Performance of adaptive bayesian equalizers in outdoor environments

Outdoor communications are affected by multipath propagation that imposes an upper limit on the system data rate and restricts possible applications. In order to overcome the degrading effect introduced by the channel, conventional equalizers implemented with digital filters have been traditionally used. A new approach based on neural networks is considered. In particular, the behavior of the adaptive Bayesian equalizer implemented by means of radial basis functions applied to the channel equalization of radio outdoor environments has been analyzed. The method used to train the equalizer coefficients is based on a channel response estimation. We compare the results obtained with three channel estimation methods: the least sum of square errors (LSSE) channel estimation algorithm, recursive least square (RLS) algorithm employed only to obtain one channel estimation and, finally, the RLS algorithm used to estimate the channel every decided symbol for the whole frame.Peer ReviewedPostprint (published version

Equalization Methods in Digital Communication Systems

Tato práce je psaná v angličtině a je zaměřená na problematiku ekvalizace v digitálních komunikačních systémech. Teoretická část zahrnuje stručné pozorování různých způsobů návrhu ekvalizérů. Praktická část se zabývá implementací nejčastěji používaných ekvalizérů a s jejich adaptačními algoritmy. Cílem praktické části je porovnat jejich charakteristiky a odhalit činitele, které ovlivňují kvalitu ekvalizace. V rámci problematiky ekvalizace jsou prozkoumány tři typy ekvalizérů. Lineární ekvalizér, ekvalizér se zpětnou vazbou a ML (Maximum likelihood) ekvalizér. Každý ekvalizér byl testován na modelu, který simuloval reálnou přenosovou soustavu s komplexním zkreslením, která je složena z útlumu, mezisymbolové interference a aditivního šumu. Na základě implenentace byli určeny charakteristiky ekvalizérů a stanoveno že optimální výkon má ML ekvalizér. Adaptační algoritmy hrají významnou roli ve výkonnosti všech zmíněných ekvalizérů. V práci je nastudována skupina stochastických algoritmů jako algoritmus nejmenších čtverců(LMS), Normalizovaný LMS, Variable step-size LMS a algoritmus RLS jako zástupce deterministického přístupu. Bylo zjištěno, že RLS konverguje mnohem rychleji, než algoritmy založené na LMS. Byly nastudovány činitele, které ovlivnili výkon popisovaných algoritmů. Jedním z důležitých činitelů, který ovlivňuje rychlost konvergence a stabilitu algoritmů LMS je parametr velikosti kroku. Dalším velmi důležitým faktorem je výběr trénovací sekvence. Bylo zjištěno, že velkou nevýhodou algoritmů založených na LMS v porovnání s RLS algoritmy je, že kvalita ekvalizace je velmi závislá na spektrální výkonové hustotě a a trénovací sekvenci.The thesis is focused on the problem of equalization in digital communication systems. Theoretical part includes brief observation of different approaches of equalizer designing. The practical part deals with implementation of the most often used equalizers and their adaptation algorithms. The aim of practical part is to make a comparison characteristic of different type of equalizers and reveal factors that influence the quality of equalization. Within a framework of the problem of equalization three types of equalizers were researched: linear equalizers, decision feedback equalizers (DFE) and maximum likelihood equalizers (ML). Each equalizer was tested on the model which approximates the real transmission system with complex distortion consisted of attenuation, intersymbol interference and additive noise. The comparison characteristics of equalizers were revealed on the basis of implementation. It was ascertained that ML equalizer has the optimum performance among three equalizers. The adaptation algorithm play significant role in performance of mentioned equalizers. Two groups of algorithms were studied: stochastic and deterministic. The first one includes following algorithms: least-mean-square algorithm (LMS), normalized LMS algorithm (NLMS) and variable step-size LMS algorithm (VSLMS). The second one is represented by RLS algorithm. It was determined that RLS algorithm converges much faster than LMS-based algorithms. The several factors that influenced the performance of all algorithms were studied. One of the most important factors that influences the speed of convergence and stability of the LMS algorithm is step-size parameter. Another very important factor is selecting the training sequence. The big disadvantage of LMS-based algorithms compare to RLS-based algorithms was found: the quality of equalization is highly dependent on the power spectral density of the training sequence.

Adaptive estimation and equalisation of the high frequency communications channel

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Least mean M -estimate algorithms for robust adaptive filtering in impulse noise

This paper proposes two gradient-based adaptive algorithms, called the least mean M-estimate and the transform domain least mean M -estimate (TLMM) algorithms, for robust adaptive filtering in impulse noise. A robust M -estimator is used as the objective function to suppress the adverse effects of impulse noise on the filter weights. They have a computational complexity of order O(N) and can be viewed, respectively, as the generalization of the least mean square and the transform-domain least mean square algorithms. A robust method for estimating the required thresholds in the M -estimator is also given. Simulation results show that the TLMM algorithm, in particular, is more robust and effective than other commonly used algorithms in suppressing the adverse effects of the impulses. © 2000 IEEE.published_or_final_versio

A fast recursive least-squares adaptive nonlinear filter

Journal ArticleThis paper presents a fast, recursive least-squares (RLS) adaptive nonlinear filter. The nonlinearity in the system is modeled using the Hammerstein model, which consists of a memoryless polynomial nonlinearity followed by a finite impulse response linear system. The complexity of our method is about 3NP2+7NP+N+10P2+6P multiplications per iteration and is substantially lower than the computational complexities of fast RLS algorithms that are direct extensions of RLS adaptive linear filters to the nonlinear case