Convergence analysis of stochastic diffusion search

In this paper we present a connectionist searching technique - the Stochastic Diffusion Search (SDS), capable of rapidly locating a specified pattern in a noisy search space. In operation SDS finds the position of the pre-specified pattern or if it does not exist - its best instantiation in the search space. This is achieved via parallel exploration of the whole search space by an ensemble of agents searching in a competitive cooperative manner. We prove mathematically the convergence of stochastic diffusion search. SDS converges to a statistical equilibrium when it locates the best instantiation of the object in the search space. Experiments presented in this paper indicate the high robustness of SDS and show good scalability with problem size. The convergence characteristic of SDS makes it a fully adaptive algorithm and suggests applications in dynamically changing environments.

A self-structured adaptive decision feedback equalizer

In a decision feedback equalizer (DFE), the structural parameters, including the decision delay, the feedforward filter (FFF), and feedback filter (FBF) lengths, must be carefully chosen, as they greatly influence the performance. Although the FBF length can be set as the channel memory, there is no closed-form expression for the FFF length and decision delay. In this letter, first we analytically show that the two-dimensional search for the optimum FFF length and decision delay can be simplified to a one-dimensional search and then describe a new adaptive DFE where the optimum structural parameters can be self-adapted.

Equalisation with adaptive time lag

In an adaptive equaliser, the time lag is an important parameter that significantly influences the performance. Only with the optimum time lag that corresponds to the best minimum-mean-square-error (MMSE) performance, can there be best use of the available resources. Many designs, however, choose the time lag either based on preassumption of the channel or simply based on average experience. The relation between the MMSE performance and the time lag is investigated using a new interpretation of the MMSE equaliser, and then a novel adaptive time lag algorithm is proposed based on gradient search. The proposed algorithm can converge to the optimum time lag in the mean and is verified by the numerical simulations provided.

Structure adaptation of linear MMSE adaptive filters

The tap-length, or the number of the taps, is an important structural parameter of the linear MMSE adaptive filter. Although the optimum tap-length that balances performance and complexity varies with scenarios, most current adaptive filters fix the tap-length at some compromise value, making them inefficient to implement especially in time-varying scenarios. A novel gradient search based variable tap-length algorithm is proposed, using the concept of the pseudo-fractional tap-length, and it is shown that the new algorithm can converge to the optimum tap-length in the mean. Results of computer simulations are also provided to verify the analysis.