Adaptive equalization for high speed optical MIMO wireless communications using white LED

Abstract

Light emitting diode (LED) is one of the most important light sources in the 21st century and has broad prospects in the illumination. Currently, the white LED is used not only for illumination, but also for transmission data. A new technique referred as visible light communication (VLC) is rapidly growing in optical communication. In order to enhance the performance of the communication link, we present optical multiple input and multiple output (MIMO) communication system to achieve high data rate, which can mitigate the shadow effect of indoor communication. Moreover, the MIMO will bring about multi-path effect, which causes inter-symbol interference (ISI) to degrade the performance of the link. Hence, an adaptive equalization technique has been used in the receiver system, which can reduce the ISI when the system is determined to receive symbol. Finally, we have simulated the MIMO system with adaptive equalization. The simulation results show significant improvement in the transmission rate using on off keying (OOK) and the average signal to noise ratio (SNR) in this channel has increased 13.5 dB after equalization.

Keywords

optical multiple input multiple output (MIMO) / adaptive equalization / indoor optical wireless communication / white light emitting diode (LED)

1 Introduction

White light emitting diode (LED) devices are being used for indoor lighting for their higher power efficiency, longer life expectancies, higher tolerance to humidity, lower heat generation and smaller size, which make these devices strong candidates for present and future lighting technology [1]. Moreover, it is possible to extend its usage to transfer data in an indoor optical wireless communication system for its intrinsic characteristics of LED, which is usually referred as visible light communication (VLC) [2]. With recent high power LED, these advantages can be explored by VLC system, Pang et al. [3] firstly proposed an optical wireless broadcasting system to transfer audio signal using visible light LED; Akanegawa with his colleague [4] proposed in the traffic information and communication system, and then established Visible Light Communication Consortium in November, 2003 [2]. Komine et al. [1,5-7] presented the integration of white LED communication into power line communication. These authors were the pioneers to present the utilization of high power LED to transmit data. Today, there are a lot of groups in Europe engaged in this technology research, such as the group in Fraunhofer Institute for Telecommunications, Heinrich-Hertz-Institute [8,9], the group in university of Oxford [10], and the group international university Bremen [11,12].

Indoor illumination for offices work requires 300 to 1500 lx [1], though a higher-power LED produces up to 130 lm per device, a single LED still cannot provide sufficient illumination for indoor illumination. Several LEDs must be mounted on the panels to obtain practical luminous power. In this case, optical multiple input and multiple output (MIMO) communication is proposed for indoor illumination and communication [13]. The MIMO technology is widely used in radio communications, which the channel has higher capacity than the single input single output (SISO) system, and has potentials to mitigate the shadow effect. Although there has been a large amount of research in radio communication, still there has a small amount research in optical MIMO communication with white LED for indoor wireless communication. Non-imaging optical MIMO system using LED array has been reported in Ref. [13]. Reference [14] proposed a multispot-diffuse MIMO approach to broad-band optical infrared wireless communications. Reference [15] presented MIMO optical wireless communication system for imaging communication. O’brien et al. [16] used 1 × 2 laser arrays of transmitters and 3 × 3 photodiode array to achieve high data rates line of sight ( LOS ) MIMO optical link. Indoor wireless communication with four channel MIMO system used white LED has been demonstrated [17]. Reference [18] presented MIMO characterization of indoor wireless optical link using a diffuse transmission configuration that used infrared radiation, and obtained the impulse response for the direct path and the diffuse path.

When the transmission data rate exceeds 2-3 Mbit/s, the inter-symbol interference (ISI) occurs due to multi-path effect which significantly degrades the system performance. References [19,20] reported the zero forcing decision feedback equalizer (ZF-DFE) based on pulse position modulation to mitigate the effects of ISI in infrared wireless communication. Komine et al. [6,21] proposed adaptive equalization, which included the decision feedback equalization (DFE), the least mean square (LMS) algorithm to mitigate ISI for visible wireless communication using multiple white LED.

