Adaptive soft-input soft-output algorithms for iterative detection with parametric uncertainty

The soft-input soft-output (SISO) module is the basic building block for established iterative detection (ID) algorithms for a system consisting of a network of finite state machines. The problem of performing ID for systems having parametric uncertainty has received relatively little attention in the open literature. Previously proposed adaptive SISO (A-SISO) algorithms are either based on an oversimplified channel model, or have complexity that grows exponentially with the observation length (or the smoothing lag ). In this paper, the exact expressions for the soft metrics in the presence of parametric uncertainty modeled as a Gauss–Markov process are derived in a novel way that enables the decoupling of complexity and observation length. Starting from these expressions, a family of suboptimal (practical) algorithms is motivated, based on forward/backward adaptive processing with linear complexity in . Recently proposed A-SISO algorithms, as well as existing adaptive hard-decision algorithms are interpreted as special cases within this framework. Using a representative application—joint iterative equalization-decoding for trellis-based codes over frequency-selective channels—several design options are compared and the impact of parametric uncertainty on previously established results for ID with perfect channel state information is assessed.