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

Abstract

Abstract. 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.

Information rate analysis of the oversampled phase-noise channel

“…In the absence of phase noise, if sampling with period T s < 1/(2B h ) is performed as in Fig. 1, the sampled sequence {y i } is a sufficient statistic for the detection of the data sequence [8], [9]. Moreover, we can consider |H(f )| 2 with vestigial symmetry with respect to 1/(2T s ), so that sampling at the time instants t = iT s leads to independent and identically distributed (i.i.d.)…”

The condition for the applicability of the Viterbi algorithm with implications for fading channel MLSD

“…A full investigation of the problem requires simulation for various combinations of and for different channel statistics. Some aspects of this problem have been considered in [19] and [20].…”

Sequence detection in nonlinear channels: a convenient alternative to analog predistortion

“…Based on the results of [18] and [19], and in particular on the reversibility principle, the set of samples obtained by sampling the output of this filter with rate is a sufficient statistic for the detection of the transmitted sequence . We then refer to the receiver structure shown in Fig.…”

“…Hence, the path chosen by the receiver in the trellis diagram differs from the correct one by state transitions, the first starting at time , where is called the duration of the error event, and the error sequence includes nonzero error symbols (at most, ). The square distance of the error event is defined as (19) where is the entire transmission period and the double summation extends only over the nonzero terms. Note that the square distance is defined in terms of the time-continuous noiseless signals entering the sampler in Fig.…”