In this paper, we focus on white LED arrays to provide both illumination and transmit data that uses MIMO configuration in indoor environment. This paper is organized as follows: in Section 2, we propose the outline of the indoor illumination, the optical MIMO communication system and the channel model. In Section 3, we report the least mean square error algorithm of the adaptive equalization used in the optical MIMO system. In Section 4, we give out the simulation result of the impulse of the MIMO channel and the performance of the system. And finally, we give out our conclusion in Section 5.

2 Optical MIMO system

The general communication system using white LED for indoor illumination and communication is shown in Fig. 1. In this system, there are four lamps for optical downlink which are made of white LED arrays for illuminating the room, each of them can independently transmit data simultaneously, and they can replace incandescent lamps mounted on the ceiling. There are four photo detectors on the desk plane above the floor, which can receive the data stream from the LED lamps.

Fig.1 Optical MIMO system using white LEDs

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To describe the process of this design method clearly, we set up a coordinate system in Fig. 1, defining the floor as the X-Y plane, the height direction as the Z-axis, and point O is the coordinate origin. Figure 1 shows the optical MIMO system in a configuration used in the literatures [1,13]. We adopt LUXEON K2 LED [22] for lighting system and optical MIMO communication system. The room size is 5.0 m × 5.0 m × 3.0 m, and the distance between the ceiling and the receivers’ plane is 2.15 m. The LEDs fixed on the ceiling of the room are arranged in the square arrays, which are like that of the literatures [23,24]. Furthermore the, LED’s luminous intensity is isotropic, and consequently the LED-to-LED of the lamp has the same spacing. In the configuration of the square LED array, the LED-to-LED have same separation, $d=\mathrm{0.25}\mathrm{m}$. Generally, the luminance of lights is standardized by International Organization for Standardization (ISO). According to the ISO standard, the luminance of 300-1500 lx is required for a work office, but the typical luminous power of LUXEON K2 LED is only 130 lm from the datasheet, therefore, 64 LEDs can provide sufficient illuminance in this system. Each LED lamp has 4 × 4 LEDs. The center positions of lamps are A: (1.575, 1.575, 3.0), B: (3.525, 1.575, 3.0), C: (3.525, 3.525, 3.0) and D: (1.575, 3.525, 3.0). It is assumed that all LED lamps are driven by different modulation circuits to achieve high speed transmission. The ceiling, the wall and the floor respectively have reflective index values of 0.8, 0.5, 0.2. Four receivers are set on the desk, each of them contains an optical concentrator, followed by a photo detector and preamplifier, and the center position of the receivers (Rs) is R₁: (2.5, 2.5, 0.8), R₂: (1.5, 1.5, 0.8), R₃: (0.5, 0.5, 0.8) and R₄: (2.5, 0.5, 0.8).

2.1 Optical MIMO model

The relation between the input and output of an optical MIMO link is shown in Fig. 2. We take the general system as a linear, diffuse, and noisy digital communication system, so the model of optical MIMO can be described as

(1)$$\mathit{y}=\mathit{H}\mathit{x}+\mathit{n},$$

where BoldItalic is the $n_T\times \mathrm{1}$ transmitter signal vector, BoldItalic is the $n_R\times \mathrm{1}$ receiver power vector of photo detector, BoldItalic is the $n_R\times n_T$ channel matrix, and defined as the channel transfer matrix or the channel gain matrix. BoldItalic is the $n_R\times \mathrm{1}$ additive white Gaussian noise (AWGN) vector.

