Estimation and Detection on Uniform Hexagonal Array Models

Magnetic recording at the highest areal density on conventional granular recording media uses $\sim 10$ grains to carry each bit of customer data. Efforts to reduce this number have focused on improving the resolution of the writing and reading processes and, in particular, on improving uniformity of the recording medium and on incorporating knowledge of the recording medium statistics into the detection process. This paper considers the extreme case of data detection on a perfect hexagonal array of grains. This paper looks at two aspects: 1) the estimation of the angle and positioning of the array with respect to the bit-steam and 2) the use of that information to assist data detection. At aggressive densities with very few grains per bit (GPB), the estimation proceeds well and the extra information is helpful in detection. With more GPB, the gains become small.