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 a complexity that grows exponentially with the observation length N (or the smoothing lag D). 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 N. Previously 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.