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It is well accepted that acquiring downlink channel state information in frequency division duplexing (FDD) massive multiple-input multiple-output (MIMO) systems is challenging because of the large overhead in training and feedback. In this paper, we propose a deep generative model (DGM)-based technique to address this challenge. Exploiting the partial reciprocity of uplink and downlink channels, we first estimate the frequency-independent underlying channel parameters, i.e., the magnitudes of path gains, delays, angles-of-arrivals (AoAs) and angles-of-departures (AoDs), via uplink training, since these parameters are common in both uplink and downlink. Then, the frequency-specific underlying channel parameters, specifically, the phase of each propagation path, are estimated via downlink training using a very short training signal. In the first step, we incorporate the underlying distribution of the channel parameters as a prior into our channel estimation algorithm. We use DGMs to learn this distribution. Simulation results indicate that our proposed DGM-based channel estimation technique outperforms, by a large gap, the conventional channel estimation techniques in practical ranges of signal-to-noise ratio (SNR). In addition, a near-optimal performance is achieved using only few downlink pilot measurements. [ABSTRACT FROM AUTHOR]

In harmonic radar (HR), the transmitter illuminates a nonlinear target (the tag), causing the return signal to consist of harmonics at multiples of the transmitted carrier frequency. Of them, the second harmonic is usually the strongest and the one to which the receiver is tuned. This frequency difference distinguishes the tag reflection from environmental clutter, which remains at the illuminating frequency. However, the passive nature of HR tags severely limits the reflected power, and therefore the operational range of a HR system. We propose to increase the range and/or signal to noise ratio (SNR) by novel restructuring at the physical and signal levels. For this, we accompany the original transmitter with auxiliary transmitters able to send simple tones that are synchronized to arrive at the tag in phase, and we design the receiver to detect an intermodulation component. The resulting range and SNR are much greater than those of the original, conventional HR system, even if the original system were to transmit with power equal to the aggregate power of the proposed system. Achieving mutually coherent, (in phase), arrival of the tones at the tag is the focus of the present paper. We provide a system framework that models the tag, then present the adaptive phase coherence algorithm and analyze the probabilistic growth of the output signal power. We also account for the effects of frequency shifts due to transmitter mobility and the frequency offset errors in the transmitter local oscillators. [ABSTRACT FROM AUTHOR]

Extremely low-resolution (e.g. one-bit) analog-to-digital converters (ADCs) and digital-to-analog converters (DACs) can substantially reduce hardware cost and power consumption for MIMO radar especially with large scale antennas. In this paper, we focus on the detection performance analysis and joint design for the MIMO radar with one-bit ADCs and DACs. Specifically, under the assumption of low signal-to-noise ratio (SNR) and interference-to-noise ratio (INR), we derive the expressions of probability of detection ($\mathcal {P}_{d}$) and probability of false alarm ($\mathcal {P}_{f}$) for one-bit MIMO radar and also the theoretical performance gap to infinite-bit MIMO radars for the noise-only case. We further find that for a fixed $\mathcal {P}_{f}$ , $\mathcal {P}_{d}$ depends on the defined quantized signal-to-interference-plus-noise ratio (QSINR), which is a function of the transmit waveform and receive filter. Thus, an optimization problem arises naturally to maximize the QSINR by joint designing the waveform and filter. For the formulated problem, we propose an alternating waveform and filter design for QSINR maximization (GREET). At each iteration of GREET, the optimal receive filter is updated via the minimum variance distortionless response (MVDR) method, and due to the difficulty in global optimality, an alternating direction method of multipliers (ADMM) based algorithm is devised to efficiently find a high-quality suboptimal one-bit waveform. Numerical simulations are consistent to the theoretical performance analysis and demonstrate the effectiveness of the proposed design algorithm. [ABSTRACT FROM AUTHOR]

In this paper, two different timing-mismatch compensation strategies for two-channel time-interleaved analog-to-digital converters are comprehensively analyzed and compared. In the first strategy (SA), one channel serves as a reference channel, and the other channel is compensated to match the reference channel using the timing mismatch between the channels. In the second strategy (SB), both channels are compensated to match each other, using half the value of the channel mismatch with different signs. For SB, the paper introduces a novel compensation structure that utilizes parallel differentiator-multiplier (PDM) branches. Expressions for the spurious-free dynamic range (SFDR) after compensation are derived for both strategies. These expressions reveal that the novel PDM structure achieves a remarkably greater SFDR than the existing cascaded differentiator-multiplier (CDM) compensation structure which can be used for both SA and SB. This is because, after compensation, the remaining aliasing distortion in the proposed PDM structure is shown to be of higher approximation order (in terms of the mismatch value) and thus substantially smaller than in the CDM structure. Simulations included in the paper validate the theoretical results. [ABSTRACT FROM AUTHOR]

Symbol-level precoding (SLP) has recently emerged as a new paradigm for physical-layer transmit precoding in multiuser multi-input-multi-output (MIMO) channels. It exploits the underlying symbol constellation structure, which the conventional paradigm of linear precoding does not, to enhance symbol-level performance such as symbol error probability (SEP). This paper aims to better understand the relationships between SLP and linear precoding, subsequent design implications, and further connections beyond the existing SLP scope. Focused on the quadrature amplitude modulation (QAM) constellations, our study is built on a basic signal observation, namely, that SLP can be equivalently represented by a zero-forcing (ZF) linear precoding scheme augmented with some appropriately chosen symbol-dependent perturbation terms, and that some extended form of SLP is equivalent to a vector perturbation (VP) nonlinear precoding scheme augmented with the above-noted perturbation terms. We examine how insights arising from this perturbed ZF and VP interpretations can be leveraged to i) substantially simplify the optimization of certain SLP design criteria, namely, total or peak power minimization subject to SEP quality guarantees; and ii) draw connections with some existing SLP designs. We also touch on the analysis side by showing that, under total power minimization, the basic ZF scheme is a near-optimal SLP scheme when the QAM order is very high—which gives a vital implication that SLP is more useful for lower-order QAM cases. Numerical results further indicate the merits and limitations of the different SLP designs derived from the perturbed ZF and VP interpretations. [ABSTRACT FROM AUTHOR]

We consider thetwo-dimensional multi-target detection problem of recovering a target image from a noisy measurement that contains multiple copies of the image, each randomly rotated and translated. Motivated by the structure reconstruction problem in single-particle cryo-electron microscopy, we focus on the high noise regime, where the noise hampers accurate detection of the image occurrences. We develop an autocorrelation analysis framework to estimate the image directly from a measurement with an arbitrary spacing distribution of image occurrences, bypassing the estimation of individual locations and rotations. We conduct extensive numerical experiments, and demonstrate image recovery in highly noisy environments. [ABSTRACT FROM AUTHOR]

