Noise analysis and massive MIMO modelling in VLC for 5G networks using EKF with SCFDM

Visible Light Communications (VLC) is the type of communication, which processes high-speed data transmission using the visible Light Emitting Diodes (LED). The VLC acts as an important supplementary that is used to define the hotspots for heterogeneous networks and plays an important role for 5G networks in wireless communications. However, performance of visible light systems is affected by various noises and Allan variance is used to analyze such noises in 5G networks. The Massive Multiple-Input and Multiple-Output (M-MIMO) technique is used for noise modeling which utilizes the mitigation circuit to find whether the noise is white noise, shot noise, random walk noises or typical noises. The existing Kalman Filter approach failed to attain the required bandwidth and higher spectral efficiency. Therefore, to achieve high data rates, the spectral efficient technologies such as Single Carrier Frequency Division Multiplexing (SCFDM) is performed in the research. The Allan Variance is utilized for analyzing the time-series that extracts the noise features of the data and the major noise is verified and considered by the M-MIMO technique. The present research uses the Extended Kalman Filter (EKF) which determines the observation models and the state transition that does not need linear functions to define the states. The proposed SCFDM was constructed based on the VLC for 5G networks that analyzes in terms of Bit Error Rate (BER) and Signal to Noise Ratio (SNR). The proposed SCFDM obtains a high SNR of 14% for the channels with white LED option when compared to the existing methods.


Introduction
In recent years, Optical Wireless Communication has received the huge attention of researchers due to its visible light spectrum in the wireless communication and also it offered a high bandwidth for high speed data transmission in wireless communication [1]. Additionally, it is possible to elaborate the usage of transfer data at an indoor optical wireless communication which carries the intrinsic characteristics of LED in VLC. To enhance the performance of the communication link, an optical MIMO communication is setup to achieve a high data rate transmission for mitigating shadow effects through indoor communication [2]. MIMO with OFDM is utilized for Optical wireless Communications that increase the data rate and spatial gain [3,4]. The OFDM and its modified versions modulate intensity that are directed to determine the intensity behaviour of VLC channels [5]. However, the intensity modulation and direct detection of VLC systems limit the direct application of MIMO and OFDM theory from wireless communications [6]. A dominant noise source is embedded on wireless optical channel which induces a shot noise in an indoor wireless optical channel which is being modelled with an Additive White Gaussian Noise (AWGN) [7]. An additive noise is added to the MIMO-VLC system such as constant stray light noise, shot noise, thermal noise, clipping noise, readout noise [8,9] to increase the Bit Error Rate (BER) of the system. A multipath channel model for MIMO-VLC was developed in the existing methods to improve the channel capacity by performing the combination of M-MIMO-OFDM. In order to analyze such noises, VLC system uses Allan 1 3 variance for noise modelling and the mitigation circuit finds whether the noise is white noise or shot noise or random walk noises. Inside the mitigation circuit, digital signal processor is computed using Kalman filter. The SCFDM is proposed in VLC to decrease the complexity of the channel capacity and also it mitigates the noise using MIMO-OFDM. The time-correlated noises that existed in the VLC system are analyzed in the experimental studies.
The organization of this research paper is given as follows: Sect. 2 analyses the various research papers on noise detection in VLC systems. A detailed explanation of the proposed SCFDM is given in Sect. 3. Section 4 discusses the results in terms of quantitative and comparative analysis. The conclusion and future work of the proposed method is explained in Sect. 5.

