A unified approach to the steady-state analysis of quantized adaptive filtering algorithms

On the convergence of blind adaptive equalizers for constant modulus signals

“…SATO'S ALGORITHM We now extend the results to Sato's algorithm (7). In this case, we introduce the functions and, for (26) Then, it is straightforward to verify that the error signals are now related via Moreover, it further holds that so that the same feedback structure of Fig. 1 will still hold with the gain in the feedback path replaced by…”

A feedback approach to the steady-state performance of fractionally spaced blind adaptive equalizers

“…(20) further ahead], which actually holds for very general adaptive schemes and not just CM algorithms, as explained in [6]. This energy relation was noted and exploited by Sayed and Rupp in [26]- [29] in studies on the robustness and -stability of adaptive filters from a deterministic point of view (see [29]).…”

“…In this case, we select (6) and the update equation for the weight estimates is given by (7) with a step-size µ and where now, is the output of the adaptive equalizer. Here, the symbol denotes complex conjugate transposition.…”

“…(Applications to other classes of adaptive algorithms, in addition to tracking analyzes, are given in [6]- [8].) By taking expectations of both sides of (20), we get (21) Now, recall that our objective in this paper is to evaluate the MSE of CM algorithms in steady state.…”

“…Our conclusions will further confirm the superior performance of CMA2-2. The approach in this paper exploits a fundamental energypreserving relation that, in fact, holds for a general class of adaptive filters and not just CM algorithms [6]. This relation allows us to avoid working directly with the nonlinear update that is characteristic of CM algorithms; it focuses instead on the propagation of error energies through a feedback structure that consists of a lossless feedforward block and a feedback path.…”