In this paper, a new method for 2-D frequency estimation of multiple damped sinusoids in additive white Gaussian noise is proposed. The key idea is to combine the subspace-based technique and projection separation approach. The frequency parameters in the first dimension are estimated by the MUSIC-based method, and then a set of projection separation matrices are constructed by the estimated frequency parameters. In doing so, the frequency parameters in the second dimension can be separated by the constructed projection separation matrix. Finally, each frequency parameter in the second dimension is estimated by multiple 1-D MUSIC-based methods. The estimated frequency parameters in two dimensions are automatically paired. Computer simulations are included to compare the proposed algorithm with several existing methods.

An algorithm for estimating sinusoidal parameters is presented. In this paper, it is assumed that an observed signal is a single sinusoidal signal contaminated by white Gaussian noise. Based on this assumption, the sinusoidal parameters can be found by minimizing a cost function using the mean squared error (MSE) between the observed signal and a sinusoidal signal with arbitrary sinusoidal parameters. Because the cost function is nonlinear and not convex, it has undesirable local minima. To solve the minimization problem, we propose to use the roots of an algebraic equation. The algebraic equation is derived straightforwardly from the cost function. We show that the global solution is formulated by using the roots of the algebraic equation.

Frequency estimation of a complex single-tone in additive white Gaussian noise from irregularly-spaced samples is addressed. In this Letter, we study the periodogram and weighted phase averager, which are standard solutions in the uniform sampling scenarios, for tackling the problem. It is shown that the estimation performance of both approaches can attain the optimum benchmark of the Cramér-Rao lower bound, although the former technique has a smaller threshold signal-to-noise ratio.

In this Letter, the maximum likelihood (ML) estimator for the parameters of a real sinusoid in additive white Gaussian noise using irregularly-spaced samples is derived. The ML frequency estimate is first determined by a one-dimensional search, from which optimum amplitude and phase estimates are then computed. It is shown that the estimation performance of the ML method can attain Cramér-Rao lower bound when the signal-to-noise ratio is sufficiently large.

Based on the least square (LS) approximation of sinusoidal signal in frequency domain by sample data, a frequency estimator is derived. Since sinusoidal signals are narrow-banded whereas white noise spreads equally in the whole spectrum, only narrow-band approximation around the actual tone is needed, and thus the influence of noise can be decreased significantly with high computational efficiency. Experimental results show that, without any iterations, the performance of the proposed estimator is close to the Cramer-Rao Bound (CRB), and has a lower SNR threshold compared with other existing estimators.

In this Letter, the problem of estimating the time-difference-of-arrival between signals received at two spatially separated sensors is addressed. By taking discrete Fourier transform of the sensor outputs, time delay estimation corresponds to finding the frequency of a noisy sinusoid with time-varying amplitude. The generalized weighted linear predictor is utilized to estimate the time delay and it is shown that its estimation accuracy attains Cramér-Rao lower bound.

In this letter, a novel blind maximum Doppler frequency estimation algorithm for OFDM based systems is proposed. We only utilize part of the subcarriers which are modulated by constant-envelope modulation such as QPSK. The received magnitude of these subcarriers is obtained and its power spectral density (PSD) is estimated by classic periodogram method. The maximum Doppler frequency is derived by finding the edge point of PSD. Different from the conventional PSD method, our method does not need the channel estimates, the estimation precision is also increased. Simulation results show that the performance of our method is good for a wide range of Doppler spread values.

By utilizing the second and fourth order linear prediction errors, a novel estimator for a single noisy sinusoid is devised. The frequency estimate is obtained from a solving a cubic equation and a simple root selection procedure is provided. Asymptotical variance of the estimated frequency is derived and confirmed by computer simulations. It is demonstrated that the proposed estimator is superior to the reformed Pisarenko harmonic decomposer, which is the improved version of Pisarenko harmonic decomposer.

A new adaptive filter algorithm based on the linear prediction property of sinusoidal signals is proposed for unbiased estimation of the frequency of a real tone in white noise. Similar to the least mean square algorithm, the estimator is computationally simple and it provides unbiased as well as direct frequency measurements. Learning behavior and variance of the estimated frequency are derived and confirmed by computer simulations.

It is well known that Pisarenko's frequency estimate for a single real tone can be computed easily using the sample covariance with lags 1 and 2. In this Letter, we propose to use alternative covariance expressions, which are inspired from the modified covariance (MC) frequency estimator, in Pisarenko's algorithm. Computer simulations are included to corroborate the theoretical development of the variant and to demonstrate its superiority over the MC and Pisarenko's methods.