Fig.2 Optical MIMO communication system model

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The channel transfer matrix $\mathit{H}$ is formed by the gains between the transmitter and the receiver, and given by ${(h_{ij})}_{N_R\times N_T}$. $h_{ij}$ can be estimated by the gain between the ith receiver and the jth transmitter, and obtained by [13]

(2)$$h_{ij}=\{\begin{array}{ll}{\displaystyle \frac{A^j}{d_{ijk}}}I({\varphi }_{ijk})g({\phi }_{ijk})\cos ({\phi }_{ijk}),\hfill & \mathrm{0}\le {\phi }_{ijk}\le {\phi }_c,\hfill \\ \mathrm{0},\hfill & {\phi }_{ijk}>{\phi }_c.\hfill \end{array}$$

Here, $A^j$ is the receiver collection area of the jth receiver, and its physical detection is 1.0 cm². $d_{ijk}$ is the distance between the kth LED in the ith transmitter and the jth receiver. $I({\varphi }_{ijk})$ is the luminous intensity of the kth LED in the ith transmitter array, and ${\varphi }_{ijk}$ is the irradiance angle of the kth LED in the ith transmitter. ${\phi }_{ijk}$ is the incident angle between the kth LED in the ith transmitter and the jth receiver. ${\phi }_c$ is the receiver angle of a field of view (FOV) that is 60°. The communication system we design has 4 transmitters each of which contains 16 high-power LEDs, and each transmitter has been arranged as the square LED array in Fig. 1. The system also has four receivers installed by four photo detectors with an amplifier. Therefore, i is in the range of 1 to 4, j is also the scope of this, and it is straightforward to show that lets $k\in \{\mathrm{1},\mathrm{2},\mathrm{3},\cdots ,\mathrm{16}\}$. $g({\phi }_{ijk})$ is the optical concentrator of the jth receiver, and can be given as [25]

(3)$$g({\phi }_{ijk})=\{\begin{array}{l}\begin{array}{ll}{\displaystyle \frac{m^{\mathrm{2}}}{{\sin }^{\mathrm{2}}({\phi }_c)}},& \mathrm{0}\le {\phi }_{ijk}\le {\phi }_c,\end{array}\hfill \\ \mathrm{0},{\phi }_{ijk}>{\phi }_c,\hfill \end{array}$$

where m denotes the refractive index.

If we only consider the LOS type communication, the optical MIMO channel model can be exactly depicted by ${(h_{ij})}_{N_R\times N_T}$. We can estimate the vector BoldItalic by the receiver vector BoldItalic and the inverse channel gain matrix ${\mathit{H}}^{-\mathrm{1}}$. Here ${\mathit{H}}^{-\mathrm{1}}$ is assumed to be calculated by a controller or four controllers, and defined as the inverse channel transfer matrix or the inverse channel gain matrix. The demodulated signal can be obtained by

(4)$$\mathit{y}={\mathit{H}}^{-\mathrm{1}}\mathit{x}.$$

In fact, the signal propagation by way of non-line-of-sight (non-LOS) should be also considered. Firstly, the divergence angle of the LED is large, the contribution from the non-LOS paths should be considered here since the light contribution to the receivers is distributed over all the area of the room due to its diffuse. Secondly, the time that the light arrives at the receivers by way of different path is not the same, so there is ISI in the communication system. If we only consider the LOS type, the model of the channel is incomplete. Thirdly, the higher modulation rate is, the more apparent multi-path effects are. In this case, we transform Eq. (1) into Eq. (5) and Eq. (2) into Eq. (6).

(5)$$\mathit{y}=(\mathit{H}+\delta \mathit{H})\mathit{x}+\mathit{n},$$

(6)$$h_{ij}=\{\begin{array}{l}{\displaystyle \frac{A^j}{d_{ijk}^{\mathrm{2}}}}I({\varphi }_{ijk})g({\phi }_{ijk})\cos ({\phi }_{ijk})+{\displaystyle \sum _{l=\mathrm{1}}^N{\displaystyle \frac{A^j}{d_l^{\mathrm{2}}}}}{\rho }_l{I}_{l}g({\phi }_l)\cos ({\phi }_l),\mathrm{0}\le {\phi }_{ijk}\le {\phi }_c,\mathrm{0}\le {\phi }_l\le {\phi }_c,\hfill \\ \mathrm{0},{\phi }_{ijk}>{\phi }_c,\hfill \end{array}$$