Literature review
The various noises degrade the optical signal during transmission in the VLC system and this section reviews about distinct methodologies that were implemented to remove the noises in MIMO.
Li et al. [10] developed a multi-layered optical OFDM for high spectral efficiency in the visible light communication system. The noises such as AWGN, shot noise and thermal noise were analyzed in the developed system. The developed schemes were employed using Generalized Spatial Modulation with MIMO that performed coded modulation for the optical signals. However, the developed optical OFDM attained bandwidth utilization and it failed to achieve spectral efficiency at higher rate.
Farahneh et al. [11] developed an Adaptive optical OFDM scheme in the VLC system that executed by a Vehicular communication network for realistic environment. The developed model showed an improvement in data rates up to 50 Mbps that achieved BER reduction under LOS and non-LOS conditions (high noise). The results obtained from the developed model showed the increase in data rate up to 50 Mbps with minimized BER under LOS and non-LOS conditions. However, the effect of various weather conditions such as rain, fog were not taken into consideration in this developed method.
Li et al. [12] analysed the spatial correlation for imaging MIMO operated underwater VLC. The channel capacity for the developed model consisted of upper bounds to solve power allocation problems. The added noise such as thermal noise and shot noise were removed from the developed model to improve the overall performance. The water injection method was utilized to achieve SNR at lower rates under the same channel. However, increased SNR values of the system lead to a power allocation problem during water injection.
Dang et al. [13] developed a Novel Receiver for Asymmetrically Clipped Optical (ACO) OFDM in VLC. The developed ACO-OFDM are distorted due to the presence of subcarriers with the help of clipping noise. The novel receiver collected a minimum MSE which exploited the subcarriers to improve the BER performance. In general, the developed model showed highest complexity in the ACO-OFDM which lowered the system performances.
Abdulkafi et al. [1] developed a 2 × 2 imaging MIMO system which was designed based on LED VLC that employed a space balanced coding for Positive Intrinsic Negative (PIN) array reception. In the developed model, noises such as AWGN and phase were added and modelled using PIN array reception. However, this developed model failed to achieve higher data and transmission for long distance system.

Proposed system
An overview of the proposed VLC model is shown in Fig. 1.
The VLC system consists of SCFDM Transmitter, DC Bias Circuit, LED, Photo detector, Allan Variance, Noise Mitigation circuit, Kalman filter, SCFDM Receiver and random noises like white noise. The present research is efficient to analyze the noise during data transmission using Allan variance. The photoelectric sensor is used in this proposed SCFDM model to influence the VLC signal and other noises.

Allan variance for noise measurement
The noise measurement modules are used in the developed model for estimating Allan variance at every light source. The time-series analysis method uses Allan variance for extracting the noise and to remove the unwanted noise data. Allan variance is used for reducing random Gaussian noise as it is positively related to the power of the received signal due to its dominant noise component. The RMSE values obtained by the randomly generated drift was based on the average time equation [14]. Allan Variance method is used to perform data instability with respect to distinct sampling time. The principles that are needed to be followed for noise measurement are given as follows: N S represents the consecutive sampling data points, t 0 is a sampling interval.
The n consecutive sampling points at the first points are used for a cluster n < where k = 1, 2, … , n.
The difference among the two adjacent data clusters are used for the next step by using the equation given in Eq. (2).
The Allan Variance consists of clusters and the length of clusters is represented in Eqs. (3) and (4).
The continuously occurring random process is defined as the Power Spectral Density (PSD) which is represented as S X (f ) . The relationship between the Allan Variance and the PSD is expressed in Eq. (5).
The Allan Variance is used to detect Gaussian white noise that is calculated using Eq. (6).
Here, N indicates the Gaussian white noise coefficient. The Allan Variance for the curve slope is − 1 2 . Where N is represented in Eq. (7).
On the basis of Eq. (6), a linear log of T is used, where is used as a percentage error. Allan Variance is estimated using T as a specific cluster length expressed using the Eq. (8).
Allan Variance obtains an accurate high sampling time.

Extended Kalman filter (EKF) algorithm for noise mitigation
The EKF is an improvised version of Kalman filter which linearizes the values of covariance and mean. The welldefined transition models are considered as a theory for Fig. 1 Overview of the proposed method nonlinear state estimation and for navigation of the systems. Therefore, major noise is particularly verified and considered for noise mitigation as the filters are applicable for real-time tracing. The mathematical expressions for the EKF to remove noise is done using Eqs. (9) and (10).
Here w k and v k are the process and observation noises and u k is the control vector.
f is the function used to calculate the present state based on the previous estimation of function.
h is the function is used to compute the predicted measurement from predicted states. The Kalman filter and particle filter performs the operation at the noise position to make the noise well fined. The present research uses EKF that performs dynamic test, thereby compensating for the difficulty of Kalman filter that works for non-linear systems. The EKF is transformed using Taylor series that obtains an approximation linearization model [15]. The co-variance matrix R is formed based on the signal noise for Allan Variance utilization. The working process of EKF is explained as follows, Input: s k−1 , P k−1 is the state for the covariance at time phase k − 1. m k time step measurement at time k.

