# Indoor Wavelet OFDM VLC-MIMO System: Performance Evaluation

^{*}

## Abstract

**:**

^{−3}bit error rate (BER) target. Hence, the proposed technique can be potentially executed in indoor VLC-MIMO systems.

## 1. Introduction

#### 1.1. State of the Art Regarding FFT-OFDM and DWT-OFDM

#### 1.2. Frame Work

^{−3}. In comparison with the system which uses only Pre-FDE, a communication coverage improvement by 52.6% is achieved in our system.

## 2. System Model

#### 2.1. The Transmitter

- 1.
- Firstly, the series input information is separated into N streams (according to N-transmitters), the positions of the LED modules are listed in Table 1. The data stream is converted from the data line to the data array, via a serial-to-parallel (S/P) converter.
- 2.
- The data is mapped to symbols by using quadrature amplitude modulation (QAM). The transmitter utilizes a 64 QAM digital modulation to map the serial bits into the OFDM symbols ${\mathsf{{\rm X}}}_{\mathrm{N}}\left(\mathrm{i}\right)$ as N is the LED modules number and$0\le \mathrm{i}\le \mathrm{s}-1,$ while s is the number of the parallel data stream.
- 3.
- Then, Hermitian symmetry (HS) is enforced to produce real values data.
- 4.
- 5.
- Wavelet transform for modulation is performed. As shown in Figure 1, the block named IDWT is a function in the MATLAB toolbox which utilizes Low Pass Filter (LPF) and High Pass Filter (HPF). WT utilizes filters like a vector of approximation coefficient (CA) and a vector of detail coefficients (CD). The signal is divided into sub-bands which are divided into low and high frequencies. OFDM symbol 〖Χ〗_N (i) is converted from parallel to serial. It has a vector YY that may be transposed into CA as represented in Figure 2 which is called approximated coefficients.

- A parallel-to-serial (P/S) operation is performed to obtain the time domain signal.
- Pre-SDE is implemented by normalizing all data streams to ensure that the detected N-data have the same value of SNR. The Pre-SDE concept of an optical DCO-OFDM system is based on the VLC-MIMO N-channel imaging technique. The output optical power and the modulation index for every LED are P
_{opt}and ξ, respectively. Pre-SDE is performed by using power allocation matrix A = diag (a_{1}; a_{2}; ⋯⋯; a_{N}) which adjusts all electrical powers modulating data.

_{opt}(1 + ξ A x).

_{Re}+ j x

_{Im},

_{1}x

_{2}, ⋯⋯ x

_{N})

^{T}is a vector of modulating signals and x

_{i}(i = 1, 2, ⋯⋯, N) is the normalized bipolar OFDM signal with variance σ

^{2}

_{xi}= 1.

_{i}, satisfy the following equation [22]:

#### 2.2. Channel Estimation

#### 2.2.1. White Gaussian Noise Estimation

_{N}, which is the sum of shot noise and thermal noise besides the ICI contributions using the optical path difference. We disregard the noise contributions from gate leakage current and 1/f noise:

_{rISI}by ICI is [26]:

_{bg}is background current. The noise bandwidth factors I

_{2}= 0.562.

_{K}is the absolute temperature, G is the open-loop voltage gain, η is the constant photodetector capacitance (PD) per unit area, Γ is the FET channel noise factor, ${\mathrm{g}}_{\mathrm{m}}$ is the FET trans-conductance, I

_{3}= 0.0868, ${\mathrm{T}}_{\mathrm{k}}$ = 295 K, Γ is the FET channel noise, G = 10 dB, g

_{m}= 30 m

_{S}, Ƞ = 1.5, Γ = 112 pF/cm

^{2}, even B = 100 Mbps. In our work, the surrounding current comes from the direct sum light [27].

#### 2.2.2. Non-Imaging LOS Channel Gain

_{R}, Y

_{R}, Z

_{R}]–[X

_{S}, Y

_{S}, Z

_{S}], where [X

_{S}, Y

_{S}, Z

_{S}] and [X

_{R}, Y

_{R}, Z

_{R}] are the positions of transmitter and receiver, respectively [28]. The optical LOS channel gain between the tth LED lamp and the rth PD is proved by:

_{1}

_{/2}) is the emitted lighting order with Ψ

_{1/2}is the semi-angle of the transmitter at half power, A

_{PD}is the PD active area, d

_{rt}is the distance between the tth LED lamp and the rth PD, μ and η are the optical filter gain likewise the optical lens, respectively, ϕ

_{rt}is the emission angle, and θ

_{rt}is the incident angle. Moreover, if θ

_{rt}is outside the Field of View (FOV) of the receiver, the optical gain h

_{rt}is zero and when an imaging non-diversity receiver (ImADR) is used, θ

_{rt}becomes zero.