where $\delta \mathit{H}$ is the disturbance of the channel matrix due to signal propagation in the non-LOS path. ${\displaystyle \sum _{l=1}^N{\displaystyle \frac{A^j}{d_l^2}}{\rho }_l{I}_{l}g\left({\phi }_l\right)\cos \left({\phi }_l\right)}$ is the contribution of the non-LOS channel. $d_l$ is the distance by the way of the lth propagation path to the receiver, and ${\rho }_l$ is the reflectivity of the path. ${\phi }_l$ is the incident angle. We have to explain here, the second part that we append to Eq. (6) might not be all the part of ISI, when the transmission rate of the system is low or the receiver is moved in the spatial, it may not interfere with other symbol, it is probable to be the part of current symbol.

2.2 Channel impulse response calculation

Fig.3 Impulse response in (1.0, 0.5, 0.85)

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The impulse response of the channels can be divided into LOS and non-LOS according to the propagation path of the ray. Two steps are adopted to simulate the procedure of the channel. Firstly, the time is separated into many equivalent time slots, which is 0.5 ns, and then the power is summed for every time slot. Secondly, the wall and the ceiling and the floor are divided into 100 × 100 differential elements. When the incident light strikes the small elements, it is assumed that it reflects as a Lambertian source. In order to calculate the impulse response of the optical MIMO, the ray tracing method is used to estimate the impulse response of the receiver, which is located at different position of the room. It is hypothesized that each transmitter simultaneously sends a very short pulse. Every receiver is installed in a different position. Consequently, it has different responses. In order to clearly explain this process, the receiver is assumed to be installed in (1.0, 0.5, 0.85). The impulse response of the receiver is shown in Fig. 3.

We calculated the impulse response and considered only the direct radiation, the first reflection, the second and third reflection. There are four obvious peaks, as indicated in the Fig. 3. It can be observed the first reflection exceeds the direct radiation. When the transmission rate is relatively high, it is considered to cause ISI.

2.3 Signal to noise ratio (SNR)

SNR stands for the reliability of the communication system. Here, a noise model is thought as an AWGN model. In the optical MIMO channel, the communication links is dominated by the shot noise and the thermal noise. Another principal component of received signal is the ISI for its non-LOS, the SNR of the links can be expressed by

(7)$$\mathrm{S}\mathrm{N}\mathrm{R}={\displaystyle \frac{{(R{P}_{\mathrm{r}})}^{\mathrm{2}}}{{\sigma }_{\mathrm{s}\mathrm{h}\mathrm{o}\mathrm{t}}^{\mathrm{2}}+{\sigma }_{\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{r}\mathrm{m}\mathrm{a}\mathrm{l}}^{\mathrm{2}}+{(R{P}_{\mathrm{I}\mathrm{S}\mathrm{I}})}^{\mathrm{2}}}},$$

where R is the detector responsivity, and $R=\mathrm{0.4}$ A/W, $P_{\mathrm{r}}$ is the received power. The shot noise variance is given by [6,25]

(8)$${\sigma }_{\mathrm{s}\mathrm{h}\mathrm{o}\mathrm{t}}^{\mathrm{2}}=\mathrm{2}qR{P}_{\mathrm{r}}B+\mathrm{2}q{I}_{\mathrm{b}\mathrm{g}}{I}_{\mathrm{2}}B,$$

where $I_{\mathrm{b}\mathrm{g}}$ is background current, $I_{\mathrm{2}}$ noise bandwidth factor, q is the electronic charge, and B is noise bandwidth. The thermal noise variance is given by [6,25]

(9)$${\sigma }_{\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{r}\mathrm{m}\mathrm{a}\mathrm{l}}^{\mathrm{2}}={\displaystyle \frac{\mathrm{8}\mathrm{\pi }k{T}_{\mathrm{k}}\eta A{I}_{\mathrm{2}}{B}^{\mathrm{2}}}{G}}+{\displaystyle \frac{\mathrm{16}{\mathrm{\pi }}^{\mathrm{2}}k{T}_{\mathrm{k}}\mathrm{\Gamma }{\eta }^{\mathrm{2}}{A}^{\mathrm{2}}{I}_{\mathrm{3}}{B}^{\mathrm{3}}}{g_{\mathrm{m}}}},$$