We address here the issue of jointly estimating the angle parameters of a single sinusoid with Wiener carrier phase noise and observed in additive, white, Gaussian noise (AWGN). We develop the theoretical foundation for time-domain, phase-based, joint maximum likelihood (ML) estimation of the unknown carrier frequency and the initial carrier phase, with simultaneous maximum a posteriori probability (MAP) estimation of the time-varying carrier phase noise. The derivation is based on the amplitude and phase-form of the noisy received signal model together with the use of the best, linearized, additive observation phase noise model due to AWGN. Our newly derived estimators are closed-form expressions, consisting of both the phase and the magnitude of all the received signal samples. More importantly, they all have a low-complexity, sample-by-sample iterative processing structure, which can be implemented iteratively in real-time. As a basis for comparison, the Cramer-Rao lower bound (CRLB) for the ML estimators and the Bayesian CRLB (BCRLB) for the MAP estimator are derived in the presence of carrier phase noise, and the results simply depend on the signal-to-noise ratio (SNR), the observation length and the phase noise variance. It is theoretically shown that the estimates obtained are unbiased, and the mean-square error (MSE) of the estimators attain the CRLB/BCRLB at high SNR. The MSE performance as a function of the SNR, the observation length and the phase noise variance is verified using Monte Carlo simulation, which shows a remarkable improvement in estimation accuracy in large phase noise. [ABSTRACT FROM AUTHOR]

We consider the problem of robust deconvolution, and particularly the recovery of an unknown deterministic signal convolved with a known filter and corrupted by additive noise. We present a novel, non-iterative data-driven approach. Specifically, our algorithm works in the frequency-domain, where it tries to mimic the optimal unrealizable non-linear Wiener-like filter as if the unknown deterministic signal were known. This leads to a threshold-type regularized estimator, where the threshold at each frequency is determined in a data-driven manner. We perform a theoretical analysis of our proposed estimator, and derive approximate formulas for its Mean Squared Error (MSE) at both low and high Signal-to-Noise Ratio (SNR) regimes. We show that in the low SNR regime our method provides enhanced noise suppression, and in the high SNR regime it approaches the optimal unrealizable solution. Further, as we demonstrate in simulations, our solution is highly suitable for (approximately) bandlimited or frequency-domain sparse signals, and provides a significant gain of several dBs relative to other methods in the resulting MSE. [ABSTRACT FROM AUTHOR]

Time-of-arrival (TOA) based localization plays a central role in current and future localization systems. Such systems, exploiting the fine delay resolution properties of wideband and ultra-wideband (UWB) signals, are particularly attractive for ranging under harsh propagation conditions in which significant multipath may be present. While multipath has been traditionally considered detrimental in the design of TOA estimators, it can be exploited to benefit ranging. This paper investigates the impact of a priori multipath information on TOA estimation. To this end, bounds on the performance of TOA estimation in dense multipath channels are provided and discussed under different operating conditions. The effects of channel dispersion and transmission bandwidth on ranging systems are investigated showing that, contrary to communication systems, diversity behavior is only exhibited in the medium signal-to-noise ratio regime. [ABSTRACT FROM AUTHOR]

A full performance analysis of the widely linear (WL) minimum variance distortionless response (MVDR) beamformer is introduced. While the WL MVDR is known to outperform its strictly linear counterpart, the Capon beamformer, for noncircular complex signals, the existing approaches provide limited physical insights, since they explicitly or implicitly omit the complementary second-order (SO) statistics of the output interferences and noise (IN). To this end, we exploit the full SO statistics of the output IN to introduce a full SO performance analysis framework for the WL MVDR beamformer. This makes it possible to separate the overall signal-to-interference plus noise ratio (SINR) gain of the WL MVDR beamformer w.r.t. the Capon one into the individual contributions along the in-phase (I) and quadrature (Q) channels. Next, by considering the reception of the unknown signal of interest (SOI) corrupted by an arbitrary number of orthogonal noncircular interferences, we further unveil the distribution of SINR gains in both the I and Q channels, and show that in almost all the spatial cases, these performance advantages are more pronounced when the SO noncircularity rate of the interferences increases. Illustrative numerical simulations are provided to support the theoretical results. [ABSTRACT FROM AUTHOR]

Time-frequency representation (TFR) plays a significant role in interpreting and analyzing nonstationary multi-mode signals. However, currently, it is still challenging to handle multi-mode signals with closely-spaced or spectrally-overlapped instantaneous frequencies (IFs), especially under low signal-to-noise ratio (SNR) conditions. To address this issue, we propose an enhanced TFR and mode decomposition (ETFR-MD) method, which is especially suitable to represent and decompose multi-mode signals with such complex IFs. The proposed ETFR-MD method exploits both the IFs and instantaneous amplitudes (IAs) of the signal under investigation. First, we design an initial IF estimation method to deal with overlapped IFs. Then, a low-complexity mode enhancement scheme is proposed so that the enhanced IFs could better fit the underlying IF laws. After that, three alternatives, i.e., short-time Fourier transform (STFT) coefficients, de-chirping, and intrinsic chirp component decomposition (ICCD), are considered for IA recovery. Finally, the extracted IAs are combined with the enhanced IFs to reconstruct each signal mode, respectively. To gain more insights, we quantitatively analyze the interference during mode decomposition and derive the optimal window length for mode separation. Experimental results implemented on both simulated and real-world data confirm the superior performance of the ETFR-MD compared with the state-of-the-art solutions. [ABSTRACT FROM AUTHOR]

It has been shown that direct target localization in distributed multiple input multiple output (MIMO) radar can outperform indirect localization significantly, but conventional direct localization methods suffer from both high computational complexity and high communication cost. In this work, we address the issues by designing an efficient factor graph based message passing approach to direct localization, which greatly reduces the computational complexity and communication cost. First, a factor graph representation for the problem of direct localization is developed, which, however, involves difficult local functions. Inspired by expectation propagation (EP), we design an iterative method to solve the problem, where both EP and belief propagation (BP) are used to make message passing in the factor graph tractable, leading to a low complexity message passing iterative method. We show that the message passing based method are very suitable for decentralized processing and can be employed in distributed radars with different configurations. Extensive comparisons with state-of-the-art indirect and direct methods are provided, which show that the proposed method can achieve similar performance to the exhaustive search-based direct localization methods while with much lower computational complexity and communication cost, and it outperforms significantly indirect localization methods at low signal to noise ratios. [ABSTRACT FROM AUTHOR]

