.

In this paper, we optimize probability of detection and probability of false alarm in cognitive radio network to minimize probability of error of a particular SU in a centralized cognitive radio network using Genetic algorithm (GA). Our objective is to minimize probability of error and find out optimum values of probability of occupancy detection or probability of detection and probability of false alarm. We use Genetic Algorithm to solve this optimization problem. The result is compared with Differential Evolution algorithm and it is evident from the comparison that DE finds better solution and takes much lesser number of evaluations to find optimum solution.