#### 2.2.3. Non-Imaging LOS Channel Matrix

#### 2.3. The Receiver

- An A/D conversion is utilized to convert the analog signals to digital. The 3-dB modulation bandwidth of LED is adjusted as 50 MHz.

#### 2.3.1. Received Wavelet-OFDM Data

#### 2.3.2. Pre-SDE Equations

#### 2.3.3. SNR Estimation

_{i}= (R P

_{opt}ξ h

_{ii})

^{2}σ

^{2}

_{xi}/σ

^{2}

_{ni}, i = 1, 2, ….., N. R is the photodiode responsivity, P

_{opt}is the LED output power, ξ is the modulation index, and h

_{ii}are the elements of the H matrix.

^{2}

_{1}SNR

_{1}= a

^{2}

_{2}SNR

_{2}= ⋯⋯ = a

^{2}

_{N}SNR

_{N}.

#### 2.3.4. Received Data Estimation

_{est}and decompose the detected streams of Y, a matrix inversion and multiplication should be required:

_{i}(i = 1, 2, ⋯⋯, N) is represented as a zero-mean real-valued AWGN through variance σ

^{2}

_{ni}. Both shot and thermal noises, given by Equations (7) and (8), respectively, are jointly added to total noise. The notation ${(.)}^{-1}$ indicates the inverse operator. diag(.) symbolized to the diagonal items, which are the results, are given within the rounded brackets. All blocks except the DWT-OFDM ones are explained in Ref. [22]. Here, we focus on DWT-OFDM blocks in detail.

## 3. Simulation Results and Discussion

#### 3.1. Simulation Parameters

#### 3.2. Simulation Results of Dmey Wavelet-OFDM and Discussion

^{−3}, and it is gradually reduced if Pre-FDE is used. The BER is substantially decreased when Pre-FDE and Pre-SDE are used in either ImR or ImADR. We notice that, in the ImADR case, the efficiency of BER is preferable to that of ImR. This is because of the ImADR’s high optical performance. For N = 1, with performing the Pre-SDE after Pre-FDE, the BER is decreased from 10

^{−2}to 10

^{−4}, which is when the ImADR is used instead of ImR. When N = 2, 3, and 4, as noticed in Figure 8a–c, the BER is improved for the overall channel according to SNR improvement.

^{−3}when Pre-FDE is not used. In addition, when the Pre-FDE is utilized, the BER progressively starts to reduce. Similarly, by using the Pre-SDE after Pre-FDE for FFT-OFDM, BER has reached 2 × 10

^{−2}for N = 4 while it is reached 4 × 10

^{−2}for WT-OFDM. By using either ImR or ImADR, the system has to meet improvement. Though, the system is more improved by using ImADR than by using ImR. The BER is reduced to less than 10

^{−5}for FFT-OFDM and is reduced to less than 5 × 10

^{−6}for DWT-OFDM for ImADR along the X-direction. As noticed, the BER is improved by using DWT-OFDM than FFT-OFDM.

^{−3}BER target for N = 1, 2, 3, and 4 is calculated, for the N- channel imaging VLC-MIMO technique. The coverage with Pre-FDE ImADR is larger than that of the Pre-FDE ImR as shown in Figure 9. For N = 1, as shown in Figure 9a, the coverage is almost identical for both Pre-FDE individually and for Pre-SDE after Pre-FDE ImR. In addition, for ImADR, it is identical for both Pre-FDE individually and for Pre-SDE after Pre-FDE. For N = 2 and 3, the contour coverage is increased, performing the Pre-FDE after Pre-SDE ImADR coverage is greater than that of the Pre-FDE after Pre-SDE ImR coverage. The ImADR coverage for N = 4 for Pre-FDE individually or before Pre-SDE is like a circle. We can calculate the coverage area by calculating the areas of the circles. The diameters for Pre-FDE individually or before Pre-SDE ImADR are 4 and 4.7 m, respectively, and for ImR are 2.3 and 3 m, respectively. The coverage along the direction of X is increased while it has no difference along the direction of Y. This is because the SNR of channel 1 is almost the same as channel 2. The SNR for all numbers of LED modules is the same whenever Pre-SDE is applied with Pre-FDE ImADR. Furthermore, X is the width, as well as, Y is the length of the room, respectively, as shown in Table 2. Coverage always increases and improvement achieved when Pre-SDE is applied with Pre-FDE in space-frequency domain pre-equalization technique as shown in Figure 9.

