Space is becoming increasingly congested and contested, which calls for effective means to conduct effective monitoring of high-value space assets, especially in Space Situational Awareness (SSA) missions, while there are imperfections in existing methods and corresponding algorithms. To overcome such a problem, this letter proposes an algorithm for accurate Connected Element Interferometry (CEI) in SSA based on more interpolation information and iterations. Simulation results show that: (i) after iterations, the estimated asymptotic variance of the proposed method can basically achieve uniform convergence, and the ratio of it to ACRB is 1.00235 in δ0 ∈ [-0.5, 0.5], which is closer to 1 than the current best AM algorithms; (ii) In the interval of SNR ∈ [-14dB, 0dB], the estimation error of the proposed algorithm decreases significantly, which is basically comparable to CRLB (maintains at 1.236 times). The research of this letter could play a significant role in effective monitoring and high-precision tracking and measurement with significant space targets during futuristic SSA missions.

This paper investigates an adaptive notch digital filter that employs normal state-space realization of a single-frequency second-order IIR notch digital filter. An adaptive algorithm is developed to minimize the mean-squared output error of the filter iteratively. This algorithm is based on a simplified form of the gradient-decent method. Stability and frequency estimation bias are analyzed for the adaptive iterative algorithm. Finally, a numerical example is presented to demonstrate the validity and effectiveness of the proposed adaptive notch digital filter and the frequency-estimation bias analyzed for the adaptive iterative algorithm.

A narrowband active noise control (NANC) system is very effective for controlling low-frequency periodic noise. A frequency mismatch (FM) with the reference signal will degrade the performance or even cause the system to diverge. To deal with an FM and obtain an accurate reference signal, NANC systems often employ a frequency estimator. Combining an autoregressive predictive filter with a variable step size (VSS) all-pass-based lattice adaptive notch filter (ANF), a new frequency estimation method is proposed that does not require prior information of the primary signal, and the convergence characteristics are much improved. Simulation results show that the designed frequency estimator has a higher accuracy than the conventional algorithm. Finally, hardware experiments are carried out to verify the noise reduction effect.

To estimate angle, velocity, and range information of multiple targets jointly in FMCW MIMO radar, two-dimensional (2D) MUSIC with matched filtering and FFT algorithm is proposed. By reformulating the received FMCW signal of the colocated MIMO radar, we exploit 2D MUSIC to estimate the angle and Doppler frequency of multiple targets. Then by using a matched filter together with the estimated angle and Doppler frequency and FFT operation, the range of the target is estimated. To effectively estimate the parameters of multiple targets with large distance differences, we also propose a successive interference cancellation method that uses the orthogonal projection. That is, rather than estimating the multiple target parameters simultaneously using 2D MUSIC, we estimate the target parameters sequentially, in which the parameters of the target having strongest reflected power are estimated first and then, their effect on the received signal is canceled out by using the orthogonal projection. Simulations verify the performance of the proposed algorithm.

The windowed interpolation DFT methods have been utilized to estimate the parameters of a single frequency and multi-frequency signal. Nevertheless, they do not work well for the real-valued sinusoids with closely spaced positive- and negative- frequency. In this paper, we describe a novel three-point windowed interpolation DFT method for frequency measurement of real-valued sinusoid signal. The exact representation of the windowed DFT with maximum sidelobe decay window (MSDW) is constructed. The spectral superposition of positive- and negative-frequency is considered and calculated to improve the estimation performance. The simulation results match with the theoretical values well. In addition, computer simulations demonstrate that the proposed algorithm provides high estimation accuracy and good noise suppression capability.

Many autocorrelation-based frequency estimation algorithms have been proposed. However, some of them cannot construct a strict linear prediction (LP) property among the adjacent autocorrelation lags, which affects the estimators' performance. To improve the precision of frequency estimation, two novel autocorrelation based frequency estimation methods of the real sinusoid signal in additive white Gaussian noise (AWGN) are proposed in this paper. Firstly, a simple method is introduced to transform the real sinusoid signal into the noncircular signal. Secondly, the autocorrelation of the noncircular signal is analyzed and a strict LP property is constructed among the adjacent autocorrelation lags of the noncircular signal. Thirdly, the least squares (LS) and reformed Pisarenko harmonic decomposer (RPHD) frameworks are employed to improve estimation accuracy. The simulation results match well with the theoretical values. In addition, computer simulations demonstrate that the proposed algorithm provides high estimation accuracy and good noise suppression capability.

A novel time-series relationship among four consecutive real-valued single-tone sinusoid samples is proposed based on their linear prediction property. In order to achieve unbiased frequency estimates for a real sinusoid in white noise, based on the proposed four-point time-series relationship, a constrained least squares cost function is minimized based on the unit-norm principle. Closed-form expressions for the variance and the asymptotic expression for the variance of the proposed frequency estimator are derived, facilitating a theoretical performance comparison with the existing three-point counterpart, called as the reformed Pisarenko harmonic decomposer (RPHD). The region of performance advantage of the proposed four-point based constrained least squares frequency estimator over the RPHD is also discussed. Computer simulations are conducted to support our theoretical development and to compare the proposed estimator performance with the RPHD as well as the Cramer-Rao lower bound (CRLB).

