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This work aims to study the effect of unwanted peaks and enhance the performance of wireless systems on the basis of tackling such peaks. A new proposition has been made based on wavelet transform method and its entropy. Signals with large peak-to-average power ratio (PAPR) will be examined such as the ones that are considered as the major Orthogonal Frequency Division Multiplexing (OFDM) systems drawbacks. Furthermore, aspatial diversity Multiple-Input Multiple- Out-put (MIMO) technology is used to overcome the complexity addition that could arise in our proposition. To draw the best performance of this work, a MATLAB simulation has been used; it is divided into three main stages, namely, MIMO-OFDM symbols’ reconstruction based on wavelet transform, a predetermined thresholding formula, and finally, moving filter. This algorithm is called Peaks’ detection based Entropy Wavelet Transform; PD-EWT. Based on the simulation, and under some constrains such as the bandwidth occupancy and the complexity structure of the transceivers, a peak detection ratio has been achieved and reaches around 0.85. Comparing with our previously published works, the PD-EWT enhances detection ratio for 0.25 more peaks.

The overwhelming huge data due to the highly demand for the various wireless and cellular system’s applications attract the researchers’ interest to handle these effects on the wireless systems. Thus, and during the last two decades, their attentions have been focused on the combination between the Orthogonal Frequency Division Multiplex (OFDM) modulation technique and the Multiple-Input Multiple-Output (MIMO) technology.

Therefore, we are talking a data rate of around more than 100 Mbps for such systems. The OFDM systems use the parallel transmission, while the MIMO technologies have been employed to reduce the effect of the rich scattering environments.

Moreover, the OFDM has been adopted at the both wireless and wired application to the high data rates as significant advantages over the conventional ones, and shows robustness to multipath fading and a greater simplification of channel equalization.

Furthermore, the multiple antennas have been employed to support the extraordinary data rates due to the rapid growth of the wireless systems and to make use of the rich scattered environments [

OFDM technique is considered as a multi-carrier system that utilizes a parallel processing technique and allowing the simultaneous transmission of data on many closely spaced, orthogonal sub-carriers. This is attained by making use of the Inverse fast Fourier transforms (IFFT) and fast Fourier transform. However, the peak-to- average power ratio (PAPR) is found as a major deficiency of the OFDM signal, which limits the efficiency of the non-linear devices such as the power amplifiers, mixers, and analog to digital converters. Therefore, the wavelet transform method has been used to tackle the effect of such deficiency as will be discussed in section two [

P_{peak} is the maximum power of an OFDM symbol, and P_{avg} is the average power. The PAPR can be reformulated as given in (2). T is the symbol duration, x(t) is the OFDM symbol at time, t. X_{n} is the data modulating the n^{th} sub-carrier and f_{o} is the nominal subcarrier frequency spacing. Moreover, the average power of the OFDM symbol presented in Equation (2) will be given in Equation (3):

Here, c_{v} is the magnitude of the modulated data. For the sake of simplicity;

From [

Another technique to compare with could be found in

1) Read a segment of the OFDM signal.

2) Denoise the OFDM signal from additive white Gaussian noise (AWGN) using wavelets technique [

- Applying discrete wavelet transform DWT to the noisy signal.

- Applying soft thresholding operator (wavelet shrinkage) [

- Applying inverse discrete wavelet transform IDWT to the thresholded wavelet coefficients to reconstruct a denoised OFDM signal.

In this work, the wireless systems’ performance will be drawn for the PD-EWT and compared to the previously published work in [

Let us define first the received OFDM symbol as shown below in Equation (5)

where s_{0} is the useful information, s_{1} is the interference signals. After that, the SINR expression could be deduced as

Then, the BER comes from defining the relationship between the bit error probabilities with the SINR. Thus, a mapping function could be defined through the link level simulation with the needed channel. Making use of the definition that is found in [

The rest of paper is organized as follows; the introduced structure of the proposed algorithm in the MIMO- OFDM wireless system is defined in Section 2, the simulation results are presented in Section 3, while the last section summarizes the conclusion.

From

In

The generated OFDM signal will pass through the second stage which is capable of detecting the high PAPR peaks and overcoming their effect. The whole work in this stage could be divided into four blocks as shown in

The continuous wavelet transform (CWT) is attained as a sum of time signals multiplied by a scaled and a shifted version of small wavy functions that are proficiently limited duration with an average of zero. Moreover, and if these scaled versions have been generated based on powers of two, therefore the discrete wavelet transform (DWT) will be obtained. In addition to the wavelet transforms that are based on the decomposition high and low pass filters namely wavelet packet transform is the WP. A pair of low and high pass filters is used to recognize two sequences capturing dissimilar frequency sub-band features of the original signal. These sequences are then decimated (dissembled by a factor of two). It was indicated by many works that WP features have better presentation than the DWT [

In [

H is the entropy, a_{i} are the discrete random variable, X, possible values. This equation reflects the disorder degree that the variable acquires. Then, the discrete wavelet decomposition for sampled values of the signal S(t) could be written as:

The signal S(t) is given by the sampled values, C_{j}(k) is the wavelet coefficient and limited to following frequency interval

Moreover, the wavelet entropy could be defined in terms of wavelet coefficients relative wavelet energy as follows:

E_{j} is the energy at each j resolution level, E_{total} is the sum of E_{js},

The preprocess stage:

- Remove the noise from a signal using wavelet technology.