^{−3}BER over the system which uses Pre-SDE after Pre-FDE for N = 4, at which the improvement remains the same when N = 1. The improvement is changed with a different number of LED modules. This makes the average percentage of the improvement of the 4- LED modules equals 20% over the system which uses Pre-SDE after Pre-FDE.

^{6}samples/sec. The bit rate for the overall system is equal to (200 × 10

^{6}samples/sec) × (log

_{2}62) = 1.2 Gbps, where the QAM constellation order is 64. In the case where the number of channels equals 4, the data rate for all the systems is divided into 4 sections according to 4 LED modules. So, the data rate for every channel is equal to the data rate for the overall system divided by 4. For this reason, the expected data rate capacity is the capacity of all the system itself = 1.2 Gbps.

^{6}samples/sec) × (1-6.25/100) × (1-6/100) × (1-7/100) × log

_{2}64 = 983.6 Mbps, where (6.25/100) is the CP percentage, (6/100) is the training sequence percentage (TS), and (7/100) is the forward error correction/channel coding (FEC) percentage as mentioned in [31], where all are added to data transmission.

^{6}samples/sec) × (1-0) × (1-6/100) × (1-7/100) × log

_{2}64 = 1049 Gbps, where 0 is related to no CP percentage added, (6/100) is the TS percentage, and (7/100) is the FEC percentage as mentioned in [31], where all are added to data transmission.

^{3}. When the room dimensions are increased, only the numbers of transmitters and receivers will increase. For example, if we choose a standard room with dimensions 9 × 9 × 3 m

^{3}, the number of LED modules will be 6 modules. So, one needs 6 transmitters and 6 receivers, not 3 as in room dimensions with 5 × 5 × 3 m

^{3}. These numbers depend on the proper distribution for proper lighting distribution. Hence, the proposed system can also be applied to meeting rooms, hospitals, museums, hotels, police stations, and so on..., with different room dimensions and corresponding numbers of transmitters and receivers. The proposed system is considered environmentally friendly, cheaper, less power consumption, more secure, higher data rate compared to RF systems. Thus, the proposed system has advantage over the conventional systems [22]. Implementing a hardware simulation and producing patents for the proposed system are a very good attempt for more validation.

## 4. Conclusions

^{−3}. The proposed system is evaluated and compared with the system based on the traditional-OFDM, in terms of the coverage contour and bit rate for various channels. The obtained results revealed that our proposed DWT-OFDM system is preferable over the FFT-OFDM, where the transmission distance and coverage contour are increased by an average of 20% over the FFT-OFDM technique, and the bit rate is increased to 1.049 Gbps. It is noted that, the suggested technique can be repeated for a large number of channels with different room dimensions. In addition, it is viable for the non-LOS channel. Furthermore, the pre-distortion can be used individually or with a pre-equalizer for more improvement. Moreover, the receiver locations can be changed to the center scenario. To conclude, the proposed system can be a good candidate for the indoor VLC applications. Implementing a hardware simulation and producing patents for the proposed system are a very good attempt for future work.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 1.**A wavelet-Orthogonal Frequency Division Multiplexing (OFDM) indoor imaging Visible Light Communication- Multiple Input Multiple Output (VLC-MIMO) transmitter utilizing the hybrid Pre Space Domain Equalization (Pre-SDE) system.

**Figure 2.**Proposed transmitter model of Discrete Wavelet Transform (DWT)-Orthogonal Frequency Division Multiplexing (OFDM).

**Figure 3.**Line of Sight (LOS) channel configuration [28].

**Figure 6.**Three-dimensional configuration of the imaging VLC-MIMO technique for N-channel [22].

**Figure 7.**Signal to Noise Ratio (SNR) performance using Imaging Receiver (ImR) without using Pre- Frequency Domain Equalization (Pre-FDE) and without using Pre-Space Domain Equalization (Pre-SDE), Imaging Angle Diversity Receiver (ImADR) without using Pre-FDE and without using Pre-SDE, ImADR with using only Pre-FDE and ImADR with using Pre-FDE and Pre-SDE, at corner scenario (0, 0, 0.85) of the receiving plane for (

