A simple algorithm for generating discrete prolate spheroidal sequences

Receive antenna selection (AS) has been shown to maintain the diversity benefits of multiple antennas while potentially reducing hardware costs. However, the promised diversity gains of receive AS depend on the assumptions of perfect channel knowledge at the receiver and slowly time-varying fading. By explicitly accounting for practical constraints imposed by the next-generation wireless standards such as training, packetization and antenna switching time, we propose a single receive AS method for time-varying fading channels. The method exploits the low training overhead and accuracy possible from the use of discrete prolate spheroidal (DPS) sequences based reduced rank subspace projection techniques. It only requires knowledge of the Doppler bandwidth, and does not require detailed correlation knowledge. Closed-form expressions for the channel prediction and estimation error as well as symbol error probability (SEP) of M-ary phase-shift keying (MPSK) for symbol-by-symbol receive AS are also derived. It is shown that the proposed AS scheme, after accounting for the practical limitations mentioned above, outperforms the ideal conventional single-input single-output (SISO) system with perfect CSI and no AS at the receiver and AS with conventional estimation based on complex exponential basis functions.

Channel state information (CSI) is required at the transmitter for achieving the maximum potentials of multiple-input multiple-output (MIMO) systems. In fast time-variant vehicular communications channels high data rate feedback lines are required in a frequency division duplex (FDD) transceiver for updating the transmitter with the rapidly changing CSI. Even with high data rate feedback lines, the delay caused by channel estimation and feedback may lead to outdated CSI at the transmitter. To reduce both the feedback load and CSI delay, this paper presents a reduced rank autoregressive (AR) channel predictor based on low dimensional discrete prolate spheroidal (DPS) sequences. The new subframe-wise DPS basis expansion model (DPS-BEM) channel predictor properly exploits the channel's restriction to low dimensional subspaces for reducing the prediction error and the computational complexity. The proposed channel predictor can be applied for updating the precoding matrix in time-variant MIMO systems. Simulation results demonstrate that the proposed channel predictor outperforms the DPS based minimum energy (ME) predictor at different Doppler frequencies and has better performance than the conventional Wiener predictor for slower time-variant channels and almost similar performance for very fast time-variant channels with reduced amount of computational complexity.

We propose a parametric waveform design approach for improved detection of extended targets embedded in uncorrelated signal-dependent clutter and noise, whose spectral densities are assumed to be known. Unlike canonical waveform design approaches, the transmit waveform is represented as a weighted linear combination of discrete prolate spheroidal sequences. In the optimization problem, the probability of detection is maximized with respect to the weighting factors of the associated discrete prolate spheroidal sequences under the transmit energy constraint. The weighting factors, which are resolved using a numerical method, lead directly to the desired transmit waveform in the time domain. In comparison to the canonical waveform design approaches, the extra step for time sequence synthesis is avoided and the loss in probability of detection produced therein is remedied. Simulation results demonstrate the improvement in the probability of detection for the proposed approach. However, the improvement comes at the cost of higher computational complexity.

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

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.

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 & 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. >

This paper investigates channel estimation for linear time-varying (LTV) wireless channels under <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">double sparsity</i>, i.e., sparsity in both the delay and Doppler domains. An on-grid approximation is first considered, enabling rigorous hierarchical-sparsity modeling and compressed sensing-based channel estimation. Guaranteed recovery conditions are provided for affine frequency division multiplexing (AFDM), orthogonal frequency division multiplexing (OFDM) and single-carrier modulation (SCM), highlighting the superiority of AFDM in terms of doubly sparse channel estimation. To address arbitrary Doppler shifts, a relaxed version of the on-grid model is introduced by utilizing multiple elementary Expansion Models (BEM) each based on Discrete Prolate Spheroidal Sequences (DPSS). Next, theoretical guarantees are provided for the precision of this off-grid model before further extending it to tackle channel prediction by exploiting the inherent DPSS extrapolation capability. Finally, numerical results are provided to both validate the proposed off-grid model for channel estimation and prediction purposes under the double sparsity assumption and to compare the corresponding mean squared error (MSE) and overhead performance when different wireless waveforms are used.

Multiplication is an important fundamental function in arithmetic operations. Multiplication-based operations such as Multiply and Accumulate(MAC) and inner product are among some of the frequently used computation Intensive Arithmetic Functions(CIAF) currently implemented in many Digital Signal Processing (DSP) applications such as convolution, Fast Fourier Transform(FFT), filtering and in microprocessors m its arithmetic and logic unit. Since multiplication dominates the execution tune of most DSP algorithms, so there is a need of high speed multiplier. Currently, multiplication time is still the dominant factor in determining the instruction cycle time of a DSP chip. The demand for high speed processing has been increasing as a result of expanding computer and signal processing applications. Higher throughput arithmetic operations are important to achieve the desired performance in many real-time signal and image processing applications . One of the key arithmetic operations in such applications is multiplication and the development of fast multiplier circuit has been a subject of interest over decades. Multiplier based on Vedic Mathematics is one of the fast and low power multiplier. Employing this technique in the computation algorithms will reduce the complexity, execution time, power etc. This vedic based multiplier is compared with binary multiplier(partial products method).

Integrated silicon waveguides serve as a transmission medium for on-chip signaling, and they are also used to form various types of devices for communication and signal processing applications. In this paper, we present some recent progress in tailoring the physical properties of the silicon waveguides such as chromatic dispersion and nonlinearity. Using slot structures, both dispersion and nonlinearity can be tailored by more than an order of magnitude, which is a very useful feature in many signal processing applications.