An effective communication application necessitates the cancellation of Impulsive Noise (IN) from Orthogonal Frequency Division Multiplexing (OFDM), which is widely used for wireless applications due to its higher data rate and greater spectral efficiency. The OFDM system is typically corrupted by Impulsive Noise, which is an unwanted short-duration pulse with random amplitude and duration. Impulsive noise is created by humans and has non-Gaussian characteristics, causing problems in communication systems such as high capacity loss and poor error rate performance. Several techniques have been introduced in the literature to solve this type of problem, but they still have many issues that affect the performance of the presented methods. As a result, developing a new hybridization-based method is critical for accurate method performance. In this paper, we present a hybrid of a state space adaptive filter and an information coding technique for cancelling impulsive noise from OFDM. The proposed method is also compared to Least Mean Square (LMS), Normalized Least Mean Square (NLMS), and Recursive Least Square (RLS) adaptive filters. It has also been tested using the binary phase-shift keyed (BPSK), four quadrature amplitude modulation (QAM), sixteen QAM, and thirty-two QAM modulation techniques. Bit error Rate (BER) simulations are used to evaluate system performance, and improved performance is obtained. Furthermore, the proposed method is more effective than recent methods.

The Orthogonal Frequency Division Multiplexing (OFDM) is a digital modulation technique which splits single wideband into narrowband or smaller dividing into parallel bit streams. The narrow band stream of each is modulated separately on different orthogonal sub-carriers and is then frequency multiplexed. OFDM is extensively used in wireless applications due to its high data rate and higher spectral efficiency. Moreover there is more resistance of orthogonal frequency-division multiplexing (OFDM) to IN inherently than the modulation of single carrier, still performance of system is degraded if the power of IN is exceeded with specified threshold and it affects all subcarriers [

OFDM based communication systems are usually corrupted by Impulsive noise, unwanted pulses of short duration that have random amplitude at random duration. Impulsive noise is human made noise having non Gaussian characteristics, exhibiting adverse effects in communication systems such as great capacity loss and poor error rate performance [

The paper’s organization is as follows, in Section 2 related work is described. Section 3 explains proposed methodology, Section-4 presents decoding

Various techniques have been presented in literature for the suppressing impulsive noise from OFDM systems. Researchers are finding solutions for mitigating impulsive noise from OFDM systems, thus improving performance of the system by means of Bit Error Rate (BER) and Mean square error (MSE). Impulsive noise mitigation through conventional method is median filter with some signal degradation was proposed in [

In OFDM, for correction of impulsive noise based on Reed Solomon (RS) code for broadband power line transmission has been proposed where the decoding algorithm with emphasis on low implementation and complexity [

In the [

In this research, suppression of impulsive noise is investigated by implementing hybrid LDPC code and SSRLS on OFDM system.

A multicarrier modulation (MCM) system i.e Orthogonal Frequency Division Multiplexing (OFDM), with multiple sub bands and multiple sub carriers where transmission is parallel. This multi carrier transmission divides the single wideband into number of narrowband or smaller dividing into parallel bit streams. Narrow band stream of each is modulated on carrier and then is frequency multiplexed. The proposed block diagram of SSRLS and LDPC coded OFDM system is demonstrated in

Impulsive noise results in different type of sources like inadequate synchronization in communication, electromagnetic system, switching noise etc. The Impulsive noise sequence can be demonstrated by modelling it using Bernoulli Gaussian model. In this model, Gaussian distribution is used to model amplitude and occurrence of all impulses

From the above equation,

Probability density function of a Gaussian model of impulsive noise with zero mean having amplitudes distributed randomly and

The mean

Auto correlation of impulsive noise as binary state can be expressed as

As Kronecker delta function is represented by symbol

Adaptive filters are used for the reduction of noise.

The Recursive Least Square (RLS) adaptive filter finds coefficient of filter recursively, useful for minimizing a cost function that is concerning to deterministic input signal. In RLS estimation of matrix autocorrelation is utilized for de correlating the present (current) input data. RLS exhibits computational complexity and extremely fast convergence when compared with all variants of Least Mean Square. In RLS, where wt denotes the filter weights are recursively updated using the equations below [