- Perform P-level Haar wavelet decomposition of a signal (P = 8).

- Construct the approximations, CAP and the details CDP.

Zero Crossing mechanism

The entropy Calculation

Case studies based on decomposition process using the depicted flowchart in

- Case Study 1: Detect true and false local extremes points using all details coefficients (CDP1-CDP8)

- Case Study 2: Detect true and false local extremes points using details coefficients (CDP1,CDP2)

- Case Study 3: Detect true and false local extremes points using all details coefficients except (CD3, CD7 and CD8).

Thresholding process

Moving average (MA) filter.

In this section, a new technique has been proposed to allocate peaks in the OFDM signal based on the entropy wavelet packets. It is clearly seen in

P level | Entropy | Decomposition Acceptance^{*} | |||
---|---|---|---|---|---|

CDp | CAp | Summation | Original Signal | ||

1 | 13.3924 | 60.8508 | 74.2432 | 100.4268 | Accepted |

2 | 26.5319 | 32.917 | 59.4489 | Accepted | |

3 | 16.3553 | 20.7162 | 37.0715 | Not Accepted | |

4 | 8.2519 | 9.7128 | 17.9647 | Accepted | |

5 | 6.3765 | 3.2822 | 9.6587 | Accepted | |

6 | 1.6068 | 0.93369 | 2.5405 | Accepted | |

7 | 1.541 | 0.54864 | 2.0897 | Not Accepted | |

8 | 0.62314 | 0.059486 | 0.68262 | Not Accepted |

(^{*}) Accepted, if the sum of the entropies at certain level is less than the entropy above this level.

The MATLAB simulation program was performed and limited to the use of

Theoretical randomly generated test data,

Simple linear convolutional encoder,

16-Quadrature Amplitude Modulation (16 QAM) and Binary-Phase Shift Keying (BPSK),

IFFT size of 256.

The novelty in this work rises from the way of dealing with the entropy of the wavelet coefficients to determine the peaks in the OFDM signal before the transmission. For checking the system performance, two main key factors will be studied; the bit error rate (BER) and the complementary cumulative distribution function (CCDF) curves for the processed OFDM signal.

As a comparison,

The CCDF plots that are shown in ^{−3} while it was 53 × 10^{−2}. Moreover, it shows an extra 15% reduction percentage over the PAPR combating technique that is in [^{−2} to 36 × 10^{−2}.

A new proposition has been made in this paper; PD-EWT. This work introduces a new OFDM transceivers design. It is based on allocating the peaks and valleys of OFDM signal to be analyzed. In the PD-EWT, the entropy of DWT has been analyzed and used to specify those peaks. The allocated peaks then will be processed using a special thresholding algorithm to overcome its effect.

Making use the analytical derivation of this technique to build a MATLAB simulation, which ease the study of its feasibility. This is in order to enhance the MIMO-OFDM wireless systems’ performance even in a condensed Multipath channel using two different modulation techniques; BPSK and 16 QAM.

Modulation Technique | PAPR (dB) | Additional Reduction (%) | ||||||
---|---|---|---|---|---|---|---|---|

No Coding | Based SLM | Based on [ | Based on [ | SLM | Convolutional Coding | Work [ | ||

16 QAM | Case study I | 7.9 | 3.6 | 3.5 | 2.7 | 72.1 | 44.5 | 11 |

Case study II | 3.81 | 2.73 | 1.92 | 81.62 | 60 | 15 | ||

Case study III | 4.2 | 3.9 | 3.1 | 65.6 | 35.9 | 8 | ||

BPSK | Case study I | 12.3 | 5.6 | 4.1 | 3.7 | 51.6 | 32.3 | 9.8 |

Case study II | 6.4 | 3.5 | 3.2 | 62 | 51.43 | 14 | ||

Case study III | 6.9 | 4.7 | 4.2 | 42.9 | 26.5 | 9 |

This work contains three case studies based on the entropy level of the DWT. Thus, a comparison among PD-EWT, our previously published work, and the SLM has been made. The results show that we can use just the first two detailed parameters where the decomposition status after that is not accepted. From this comparison, the PD-EWT shows extraordinary promising results in allocating and combating the high peaks. The achieved performance improvement for allocating and combating the effect of the PAPR is between 8%-81% over the limitations that have been taken into consideration. Moreover, the BER for the best scenario has been reduced to 36 × 10^{−2} from 48 × 10^{−2} that has been achieved in our previously work.

Ahlam Damati,Omar Daoud,Qadri Hamarsheh, (2016) Enhancing the Odd Peaks Detection in OFDM Systems Using Wavelet Transforms. International Journal of Communications, Network and System Sciences,09,295-303. doi: 10.4236/ijcns.2016.97026