This paper addresses joint estimation of the frequency and the direction-of-arrival (DOA), under the relaxed condition that both snapshots in the temporal domain and sensors in the spacial domain are sparsely spaced. Specifically, a novel coprime sparse array allowing a large range for interelement spacings is employed in the proposed joint scheme, which greatly alleviates the conventional array's half-wavelength constraint. Further, by incorporating small-sized DFT spectrum correction with the closed-form robust Chinese Remainder Theorem (CRT), both spectral aliasing and integer phase ambiguity caused by spatio-temporal under-sampling can be removed in an efficient way. As a result, these two parameters can be efficiently estimated by reusing the observation data collected in parallel at different undersampling rates, which remarkably improves the data utilization. Numerical results demonstrate that the proposed joint scheme is highly accurate.

Computing autocorrelation coefficient can effectively reduce the influence of additive white noise, thus estimation precision will be improved. In this paper, an autocorrelation-like function, different from the ordinary one, is defined, and is proven to own better linear predictive performance. Two algorithms for signal model are developed to achieve frequency estimates. We analyze the theoretical properties of the algorithms in the additive white Gaussian noise. The simulation results match with the theoretical values well in the sense of mean square error. The proposed algorithms compare with existing estimators, are closer to the Cramer-Rao bound (CRLB). In addition, computer simulations demonstrate that the proposed algorithms provide high accuracy and good anti-noise capability.

In this letter, a new rapid and accurate synchronization scheme based on PMF-FFT for high dynamic GPS receiver is proposed, with a fine Doppler frequency estimation inserted between the acquisition and tracking modules. Fine Doppler estimation is firstly achieved through a simple interpolation of the PMF-FFT outputs in terms of LSE criterion. Then a high dynamic tracking loop based on UKF is designed to verify the synchronization speed and accuracy. Numerical results show that the fine frequency estimation can closely approach the CRB, and the high dynamic receiver can obtain fine synchronization rapidly just through a very narrow bandwidth. The simplicity and low complexity give the proposed scheme a strong and practical-oriented ability, even for weak GPS signals.

In order to significantly reduce the time and space needed, compressive sensing builds upon the fundamental assumption of sparsity under a suitable discrete dictionary. However, in many signal processing applications there exists mismatch between the assumed and the true sparsity bases, so that the actual representative coefficients do not lie on the finite grid discretized by the assumed dictionary. Unlike previous work this paper introduces the unified compressive measurement operator into atomic norm denoising and investigates the problems of recovering the frequency support of a combination of multiple sinusoids from sub-Nyquist samples. We provide some useful properties to ensure the optimality of the unified framework via semidefinite programming (SDP). We also provide a sufficient condition to guarantee the uniqueness of the optimizer with high probability. Theoretical results demonstrate the proposed method can locate the nonzero coefficients on an infinitely dense grid over a wide range of SNR case.

In this letter, a new and accurate frequency estimation method of complex exponential signals is proposed. The proposed method divides the signal samples into several identical segments and sums up the samples belonging to the same segment respectively. Then it utilizes fast Fourier transform (FFT) algorithm with zero-padding to obtain a coarse estimation, and exploits three Fourier coefficients to interpolate a fine estimation based on least square error (LSE) criterion. Numerical results show that the proposed method can closely approach the Cramer-Rao bound (CRB) at low signal-to-noise ratios (SNRs) with different estimation ranges. Furthermore, the computational complexity of the proposed method is proportional to the estimation range, showing its practical-oriented ability. The proposed method can be useful in several applications involving carrier frequency offset (CFO) estimation for burst-mode satellite communications.

This paper presents a wideband differential amplifier operating at 141GHz in 40-nm CMOS. It is composed of five differential common source stages with cross-coupled capacitors. A small-signal gain of 20dB and a 3-dB bandwidth of 22GHz are achieved. It consumes 75mW from a 0.94-V voltage supply. The die area with balun and pads is 945×842µm2 and the size of the core not including input/output matching networks is 201×284µm2. The small core area is made possible by using a refined “fishbone” layout technique.