Direction of arrival (DOA) estimation is a classical topic in source localization. Notably, a reliable grid-free sparse representation algorithm, called FRI (finite rate of innovation) algorithm, was proposed to recover the finite number of Dirac pulses from a stream of 1D temporal samples, which also offers a efficient solution to the DOA estimation problem. Typically, FRI method assumes uniform sampling with single snapshot. However, the actual situation is richer and more diverse. Motivated by the requests of practical applications (e.g. array deployment, algorithm run-speed, etc.), a generic FRI method is proposed to tackle the more general case in practice, i.e. non-uniform sampling with multiple snapshots. Instead of annihilating the measured sensor data, a model-fitting method is used to robustly retrieve the sparse representation (i.e. DOAs and associated amplitudes) of the 1D samples. We demonstrate that our algorithm can handle challenging DOA tasks with high-resolution, which we validate in various conditions, such as multiple coherent sources, insufficient signal snapshots, low signal-to-noise ratio (SNR), etc. Moreover, we show that the computational complexity of our algorithm mainly scales with the number of sources and varies very slowly with the number of samples and snapshots, which meets the needs of a wider range of practical applications. [ABSTRACT FROM AUTHOR]

A class of Cramér-Rao bounds (CRBs) for wideband direction-of-arrival (DOA) estimation under the subband (or frequency bin) model is studied for the underdetermined case, where the number of sources is no less than that of physical sensors. A unified framework is proposed to encompass the closed-form CRB expressions for DOAs in four cases where the sources are known a priori to 1) have flat spectra/cross spectra, 2) be spatially uncorrelated, 3) be spatially uncorrelated and have proportional spectra up to unknown factors, 4) be spatially uncorrelated and have flat spectra. The relationship between the wideband CRBs and the subband ones is investigated, and the order relationship among the derived CRBs are provided. The asymptotic behavior of the CRBs with respect to the number of snapshots and the signal-to-noise ratio (SNR) is discussed. Two asymptotic expressions for sufficiently large SNR are derived in both overdetermined and underdetermined cases. Existence of the derived CRBs is examined through rank conditions of the introduced matrices, which yields upper bounds on the resolution capacities. Different from the narrowband scenario, underdetermined wideband DOA estimation is feasible even if a sparse array is not used given different a priori knowledge about the source spectra. It is possible to resolve more wideband Gaussian sources than the number of DOFs offered by the difference co-array. Finally, further interpretations of the subband model are provided, revealing the underlying connections with the multi-frequency co-array augmentation concept and the non-coherent subarray system. [ABSTRACT FROM AUTHOR]

A Savitzky-Golay (SG) filter, widely used in signal processing applications, is a finite-impulse-response low-pass filter obtained by a local polynomial regression on noisy observations in the least-squares sense. The problem addressed in this paper is one of optimal order (or filter length) selection of SG filter in the presence of non-Gaussian noise, such that the mean-squared-error (or risk) between the underlying clean signal and the SG filter estimate is minimized. Since mean-squared-error (MSE) depends on the unknown clean signal, direct minimization is impractical. We circumvent the problem within a risk-estimation framework, wherein, instead of minimizing the original MSE, an unbiased estimate of the MSE (which depends only on the noisy observations and noise statistics) is minimized in order to obtain the optimal order. The proposed method gives an unbiased estimate of the MSE considering SG filtering in the presence of additive noise following any distribution with finite first- and second-order statistics and independent of the signal. The SG filter's order and length are optimized by minimizing the unbiased estimate of MSE. The denoising performance of the optimal SG filter is demonstrated on real-world electrocardiogram (ECG) signals as well as signals from the WaveLab Toolbox under Gaussian, Laplacian, and Uniform noise conditions. The proposed denoising algorithm is superior to four benchmark algorithms in low-to-medium input signal-to-noise ratio (SNR) regions ($-5$ dB to 12.5 dB) in terms of the SNR gain. [ABSTRACT FROM AUTHOR]

Pulse Doppler radars suffer from range-Doppler ambiguity that translates into a trade-off between the maximal unambiguous range and velocity. Several techniques, like the multiple PRFs (MPRF) method, have been proposed to mitigate this problem. The drawback of the MPRF method is that the received samples are not processed jointly, decreasing signal to noise ratio (SNR). To overcome the drawbacks of MPRF, we employ a random pulse phase coding approach to increase the unambiguous range region while preserving the unambiguous Doppler region. Our method encodes each pulse with a random phase, varying from pulse to pulse, and then processes the received samples jointly to resolve range ambiguity. This technique increases the SNR through joint processing without the parameter matching procedures required in MPRF. The recovery algorithm is designed based on orthogonal matching pursuit so that it can be directly applied to either Nyquist or sub-Nyquist samples. The unambiguous delay-Doppler recovery condition is derived using compressed sensing theory in noiseless settings. In particular, an upper bound on the number of targets is given, with respect to the number of samples in each pulse repetition interval and the number of transmit pulses. Simulations show that in both regimes of Nyquist and sub-Nyquist samples our method outperforms the popular MPRF approach in terms of hit rate. [ABSTRACT FROM AUTHOR]

This paper proposes an efficient algorithm for robust sensor placement with the purpose of recovering a source signal from noisy measurements. To model uncertainty on the spatially-variant sensors gain and on the spatially correlated noise, we assume that both are realizations of Gaussian processes. Since the signal to noise ratio (SNR) is also uncertain in this context, to achieve a robust signal extraction, we propose a new placement criterion based on the maximization of the probability that the SNR exceeds a given threshold. This criterion can be easily evaluated using the Gaussian process assumption. Moreover, to reduce the computational complexity of the joint maximization of the criterion with respect to all sensor positions, we suggest a sequential maximization approach, where the sensor positions are chosen one at a time. Finally, we present numerical results showing the superior robustness of the proposed approach when compared to standard sensor placement criteria aimed at interpolating the spatial gain and to a recently proposed criterion aimed at maximizing the average SNR. [ABSTRACT FROM AUTHOR]

We consider multi-carrier two-way relaying networks consisting of two user transceivers and multiple filter-and-forward (FF) relays. The FF relaying technique along with the multi-carrier schemes at the transceivers are utilized to suppress the inter-symbol-interference caused by the frequency-selectivity of the end-to-end channel. We jointly optimize subcarrier power allocation at the transceivers and the FIR filters at the FF relays to minimize the total transmit power subject to two quality of service constraints measured by sum-rates at the transceivers. We propose two approaches to tackle this problem: a gradient steepest descent technique, and a semi-closed-form method, which enforces a new constraint on the optimization such that at the optimum, the frequency-selective end-to-end channel is turned into a frequency-flat one. Furthermore, we show that the second method can be used as an initial point for the gradient steepest descent technique. Aiming to evaluate the performance of the proposed methods with a benchmark, we obtain a lower bound for the minimum transmit power at the network. We show that the proposed techniques are within 3 dB of this lower bound. Our numerical results further show that the proposed methods outperform existing solutions for similar networks. [ABSTRACT FROM AUTHOR]

