In this paper, an efficient Weighted Fourier transform and RELAXation based algorithm (referred to as WRELAX) is first proposed for the well-known time delay estimation problem. WRELAX involves only a sequence of weighted Fourier transforms. Its resolution is much higher than that of the conventional matched filter approach. One disadvantage associated with WRELAX is that it converges slowly when the signals are spaced very closely. To overcome this problem, the well-known high resolution MODE (method of direction estimation) algorithm, which was originally proposed for angle estimation in array processing, is modified and used with WRELAX for super resolution time delay estimation. The latter method is referred to as MODE-WRELAX. MODE-WRELAX provides better accuracy than MODE and higher resolution than WRELAX. Moreover, it applies to both complex- and real-valued signals (including those with highly oscillatory correlation functions). Numerical results show that the MODE-WRELAX estimates can approach the corresponding the Cramer-Rao bounds.

We propose a receiver diversity based code-timing estimator for DS-CDMA systems. The systems are assumed to work in a flat fading and near-far environment, where an arbitrary antenna array is used at the receiver of the system to achieve the spatial diversity. The algorithm is derived by modeling the known training sequence as the desired signal and all other signals including the multiuser interfering signals and the additive noise as unknown colored Gaussian noise so that a knowledge of the number of active users is not required. We show that by utilizing the information collected via multiple antenna sensors, the length of the training sequences can be greatly reduced. We also show that the algorithm is an asymptotic maximum Likelihood estimator. As a result, the mean-squared error of the code-timing estimates obtained by the algorithm approaches the Cramer-Rao lower bound (CRB) as the length of the training sequence increases. Moreover, the algorithm does not require the search over a parameter space and the code-timing is obtained by rooting a second-order polynomial, which is computationally very efficient. Simulation results show that the algorithm is quite robust against the near-far problem and requires a much shorter training sequence than the existing estimators.

We propose an efficient algorithm for estimating the code timing of direct-sequence code-division multiple-access (DS-CDMA) systems that consist of an arbitrary antenna array at the receiver and work in a flat-fading and near-far environment. The algorithm is an asymptotic (for large number of data samples) maximum-likelihood (ML) estimator that is derived by modeling the known training sequence as the desired signal and all other signals including the interfering signals and the additive noise as unknown colored Gaussian noise. The algorithm does not require the search over a parameter space and the code timing is obtained by rooting a second-order polynomial, which is computationally very efficient. Simulation results show that the algorithm is quite robust against the near-far problem and channel fading. It requires a shorter training sequence than the single-antenna-based estimators.

We present a comparative study of using the IQML (iterative quadratic maximum likelihood) algorithm and the MODE (method of direction estimation) algorithm for direction-of-arrival estimation with a uniform linear array. The consistent condition and the theoretical mean-squared error for the parameter estimates of IQML are presented. The computational complexities of both algorithms are also compared. We show that the frequency estimates obtained via MODE are asymptotically statistically efficient, while those obtained via IQML are almost always inconsistent and hence inefficient. We also show that the amount of computations required by IQML is usually much larger than that required by MODE, especially for low signal-to-noise ratio and large number of snapshots.

As one of the key steps in the feature extraction of targets consisting of both trihedral and dihedral corner reflectors via synthetic aperture radar, this paper studies the problem of estimating the parameters of a single dihedral corner reflector. The data model of the problem and the Cramer-Rao bounds (CRBs) for the parameter estimates of the data model are presented. Two algorithms, the FFTB (fast Fourier transform based) algorithm and the NLS (non-linear least squares) algorithm, are devised to estimate the model parameters. Numerical examples show that the parameter estimates obtained with both algorithms approach the CRBs as the signal-to-noise ratio increases. The parameter estimates obtained with the NLS algorithm start to achieve the CRB at a lower SNR than those with the FFTB algorithm, while the latter algorithm is computationally more efficient.