# Optimized threshold calculation for blanking nonlinearity at OFDM receivers based on impulsive noise estimation

- Zehra Ali
^{1}, - Ferheen Ayaz
^{2}Email author and - Chang-Soo Park
^{1}Email author

**2015**:191

https://doi.org/10.1186/s13638-015-0416-0

© Ali et al. 2015

**Received: **23 December 2014

**Accepted: **18 June 2015

**Published: **14 July 2015

## Abstract

Impulsive noise (IN) degrades the performance of OFDM-based communication systems. Performance degradation is usually measured in terms of signal-to-noise ratio (SNR) and symbol-error rate (SER). To improve the performance of the system of OFDM receivers, one of the effective methods is to use blanking nonlinearity. In this method, the samples whose magnitudes exceed a certain fixed threshold are considered to be IN-affected and are therefore blanked. A fixed threshold does not always determine the IN-affected samples truly for all probabilities of IN occurrence. This paper proposes an optimized threshold-calculation method for blanking nonlinearity which is based on distribution characteristics of the received signal, i.e., mean, median, and peak. The proposed method can calculate an optimized threshold for all probabilities of impulsive noise occurrence. Simulation results show over 2.2-dB gain in SNR and lower SER by using the proposed method as compared to fixed threshold.

## Keywords

## 1 Introduction

Impulsive noise (IN) is one of the most challenging factors of performance degradation in power line communications [1]. One of the most widely used modulation techniques for PLC and wireless/wired channels is orthogonal frequency division multiplexing (OFDM). It offers many advantages like increased data rates, robustness in multipath, and resistance to noise [2].

Various methods to find optimal threshold have been reported in [7] and [8]. However, these methods are purely theoretical. A direct relationship between the peak of the transmitted signal and optimal threshold is derived in [8], but it is not feasible to determine the exact peak of transmitted signal of OFDM receivers. In this paper, we propose an optimized threshold-calculation method for blanking nonlinearity based on impulsive noise estimation (INE) by using distribution characteristics of the received signal, i.e., peak (maximum value), median, and mean. The use of median and mean in filtering and removing impulsive noise has already resulted in many well-established algorithms in [9] and [10]. The optimized threshold-calculation method proposed in this paper is independent of the probability of IN occurrence and can be adapted to a receiver even if the probability of IN occurrence in the channel is not known. Since the proposed method determines the optimized threshold using the characteristics of the received signal, instead of the transmitted signal, it can be used in practical scenarios.

The paper is organized as follows. Section OFDM system model and optimized threshold-calculation method describes the system model and optimized threshold-calculation method. The system performance of the proposed optimized threshold (OT) is compared with a fixed threshold (FT) by simulations at different probabilities in Section Simulation results and discussions. Conclusions are presented in Section Conclusions.

## 2 OFDM System model and optimized threshold-calculation method

### 2.1 OFDM system model

*s*(

*t*) is obtained by taking the inverse Fourier transform of the frequency-domain signal by using

*S*

_{ k }denotes the frequency-domain signal, \( j=\sqrt{-1} \),

*N*is the number of subcarriers, and

*T*

_{ s }is the active symbol interval. The transmitted signal is passed through an additive transmission channel, including additive white Gaussian noise (AWGN) and additive IN. AWGN is denoted by

*w*

_{ k }and has variance. \( {\sigma}_w^2=\left(1/2\right)E\left[{\left|{w}_k\right|}^2\right] \). IN is denoted by

*i*

_{ k }and is modeled as a Bernoulli-Gaussian random process [4] as follows:

*b*

_{ k }is the Bernoulli process of sequence ‘

*b*

_{ k }

*=*1’ or ‘

*b*

_{ k }

*=*0’ with probability of

*p*or 1 −

*p*, respectively, and

*g*

_{ k }is the complex–zero mean white Gaussian noise with variance \( {\sigma}_i^2=\left(1/2\right)E\left[{\left|{g}_k\right|}^2\right] \). Thus, the noisy channel can be characterized by the signal-to-AWGN ratio \( SNR=10{ \log}_{10}\left(1/{\sigma}_w^2\right) \) and signal-to-IN ratio \( SINR=10{ \log}_{10}\left(1/{\sigma}_i^2\right) \). The received time-domain signal (