The framework of this paper is that of adaptive detection in Gaussian noise with unknown covariance matrix when the training samples do not share the same covariance matrix as the vector under test. We consider a class of constant false alarm rate detectors which depend on two statistics (β,t) whose distribution is parameter-free in the case of no mismatch and we analyze the impact of covariance mismatched training samples. More precisely, we provide a statistical representation of these two variables for an arbitrary mismatch. We show that covariance mismatch induces significant variations of the probability of false alarm and we investigate a way to mitigate this effect. [ABSTRACT FROM AUTHOR]

We present a novel and computationally simple solution to the problem of detecting the number of signals, which is applicable to both white and colored noise, and to a very small number of samples. The solution is based on a novel and non-asymptotic goodness-of-fit metric, referred to as signal subspace matching (SSM), which is aimed at matching a model-based signal subspace to its sampled-data-based counterpart. We form a set of hypothesized signal subspace models, with the k-th model being a projection matrix composed of the k leading eigenvectors of the sample-covariance matrix. This set of hypothesized models is compared to their sampled-data-based counterpart – a projection matrix constructed from the sampled data – via the SSM metric, and the model minimizing this metric is selected. We show that this solution involves the principal angles between the column span of the model and the column span of the model. We prove the consistency of this solution for the high signal-to-noise-ratio limit and for the large-sample limit. The large-sample consistency is shown to be conditioned on the signal-to-noise ratio (SNR) being higher than a a certain threshold. Simulation results, demonstrating the performance of the solution for both colored and white noise, are included. [ABSTRACT FROM AUTHOR]

We present a novel solution to the problem of estimating the array response of the signal of interest (SOI) in case it is constrained to lie in a known subspace, aimed at coping with model errors in the known subspace. The solution is based on a novel formulation of the problem, targeted at matching the error-contaminated model-based signal subspace to its sampled-data counterpart. The solution turns out to minimize the angle between these two subspaces, which is intuitively very pleasing. We solve the problem for three different characterization of the spatial interference: (i) the spatial interference is known, (ii) the spatial interference is unknown, and (iii) the spatial interference is constrained to lie in a known subspace. We present a closed-form solution for the first case and iterative solutions for the other two cases. Based on these solutions, we derive the corresponding estimators for the SOI’s waveform and their signal-to-interference+noise ratio (SINR). Simulation results, demonstrating the superiority of the derived solutions over the corresponding deterministic maximum likelihood (DML) solutions, are included. [ABSTRACT FROM AUTHOR]

This paper proposes an integrated time-frequency rate distribution (TFRD) technique, i.e., coherently integrated trilinear autocorrelation function (CITAF), for the detection and parameter estimation of quadratic frequency modulated (QFM) signal embedded in white Gaussian noise. The basic idea is to design a trilinear autocorrelation function (TAF) enabling a coherent integration of the signal energy in both of the time and lag-time domains. Theoretical analysis and numerical simulations show that this new method has a lower signal to noise ratio (SNR) threshold and higher estimation accuracy in comparison with several state-of-the-art algorithms. Furthermore, the coherently integrated nonuniform TAF (CINTAF) is briefly introduced. [ABSTRACT FROM AUTHOR]

Molecular communications rely on diffusive propagation to transport information, which is attractive for a variety of nano-scale applications. Due to the long-tail channel response, spatial-temporal coding of information may lead to severe inter-symbol interference (ISI). Classical linear signal processing in wireless communications is usually operating with high complexity and high signal-to-noise ratios, whereas signal processing in molecular communication system requires operating in opposite conditions. In this work, we propose a novel signal processing paradigm inspired by the biological principle, which enables low-complexity signal detection in extremely noisy environments. We first propose a non-linear filter inspired by stochastic resonance, which is found in a variety of biological systems, and it can significantly improve the output SNR by converting noise to useful signals. Then, we design a non-coherent detection method, one which exploits the generally transient trend of observed signals (i.e. quick-rising and slow-decaying) rather than hidden channel state information (CSI), thus excluding CSI estimation and involving only summations. Implementation issues are also discussed, including parameters configuration and adaptive threshold. Numerical results show that the proposed bio-inspired scheme can improve the performance remarkably over classical approaches. Even compared with the optimal linear methods, the required SNR of the proposed scheme can be reduced by 7 dB, which reaffirms why it can be used in noisy biological environments. As the first attempt to design bio-inspired molecular signal detectors, the proposed non-linear processing paradigm may provide the great promise to the emerging nano-machine applications. [ABSTRACT FROM AUTHOR]

We investigate synthesis of a large effective aperture using a sparse array of subarrays. We employ a multi-objective optimization framework for placement of subarrays within a prescribed area dictated by form factor constraints, trading off the smaller beam width obtained by spacing out the subarrays against the grating and side lobes created by sparse placement. We assess the performance of our designs for the fundamental problem of bearing estimation for one or more sources, comparing performance against estimation-theoretic bounds. Our tiled architecture is motivated by recent progress in low-cost hardware realizations of moderately sized antenna arrays (which play the role of subarrays) in the millimeter wave band, and our numerical examples are based on 16-element ($4 \times 4$) subarrays in the 60 GHz unlicensed band. [ABSTRACT FROM AUTHOR]

The paper considers sparse array design for receive beamforming achieving maximum signal-to-interference plus noise ratio (MaxSINR) for both single point source and multiple point sources, operating in an interference active environment. Unlike existing sparse design methods which either deal with structured environment-independent or non-structured environment-dependent arrays, our method is a hybrid approach and seeks a full augumentable array that optimizes beamformer performance. This approach proves important for limited aperture that constrains the number of possible uniform grid points for sensor placements. The problem is formulated as quadratically constraint quadratic program (QCQP), with the cost function penalized with weighted $l_1$ -norm squared of the beamformer weight vector. Simulation results are presented to show the effectiveness of the proposed algorithms for array configurability in the case of both single and general rank signal correlation matrices. Performance comparisons among the proposed sparse array, the commonly used uniform arrays, arrays obtained by other design methods, and arrays designed without the augmentability constraint are provided. [ABSTRACT FROM AUTHOR]

