A signal-dependent autoregressive channel model

Multidimensional signal processing and detection for storage systems with data-dependent transition noise

“…The application of the chain factorization rule in (15) allows us to factor the multidimensional conditional pdf in (12) as a product of one-dimensional conditionally Gaussian pdfs, completely defined by the conditional means and the conditional variances It should be now clear that and can be interpreted as linear predictive estimates of , and , respectively, and and as the relevant MMSPEs [35]. It is also possible to express explicitly the conditional means as 4 (17) (18) (19) 4 We note that the prediction process is not homogeneous [36].…”

“…The method can be applied to both longitudinal and perpendicular recording systems, as well as optical storage systems. The signal at the output of the channel can be expressed as 2 (5) where is a data information vector, is a random vector collecting the unknown parameters affecting the observable, i.e., the sequences of random variables and , is an additive white Gaussian thermal noise process with monolateral power spectral density and is defined as in (4). Given a probabilistic model of with realizations in a suitable space and noting that, for any finite number of transmitted bits, an information lossless discretization of signal by expansion over an orthonormal finite-dimensional basis can be achieved, the detection strategy can be formulated as (6) where is the a priori probability of the information sequence and is the conditional probability density function (pdf) of the observation vector , given the information sequence .…”

“…In the literature, a few channel models have been proposed to enable the analysis and design of optimum detectors, among which the microtrack model [3], the signal-dependent autoregressive channel model [4], and the position jitter and width variation model [2], [5]. The latter is used in this paper.…”

Oversampled Detector for Transition-Noise-Limited Digital Storage Systems

“…The application of the chain factorization rule to (7) allows us to factor the multidimensional conditional pdf in (6) as a product of β one-dimensional conditional Gaussian pdfs, completely defined by the conditional mean as the relevant MMSPE [12]. 2 Note that the size of the observation vector x is β times the size of the data vector a.…”

“…In the literature, a few channel models have been proposed to enable the analysis and design of optimum detectors [1], [2]. In this paper the position jitter and width variation model [3], [4] is used.…”