Near minimum bit-error rate equalizer adaptation for PRML systems

Abstract

Abstract-Receivers for partial response maximum-likelihood systems typically use a linear equalizer followed by a Viterbi detector. The equalizer tries to confine the channel intersymbol interferenceto a short span in order to limit the implementation complexity of the Viterbi detector. Equalization is usually made adaptive in order to compensate for channel variations. Conventional adaptation techniques, e.g., LMS, are, in general, suboptimal in terms of bit-error rate (BER). In this paper, we present a new equalizer adaptation algorithm that seeks to minimize the BER at the Viterbi detector output. The algorithm extracts information from the sequenced amplitude margin (SAM) histogram and incorporates a selection mechanism that focuses adaptation on particular data and noise realizations. The selection mechanism is based on the reliability of the add compare select (ACS) operations in the Viterbi detector. From a complexity standpoint, the algorithm is essentially as simple as the conventional LMS algorithm. Moreover, we present a further simplified version of the algorithm that does not require any hardware multiplications. Simulation results, for an idealized optical storage channel, confirm a substantial performance improvement relative to existing adaptation algorithms.Index Terms-Adaptive equalizers, intersymbol interference, partial response signaling, sequenced amplitude margin (SAM), Viterbi detection.

GEN04-6: Near Minimum-BER all-Adaptive Partial Response Equalization For High Density Recording Systems

“…It can be seen already that optimization of the target response based on ∆ e will tend to decrease error signal coloration in the direction of δ e and increase the Euclidian weight of the bit-error event e k . The thresholding in (1) expresses the focusing of adaptation on bit sequences, bit-error events and noise realizations that lead to non-reliable decisions in the VD [17]. For example, if we consider mis-equalization ISI then the thresholding is equivalent to focusing the adaptation effort only on bit sequences and bit-error events for which ISI is destructive.…”

“…The adaptation criterion and the near-minimum bit-error rate (NMBER) equalizer adaptation for a fixed target were presented in [17]. Because the equalizer adaptation used in this paper is similar to that in [17], we focus in the sequel primarily on target adaptation.…”

“…The detector selects the sequence that leads to the smallest path metric in the trellis [1]. In [17], an analysis of the performance of the VD was presented and a criterion, which was shown to be directly linked to the probability of detection error, was highlighted. For a given bit sequence b k and an admissible biterror event e k , i.e.…”

“…In order to minimize the overall BER, it was shown in [17] that the different cost functions ∆ e must be combined with different weights for different bit-error events. The weight for a bit-error event e k was shown to be proportional to its Hamming weight H w (e), i.e.…”

“…The coefficient η (e) denotes the target adaptation constant and is proportional to the Hamming weight of e k [17]. Upon replacing the expectation of X e in (3) by its instantaneous realization and taking its gradient, (4) yields…”