16-08-2012, 02:26 PM
Implementation of Adaptive channel equalizers using Variants of LMS
Implementation of Adaptive channel equalizers using Variants of LMS.doc (Size: 1,005.5 KB / Downloads: 44)
Overview
Efficient and successful communication of messages via imperfect channels is one of the major issues of information technology today. With more and more users desiring to share communication channels, the importance of clever use of the bandwidth becomes paramount. How can we support the exceedingly high data rates and capacity required for various applications with the severely restricted resources offered in a wireless channel? The answer of this question is lie on idea of efficient use of types of Filters which reduces the attenuation and noise.
Digital signal processing has played a key role in the development of communication systems over the last two decades. In recent years digital filter have been occupying an increasingly important role in both wireless and wire line communication systems. In numerous applications of signal processing and communication we are faced with the necessity to remove noise and distortion from the signals. These phenomena are due to time-varying physical processes, which sometimes are unknown. One of these situations is during the transmission of a signal (message) from one point to another. The medium (wires, fibers, microwave beam, etc.), which is known as channel introduces noise and distortion due to variations of its properties. These variations may be slow varying or fast varying. Since most of the time the variations are unknown, it is the use of adaptive filtering that diminishes and sometimes completely eliminates the signal distortion. The most common adaptive filters, which are used during the adaptation process, are the finite impulse response filers (FIR) types. These are preferable because they are stable; no special adjustments are needed for their implementation. The adaptation approaches, which we will introduce in this project is VARIANTS OF LMS (least mean square) algorithm. Signal to Noise ratio (SNR) values are observed for different orders of the filter.
Along with SNR, Root Mean Square Error (RMSE) is also calculated with the help of formulas to find the minimum error. This shows the performance of the algorithm and SNR versus RMSE is also drawn.
INTRODUCTION
The channel as a physical medium for transmitting data can, e.g., be a copper cable, an optical fiber, or air—three example channels that are used for telephony. More generally, a channel can also be a magnetic or optical. The channel influences the signal to be transmitted. It is desirable to find a mathematical model. A copper cable, e.g., can roughly be modeled as a band pass filter with a pass band of 300 − 3300 Hz. An adequate mathematical model of the channel constitutes the basis for compensating the channel’s influence, which is referred to as channel equalization. In case the inverse of the channel exists, the channel is said to be invertible. If the inverse does not exist, often an approximation can be found.
An algorithm that implements the channel equalization optimally in the maximum likelihood sense is the so called Viterbi algorithm. The implementation of such a rather sophisticated algorithm is comparably expensive. Depending on the channel and the application, a simple FIR-filter may be used for equalization, which is a low complexity solution.
In many practical cases the channel cannot be inverted, which may have various reasons. Hence, there exists no equalizer. The properties of, e.g., a radio channel may depend on the atmospheric conditions, possibly existing reflecting objects, and the movement of both transmitter and receiver. A copper cable appears to be a much more static channel; however, the actual transfer function of a randomly choosen pair may differ substantially from the theoretical model since several parameters as well as their influence on the cable’s behavior are unknown. The temperature of the cable, the age of the cable, and the exact arrangement of the cable with respect to ground as well as other cables and conductors are examples for such parameters. Hence, a priori an accurate channel model is not available.
Once the channel properties have been determined exactly, they may change with time. This is obvious for the radio channel; however, even the properties of the copper cable may change, for example due to a change of the cable’s temperature caused by the weather. Thus adaptive channel equalization, i.e. equalization that can adapt to different channel conditions and track changes, is required.
Adaptation employs the receive signal to obtain an estimate of the channel. A possible solution is that the transmission starts with a data sequence that is known at the receiver, a so called training sequence. The training sequence is designed to permit an equalizer at the receiver to acquire the proper filter coefficients in the worst possible channel conditions, when the training sequence is finished. Therefore filter coefficients are near their optimal values for reception of user data. An adaptive equalizer at the receiver uses a recursive algorithm to evaluate the channel and estimate filter coefficients to compensate for the channel.
A more sophisticated alternative is blind equalization, which does not required knowledge of the transmitted data. After an initial equalization phase (either done blindly or employing a training sequence), it is advantageous to switch to decision feedback equalization, which uses the data obtained by a decision device in the receiver. As a result of successful channel equalization the data rate can be increased substantially. A problem with channel equalization is that the effect of interference present at the receiver input can be increased by the equalizer.
Data transmission over the channel
When transmitting data, e.g. fax, video streams, or web contents, over the copper cable, the transmitted symbols suffer from inter symbol interference (ISI). The responses of consecutively transmitted data symbols influence each other at the receiver due the dispersive nature of the channel.
The response of a transmitted symbol overlaps with the response of the next symbol in time domain, which makes the reception more complicated. So far we did not consider that the signal is modulated, i.e., the information is transmitted in a high frequency band modulated onto a carrier. For data transmission over the copper channel this corresponds to a band that it centered in the pass band. Channel equalization can be investigated in the baseband, i.e., without taking into account modulation and demodulation in the model, if the channel is transformed into an equivalent baseband channel. After sampling, a discrete time model of the system can be employed as shown in Fig.1.In general, a data transmission system consists of a modulator, a channel, and a demodulator. The channel equalization problems are considered as independent of the modulation and hence concentrate only on the base band equivalent.