We show the equivalence between the conventional frame synchronization in single-carrier systems and integer part estimation of frequency offset in OFDM systems and propose an efficient synchronization scheme. The proposed scheme achieves both OFDM symbol/frame timing and frequency offset estimation with only one well-designed OFDM training symbol, while previous synchronization algorithms need two OFDM training symbols at least. Numerical analysis shows that the proposed frequency estimator nearly achieves the Cramér-Rao lower bound for the variance of the frequency offset estimate, despite the reduction in the training sequence length.

The modified covariance (MC) method provides a computationally attractive and closed-form solution for frequency estimation of a single real sinusoid. In this paper, the performance measures of the MC estimator, namely, mean and mean square error, are derived in closed-form and confirmed by computer simulations.

This letter proposes a low-complexity estimation method of integer frequency offset in orthogonal frequency division multiplexing (OFDM) systems. The performance and complexity of the proposed method are compared with that of Morelli and Mengali's method based on maximum likelihood (ML) technique. The results show that the performance of the proposed method is comparable to that of M&M method with reduced complexity.

A nonlinear harmonic estimator (NHE) is proposed for extracting a harmonic signal and its fundamental frequency in the presence of white noise. This estimator is derived by applying an extended complex Kalman filter (ECKF) to a multiple sinusoidal model with state-representation and then efficiently specializing it for the case of harmonic estimation. The effectiveness of the NHE is verified using computer simulations.

Multiple-input multiple-output (MIMO) systems using eigenbeam space division multiplexing (E-SDM) perform well and have increased capacities compared with those using conventional space division multiplexing (SDM). However, channel state information (CSI) is required at a transmitter, and the performance of E-SDM systems depends much on the accuracy of the CSI at a transmitter and a receiver. In time-varying fading environments, the channel change between the transmit weight determination time and the actual data transmission time causes the system performance to degrade. To compensate for the channel error, a linear extrapolation method has been proposed for a time division duplexing system. Unfortunately, the system performance still deteriorates as the maximum Doppler frequency increases. Here, two new techniques of channel extrapolation are proposed. One is second order extrapolation, and the other is exponential extrapolation. Also, we propose maximum Doppler frequency estimation methods for exponential extrapolation. Simulation results for 4tx 4rx MIMO systems showed that using the proposed techniques, E-SDM system performs better in a higher Doppler frequency region.

A parallel notch filter (PNF) for eliminating a sinusoidal signal whose frequency and phase are unknown, has been proposed previously. The PNF achieves both fast convergence and high estimation accuracy when the step-size for adaptation is appropriately determined. However, there has been no discussion of how to determine the appropriate step-size. In this paper, we derive the convergence condition on the step-size, and propose an adaptive algorithm with variable step-size so that convergence of the PNF is automatically satisfied. Moreover, we present a new filtering structure of the PNF that increases the convergence speed while keeping the estimation accuracy. We also derive a variable step-size scheme for the new PNF to guarantee the convergence. Simulation results show the effectiveness of the proposed method.

The frequency estimate for a real sinusoid provided by the periodogram has a bias which is particularly severe for a short observation interval. In this paper, two improvements to the periodogram are proposed to reduce this bias. The first method transforms the real tone to a complex sinusoid while the second algorithm subtracts the negative spectral line from the received signal, prior to applying the periodogram. The performance of the two methods is illustrated by comparing with the periodogram and Quinn's interpolation as well as Cramér-Rao lower bound.

Recent studies show that several FFT-based high-accuracy frequency estimation methods achieve very good performance. In this letter, we select three methods, which are the zero-padding, weighted multipoint interpolated DFT, and phase difference approximation respectively, and discuss the window selection for each method. Experiments show that the window selection primarily depends on the signal-to-noise ratio (SNR). As a result, the optimal window selection for each method and, reversely, the optimal selection of the estimation method for a specific window are discussed as a function of SNR. Consideration on the computational load and the resolution problem is also briefly discussed.

Tufts-Kumaresan (TK) method, which is based on linear prediction approach, is a standard algorithm for estimating the frequencies of sinusoids in noise. In this Letter, the TK algorithm is improved by attenuating the noise in the observation vector with the use of the reduced rank data matrix. It is shown that the proposed modification can provide smaller mean square frequency errors with lower threshold signal-to-noise ratios than the TK method and a total least squares solution.

Borrowing the notion of instantaneous frequency that was developed in the context of time-frequency signal analysis, an instantaneous frequency amplitude spectrum (IFAS) is introduced for estimating fundamental frequency of speech signal in both noiseless and adverse environments. We define harmonicity measure as a quantity that indicates degree of periodical regularity in the IFAS and that shows substantial difference between periodic signal and noise-like waveform. The harmonicity measure is applied to estimate the existence of fundamental frequency. We provide experimental examples to demonstrate the general applicability of the harmonicity measure and apply the proposed procedure to Japanese continuous speech signals. The results show that the proposed method outperforms the conventional methods with or without the presence of noise.