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Encyclopedia > Blind equalization

Blind equalization is a digital signal processing problem in which the channel impulse response and the transmitted signal are inferred from the received signal. In contrast to the equalization problem, the input signal is not assumed to be known, save its statistics. Digital signal processing (DSP) is the study of signals in a digital representation and the processing methods of these signals. ... Channel, in communications (sometimes called communications channel), refers to the medium used to convey information from a sender (or transmitter) to a receiver. ... In the language of mathematics, the impulse response of a linear transformation is the image of Diracs delta function under the transformation. ... For information about computer bandwidth management, see Equalization (computing). ... In the fields of communications, signal processing, and in electrical engineering more generally, a signal is any time-varying quantity. ...

Blind equalization is essentially blind deconvolution formulated as a digital communications problem. None the less, the emphasis in blind equalization is on online computation of the equalizer, which is the inverse of the channel impulse response, rather than computation of the channel impulse response itself. This is due to blind equalization common mode of usage in digital communications systems. To meet Wikipedias quality standards, this article or section may require cleanup. ... Digital communication, as opposed to analogue communication refers to all emerging communications and technologies via a digital platform usually combining text, graphics, sound, and video, utilising computer or mobile technology. ... In computer science, an online algorithm is one that can process its input piece-by-piece, without having the entire input available from the start. ... An equalization (EQ) filter is a filter, usually adjustable, chiefly meant to compensate for the unequal frequency response of some other signal processing circuit or system. ...

## Contents

### Noiseless model

The channel is modeled as an LTI system whose impulse response will be denoted . The noiseless model of the blind equalization problem relates the received signal r[k] to the transmitted signal s[k] via In electrical engineering, specifically in signal processing and control theory, LTI system theory investigates the response of a linear, time-invariant system to an arbitrary input signal. ...

The blind equalization problem can now be formulated as follows; Given the received signal r[k], find a filter w[k], called an equalization filter, such that

The solution s[k] to the blind equalization problem is not unique. In fact, it may be determined only up to a signed scale factor and an arbitrary time delay. That is, if are estimations of the transmitted signal and channel impulse response, respectively. Than give rise to the same received signal r[k] for any choice of a real scale factor c and an integral time delay d. In fact, the role of s[k] and h[k] in the above formula is symmetric.

### Noisy model

In the noisy model includes an additional additive term n[k] representing additive noise. The model is therefore

## Algorithms

Many algorithms have been suggested over the years for the solution of the blind equalization problem. As in practice, one usually has access to only a finite number of samples from the received signal r(t), further restrictions must be imposed over the mathematical models described above, in order to render the problem tractable.

### Bussgang methods

The Bussgang methods further assume that the channel has a finite impulse response. Specifically, the channel impulse response is assumed to be of the form , where N is an arbitrary natural number. This assumption may be justified over physical ground, as any physical signal must have finite energy, and consequently, its impulse response must tend to zero. Thus, it may be assumed that beyond a certain index, all coefficients are negligibly small. A finite impulse response (FIR) filter is a type of a digital filter. ...

### Polyspectra techniques

Polyspectra techniques utilize higher order statistics in order to compute the equalizer.

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