$k$ is Boltzmann’s constant, $T_{\mathrm{k}}$ is absolute temperature. $\eta$ is the fixed capacitance per unit area. A is the detector area. G is the voltage gain. $\mathrm{\Gamma }$ is the channel noise factor, $g_{\mathrm{m}}$ is FET transconductance. And all the parameter of above will be listed in Section 4. $P_{\mathrm{I}\mathrm{S}\mathrm{I}}$ is expressed by $P_{\mathrm{I}\mathrm{S}\mathrm{I}}=\delta \mathit{H}\mathit{x}$.

3 Adaptive equalization

The quality of digital communication system is depended on the channel characteristics. The fading channel, the multipath transmission and the Gaussian additive noise are the principal factors that influence the communication quality. The adaptive equalization is quite suitable for the channel equalization. In this section, the adaptive equalization technique is introduced to the optical MIMO communication links. Each sub-system is connected with the optical MIMO system as shown in Fig. 2 to replace the algorithm to calculate the inverse of the matrix BoldItalic. Hence, there are four sub-systems in the communication links, and one of them is generally illustrated here. And two typical method of adaptive equalization are selected, one is ZF-DFE, the other is the least mean square algorithm. The former is a non-linear equalization, and the latter is a linear equalization.

Widrow and Stearns presented the least mean square (LMS) error algorithm in 1960’s [26], and this method is very suitable for channel equalization. The structure of least mean square equalizer (LMSE) is similar to that of ZF-DFE. This method has advantages of easy implementation, simple structure and robustness, but its disadvantage is slow convergence. Since adaptive equalization can compensate an unknown and time-varying channel to mitigate the ISI, it requires a specific algorithm to update the equalizer coefficients and track the channel variation [6]. Here we use the least mean square error algorithm to compensate the channel defects. Here, we will introduce the LMSE algorithm principle, which usually use the transversal filter as shown in Fig. 4 to implement. Here we assume the input signals as a vector are

(10)$$\mathit{X}(n)={[x(n),x(n-\mathrm{1}),\cdots ,x(n-N+\mathrm{1}),x(n-N)]}^{\mathrm{T}}.$$

The weight coefficients are given as a vector as

(11)$$\mathit{W}(n)={[w_{\mathrm{0}}(n),w_{\mathrm{1}}(n),\cdots ,w_{N-\mathrm{1}}(n),w_N(n)]}^{\mathrm{T}}.$$

The output signals are given by

(12)$$\mathit{Y}(n)={[y(n),y(n-\mathrm{1}),\cdots ,y(n-N+\mathrm{1}),y(n-N)]}^{\mathrm{T}}.$$

The error signals $e(n)$ are given by

(13)$$e(n)=f(n)-y(n),$$

$f(n)$ is the reference signal, the relationship between the input signal and the output signal are given by

(14)$$y(n)={\displaystyle \sum _{i=\mathrm{0}}^N{w}_i(n)x(n-i)}={\mathit{W}}^{\mathrm{T}}(n)\mathit{X}(n).$$

Fig.4 LMSE structure

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The weight coefficients vector is updated by Eq. (15).

(15)$$\mathit{W}(n+\mathrm{1})=\mathit{W}(n)+\mu e(n)\mathit{X}(n),$$

$\mu$ is an adaptive iterative step size, and requires to satisfy $\mathrm{0}<\mu <2/{\lambda }_{\max }$, where ${\lambda }_{\max }$ is the largest eigenvalue of the correlation matrix of the input signal $E(X(n)X^H(n))$. Equations (13)-(15) consist of the iterative LMSE algorithm. Here, the part of Fig. 4 can be considered as a component connected to replace one part of ${\mathit{H}}^{-\mathrm{1}}$ in Fig. 2. Therefore it requires four components similar to Fig. 4 to make of the communication receivers system as Fig. 2.

