Author : Deepmala Singh Parihar, Prof. Ravi Mohan

International Journal of Scientific & Engineering Research Volume 3, Issue 1, January-2012

ISSN 2229-5518

Download Full Paper : PDF**Abstract - **The channel estimation has become very vast field due to different types of interference present in wireless channel and in equipments. In this thesis, estimation algorithms for digital communications systems in the presence of Additive White Gaussian noise and Multipath environment are explored and their performance is investigated. In particular, least square Error and Zero forcing equalizers are used to provide the optimum solution and compensate for Inter-Symbol error. As the BER performance of equalizers in variable in multipath fading channel therefore we have combined Equal Gain combining and Maximal Ratio Combing Diversity techniques, and searched that Maximal Ratio combining techniques is able to fight with Co-Channel interference and Inter-symbol interference problem.

**Keywords: **- OFDM, Equalizer, Diversity, QAM

**1 INTRODUCTION**Wireless communication [1] systems require signal processing techniques that improve the link performance in hostile mobile radio environments. Complex channel estimation i.e. estimation of channel gain, which includes phase and amplitude. Equalization, diversity and channel coding are three techniques which can be used independently or in tandem to improve received signal quality and link performance over small scale times and distances. In flat fading environment, estimation of the channel using trained sequence of the data has been studied and implemented in [2]. Then pilot data of some required percentage of data length is inserted into the source data. It is used to estimate the random phase shift of the fading channel and train the decision to adjust the received signal with phase recover. So, finally phase estimation using training symbol is implemented in flat fading environment. The radio channels in mobile radio systems are usually multipath fading channel, which are causing intersymbol interference (ISI) and intercarrier interference (ICI) in the received signal. To remove ISI and ICI from the signal many kind of equalizers and diversity algorithms can be used. Detection algorithms based on trellis search like Least square error (LSE) and Zero forcing (ZF) algorithms for equalization[3] and Maximal ratio combining (MRC) and Equal gain combining (EGC) for diversity techniques[4] offer a good receiver performance, but still often not much computation. Therefore, these algorithms are currently quite popular. Channel estimation in frequency selective has different approach then compared with flat fading environment.

Semi analytical method to evaluate BER of quadrature amplitude modulation (QAM) and additive noise where pilot assisted linear channel estimation and channel equalization. A novel channel estimation scheme for OFDMA uplink packet transmissions over doubly selective channels was suggested in [5].

**2 OFDM **OFDM is a spectrally efficient modulation technique [6]. It is conveniently implemented using IFFT and FFT operation. There are very fast and efficient implementation of the FFT and IFFT, which is the big reason of the popularity of OFDM. It handles frequency selective channels well when combined with error correction coding. In other words OFDM is frequency division multiplexing of multicarriers which are orthogonal to each other i.e. they are placed exactly at the nulls in the modulation spectra of each other. In OFDM data is divided into several parallel data streams or sub-channels, one for each sub carrier which are orthogonal to each other although they overlap spectrally. Each subcarrier is modulated with a conventional modulation scheme (QAM or QPSK) at a low symbol rate, maintaining total data rates similar to conventional single carrier modulation schemes in the same bandwidth.

Figure 1 Subdivision of the channel bandwidth W into narrowband sub channels of equal width ∆f

The advantages of OFDM include its robustness to narrowband cochannel interference. High spectral efficiency and its low sensitivity to time synchronization errors. Besides these advantages it has some disadvantages like its complexity and sensitive to Doppler shift and frequency synchronization problems. OFDM requires a more linear power amplifier.

Figure 2 Block diagram of OFDM transmitter and receiver

FFT is written as

... (1)

WN be the complex-valued phase factor

Thus, X (k) becomes

... (2)

Similarly IFFT is written as,

… (3)

**3 EQUALIZERS**Equalization is the process of adjusting the balance between frequency components within an electronic signal. The circuit or equipment used to achieve equalization is called Equalizer [7]. Equalization compensates for ISI created by multipath within time dispersive channels. If the modulation bandwidth exceeds the coherence bandwidth of the radio channel, ISI occurs and modulation pulses are spread in time into adjacent symbols. An equalizer within a receiver compensates for the average range of expected channel amplitude and delay characteristics. Equalizers must be adaptive since the channel is generally known and time varying. So, an adaptive equalizer compensates for an unknown and time varying channel, it requires a specific algorithms to update equalizer coefficients and track the channel variations, we use zero forcing (ZF) algorithm and least square error (LSE) algorithm.

3.1 Zero Forcing Algorithms:

In a zero forcing equalizer, the equalizer coefficients Cn are chosen to force the samples of the combined channel and equalizer impulse response to zero at all. For a channel with frequency response F(f) the ZF equalizer . Thus the combination of channel and equalizer gives a flat frequency response and linear phase must satisfy Nyquists criterion.

.... (4)

Zero Forcing equalizer has the disadvantage that the inverse filter may excessively amplify noise at frequencies where the folded channel spectrum has high attenuation.

3.2 Least Mean Square Algorithms:

A more robust equalizer is the LMS equalizer where the criterion used is the minimization of the MSE between the desired equalizer output and the actual equalizer output. Define the input signal to the equalizer as a vector yk.

Mean Square Error is

… (5)

Equalization can be used to any signal processing operation that minimizes intersymbol interference (ISI). Since the mobile fading channel is random and time varying, equalizer must track the time varying characteristics of the mobile channel and thus are called adaptive equalizer.

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