Output:
s k , P k state for the covariance at time phase k.

Process:
1. The initial state is set at k that is based on the start point location to provide the values using ALSQ (Adaptive Least Square) algorithm. The initial covariance is set as P k with non-zero matrix R and it also consists of noise element noise . 2. Linearization process is performed using the Eq. (11).

For
. End For 10. Final.

Single channel frequency division multiplexing model
The block diagram of the SCFDM system in VLC is represented in Figs. 2 and 3. Figure 2 shows the diagram of the SCFDM system in VLC (Transmitter) and Fig. 3 shows the diagram of the SCFDM system in VLC (Receiver). The proposed SCFDM-VLC system is used for mapping and it generated the sequence into 64 sub-carriers using BPSK and 16-bit QAM modulations. The PSK is used as a common digital modulation where the data transmission is performed to alter the phase of signal reference frequency. The QAM is used for both amplitude components and phases that consider the reference frequency signal. The QAM is utilized for both amplitude and phase components that deliver to form modulation at high level spectrum efficiency. The Selective Mapping (SLM) technique is applied Fig. 2 The diagram of the SCFDM system in VLC (Transmitter) for PAPR reduction that chooses the phase rotation factors effectively [9,16]. The SCFDM-VLC system used to transmit the sub-carrier signals which makes the small bandwidth difficult for few concerns such as demodulation errors, Inter-Symbol Interference (ISI), and orthogonality between the sub-carriers. In order to overcome such consequences, the Cyclic Prefix (CP) is used for the channel that estimates the time length based on the delay. Figures 2 and 3 indicates the graphical depiction of proposed SCFDM based VLC system. The zero forcing operation is mathematically denoted in Eq. (12).
Here X is transmitted signal, n is noise term, Y is the frequency of received signal, C is frequency response for the channel.
The frequency response of the channel is defined using the training sequences. The equalizer coefficients reduce MMSE criterion where ISI and additive noise affect the system. The equalizer coefficients are minimized using Eq. (13).
where 2 w is variance obtained using additive noise, H is channel matrix for the transmitter and receiver, and 2 X are data symbols that are transmitted.

White LED characteristics
In the present research, white LED is used as a lighting device with the property of robustness, high lifetime, energy efficiency and decent temporal stability. The White LED consists of two features such as luminous intensity and transmitted optical power. The luminous intensity is denoted based on the white LED brightness which is calculated using the Eq. (14).
where is luminous flux, luminous flux e is denoted using Eq. (15).
where K m is the maximum visibility having the range of 680 lm/W at = 555 nm , v( ) is known called as luminosity curve. The energy flux integral e at the transmitted optical power P t for all the direction is expressed using the Eq. (16).
where ∧ max and ∧ min are sensitivity curve for the photodiode. At the angle luminous intensity is expressed mathematically using the Eq. (17). irradiance, d is known as the distance between the detector surface of an LED, m is known as the lambertain emission expressed mathematically using the Eq. (19). The parameter settings of white LEDs used in this research are shown in the Table 1 as follows:

PAPR reduction using selective mapping
Initially, the SCFDM -VLC is divided into equal spaced signals to achieve lesser signal distortions for wireless communication system that achieves data transmission at higher rate. The input frequency domain sequences are denoted mathematically using the Eq. (20) where x is an input data, n is data dimension. The signals are modulated from the input for every time domain set which is computed using the SCFDM-VLC that encoded the digital data for each and every carrier frequency. The processed IFFT signals are expressed mathematically using the Eq. (21).
where kN is value for the single carrier frequency, X N is the signal that is processed using IFFT.
The high power generation is represented based on the calculation of the ratio between the average and maximum power that is expressed mathematically using the Eq. (22).
where E | | S N | | 2 is known as the average power generated for X N . The IFFT output applied for SLM is calculated using the Eq. (23).
where x N known modified input signal at L = 5.

Sub-block partition optimization using BCS algorithm
The BCS algorithm is an optimization based algorithm that mimics the crow's behaviour. For the optimization algorithms, the crows position i is specified using the mathematical Eq. (24).
From the Eq. (24), i is the value which ranges from 1 to N, t ranges from 1 to t max.
Similarly, the crows memorize the best locations or positions where it will get best food source which is denoted in Eq. (25). The BCS algorithm is used to update the position of crows in two dissimilar ways as mentioned in Eq. 25. where fl i,t indicated as flight length of crow, i is the iteration at t, and r j is represented as random number that ranges between [0, 1].
Case 2: Crow j knows crow i position. When the crow j distracts crow i by moving elsewhere in the search space to protect its hiding place, a novel position of the crow i is randomly updated as expressed in the Eq. (27).
where AP i,t is known as the Awareness Probability (AP) of crow at the j generation.