4 Performance of communication system

4.1 Simulation parameter

We implement the LMS algorithm described in the previous section, and the simulation parameters of the LED are listed in Table 1. We only considered downlink transmission based on on off keying (OOK) modulation.

Tab.1 Simulation parameters of LED

parameters	values
LED array	4
number of LED per array	4 × 4
transmitted power	1 W
LED pitch	0.25 m
LED array size	0.75 × 0.75
transmitter semi-angle	100°

The simulation parameters of the receiver system are described in Table 2.

Tab.2 Simulation parameters of photo detector

parameters	values
PD responsivity R	0.4 A/W
detector area of a PD	1.0 cm2
FOV at a receiver	60°
gain of an optical filter	1.0
refractive index of a lent at PD	1.5
pre-amplifier noise sensity	5 pA/Hz-1/2
receiver bandwidth	100 Mb/s
ambient light photocurrent Ibg	5100 μA

We also choose the following parameter for estimating the shot noise variance and thermal noise variance: noise bandwidth factor $I_{\mathrm{2}}=\mathrm{0.562}$, $T_{\mathrm{k}}=\mathrm{298}\mathrm{K}$, the fixed capacitance per unit area $\eta =\mathrm{1.12}{\mathrm{e}}^{-\mathrm{6}}\mathrm{F}/{\mathrm{m}}^{\mathrm{2}}$, the voltage gain $G=\mathrm{10}$, and the channel noise factor is $\mathrm{\Gamma }=\mathrm{1.5}$, the FET transconductance $g_{\mathrm{m}}=\mathrm{0.03}\mathrm{S}$.

4.2 Simulation algorithm

We use following steps to simulate the LMS algorithm equalization:

1) The LED transmitters A, B, C and D respectively send different signals $x_{\mathrm{A}}(n)$, $x_{\mathrm{B}}(n)$, $x_{\mathrm{C}}(n)$ and $x_{\mathrm{D}}(n)$ which are OOK.

2) Assuming the receiver is R₁, we calculate the channel transfer matrix $h_{\mathrm{11}}$, $h_{\mathrm{12}}$, $h_{\mathrm{13}}$ and $h_{\mathrm{14}}$ according Eq. (6), find the training sequence $y_{\mathrm{0}}(n)=h_{\mathrm{11}}{x}_{\mathrm{A}}(n)$.

3) We calculate the random noise $n_{\mathrm{1}}$ generated by the channel according to Eqs. (8) and (9). Therefore, R₁ receives actual signal as follow:

(16)$$y_{\mathrm{1}}(n)=h_{\mathrm{11}}{x}_{\mathrm{A}}(n)+h_{\mathrm{12}}{x}_{\mathrm{B}}(n)+h_{\mathrm{13}}{x}_{\mathrm{C}}(n)+h_{\mathrm{14}}{x}_{\mathrm{D}}(n)+n_{\mathrm{1}}.$$

4) Determines the iterative step size $\mu$.

5) The output signals are given by

(17)$$y(n)=w(n)*y_{\mathrm{1}}(n).$$

6) The error signals $e(n)$ are given by

(18)$$e(n)=y_{\mathrm{0}}(n)-y(n).$$

7) Updates filter coefficients:

(19)$$w(n+\mathrm{1})=w(n)+\mu e(n)y_{\mathrm{1}}(n).$$

8) Repeats the step (5).

4.3 Adaptive algorithm error

In this section, we will discuss the effectiveness of the parameter of the iterative step size and training sequence for optical MIMO adaptive equalization. LED lamp A is adopted for simulation and the finite impulse filter of the LMSE structure has 5 taps. The receiver is located in the position (2.5, 2.5, 0.85), the transmitter A, B, C and D respectively sends training sequence of 1000. Figure 5 shows the relationship between the mean square error (MSE) and the length of training sequence. Here, the simulations of direct and first reflection of light are only considered.

