Reduced-complexity multi-stage blind clustering equaliser

Abstract

A multi-stage blind clustering algorithm is proposed for equalisation of M-QAM channels. A navel hierarchical decomposition divides the overall task of equalising a highorder QAM channel into much simpler sub-tasks. Each subtask can be accomplished fast and reliably using a blind clustering algorithm derived originally for 4-QAM signals. The well-known constant modulus algorithm (CMA) is used as a benchmark to assess this novel multi-stage blind equaliser and it is demonstrated that the new blind adaptive algorithm achieves much faster convergence. This multi-stage clustering equaliser only quires slightly more computations than the very simple CMA and, like the latter, its computational complexity does not increase as the levels of digital symbols increase.

Concurrent constant modulus algorithm and soft decision directed scheme for fractionally-spaced blind equalization

“…It also has an effect that a larger adaptive gain µ d can often be used, compared with the DD scheme. It is also obvious that this SDD scheme corresponds to the last stage of the bootstrap MAP scheme given in [7], [8]. The complexity of the this CMA+SDD scheme is given in Table I, where it can be seen that computational complexity per weight update of this proposed new scheme is simpler than that of the CMA+DD scheme.…”

“…Obviously this approximation is only valid when the equalization goal has been accomplished. A bootstrap optimization process however can be performed to achieve the MAP solution, as is presented in [7], [8].…”

“…At a cost of slightly more than doubling the complexity of the very simple CMA, this concurrent CMA+DD equalizer is reported to obtain a dramatical improvement in equalization performance over the CMA [6], and it represents a state-of-art technique for low-complexity blind equalization of high-order QAM channels. Another blind equalization scheme, which is relevant to the proposed concurrent CMA and soft decision-directed (SDD) blind equalizer, is the bootstrap maximum a posteriori probability (MAP) blind equalizer [7], [8].…”

“…The bootstrap MAP blind scheme was originally derived in [9] for the 4-QAM case and extended to M -QAM channels in [7], [8], and it has been shown to outperform the CMA+DD scheme, in terms of convergence rate and steady-state performance [10], [11]. A drawback of this bootstrap MAP scheme is that its adaptive process requires L-stage switchings, where L = log 2 (M )/2, and each stage of adaptation needs a different set of algorithm parameters.…”

Integration of macromolecular diffraction data using radial basis function networks

“…Therefore, a more robust approach is suggested, based on radial basis function (RBF) neural networks, a well established technique that has been applied to a wide variety of problems such as image processing (Saha et al, 1990), speech recognition (Ng & Lippmann, 1990), adaptive equalization (Chen et al, 1992) and medical diagnosis (Lowe & Webb, 1990). The technique for diffraction data processing presented in this paper extends the conventional reference pro®le-®tting method by using a concentrated RBF network design (Pokric  et al, 1999) in order to compensate for possible changes in the observed spot pro®les.…”