We consider the problem of timing recovery for bandlimited, baud-rate sampled systems with intersymbol interference and a timing offset that can be modeled as a combination of a frequency offset and a random walk. We first derive the Cramer–Rao bound (CRB), which is a lower bound on the estimation-error variance for any timing estimator. Conventional timing recovery is based on a phase-locked loop (PLL). We compare the conventional timing recovery method with the CRB for realistic timing parameters for the magnetic recording channel, and observe a 7 dB signal-to-noise ratio gap between the two. Next, we propose a PLL postprocessor based on the maximum a posteriori estimation principle that performs to within 1.5 dB of the CRB. This postprocessor performs time-invariant filtering and time-varying scaling of the PLL timing estimates. The refined timing estimates from the postprocessor are then used to get refined samples by interpolating the samples taken at the PLL's timing estimates. Finally, we present suboptimal implementations that allow a performance-complexity tradeoff.

We consider the problem of timing recovery for bandlimited, baud-rate sampled systems with intersymbol interference and a timing offset that can be modeled as a combination of a frequency offset and a random walk. We first derive the Crameacuter-Rao bound (CRB), which is a lower bound on the estimation error variance for any timing estimator. Conventional timing recovery is based on a phase-locked loop (PLL). We compare the conventional timing-recovery method with the CRB for realistic timing parameters for the magnetic recording channel, and observe a 7 dB signal-to-noise ratio gap between the two. Next, we propose a PLL postprocessor based on the maximum a posteriori estimation principle that performs to within 1.5 dB of the CRB. This postprocessor performs time-invariant filtering and time-varying scaling of the PLL timing estimates. The refined timing estimates from the postprocessor are then used to get refined samples by interpolating the samples taken at the PLL's timing estimates. Finally, we present suboptimal implementations that allow a performance-complexity tradeoff

The nonlinear write process of magnetic recording allows to write the symbols /spl plusmn/1 only. The magnetic channel is a differentiating channel. The locations of the transitions from +1 to -1 and vice versa in the input signal to the magnetic channel are important for the received waveform. This paper defines a noise enhancement constrained, finite dimensional equalizer. This equalizer trades some misequalization of the data signal for less noise enhancement after the equalizer. In a second step the misequalization is decreased by the precoding. Precoding shapes the communication signal before entering the communication channel. Since precoding works on the noise-free signal, there is no noise enhancement. Since precoding in magnetic channels is limited to shifting the positions of the transitions around, precoding does not allow for full equalization at the receiver. Therefore the equalizer in the receiver and the precoder are optimized. In order to find the optimal transition positions a linearized representation of the transition shift is produced. This representation leads to a constrained optimization problem.

The estimation of the frequencies of sinusoids in noise is a very common problem. This paper addresses the estimation of sinusoids in a low SNR environment. This sinusoidal frequency estimation problem can be used to find the carrier frequencies and baud rates of communication waveforms after some appropriate nonlinearity. If the underlying signal model is sinusoids in white Gaussian noise and we use the forward/backward prediction framework, then the forward/backward prediction equations force a Toeplitz/Hankel structure on the data matrix. If there are M distinct sinusoids in the data and no noise, then the data matrix has rank M. Cadzow and Wilkes (1991) enhance a noisy data matrix by enforcing both the structure and the rank of the data matrix, before solving for the coefficient vector of the prediction problem. Besides the Toeplitz/Hankel structure, the estimated singular values of the data matrix are also enforced. Using more information extracted from the original data matrix extends the threshold to lower SNR values.

The inverse eigenvalue problem for real symmetric Toeplitz matrices is defined. A Newton-Raphson-type algorithm is developed for the solution of the problem. The algorithm converges unsafeguarded in all the computed cases and shows the typical behavior of Newton-type algorithms: in general quadratic convergence, linear convergence near double roots. Examples of dimension 10 and 20 are presented. Known sufficient conditions for inverse eigenvalue problems of real symmetric matrices are discussed.>

A real symmetric polynomial Q(z) can be factored into the product A(z)A(z/sup -1/) if Q(z) is nonnegative on the unit circle. The authors pose a constrained minimization problem that results in the correct factorization in this case and gives an approximation to Q(z) if Q(z) does not satisfy the nonnegativity condition.>