In our previous work, we addressed a unified representation problem on Wigner distribution (WD) in linear canonical transform (LCT) domains by introducing a kind of closed-form instantaneous cross-correlation function type of Wigner distribution (CICFWD) that can be regarded as the WD's closed-form representation in the linear canonical domain. We then discussed the application of CICFWD in the detection of linear frequency-modulated (LFM) signals through the numerical simulation analysis approach, and it turns out that there is a causation between LCT free parameters and the detection performance. The main contribution of this paper is to provide a mathematical model for this causality in order to disclose the intrinsic mechanism of non-stationary signal detection performance improvement triggered by LCT free parameters. We first revisit the definition of CICFWD, and establish some related theories including its essential properties and discretization. We then formulate a mathematical theory foundation of the output signal-to-noise ratio (SNR) improvement, an output SNR inequality relation between the traditional WD and the CICFWD for a general noisy signal, and discuss how to solve this inequality to come out LCT free parameters. Within the well-established output SNR improvement analysis framework, we also explore LCT free parameters selection results on LFM signals added with white noise. Finally, numerical experiments are carried out to validate the correctness of strategies on determination LCT free parameters and the feasibility of output SNR improvement analysis approach. [ABSTRACT FROM AUTHOR]

We address a robust detection problem for MIMO radars in Gaussian noise with unknown covariance matrix, for the mismatched case where the nominal transmit (or receive) steering vector may not be aligned with the true transmit (or receive) steering vector. Subspace models are adopted for taking into account these mismatches. More specifically, the transmit (or receive) steering vector is assumed to belong to a subspace. Without requiring training data, we design adaptive detectors according to the criteria of Wald test, Rao test, and generalized likelihood ratio test (GLRT). It is found that the Rao test does not exist for the detection problem to be solved. Additionally, the proposed Wald test and GLRT exhibit constant false alarm rate properties against the noise covariance matrix. Numerical examples show that the proposed detectors compared to their existing counterparts have better robustness against the steering vector mismatches. Moreover, the proposed Wald test exhibits better robustness than the proposed GLRT in the region of high signal-to-noise ratio. [ABSTRACT FROM AUTHOR]

In the context of independent component analysis, noisy mixtures pose a dilemma regarding the desired objective. On one hand, a “maximally separating” solution, providing the minimal attainable interference-to-source-ratio (ISR), would often suffer from significant residual noise. On the other hand, optimal minimum mean square error (MMSE) estimation would yield estimates that are the “closest possible” to the true sources, often at the cost of compromised ISR. In this paper, we consider noisy mixtures of temporally diverse stationary Gaussian sources in a semi-blind scenario, which conveniently lends itself to either one of these objectives. We begin by deriving the maximum-likelihood (ML) estimates of the unknown (deterministic) parameters of the model: the mixing matrix and the (possibly different) noise variances in each sensor. We derive the likelihood equations for these parameters, as well as the corresponding Cramér–Rao lower bound, and propose an iterative solution for obtaining the ML estimates (MLEs). Based on these MLEs, the asymptotically optimal “maximally separating” solution can be readily obtained. However, we also present the ML-based MMSE estimate of the sources, alongside a frequency-domain-based computationally efficient scheme, exploiting their stationarity. We show that this estimate is asymptotically optimal and attains the (oracle) MMSE lower bound. Furthermore, for non-Gaussian signals, we show that this estimate serves as a quasi-ML-based linear MMSE (LMMSE) estimate, and attains the (oracle) LMMSE lower bound asymptotically. Empirical results of three simulation experiments are presented, corroborating our analytical derivations. [ABSTRACT FROM AUTHOR]

In the public channels, it is desirable to transmit the common signals omnidirectionally to ensure cell-wide coverage. In Part I of this two-part paper, we develop low-cost closed-form omnidirectional precoding designs for a massive multiple-input multiple-output (MIMO) system equipped with a uniform rectangular array (URA). By formulating the omnidirectional transmission design for a general URA as a feasibility optimization problem, we derive an optimal solution based on the complementary set (CS) or the complete complementary codes (CCC). We prove that the precoding vectors based on the CS or CCC sequences can generate a perfectly omnidirectional power radiation pattern. Since both CS and CCC sequences are binary and constant-modulus, the proposed schemes are well suited to be implemented in the radio frequency analog domain with low hardware cost and suppressed peak-to-average power ratio. The numerical results validate the superior performance of the proposed schemes over the existing alternatives. [ABSTRACT FROM AUTHOR]

The emerging millimeter-wave massive multiple-input multiple-output (MIMO) with lens antenna arrays, which is also known as “beamspace MIMO,” can effectively reduce the required number of power-hungry radio frequency (RF) chains. Therefore, it has been considered as a promising technique for the upcoming 5G communications and beyond. However, most current studies on beamspace MIMO have not taken into account the important power leakage problem in beamspace channels, which possibly leads to a significant degradation in the signal-to-noise ratio (SNR) and the system sum-rate. To this end, in this paper, we propose a beam-aligning precoding method to handle the power leakage problem. First, a phase shifter network (PSN) structure is proposed, which enables each RF chain in beamspace MIMO to select multiple beams to collect the leakage power. Then, a rotation-based precoding algorithm is designed based on the proposed PSN structure, which aligns the channel gains of the selected beams toward the same direction for maximizing the received SNR at each user. Furthermore, we reveal some system design insights by analyzing the sum-rate and energy efficiency (EE) of the proposed beam-aligning precoding method. In simulations, the proposed approach is found to achieve the near-optimal sum-rate performance compared with that of the ideal case of no power leakage, and obtains a higher EE than those of the existing schemes with either a linear or planar array. [ABSTRACT FROM AUTHOR]

In this paper, we study the problem of beam alignment for millimeter wave (mmWave) communications, where a hybrid analog and digital beamforming structure is employed at the transmitter (i.e., base station), and an omni-directional antenna or an antenna array is used at the receiver (i.e., user). By exploiting the sparse scattering nature of mmWave channels, the beam alignment problem is formulated as a sparse encoding and phaseless decoding problem. More specifically, the problem of interest involves finding a sparse sensing matrix and an efficient recovery algorithm to recover the support and magnitude of a sparse signal from compressive phaseless measurements. A sparse bipartite graph code algorithm is developed for sparse encoding and phaseless decoding. Our theoretical analysis shows that, in the noiseless case, our proposed algorithm can perfectly recover the support and magnitude of the sparse signal with a probability exceeding a pre-specified value from $\mathcal {O}(K^2)$ measurements, where $K$ is the number of nonzero entries of the sparse signal. The proposed algorithm has a simple decoding procedure which is computationally efficient and noise robust. Simulation results show that our proposed method renders reliable beam alignment even in the low signal-to-noise ratio regime and presents a clear performance advantage over existing methods. [ABSTRACT FROM AUTHOR]

