Reduced - State Soft - Output Trellis - Equalizationincorporating Soft

{ A novel reduced-state soft-output trellis-equalization algorithm is presented, which essentially is a combined application of the algorithms of Bahl et al. and that of Lee to a reduced-state trellis. State reduction is accomplished by a feedback of soft decisions. For this, soft decisions are calculated using a reduced-state Lee algorithm. The proposed feedback is optimum in terms of mean-squared error. We show that Lee and Bahl algorithm share a common core and can easily be combined. Simulation results for an application in the GSM system demonstrate the improved performance of the proposed algorithm , compared to a conventional reduced-state Bahl algorithm using feedback of hard decisions. 1. INTRODUCTION A major obstacle to reliable digital communications is inter-symbol interference (ISI) and noise, encountered in transmission over dispersive channels, such as copper lines or mobile communications channels. The latter suuer from multipath propagation, causing frequency-selective fading. Thus, equalization of ISI at the receiver side is necessary. Linear and decision-feedback equalization (DFE) are two common strategies to cope with ISI; however, depending on the channel characteristics, their performance may be poor. Optimum performance in terms of error event probability is achieved by maximum-likelihood sequence estimation (MLSE), which can be implemented using the Viterbi algorithm (VA) 1]. However, the complexity of the VA increases exponentially with channel length, which makes implementation diicult or even impossible for long channel impulse responses. For complexity reduction, while retaining high performance, several approaches have been discussed in literature, among which the most powerful one seems to be delayed decision-feedback sequence estimation (DFSE) 2, 3]. Here, the rst part of the impulse response is taken for a trellis deenition, while the ISI, produced by the remaining part, is removed by separate DFEs for each state. Especially if the channel impulse response is minimum-phase, which always can be guaranteed by all-pass preeltering, a considerable complexity reduction is possible by DFSE while preserving high performance. While MLSE and DFSE deliver only hard decided symbol estimates, for coded transmission, additional reliability measures are desirable for channel decoding subsequent to equalization. In 4, 5], an extended VA is proposed, which provides suboptimum soft-output information. However, high performance is achieved only for binary signalling and implementation eeort is rather high. Optimum soft-output information is produced by symbol-by-symbol maximum a posteriori (MAP) decoding algorithms, which calculate the conditional probability of each symbol, given the entire received sequence. For a continuous transmission, the symbol-by-symbol MAP …