A Novel Map-mlse Adaptive Receiver with Enhanced Performance

Several contributions have recently shown that adaptive receivers based on Symbol-by-Symbol Maximum A Posteriori (SbS-MAP) equalizers are an attractive alternative to the more common ones based on Maximum Likelihood Sequence (MLS) detectors (see, e.g., [1,6]). However, these two equalizers present advantages that, if suitably exploited in a combined form, can be used to develop high performance adaptive receivers. In this paper, a novel adaptive receiver that merges the advantages of both SbS-MAP and MLS receivers is presented. I. AN OVERVIEW ON MLS AND SBS-MAP EQUALIZERS Every equalization strategy is characterized by a decision delay and, in time-variant environments, the value of this delay greatly affects the performance of an adaptive receiver that exploits hard-decisions for channel estimation and tracking. In fact, D-delayed decisions imply the use of predicted channel estimates, the order of this prediction being D. As far as the order of the decision delay D is concerned, MLS and SbSMAP equalizers present two opposite features: MLS equalizers deliver reliable data estimates when D is very large (at least five-six times the memory d introduced by the channel) [4], whereas SbS-MAP equalizers deliver reliable decisions for low values of D (of the order of the memory introduced by the channel) [1]. The optimality criterion on which MLS receivers are based is the minimization of the error probability on a persequence basis. The complexity of this algorithm grows linearly with the sequence length and is optimum, in an MLS sense, when the decision delay D is infinite. However, nearly optimum performance can be obtained with a finite decision delay of the order of five-six times the memory introduced by the channel [4]. When the channel is time variant and unknown, a value of D=5d, may be too large for channel tracking purposes and, for this reasons, improved versions of the adaptive MLS that employ “tentative” decisions (see Fig.1) with a limited decision delay d have been proposed [2]. However, due to the low value of the delay d, these tentative decisions generally exhibit a limited reliability that, in turns, degrades the receiver performance during deep faded periods. The optimality criterion exploited by SbS-MAP receivers is the minimization of the symbol error probability [3], [4,Sect.6.6]. As it is well known, this algorithm is based on the computation of the probability of having received a symbol conditional on the past observations. Once these probabilities (A Posteriori Probabilities, APPs) are computed, the receiver selects as the decided symbol the one that has the highest a posteriori probability. The main drawback of an SbS-MAP receiver is due to its high computational complexity that is at least linear in the decision delay D [1] and this has limited their application in practical environments. However, these receivers have been recently “rediscovered” because they are able to generate soft-information in the form of APPs. For example, this soft-information is exploited in parallel concatenated coded systems during the process of iterative decoding; moreover, the APPs have been recently exploited in several other fields such as in blind equalization [5], channel estimation and tracking [6] and adaptive decoding [7]. In particular, in [6] a new channel estimator that is fed by the APPs of the states of the ISI channel (instead of the less informative hard-decisions) and that is able of generating reliable zero-delayed filtered channel estimates has been presented. This soft channel estimator represents the core of the proposed adaptive receiver. II. THE PROPOSED ADAPTIVE RECEIVER As mentioned in the previous Section, the most appealing feature of an SbS-MAP receiver is its ability of generating soft-information in the form of APPs, whereas the most appealing feature of an MLS receiver is reasonable computational complexity and nearly optimum performance for large values of D. The proposed receiver, sketched in Fig.2, combines these two features and it consists of an SbSMAP detector that feeds a nonlinear, recursive and optimum (in an MMSE sense) Kalman-like channel estimator with the soft information given by the APPs of the state sequence of the ISI channel and of an MLS equalizer which outputs harddetected data. Unlike the receiver in Fig.1, the one in Fig.2 does not utilize hard decided data for channel estimation and tracking so that unreliable “tentative” decision are not generated. This allows the receiver to build the VA trellis with more reliable zero-delayed channel estimates (in parallel with channel tracking) and to output the entire decided sequence with a decision delay equal to the length of the TDMA-slot. So doing, the proposed receiver yields to better performances than those obtained in [6] because the MLS equalizer operates at the largest decision delay (i.e., the TDMA-slot length), something an SbS-MAP receiver cannot do at a reasonable computational complexity. Referring to a TDMA-based digital link impaired by timevariant multipath phenomena and AWGN, the baud-rate sampled complex sequence {r(i)} received at the output of the equivalent low-pass randomly time-variant ISI channel can be modeled as , ) ( ) ( ) ( ) ( ) ( ) ; ( ) ( 1