Analytical characterization of detection SNR for PR target design in Viterbi-based receivers

In this paper, we address the problem of designing the optimum partial-response (PR) target that results in the best bit-error-rate (BER) performance in Viterbi-like detectors when applied for signal detection in digital magnetic recording systems. We present a detailed analysis of the effective detection signal-to-noise ratio (SNReff), which is closely related to the BER performance of a Viterbi detector. We show that SNReff is a concave function with a unique global maximum corresponding to the magnitude frequency response of the optimum targets. Thus, any simple search approach is guaranteed to reach the optimum target. We consider the cases of single dominant error event and multiple dominant error events. Numerical and simulation results are presented to corroborate our analytical results for perpendicular magnetic recording channels.