Cognitive radio (CR) is an important technology to provide high-efficiency data communication for the IoT (Internet of Things) era. Signal detection is a key technology of CR to detect communication opportunities. Energy detection (ED) is a signal detection method that does not have high computational complexity. It, however, can only estimate the presence or absence of signal(s) in the observed band. Cyclostationarity detection (CS) is an alternative signal detection method. This method detects some signal features like periodicity. It can estimate the symbol rate of a signal if present. It, however, incurs high computational complexity. In addition, it cannot estimate the symbol rate precisely in the case of single carrier signal with a low Roll-Off factor (ROF). This paper proposes a method to estimate coarsely a signal's bandwidth and carrier frequency from its power spectrum with lower computational complexity than the CS. The proposed method can estimate the bandwidth and carrier frequency of even a low ROF signal. This paper evaluates the proposed method's performance by numerical simulations. The numerical results show that in all cases the proposed coarse bandwidth and carrier frequency estimation is almost comparable to the performance of CS with lower computational complexity and even outperforms in the case of single carrier signal with a low ROF. The proposed method is generally effective for unidentified classification of the signal i.e. single carrier, OFDM etc.

The theoretically minimum length of a signal for fundamental frequency estimation in a noisy environment is discussed. Assuming that the noise is additive white Gaussian, it is known that a Cramér-Rao lower bound (CRLB) is given by the length and other parameters of the signal. In this paper, we define the minimum length as the length whose CRLB is less than or equal to the specific variance for any parameters of the signal. The specific variance is allowable variance of the estimate within an application of fundamental frequency estimation. By reformulating the CRLB with respect to the initial phase of the signal, the algorithms for determining the minimum length are proposed. In addition, we develop the methods of deciding the specific variance for general fundamental frequency estimation and pitch estimation. Simulation results in terms of both the fundamental frequency estimation and the pitch estimation show the validity of our approach.

A closed form frequency estimator is derived for estimating the frequency of a complex exponential signal, embedded in white Gaussian noise. The new estimator consists of the fast Fourier transform (FFT) as the coarse estimation and the phase of autocorrelation lags as the fine-frequency estimator. In the fine-frequency estimation, autocorrelations are calculated from the power-spectral density of the signal, based on the Wiener-Khinchin theorem. For simplicity and suppressing the effect of noise, only the spectrum lines around the actual tone are used. Simulation results show that, the performance of the proposed estimator is approaching the Cramer-Rao Bound (CRB), and has a lower SNR threshold compared with other existing estimators.

In this paper, we present a new four parameter estimator of sampled sinusoidal signals that does not require iteration. Mathematically, the four parameters (frequency, phase, magnitude, and dc offset) of sinusoidal signals can be obtained when four data points are given. In general, the parameters have to be calculated with iteration since the equations are nonlinear. In this paper, we point out that the four parameters can be obtained analytically if the four data points given are measured using a fixed sampling interval. Analytical expressions for the four parameters are derived using the signal differences. Based on this analysis, we suggest an algorithm of estimating the four parameters from N data samples corrupted by noise without iteration. When comparing with the IEEE-1057 method which is based on the least-square method, the proposed algorithm does not require the initial guess of the parameters for iteration and avoid the convergence problem. Also, the number of required numerical operations for estimation is fixed if N is determined. As a result, the processing time of parameter estimation is much faster than the least-square method which has been confirmed by numerical simulations. Simulation results and the quantitative analysis show that the estimation error of the estimated parameters is less than 1.2 times the square root of the Cramer-Rao bounds when the signal to noise ratio is larger than 20dB.

This paper investigates the non-data-aided (NDA) carrier frequency estimation of amplitude and phase shift keying (APSK) signals. The true Cramer-Rao bound (CRB) for NDA frequency estimation of APSK signals are derived and evaluated numerically. Characteristic and jitter variance of NDA Luise and Reggiannini (L&R) frequency estimator are analyzed. Verified by Monte Carlo simulations, the analytical results are shown to be accurate for medium-to-high signal-to-noise ratio (SNR) values. Using the proposed closed-form expression, parameters of the algorithm are optimized efficiently to minimize the jitter variance.

We propose an iterative frequency estimation method for accuracy improvement of discrete Fourier transform (DFT) phase-based methods. It iterates frequency estimation and phase calculation based on the DFT phase-based methods, which maximizes the signal-to-noise floor ratio at the frequency estimation position. We apply it to three methods, the phase difference estimation, the derivative estimation, and the arctan estimation, which are known to be among the best DFT phase-based methods. Experimental results show that the proposed method shows meaningful reductions of the frequency estimation error compared to the conventional methods especially at low signal-to-noise ratio.

This letter proposes two efficient schemes for the joint estimation of symbol timing offset (STO) and carrier frequency offset (CFO) in orthogonal frequency division multiplexing (OFDM) based IEEE 802.16e systems. Avoiding the effects of inter symbol interference (ISI) over delay spread by the multipath fading channel is a primary purpose in the letter. To do this, the ISI-corrupted CP is excluded when a correlation function is devised for both schemes, achieving the improved performance. To demonstrate the efficiency of the proposed methods, the performance is compared with the conventional method and is evaluated by the mean square error (MSE), acquisition range of CFO, and complexity comparison.