*r*

_{ k }) can be expressed as

*s*

_{ k }=

*s*(

*kT*

_{ s }/

*N*) is the sampled OFDM signal in time domain with a variance of \( {\sigma}_s^2=\left(1/2\right)E{\left|{s}_k\right|}^2=1 \). The received signal is passed to the nonlinear preprocessor. The output of the nonlinear preprocessor

*y*

_{ k }is then fed to the OFDM demodulator for further processing and is represented in [5] as

*T*is the blanking threshold and

*k*= 0, 1, …,

*N*− 1. The threshold value is a crucial parameter in blanking nonlinearity as it is responsible for deciding which signal is to be blanked [6].

### 2.2 The proposed optimized threshold-calculation method

## 3 Simulation results and discussions

The computer simulation of the OFDM system is carried out with 16 QAM modulation, SNR = 40 dB, SINR = −15 dB, number of subcarriers, *N* = 10^{5}, \( {\sigma}_w^2=\left(1/2\right)E\left[{\left|{w}_k\right|}^2\right] \), and \( {\sigma}_i^2=\left(1/2\right)E\left[{\left|{g}_k\right|}^2\right] \).

*p*) of IN occurrence is considered to be

*p*= 0.01, 0.03, and 0.1, which implies that 1, 3, and 10 % of the received samples will be affected by IN, respectively. Therefore, with 10

^{5}subcarriers, the average number of IN pulses received within each OFDM symbol is (pN), i.e., about 1000, 3000, and 10,000 IN pulses per OFDM symbol for

*p*= 0.01, 0.03, and

*p*= 0.1, respectively. The output SNR is obtained by

*p*= 0.1, 1.16 dB for

*p*= 0.01, and 1.73 dB for

*p*= 0.03. Figure 8 shows that the relative SNR gain is never less than 0 for all probabilities. This means that blanking nonlinearity with OT never results in lower SNR than blanking nonlinearity with FT. To further check the accuracy of the proposed method, the relative SNR gain was also plotted simulating a 64 QAM modulation. Figure 9 shows that the gain is always greater than 0 even with higher modulation index.

*p*= 0.01, 0.03, and 0.1, respectively. Table 1 shows that the minimum SER achieved by OT is always lower than that achieved by the FT method in all IN scenarios. The SER of the system is given in Eq. 11 as in [6] as follows:

Minimum SER achieved by blanking nonlinearity with OT and FT

| OT | FT |
---|---|---|

0.01 | 5.6537*10 | 7.0*10 |

0.03 | 5.53*10 | 9.11*10 |

0.1 | 3.49*10 | 4.919*10 |

Where *m* is modulation index and *Q* is *Q* function.

## 4 Conclusions

The optimized threshold for blanking nonlinearity for achieving higher SNR and lower SER is proposed. As the optimized threshold is determined according to the peak, mean, and median of the signal, it gives better results and better system performance regardless of the probability of impulsive noise occurrence. On the other hand, a fixed threshold is independent of the signal characteristics. Therefore, one fixed threshold is not suitable for all the received signals with different probabilities of impulsive noise which may occur in practical scenarios.

Moreover, in this paper, the optimum range for setting γ is introduced. Changing γ within the given range does not cause a greater change in SNR. The SNR remains higher than that achieved by setting a fixed threshold. Whereas, changing the conventional fixed threshold results in a drastic change in SNR.

## Declarations

### Acknowledgements

The authors are extremely thankful for the support and facilities provided by Gwangju Institute of Science and Technology, Gwangju, South Korea under the supervision of Professor Chang Soo Park.

## Authors’ Affiliations

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## Copyright

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