When using adaptive channel equalizer, it is assumed that A, B, C, D LED lamp respectively transmits a random sequence of length 1000. Therefore, the role of the equalizer is as follows: Firstly, the equalizer detaches received signal which are transmitted by device B, C and D from the mixed signal, and retains the signal from device A. Secondly, the equalizer detaches the signal by the way of non-LOS path from the mixed signal. Thirdly, the equalizer eliminates the random noise generating in the communication link.

Fig.5 Mean square error with 5 taps of filter in (2.5, 2.5, 0.85)

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From the figure, the iteration number is set as 1000, and the step size of 0.005, 0.05 and 0.1 is simulated respectively. It can be found that the value of the step size influence the mean square error in the initial stage. The larger the step size is, the better the tracking ability of the equalizer becomes. when $\mu =\mathrm{0.1}$, the system needs no more than 50 training sequence, namely, it can be quickly converged with such a step size.

4.4 Bit error rate (BER) performance

The average SNR of the channel after equalization increases from 0.7 to 14.2 dB according to simulation results. Figure 6 shows that distribution of BER of the optical MIMO system with the LMSE algorithm, and the transmission rate is 100 Mbit/s. It can be observed that the BER in the central position (2.5, 2.5, 0.85) is 2.2×10^-5, and the BER is gradually increases from the center to the fringe, and the performance of the system degrades in the wall corner. Here, the BER contour with ZF-FDE is not presented.

Fig.6 Bit error rate contour with LMSE at 100 Mbit/s

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4.5 MIMO channel capacity

The capacity of the optical MIMO system linearly increases with the number of receivers in the indoor channel, and the channel capacity for the MIMO system by assuming that the receiver has perfect channel state information (CSI), the channel capacity can be written by [27,28]

(20)$$\begin{gathered} C={\log }_{\mathrm{2}}\left[\det \left(I_{n_R}+{\displaystyle \frac{\rho }{n_T}}\mathit{H}{\mathit{H}}^H\right)\right] \\ ={\displaystyle \sum _{i=\mathrm{1}}^{n_T}{\log }_{\mathrm{2}}\left(\mathrm{1}+{\displaystyle \frac{\rho }{n_T}}{\lambda }_i\right)}, \end{gathered}$$

where $\rho$ is the average SNR of every receiver. ${\lambda }_i$ is the eigenvalue of the matrix $\mathit{H}{\mathit{H}}^H$. Due to the use of multiple receivers, the capacity for different signal to noise with 4 transmitters and 4 receivers is shown in Fig. 7. It is clear that when increasing the SNR the capacity is significantly increased. The simulation curve of the channel in the position of (2.5, 2.5, 0.85) and (0, 0, 0.85) is drawn for comparison. The capacity in the other corner of the room is omitted, since they are the same. The simulation results show that the capacity in the center of the room is larger than that of the corner, when the SNR exceeds 0.8 dB. Overall, the capacity of the MIMO system is higher than that of SISO system.

Fig.7 Capacity of different SNR with 4 transmitters and 4 receivers

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5 Conclusions

In this paper, the fundamental problem for indoor optical wireless communication using white LED is investigated. As we know, a single LED cannot provide sufficient illumination for indoor illumination and transmission data. Hence we propose the optical MIMO communication system, which can be used not only for indoor lighting, but also for the indoor communication. However, this approach can bring about the multipath effect that induces ISI. Consequently the adaptive equalization technique is adopted to compensate for these shortcomings. Adaptive channel equalization algorithm is a simple and easy to implement algorithm, so this method is widely used for channel equalization. The validity of the iterative step size is simulated, and the SNR distribution is calculated by adaptive equalization. Finally, the relationship between the capacity and BER is also estimated. The simulation results show that this technique can eliminate the ISI caused by the channel, and significantly improve SNR. In particular, using the fixed step size, the algorithm can quickly be converged to obtain the input signal.

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