Soft-In Soft-Out Detection Using Partial Gaussian Approximation

Abstract

This paper concerns the soft-in soft-out detection in a coded communication system, where the transmitted symbols are discrete valued, and the exact a posteriori probability (APP) detection often involves prohibitive complexity. By using the properties of Gaussian functions, an approximate approach to the APP detection is devised with the idea that, in the computation of the APP of each symbol, the remaining symbols are distinguished based on their contributions to the APP of the concerned symbol, and the symbols with less contributions are approximated as (continuous) Gaussian variables [hence the name partial Gaussian approximation (PGA)] to reduce the computational complexity. The connection between the PGA detector and the reduced dimension maximum a posteriori detector (RDMAP) is investigated. It is shown that, PGA is equivalent to RDMAP, but it has a complexity much lower than that of RDMAP, i.e., PGA can be regarded as an efficient implementation of RDMAP. In addition, the application of PGA in intersymbol interference (ISI) channel equalization is also investigated. We show that PGA allows further significant complexity reduction by exploiting the circulant structure of the system transfer matrix, which makes PGA very attractive in handling severe ISI channels with large memory length.INDEX TERMS Soft-in soft-out detection, turbo equalization, Gaussian functions, LMMSE detection, RDMAP.

Turbo Equalization Using Partial Gaussian Approximation

“…The idea is to use the original discrete messages rather than their Gaussian approximation for a selected subset of channel symbols which significantly interfere with x i . It is inspired from the PGA proposed in [10].…”

“…The complexity of the PGA algorithm in [10], which was designed for generic channel matrices, is O(N 2 + M 2 Q M ) per symbol. The main contribution to the complexity of the BP-EP-PGA is at (4), which requires L × L matrix inversions (see [8,Eq.…”

“…By contrast, to equalize one channel symbol the new equalizer combines discrete messages from the demodulatordecoder for the symbols strongly interfering with said symbol and Gaussian-converted messages for the weakly interfering symbols. The reported simulation results show that doing so leads to a significant performance improvement compared to the turbo-equalizers in [7], [10] and [8]. Finally, our turboequalizer allows for trading complexity with performance by varying the set of symbols that are considered as strong interferers.…”

“…Inspired by the partial Gaussian approximation (PGA) proposed in [10] we modify the messages returned from the equalizer and passed to the demodulator-decoder in [8]. The messages returned by the equalizer in [8] are computed from the above Gaussian-converted messages from the demodulatordecoder.…”

“…Secondly, due to the particular structure of the ISI channel model, the messages returned by our equalizer can be computed from the Gaussian messages passed to it in a simple way. This leads to a significant complexity reduction compared to the turbo-equalizer in [10].…”