Many robust adaptive wideband beamforming algorithms have been carried out to preserve the signal of interest, but their performance can be still degraded by the mismatches of steering vector and covariance matrix. Therefore, in this paper, a novel robust adaptive wideband beamformer based on the time-frequency distribution is proposed, which can achieve high output signal-to-interference-plus-noise ratio close to the optimal one even with perturbed array manifold and limited snapshots. It transforms the received signal into the time-frequency domain, and gives a method to select the single-source points of wideband signals. With the single-source points, it reconstructs the interference-plus-noise covariance matrix and estimates the steering vector without using the imprecise prior information about the array manifold, guaranteeing high estimation accuracy. Simulation results demonstrate that the proposed method outperforms other adaptive wideband beamformers, and achieves excellent output performance over a broad range of direction and sensor position errors even with small number of snapshots. [ABSTRACT FROM AUTHOR]

The paper derives the stability bound of the initial mean-square deviation of an adaptive filtering algorithm based on minimizing the 2Lth moment of the estimation error, with L being an integer greater than 1. The analysis is done for a time-invariant plant with even input probability density function. Dependence of the stability bound on the algorithm step-size, type of the noise distribution, signal-to-noise ratio (SNR), and L is studied. It is shown that the stability bound is decreasing in the step-size. The stability bound decreases as the tail of the noise probability density function becomes lighter for the same steady-state misadjustment. This result is surprising since, for example, it is expected that the stability of the least mean 2Lth algorithm for binary noise distribution is better than that for uniform distribution. The stability bound is proportional to the reciprocal of the SNR, another surprising result. Finally, the stability bound is decreasing in L, which implies a limitation on the ability to improve the performance of the adaptive filter by increasing the order of the cost function. Theoretical results are supported by simulations. [ABSTRACT FROM AUTHOR]

This paper presents a flexible array response control algorithm via oblique projection, abbreviated as FARCOP, and its application to array pattern synthesis. The proposed FARCOP algorithm stems from the adaptive array theory, and it can flexibly, precisely and simultaneously adjust the array response levels at multiple angles based on an arbitrarily given weight vector. Different from the existing approaches, the proposed FARCOP algorithm controls multi-point responses by linearly transferring the given weight vector, with a transformation matrix containing a set of parameters, each of which can be very easily determined by the desired response level (at the control angle). Owing to the fact that those parameters are independent of each other, the response levels at the control angles can be either individually or jointly and, therefore, flexibly adjusted. Since the parameter phases can be arbitrary, we take the beampattern into account and propose to uniquely choose the optimal parameters under the typical criterion of maximum white noise gain (WNG). Accordingly, a gradient projection (GP) algorithm is devised to achieve the optimal solution. Moreover, a closed-form solution is derived for the centro-symmetric array. In addition, the application of the FARCOP algorithm to pattern synthesis is discussed. Comparing to the state-of-the-art methods like multi-point accurate array response control (${\text {MA}}^2{\text {RC}}$), the proposed FARCOP algorithm controls the array responses more flexibly with lower computational complexity. Representative examples are presented to demonstrate the effectiveness and superiority of the FARCOP algorithm under various situations. [ABSTRACT FROM AUTHOR]

We consider the design of a linear sensing system with a fixed energy budget assuming that the sampling noise is the dominant noise source. The energy constraint implies that the signal energy per measurement decreases linearly with the number of measurements. When the maximum sampling rate of the sampling circuit is chosen to match the designed sampling rate, the assumption on the noise implies that its variance increases approximately linearly with the sampling rate (number of measurements). Therefore, the overall SNR per measurement decreases quadratically in the number of measurements. Our analysis shows that, in this setting there is an optimal number of measurements. This is in contrast to the standard case, where noise variance remains unchanged with sampling rate, in which case more measurements imply better performance. Our results are based on a state evolution technique of the well-known approximate message passing algorithm. We consider both the sparse (e.g. Bernoulli-Gaussian and least-favorable distributions) and the non-sparse (e.g. Gaussian distribution) settings in both the real and complex domains. Numerical results corroborate our analysis. [ABSTRACT FROM AUTHOR]

This paper studies linear distributed estimation of an unknown random parameter vector in a bandwidth-constrained multisensor network. To meet the bandwidth limitations, each sensor converts its observation into a low-dimensional datum via a suitable linear transformation. Then, the fusion center estimates the parameter vector by linearly combining all the received low-dimensional data, aiming at minimizing the estimation mean square error. The main purpose of this paper is to jointly determine the compression dimension of each sensor (referred to as dimension assignment) and design the corresponding compression matrix when the total compression dimensions is limited. Such a joint design problem can be formulated as a rank-constrained optimization problem and it is shown to be NP-hard for the first time. In addition, successive quadratic upper-bound minimization (SQUM), SQUM-block coordinate descent (SQUM-BCD) and nuclear norm regularization (NNR) methods are developed to solve it approximately. Furthermore, we show that any accumulation point of the sequence generated by the SQUM method satisfies the Karush-Kuhn-Tucker conditions of the rank-constrained optimization problem, and the Phase II algorithm of the SQUM-BCD and NNR methods (both are two-phase algorithms and have the same Phase II algorithm) guarantees convergence at least to a stationary point. Numerical experiments illustrate the advantages of the proposed methods compared with the existing method. [ABSTRACT FROM AUTHOR]

Newton's method is a widely applicable and empirically efficient method for finding the solution to a set of equations. The recently developed algebraic geometry analyses provide information-theoretic bounds on the sampling rate to ensure the existence of a unique completion. A remained open question from these works is to retrieve the sampled data when the sampling rate is very close to the mentioned information-theoretic bounds. This paper is concerned with proposing algorithms to retrieve the sampled data when the sampling rate is too small and close to the mentioned information-theoretic bounds. Hence, we propose a new approach for recovering a partially sampled low-rank matrix or tensor when the number of samples is only slightly more than the dimension of the corresponding manifold, by solving a set of polynomial equations using Newton's method. In particular, we consider low-rank matrix completion, matrix sensing, and tensor completion. Each observed entry contributes one polynomial equation in terms of the factors in the rank factorization of the data. By exploiting the specific structures of the resulting set of polynomial equations, we analytically characterize the convergence regions of the Newton's method for matrix completion and matrix sensing. Through extensive numerical results, we show that the proposed approach outperforms the well-known methods such as nuclear norm minimization and alternating minimization in terms of the success rate of data recovery (noiseless case) and peak signal-to-noise ratio (noisy case), especially when the sampling rate is very low. [ABSTRACT FROM AUTHOR]

