Optimal Channel Shortener Design for Reduced- State Soft-Output Viterbi Equalizer in Single-Carrier Systems

Abstract

We consider optimal channel shortener design for reduced-state soft-output Viterbi equalizer (RS-SOVE) in single-carrier (SC) systems. To use RS-SOVE, three receiver filters need to be designed: a prefilter, a target response and a feedback filter. The collection of these three filters are commonly referred to as the "channel shortener". Conventionally, the channel shortener is designed to transform an intersymbol interference (ISI) channel into an equivalent minimum-phase equivalent form. In this paper, we design the channel shortener to maximize a mutual information lower bound (MILB) based on a mismatched detection model. By taking the decision-feedback quality in the RS-SOVE into consideration, the prefilter and feedback filter are found in closed forms, while the target response is optimized via a gradient-ascending approach with the gradient explicitly derived. The information theoretical properties of the proposed channel shortener are analyzed. Moreover, we show through numerical results that, the proposed channel shortener design achieves superior detection performance compared to previous channel shortener designs at medium and high code-rates.

Complexity Reduction of MLSE and MAP Equalizers Using Modified Prolate Basis Expansion

“…This work is intended to highlight the use of the modified version of the Prolate basis expansion [16][17][18], in MLSE and MAP equalization processes [13,15,19,20]. The application of MPF in the time-delay domain conveys a more accurate channel representation, which leads to a reduction in the error floor.…”

“…Such a parameter corresponds to the noiseless received signal when a specific b l is transmitted through the channel h. Note thatỹ l |b l is highly dependent on the current communication channel. Moreover, the iterative computation of the objective functions Equations (13) and (16) leads to a highly demanding computational problem, which increases with the cardinality M of the transmitted alphabet and the length of the CIR. In order to deal with the latter, the use of BEM is proposed for representing h employing MPFs.…”

“…In order to reduce the computational complexity, sub-optimal algorithms [8] have been used, such as reduced state sequence estimation (RSSE), delayed decision feedback sequence estimation (DDFSE), the M-algorithm, Max-Log-MAP, Log-MAP, and other recent ideas including the reduced-state soft-output Viterbi equalizer [13] and the estimation of channel sparsity to assist in the detection of the transmitted sequence [14]. In [15], the authors presented an MLSE and a MAP equalizer using the discrete-Fourier basis expansion model (BEM) of the channel.…”

On the Design of Channel Shortening Demodulators for Iterative Receivers in Linear Vector Channels

“…Instead of fully removing the trellis-based detection, another possible approach is to reduce the memory size of the original linear vector channel through an interference cancellation (IC) based prefiltering. To the best of our knowledge, there is only limited literature [54], [62] on such a design of demodulator that combines both IC based prefiltering and a memory-size shortened BCJR in iterative receiver design. A closely related concept is delayed-decision-feedback-sequence-estimation (DDFSE) [21], [57], which also reduces the number of states in the BCJR.…”

Closed-Form Expressions for Channel Shortening Receivers Using $A\ Priori$ Information

“…Recent work on channel shortening considers the mutual information as the optimization criterion [2] and closed-form expressions for the receiving and target response filters have been obtained by assuming that input symbols follow a Gaussian distribution. Channel shortening has been extended to the optimization of the transmit filters [3] and a channel shortening receiver with an additional return filter using a priori information has been introduced in [4], [5] although no closed-form expressions have been provided for the return filter and the target response so far. In [6], the authors observe that further constraints must be put on the return channel shortening filter in order for the receiver to perform interference cancellation in a turbo equalization scheme.…”