Abstract
Multimodulus algorithms (MMA) based adaptive blind equalizers mitigate inter-symbol interference and recover carrier-phase in communication systems by minimizing dispersion in the in-phase and quadrature components of the received signal using the respective components of the equalized sequence in a decoupled manner. These equalizers are mostly incorporated in bandwidth-efficient digital receivers which rely on quadrature amplitude modulation (QAM) signaling. The nonlinearities in the update equations of these equalizers tend to lead to difficulties in the study of their steady-state performance. This paper presents originally the steady-state excess mean-square-error (EMSE) analysis of different members of multimodulus equalizers MMAp–q in a non-stationary environment using energy conservation arguments, and thus bypassing the need for working directly with the weight error covariance matrix. In doing so, the exact and approximate expressions for the steady-state mean-square-error of several MMA based blind equalization algorithms are derived, including MMA2–2, MMA2–1, MMA1–2, and MMA1–1. The accuracy of the derived analytical results is validated using Monte–Carlo experiments and found to be in close agreement.
Highlights
Blind equalizers mitigate different types of interferences such as inter-symbol interference (ISI), frequency selective fading, etc., caused by non-ideal transformations performed by the dispersive channels in a communication system
In [66], Gouptil and Palicot developed a geometrical approach to steady-state analysis for Bussgang algorithms, and derived a closed-form analytical expression for excess mean-square-error (EMSE), which when extended to tracking analysis is given as ζ μTr(R)E|φ|(a,a∗)|2 + μ−1Tr(
This paper reports the steady-state EMSE analysis of adaptive filters belonging to MMAp–q family (i.e., MMA2–2, MMA2–1, MMA1–2 and MMA1–1) by exploiting the fundamental energy relation in non-stationary environment
Summary
Blind equalizers mitigate different types of interferences such as inter-symbol interference (ISI), frequency selective fading, etc., caused by non-ideal transformations performed by the dispersive channels in a communication system. The approach that has been adopted for steadystate tracking analysis of multimodulus equalizers exploits the study of energy propagation through each iteration of an adaptive filter using a feedback structure (which consists of a lossless feedforward block and a feedback path), and it relies on energy conservation arguments [14]. The convenience of this approach is that it allows us to avoid working with nonlinear update equations and bypasses the need for working directly with the weight error covariance matrix. Our objective is not to study the conditions under which an algorithm will tend to converge successfully, rather to evaluate its expected steady-state performance once it has converged successfully
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