Pseudo code of BCS algorithm
Initialize, the crow's position N and the memory of every crow (23)

Results
The results for the proposed SCFDM is designed based on the VLC system which are simulated using MATLAB (2018a). The results obtained for the performance metrics are compared against the modulation techniques which includes 16 bit-QAM and BPSK. These are evaluated in terms of MMSE and Zero forcing that evaluates the efficiency of the proposed method. The main simulation parameters are presented in the Table 2.

Performance measure
In SCFDM, BER is evaluated using received bits along with AWGN. The AWGN is altered by performing distortion, synchronization errors, interference and noise. The SNR defines the ratio of Signal Power to the Noise Power (dB) and is expressed in Eq. (28).

Quantitative analysis
The parameters used for simulation environment are shown in the Table 2. The LEDs receive a signal and are simulated by using the Photo Detector Channel model having the random Gaussian noise, whose noise is having the variance which is set by using the Allan Variance which obtains the results for the field tests. The results which are obtained for positioning before and after the denoising are measured as shown in the Table 3.
In the proposed systems, the 16 × 16 elements evaluated in terms of SNR is compared to the existing system and simulations results are shown in Figs. 4 and 5. However, the values are mainly affected by the geometry distribution between the receiver and LED. The proposed denoised process improves the SNR rate of the VLC system when compared with the Existing Conventional SCFDMA. The SNR analysis of the proposed system for 16X16 elements is given in Table 3.  Correspondingly, Table 4 analyzed the performance of the proposed system in light of SNR for 32 × 32 elements. We use least square technique to minimize the fitting error due to gaussian noise. Table 4 consists of SNR values obtained for both existing and proposed method that are plotted in the graph as shown in the Fig. 6. Similarly, Table 4 consists of SNR values that are plotted in the graph for the existing Conventional SCFDMA method and the proposed SCFDMA which is represented as shown in Fig. 7. Table 5 shows the tabulation for BER versus SNR for hybrid Kalman Filter and SCFDMA for 16 × 16 elements. Figure 8 shows the BER versus SNR for hybrid Kalman Filter and SCFDMA for 16 × 16 elements. Table 6 shows the values for BER and SNR using the hybrid Kalman Filter for 32 × 32 elements. The values obtained from the Table 4 is graphically represented in Fig. 9 for hybrid Kalman Filter and SCFDMA.    Table 7 shows the performance executed by the existing ALSQ and EKF. The results obtained by the developed model out performed using an average filter and Allan Variance. The improvement of the SNR in existing method are that ALSQ and EKF [15] showed 19% improvement, Modelling in Visible Light Communication Using Allan Variance [14] showed 9% improvement whereas, the proposed method showed 14% improvement in SNR. Table 7 showed improved BER performance for the 6 m × 6 m × 4 m theoretical room dimension. The transmission rates of 400 Gbps is obtained when white LED is used in the dimension of 6 m × 6 m × 4 m.

Conclusion
In the research, the proposed EKF-SCFDMA model was used for noise measurement of visible light system based on the Allan Variance. A realistic VLC for 5G networks was built and field tests were developed in the simulated study that measured and evaluated the VLC noise in M-MIMO using the proposed scheme. The obtained results showed   that two types of noises namely white noise and short cluster time noise were dominant in the system. The results for simulation showed that Allan Variance obtained better performance when compared with existing methods in VLC for 5G networks. According to the field static tests, the proposed VLC system obtained SNR of 43.12 dB in 32 × 32 elements with an improvement of 14% with the existing method. The proposed SCFDMA showed that the EKF with Allan Variance removed the noise components to improve the performance in terms of SNR ratio. The results were transparent and showed that Allan Variance technique was efficient for measuring noises in VLC 5G networks. The simulation field tests showed improved SNR for room dimension of 6 m × 6 m × 4 m. In the future, the performance evaluation can be improved for large scale environment.