Long time coherent integration (LTCI) technique enhances radar detection of maneuvering weak targets. Unfortunately, range migration (RM) and Doppler frequency migration (DFM) would occur during the integration period. Existing LTCI methods are all based on the assumption that the target is of single motion model (i.e., the target's motion model is fixed) during the long integration time. However, with increasing target's maneuverability and long observation time (needed to detect weak targets), the target's motion model is often changing (i.e., target is of multiple motion models) during the integration time, which would reduce the performance of existing LTCI methods significantly. In this paper, we address the LTCI problem for detecting a maneuvering weak target with multiple motion models, where the target signal model is first established. Thereafter, the short-time generalized Radon Fourier transform (STGRFT) based LTCI algorithm is proposed. The STGRFT method could not only eliminate RM and DFM but also estimate the model-changing point (i.e., the time when target's motion model changes) and accumulate the target energy distributed in different motion stages (corresponding to different motion models). Finally, numerical and real-data experiments are carried out to demonstrate its effectiveness. The results confirm that in terms of integration gain, input–output signal-to-noise ratio performance and detection ability, STGRFT-based method is superior to the existing popular LTCI algorithms. [ABSTRACT FROM AUTHOR]

We present our results of applying wavelet theory to the classic problem of estimating the unknown parameters of a model function subject to noise. The model function studied in this context is a generalization of the second-order Gaussian derivative of which the Gaussian function is a special case. For all five model parameters (amplitude, width, location, baseline, undershoot-size), scale-dependent algebraic expressions are derived. Based on this analytical framework, our first method estimates all parameters by substituting into a given expression numerically obtained values, such as the zero-crossings of the multiscale decompositions of the noisy input signal, using Gaussian derivative wavelets. Our second method takes these estimates as starting values for iterative least-squares optimization to fit our algebraic zero-crossing model to observed numeric zero-crossings in scale-space. For evaluation, we apply our method together with three reference methods to the three-parameter Gaussian model function. The results show that our method is on average 3.7 times more accurate than the respective best reference method for signal-to-noise ratios (SNR) from $-{\text{10}}$ to 70 dB, using a synthetic test scenario proposed by a competitor. For our full five-parameter model, we investigate overall estimation error as well as per-parameter error and per-parameter uncertainty as a function of SNR and various noise models, including correlated noise. To demonstrate practical effectiveness and relevance, we apply our method to the well-studied problem of QRS complex delineation in electrocardiography signals. Out-of-the-box results show a performance comparable to the best algorithms known to date, without relying on problem-specific heuristic decision rules. [ABSTRACT FROM AUTHOR]

In this paper, we examine the normalized output signal-to-interference-plus-noise ratio (SINR) of a sample matrix inversion beamformer exploiting the persymmetry of the received data. The persymmetry commonly exists in the received data, when a symmetrically spaced linear array and/or symmetrically spaced pulse trains are utilized. An exact expression for the probability density function (PDF) of the normalized output SINR is derived in the mismatched case. This PDF is verified using Monte Carlo simulations. Numerical examples indicate that the exploitation of persymmetry is equivalent to doubling the training data size, and hence can greatly alleviate the requirement of training data in adaptive processing. [ABSTRACT FROM AUTHOR]

Spatial modulation is emerging as a promising signal transmission paradigm for future wireless communications relying on massive multiple-input multiple-output (MIMO) technology. In this paper, the receive spatial modulation (RSM) is applied to the downlink of multi-user MIMO systems with the base station equipped with a massive array of antennas. Due to the significant overhead associated with acquiring channel state information at the transmitter (CSIT) of frequency-division-duplex massive MIMO systems, herein we propose a preprocessing scheme for correlated channels that reduces the channel estimation overheads. The proposed preprocessing method relies on the partial CSIT and consists of two stages of beamforming and precoding. The beamforming is accomplished via block-diagonalization to combat multi-user interference while the precoding matrix is designed by formulating optimization problems aiming to eliminate inter-antenna interference and enhancing RSM transmission performance. The design criteria of the problems include bit-error-rate minimization and discrete-input continuous-output (DCMC) capacity maximization with a transmit power constraint. The arising non-convex problems are cast as semi-definite and second-order cone programs that can be solved efficiently. The proposed schemes are readily extended to generalized RSM as the most comprehensive case in RSM-MIMO scenarios. Simulation results demonstrate that the proposed schemes outperform the imperfect-CSIT based and two-stage zero-forcing procedures and offer similar or significant performance compared to conventional MIMO counterparts at low to mid signal-to-noise ratio regimes, depending on the configurations. [ABSTRACT FROM AUTHOR]

Model order selection (MOS) in linear regression models is a widely studied problem in signal processing. Penalized log likelihood techniques based on information theoretic criteria (ITC) are algorithms of choice in MOS problems. Recently, a number of model selection problems have been successfully solved with explicit finite sample guarantees using a concept called residual ratio thresholding (RRT). This paper proposes to use RRT for MOS in linear regression models and provide rigorous mathematical analysis of RRT. RRT is numerically shown to deliver a highly competitive performance when compared to popular MOS criteria, such as Akaike information criterion, Bayesian information criterion, and penalized adaptive likelihood, especially when the sample size is small. We also analytically establish an interesting interpretation for RRT based on ITC thereby linking these two model selection principles. [ABSTRACT FROM AUTHOR]

The design of beamformers for the multi-user multiple-input single-output downlink that provide prespecified levels of quality-of-service can be quite challenging when the channel state information is not perfectly known at the base station. The constraint of having the signal-to-interference-and-noise ratio (SINR) satisfy a given threshold with high probability is intractable in general, which results in problems that are fundamentally hard to solve. We develop a high-quality approximation of the SINR outage constraint that, along with a semidefinite relaxation, enables us to formulate the robust beamformer design problem for Gaussian channel estimation errors as a convex optimization problem that can be efficiently solved. For systems with small uncertainties, further approximations yield design algorithms based on iterative evaluations of closed-form expressions that have substantially lower computational cost. Since finding the beamforming directions incurs most of that cost, analogous power loading algorithms for predefined beamforming directions are developed and their performance is shown to be close to optimal. When the system contains a large number of antennas, the proposed power loading can be obtained at a computational cost that grows only linearly in the number of antennas. The proposed power loading algorithm provides an explicit relationship between the outage probability required and the power consumed, which allows us to precisely control the power consumption, and automatically identifies users who are consuming most of the power resources. The flexibility of the proposed approach is illustrated by developing a power loading technique that minimizes an average notion of outage. [ABSTRACT FROM AUTHOR]

