On recursive optimal detection of linear modulations in the presence of random fading

In this paper, the problem of optimal detection of a linearly modulated digital signal transmitted over a fading channel is addressed. First, the issue of preliminary front-end processing in order to extract a sufficient statistics for information sequence detection from the continuous-time received signal is considered. Then, recursive algorithms are derived, which approximate optimal detection under the assumption of a linear and noisy channel modeled by a stochastic time-varying impulse response with arbitrary known statistics. Specific solutions are proposed for the Rayleigh fading channel typical of mobile radio communications. The information symbols are assumed to be grouped into blocks which are preceded and followed by known preamble and postamble, respectively This model encompasses both Time Division Multiple Access (TDMA) schemes and pilot symbol assisted transmission. Two detection schemes are considered and relevant recursive formulations proposed. More specifically, optimal detection in complete absence of Channel State Information (CSI) (blind detection) or in presence of perfect CSI at the beginning of the data block (trained detection) are investigated. It is shown that optimal detection performance may be practically attained by sampling the received signal with few samples per symbol interval and searching a trellis diagram of adequate size by means of a Viterbi algorithm. State-complexity reduction techniques based on Per-Survivor Processing (PSP) for both types of detection schemes are also considered.