We consider the problem of training symbol placement for timing acquisition in digital magnetic recording systems that can be modeled as band-limited, baud-rate sampled systems with intersymbol interference and frequency offset. The conventional approach is to place known symbols at the start of the sector and use these at the detector to run a trained phase-locked loop (PLL). We introduce an additional degree of freedom by allowing arbitrary locations for the training symbols. We first consider a simplified system model where only the training symbols are written, or equivalently, the unknown data is assumed to be zero. We derive the modified Cramer-Rao bound (CRB) on the timing estimation error variance as a function of the training symbol locations and then derive the optimal training symbol placement strategy to minimize the CRB. The optimal strategy, called the split-preamble strategy, is to split the known symbols into two halves and place these at the beginning and at the end of the sector. Simulations with a proposed PLL-based method show that the split-preamble arrangement leads to a reduced frequency estimation error variance and also greatly reduces the occurrence of lost or added symbols, i.e., cycle slips. Finally, we present a simplified analysis of the problem when both known and unknown data are present, and show that the same arrangement also minimizes the CRB in this case.

In this paper, we investigate the benefits of exploiting the a priori information about the structure of the multipath channel on the performance of channel estimation for multiple-input multiple-output (MIMO)-orthog- onal frequency-division multiplexing (OFDM) systems. We first approach this problem from the point of view of estimation theory by computing a lower bound on the estimation error and studying its properties. Then, based on the insight obtained from the analysis, efficient channel estimators are designed that perform close to the derived limit. The proposed channel estimators compute the long-term features of the multipath channel model through a subspace tracking algorithm by identifying the invariant (over multiple OFDM symbols) space/time modes of the channel (modal anal- ysis). On the other hand, the fast-varying fading amplitudes are tracked by using least-squares techniques that exploit temporal correlation of the fading process (modal filtering). The analytic treatment is complemented by thorough numerical investigation in order to validate the performance of the proposed techniques. MIMO-OFDM with bit-interleaved coded mod- ulation and MIMO-turbo equalization is selected as a benchmark for per- formance evaluation in terms of bit-error rate. The authors are with the Dipartimento di Elettronica e Informazione, Politec- nico di Milano, Milano, Italy. Abstract—We consider the problem of creating signal constellations for trellis-coded unitary space-time communication links, where neither the transmitter nor the receiver knows the fading gains of the channel. Our study includes design techniques for trellis-coded schemes with and without parallel paths, which allows us to find a tradeoff between low complexity and high performance. We present a new formulation of the constellation design problem for trellis-coded unitary space-time modulation schemes. The two key differences in our approach against those of other authors are that we not only combine the constellation design and mapping by set par- titioning into one step, but we also use directly the Chernoff bound of the pairwise error probability as a design metric. By novelly employing a the- orem for the Clarke subdifferential of the sum of the largest singular values of the unitary matrix, we also present a numerical optimization pro- cedure for finding signal constellations resulting in high-performance com- munications systems. To demonstrate the advantages of our new design method, we report the best constellations found for trellis-coded unitary space-time modulation systems. Simulation results show that these constel- lations achieve 1 dB coding gain against the usually used constellations.

The modified Cramer-Rao bound (CRB) on frequency estimation error variance for magnetic recording channels is derived as a function of training symbol locations, and it is shown that placing the known symbols half at the beginning and half at the end of the sector minimizes the CRB. Simulation results show a 1.5 dB gain in loss-of-lock rate over having all known symbols at the start of the sector.

Summary form only given We propose an iterative scheme for jointly performing timing recovery and turbo equalization that embeds the timing recovery process inside a modified turbo equalizer. The proposed scheme is applied where a rate- 1/4 RSC encoder, an s-random interleaver, and a 1/(I /spl oplus/ D/sup 2/) precoder map blocks of 1278 bits to blocks of 5120 symbols a/sub k/ /spl isin/ {/spl plusmn/1}, which then drive a perfect PR4 pulse shape h(t) = p(t) - p(t - 2T), where p(t) = sin(/spl pi/t/1)/(/spl pi/t/7). A random-walk model is used for the timing jitter, whereby the k-th pulse is delayed by /spl tau//sub k/, and /spl tau//sub k+1/ = /spl tau//sub k/ + /spl Nscr/(0, /spl sigma//sub w//sup 2/). The channel adds white Gaussian noise.