Extracting information from a signal exhibiting damped resonances is a challenging task in many practical cases due to the presence of noise and high attenuation. The interpretation of the signal relies on a model whose order (i.e., the number of resonances) is in general unknown. In this study, the signal is modeled as a sum of Lorentzian lineshapes, and a Bayesian framework is designed to simultaneously remove the baseline distortion, select the number of resonances, and recover the parameters of each lineshape including frequency, damping factor, resonance amplitude, and noise magnitude. The Bayesian problem is solved resorting to a reversible jump Markov chain Monte Carlo (RJ-MCMC) sampling scheme. The algorithm is tested on synthetic signals as well as experimental data from a resonant ultrasound spectroscopy experiment aiming to measure elastic properties. The results show that, compared to the well-known linear prediction singular value decomposition method, the RJ-MCMC method achieves a better performance with the advantages of joint model selection, high accuracy estimation, and uncertainty evaluation. We found that when the signal-to-noise-ratio is larger than 20 dB, the average relative error for frequency extraction is smaller than $\text{0.5}\%$. Such an algorithm enables to estimate the number of resonances and extract tens of resonance parameters from a highly attenuated spectrum, which can significantly facilitate the automated processing of signals exhibiting damped resonances. [ABSTRACT FROM AUTHOR]

The linear canonical transform (LCT) is a multiparameter unitary transform that generalizes a large number of classical transforms with application to signal processing and optics. Many of its fundamental properties are already known; however, little attention has been paid to the design and implementation of matched filters in the LCT domain. The objective of this paper is to design this type of filters that maximize the output signal-to-noise ratio, dubbed the linear canonical matched filter (LCMF). We first derive some facts of the LCT spectral analysis for random signals. Then, by applying the derived results, the LCMF design theory associated with the LCT is developed. Moreover, the implementation and basic properties of the LCMF are presented. The introduction of the LCMF invites a new interpretation of the ambiguity function and the correlation function of the LCT. Finally, we provide several applications for the theoretical derivations. [ABSTRACT FROM AUTHOR]

The linear canonical transform (LCT), which includes many classical transforms, has increasingly emerged as a powerful tool for optics and signal processing. Signal reconstruction associated with the LCT has blossomed in recent years. However, many existing reconstruction algorithms for the LCT can only handle noise-free measurements, and when noise is present, they will become ill posed. In this paper, we address the problem of reconstructing an analog signal from noise-corrupted measurements in the LCT domain. A general methodology is proposed to solve this problem in which the analog signal is recovered from ideal samples of its filtered version in a unified way. The proposed methodology allows for arbitrary measurement and reconstruction schemes in the LCT domain. We formulate signal reconstruction in an LCT-based function space, which is the span of integer translates and chirp-modulation of a generating function, with coefficients derived from digitally filtering noise corrupted measurements in the LCT domain. Several alternative methods for designing digital filters in the LCT domain are also suggested using different criteria. The validity of the theoretical derivations is demonstrated via numerical simulation. [ABSTRACT FROM AUTHOR]

This paper considers the reconstruction of a discrete-valued random vector from possibly underdetermined linear measurements using sum-of-absolute-value (SOAV) optimization. The proposed algorithm, referred to as discreteness-aware approximate message passing (DAMP), is based on the idea of approximate message passing (AMP), which has been originally proposed for compressed sensing. The DAMP algorithm has low computational complexity and its performance in the large system limit can be predicted analytically via state evolution framework, where we provide a condition for the exact reconstruction with DAMP in the noise-free case. From the analysis, we also propose a method to determine the parameters of the SOAV optimization. Moreover, based on the state evolution, we provide Bayes optimal DAMP, which has the minimum mean-square-error at each iteration of the algorithm. Simulation results show that the DAMP algorithms can reconstruct the discrete-valued vector from underdetermined linear measurements and the empirical performance agrees with our theoretical results in large-scale systems. When the problem size is not large enough, the SOAV optimization with the proposed parameters can achieve better performance than the DAMP algorithms for high signal-to-noise ratio. [ABSTRACT FROM AUTHOR]

We consider optimal Bayesian detection of a slowly varying tone of unknown amplitude in situations characterized by very low signal-to-noise ratio (SNR) and a large number of measurements, as found in certain gravitational wave and passive sonar problems. We use a hidden Markov model (HMM) framework but, unlike typical HMM-based frequency line tracking methods, we develop a true track-before-detect algorithm, which does not threshold the blocked Fourier data and only considers frequency trails that have phase continuity across all HMM steps. We model the frequency and phase evolution as a phase-wrapped Ornstein–Uhlenbeck process. The resulting optimal detector is computationally efficient. The detectability improvement arising from phase continuity is characterized via comparative simulation for a mock, simplified gravitational wave search problem. [ABSTRACT FROM AUTHOR]

The successive cancellation list (SCL) decoding is the most powerful decoding algorithm for polar codes. However, the long latency makes it unsuitable for practical applications, and thus many algorithms have been presented to resolve the problem. While most of the previous algorithms have reduced the latency by pruning unnecessary operations in the middle of the process, this paper proposes an early stopping criterion. The proposed method can determine the minimum metric path without having to traverse the tree to the end if a special condition is satisfied at a certain point. The remaining bits located after the stopped bit position are decoded directly from the soft information. The simulation results show that the criterion reduces the decoding latency effectively for various code rates and list sizes without any performance loss. We also propose a hardware architecture that is efficient in realizing the proposed method. Compared to previous SCL decoding algorithms, the proposed decoder achieves 16% higher throughput and 12% improved area efficiency at an SNR of 5.0 dB when the list size is 4. [ABSTRACT FROM AUTHOR]

Finding a balance between observation duration and detection rates is the ultimate goal of the detection of ultrahigh speed targets. However, short observation durations, both across range unit, and Doppler frequency migration, may severely limit the detection performance of ultrahigh speed targets. Although, traditional coherent integration methods can efficiently accumulate signal energy to produce a high signal-to-noise-ratio measurement, they often need to search for unknown motion parameters. This search is time consuming and unacceptable for the real-time detection of ultrahigh speed targets. In this paper, a coherent-like detection method is designed based on the finite-dimension theory of Wigner matrices along with velocity identification. The proposed method can efficiently integrate signal energy without rendering motion parameters. We use the distribution and mean of the eigenvalues of the constructed matrix, i.e., an additive Wigner matrix, to identify velocities and detect ultrahigh speed targets, respectively. Simulation results validate the theoretical derivation, superiority and operability of the proposed method. [ABSTRACT FROM AUTHOR]