**a**) N = 1, (

**b**) N = 2, (

**c**) N = 3, and (

**d**) N = 4.

**Figure 8.**Bit Error Rate (BER) performances along width-direction (X) and length Y = 1.5 m of (

**a**) N = 1, (

**b**) N = 2, (

**c**) N = 3, and (

**d**) N = 4.

**Figure 9.**Communication area contour on an objective of 10

^{−3}BER (

**a**) N = 1, (

**b**) N = 2, (

**c**) N = 3, and (

**d**) N = 4.

**Table 1.**Light Emitting Diode (LED) modules locations (m) [22].

N = 1 | (2.5, 2.5, 3) |

N = 2 | (1.5, 2.5, 3) (3.5, 2.5, 3) |

N = 3 | (1.5, 1.5, 3) (3.5, 1.5, 3) (2.5, 3.5, 3) |

N = 4 | (1.5, 1.5, 3) (3.5, 1.5, 3) (1.5, 3.5, 3) (3.5, 3.5, 3) |

**Table 2.**Simulation parameters [22].

Room dimensions (width × length × height) | 5 × 5 × 3 m^{3} |

Number of LED modules = N | 4 |

Number of receivers = M | 1 |

Receiving plane height | 0.85 m |

Half power semi angle (Ψ1/2) | 60 deg |

LED optical output power (P_{opt}) | 10 W |

Modulation index (ξ) | 0.3 |

Gain of optical filter (μ) | 1 |

Lens gain (η) | 1 |

Active area of PD (A_{PD}) | 19.6 mm^{2} |

Photodiode responsivity (R) | 0.53 A/W |

Background current (I_{bg}) | 190 μA |

Bandwidth (B) | 50 MHz |

QAM | 64 |

FOV of detector | 150 deg |

Number of carriers (QAM) | 64 |

Number of frames = Number of symbols for each carrier (S) | 1 |

Wavelet used (w) | ‘Dmey’ |

Number of symbols | 1000 |

Number of data | 64 |

**Table 3.**Simulation parameters comparison between FFT-OFDM [22] as well as DWT-OFDM, and their corresponding matrix values.

Parameters | FFT-OFDM [22] | Present Work DWT-OFDM | ||
---|---|---|---|---|

Common requirements | Number of subcarriers | 64 | 64 | |

Total number OFDM symbols | 1000 | 1000 | ||

Transmitter | Input binary data | 1 × 64,000 | 1 × 64,000 | |

QAM data | 1 × 64,000 | 1 × 64,000 | ||

Parallel data transmitted | 1000 × 64 | 1000 × 64 | ||

Parallel to serial data transmitted | 1 × 64,000 | 1 × 64,000 | ||

Normalized transmitted data | 1 × 64,000 | 1 × 64,000 | ||

Receiver | Normalized received data | 1 × 64,000 | 1 × 64,000 | 1 × 64,000 |

1 × 128,000 | ||||

Serial data received | 1 × 64,000 | 1 × 64,000 | ||

Serial to parallel data received | 64 × 1000 | 64 × 1000 | ||

De-QAM data | 1 × 64,000 | 1 × 64,000 | ||

Output binary data recovery | 1 × 64,000 | 1 × 64,000 |

Comparison Parameters | FFT-OFDM (Ref. [22]) | DWT-OFDM (Present Work) | |
---|---|---|---|

Coverage contour | Diameter of the coverage contour employing only Pre-FDE ImADR (m) | 3.4 (52.6%) | 4 (70%) |

Diameter of the coverage contour employing Pre-SDE after Pre-FDE ImADR (m) | 4.2 | 4.7 | |

Diameter of the coverage contour employing only Pre-FDE ImR (m) | 2 (20%) | 2.3 (25%) | |

Bit rate | 983.6 Mbps | 1.049 Gbps | |

BER (along X direction) | Less than 10^{−5} | Less than 5 × 10^{−6} |

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**MDPI and ACS Style**

Badawi, W.K.; El-Hossary, M.G.; Aly, M.H.
Indoor Wavelet OFDM VLC-MIMO System: Performance Evaluation. *Symmetry* **2021**, *13*, 270.
https://doi.org/10.3390/sym13020270

**AMA Style**

Badawi WK, El-Hossary MG, Aly MH.
Indoor Wavelet OFDM VLC-MIMO System: Performance Evaluation. *Symmetry*. 2021; 13(2):270.
https://doi.org/10.3390/sym13020270

**Chicago/Turabian Style**

Badawi, Waleed K., Marwa G. El-Hossary, and Moustafa H. Aly.
2021. "Indoor Wavelet OFDM VLC-MIMO System: Performance Evaluation" *Symmetry* 13, no. 2: 270.
https://doi.org/10.3390/sym13020270