^{1}

^{2}

^{2}

^{3}

^{1}

^{2}

^{3}

The paper proposes a novel technique for reducing noise in M-ary signal transmission through wireless fading channel using wavelet denoising that play the key role. The paper also explains that the conventional threshold-based technique is not capable of denoising M-ary quadrature amplitude modulated (M-QAM) signals having multilevel wavelet coefficients through wireless fading channels. A detailed step by step wavelet decomposition and reconstruction processes are discussed here to transform a signal function into wavelet coefficients using simulation software like MATLAB. A 16-QAM modulated symbol through a Rician fading channel is weighted by a control variable of complex form to force the mean of each detail coefficient except low frequency component to zero to enhance noiseless property. The bit error rate (BER) performance of the simulation results are furnished to show the effectiveness of the proposed technique. The root mean square of the deviation of the reconstruct signal from the original signal is used to express the effectiveness of the proposed technique. The traditional denoising provides very high value (above 90%) of the percentage root mean square difference (PDR) and the proposed technique provides only 10% PDR value for the symbol through a noisy channel. The result of the simulation study reveals that the BER performance can be increased using an appropriate control variable to force the mean of each detail coefficient to zero.

The signal transmitted through a wireless channel may arrive at the receiver through a number of paths with different amplitude, phase, and time delay due to multipath fading. The relative movement of either transmitter or receiver or both causes time varying multipath fading. Equalizer is used to minimize the fading effect, but the design complexity of the equalizer increases with the increase of data rate. Wavelet decomposition is in use in the area of image processing, image compression, segmentation, and denoising [

In this paper, the authors attempt to apply wavelet decomposition technique to generate wavelet coefficients of a noisy signal passing through a fading channel. The multipath fading channel has been modeled recently as reported in [

The organization of the paper is as follows. In Section

A QAM bandpass signal

Rician fading channel.

The carrier frequency is shifted from the actual one due to the relative movement of either transmitter or receiver or of both. The resultant received signal frequency is given by

pdf of Rician channel and rf represent Rician factor.

The wavelet transform provides the time-frequency representation of the signal through decomposition by passing the time domain signal through various high-pass and low-pass filters. Each filter gives output signal of various frequency bands. The wavelet coefficients after the decomposition process can be used for further processing to obtain the desired level of signal.

The coefficients are the function of scale and position and are the sum over the signal time multiplied by scale and shifted version of the wavelet function (_{ a,b} is defined as

The family

Now let us define the following equations:

Decomposition of

Similarly, the reconstruction of

The reconstruction step is shown in Figure

Wavelet reconstruction.

Multiresolution analysis analyze the signal in different frequency band and enables to observe signal in both time and frequency domain. The three level multiresolution analysis of

Wavelet multiresolution analysis.

The analysis gives the three detail coefficients

Multiresolution reconstruction.

The multiresolution reconstruction produces final three details (

Wavelet denoising is used to predict approximate detail coefficients by allowing minimum error between the detailed coefficients of threshold noisy signal and the original. A noisy random signal is represented as

Wavelet denoising of a signal

In the denoising technique, let the detail coefficients have two levels a and b as in Figure

Wavelet coefficient and threshold level.

A modulated signal

A complex weighting vector

The noise and interference associated with the wavelet detail coefficient can be discarded using the proposed denoising technique as in (

Wavelet denoising in communication signal processing.

Wavelet denoising can be used in antenna diversity technique to obtain better quality signal through a noisy channel. In antenna diversity, signal is transmitted through more than one antenna and received by a single antenna, on the other way one antenna transmits signal and more than one antenna receive the signal. The first process is called transmit diversity and second is called receive diversity. A combiner is used at the receiver to add the entire incoming signal in phase or search the path having highest signal strength [

Wavelet denoising in antenna diversity.

The simulation results in MATLAB environment of the BER performance of the AWGN channel for the 16-QAM symbol is shown in Figure

BER performance through AWGN channel.

BER performance through Rician channel.

The control variable in antenna diversity is used to reduce the noise level by a factor more than the previous case because diversity provides some noise reduction performance. Here, the BER performance in antenna diversity for the control values of values

BER performance in antenna diversity.

PDR of the reconstructed signal through a fading channel.

Three main issues regarding wireless signal denoising through a multipath fading channel are addressed in this paper. Firstly, the wavelet decomposition and reconstruction of a 16-QAM symbol through a noisy channel using MATLAB simulation software. The BER performance of a modulated signal through AWGN and Rician channel and the performance using wavelet denoising technique for the same signal through the same channel is the same as shown from Figures

The simulation result shows that the BER performance is increased with increasing tendency of the mean of the detail coefficients close to zero by selecting appropriate control variable as shown in Figures

In the future, the analysis can be done to search for far better a control variable depending on the condition of the wireless channel characteristics to obtain far more accurate results. The proposed technique can be used in multiple input multiple output (MIMO) case to send image signal at very high date rate with far better BER results through WiMAX physical layer.