From equation,

An extension to RLS method is State Space Recursive Least Squares (SSRLS). Usually represented using state space and used for noise reduction. Its performance can be evaluated in presence of impulsive noise background. The sinusoidal model for implementation of SSRLS form II filter is given in [

where

Low Density Parity Check codes (LDPC), linear error correcting codes used for purpose of transmitting an input signal over a noisy channel. One of the great uses of this code is that it performs near to Shannon limit and thus has low decoding complexity. A low-density parity-check code is one that is described by a parity-check matrix that has the following attributes: Each column has a small fixed number j geq 3 of l’s, but each row includes defined number k > j of l’s. For a fixed amount and fixed j, the usual minimum range of these codes rises linearly with block size. When combined with maximum likelihood decoding over just a sufficiently silent binary-input symmetric channel, the normal rate of decoding error decreases exponential with block length for a fixed rate and fixed j. In this paper, we consider a random sequence of bits generated and coded bits are modulated using 4 array QAM symbols and orthogonally is maintained by applying fast Fourier transform on OFDM signal. LDPC codes are represented by a matrix having almost O’s and very small number of 1’s. LDPC code mentioned here by parity check matrix H as illustrated an example in

Suppose

In this paper SPA algorithm is used for decoding, where Initialization is based on the probabilities of the modulated signal and probabilistic properties of the channel noise. The next step is to update the message, where the message bits are based on the observed value of the bit nodes by computing bit to constituent nodes and some of the messages transmitted to that bit nodes from the corresponding constituent nodes. The last step is decision, where the decoding is successfully done if and only if decision condition is satisfied or otherwise it switches direct to upcoming message update iteration.

When maximum number of iteration is done i.e., decoding is completed, the message signal is extracted.

Performance analysis of OFDM is done by applying LDPC code and SSRLS adaptive filter.

Parameters | Value |
---|---|

Subcarriers number | 52 |

Cyclic prefix size | 16 |

FFT size | 64 |

Modulation | 4-QAM |

Modulation technique used is 4-QAM, by generating random data. In this paper irregular LDPC code size of 525 × 1050 is created where the H matrix has m columns and n rows. The coding rate defined here is

Parameters | Value |
---|---|

Information bits | 1050 |

Modulation | 4-QAM |

Encoding | LDPC |

Code rate | |

Decoding | SPA |

Maximum iteration | 20 |

In this paper impulsive noise is generated as per the mentioned steps in [

Parameters | Symbol | Value |
---|---|---|

Total time | 8000 | |

Sampling frequency | 10 | |

Log-amplitude mean | A | 10 dB |

Additive Gaussian noise mean | 0 | |

Log-amplitude standard deviation | B | 5 dB |

Gaussian noise standard deviation | σ | 20 |

In this paper, AWGN and IN (impulsive Noise) are introduced into the OFDM system. A corrupted signal is first encoded using LDPC code and then filtered using SSRLS adaptive filter to reduce noise. The results of the adaptive filter and a signal known as the required signal are compared. As a result, the difference between the two signals generates an error signal, and the filter recursively upgrades its weights to mitigate the effect of the error signal. The performance of various adaptive filters, such as LMS, NLMS, RLS, and SSRLS, is compared. For NLMS algorithm, the step size parameter’s range i.e., µ lies in between 0 to 1 and the value to be selected is 0.01. While for RLS forgetting factor i.e., λ is calculated to be 0.98 from the range 0.98 to 1.

The BER vs signal to noise ratio (SNR) of the OFDM signal is depicted in

Performance of amalgamated LMS and LDPC is better than LMS filtering method. Furthermore

Moreover, for reduction of IN, RLS LDPC coded OFDM’s performance is compared with LDPC OFDM and RLS OFDM in

The hybrid method i.e., SSRLS and LDPC outperforms than RLS LDPC as well as NLMS LDPC coded OFDM system. The comparison among hybrid combination of LMS, NLMS, RLS and SSRLS based LDPC code is shown in

For

This paper presents a hybrid combination of adaptive filters amalgamated LDPC coded OFDM system. Because of recursive parameters of adaptive filters such as Normalized Least Mean Square (NLMS), Recursive Least Square (RLS), State Space Recursive Least Square (SSRLS), and LDPC code, the presented scheme exhibits better impulsive noise reduction in OFDM systems. Furthermore, the comparison was made using various modulation techniques such as BPSK, 4-QAM, and 16-QAM. The results demonstrated the good performance of the hybrid technique through lower BER. The simulation results show that SSRLS LDPC coded OFDM outperforms SSRLS, RLS, and NLMS-based OFDM. Individual filters with LDPC code mitigated impulsive noise in OFDM better than the proposed technique. In the future, this technique can be applied for several computer vision research applications such as medical [

This research was supported by the

The authors declare that they have no conflicts of interest to report regarding the present study.