On the study of a quasi-synchronous CDMA-VLC system with two channels

Danyang Chen; Zhonggui Ma; Huimin Lu; Lifang Feng; Jianping Wang

doi:10.1364/OE.27.030249

1. Introduction

Visible light communication (VLC) using light emitting diodes (LEDs) is an emerging technology, which brings wider bandwidth, lower power consumption, greater security, more convenience and no electromagnetic interference [1–3]. Owing to the tremendous growth of communication requirements over past years, it has great potential to become a compelling and optional technology for next-generation wireless communications. The rapid development of VLC brings many great challenges, which should be solved before it is widely used in the consumer market [4]. One of the main challenges is to realize the simultaneous access for a large number of users to the network, such as in hospitals, malls and so on [5,6]. Code division multiple access (CDMA) technology has been viewed as one efficient and straight forward way to reduce or eliminate multiple access interference (MAI), and has attracted increasing researchers’ attentions [7–9]. In [10], color-shift keying (CSK) modulation and mobile phone camera receivers were used in a VLC-CDMA system to enhance the capacity and practicability. Zheng et al. [11] demonstrated experimentally a VLC CDMA downlink system with 4 femtocells and 3 Mb/s transmission rate for each user. A multi-cell CDMA-VLC system has been proposed in [12], adopting two resource allocation techniques to achieve good performance in data rate. For electromagnetic-wave-free indoor healthcare service, a single cell CDMA-VLC system using 3-level amplitude signals was proposed, which was a simple and cost-effective system with a good bit error rate (BER) performance [13]. CDMA technology can also be employed to solve the mutual interference among the reference source points in visible light positioning (VLP) system [14,15].

The spreading code set is optimal when it has the maximal number of codes, maximal weight, minimal length, and the good auto-correlation and cross-correlation properties [16]. Based on these criteria, lots of unipolar optical codes which are suitable for the intensity modulation (IM) in VLC system have been constructed and introduced. A random optical codes (ROCs) with easy implementation were considered to improve the number of simultaneous users in VLC Ethernet system [17]. By optimizing the prime codes (PCs)’ correlation properties, generalized modified prime sequence codes (GMPSC) and inverted GMPSC were designed for VLC-CDMA systems, which can achieve lower intensity fluctuation and higher average light intensity [18]. An optical CDMA VLC system based on optical orthogonal codes (OOC) and balanced incomplete block design (BIBD) codes was proposed, of which numerical results show that the system could support up to 15 simultaneous users with 200 Mb/s transmission under normal lighting conditions [19].

Most of the previous works mainly focused on the improvement of BER performance of ideal synchronous CDMA system. However, it is difficult to achieve perfect synchronization among users in VLC-CDMA system due to time delay or multi-path transmission. For quasi-synchronous CDMA-VLC (QS-CDMA-VLC) system, the design of optical zero correlation zone (OZCZ) codes has been proposed with ideal correlation properties in the zero correlation zone [16,20]. The theoretical and numerical analyses indicated that OZCZ codes can effectively tolerate the inevitable time delay. Addad et al. [21] proposed a new method for generating zero cross correlation (ZCC) codes which could more significantly reduce MAI, compared with existing OZCZ codes. In the code construction mentioned above, the introduction of too many ’0’s would lead to lower dimming values, which has an impact on illumination performance and is another major concern of practicality of VLC system [22–24]. In our previous study, we presented and investigated a new construction of OZCZ code set, including a pair of unipolar and bipolar code sets with good correlation properties, which was evaluated in the QS-CDMA-VLC system by simulations and corresponding experiments with one optical channel [25].

In this paper, we construct a new OZCZ code set pair by iterating method, which has more flexible generation of initial matrix and more possibilities for constructions. The new construction consisting of unipolar and bipolar code sets has excellent correlation properties within longer zero correlation zone and greater code weight. A QS-CDMA-VLC system with two different experiment setups is designed to evaluate the proposed construction and compare with other existing code sets. The system contains two optical channels, which would practically introduce MAI and time delay among users. The BER performance of QS-CDMA-VLC system using the proposed OZCZ construction is investigated experimentally for different user numbers, sample rates and free-space transmission distance difference. Besides, we further analyze the dimming values of transmitted signal and overall bit rates of the system by simulation calculations. The results show that the new construction of OZCZ can effectively improve the illumination and communication performance of multi-users’ QS-CDMA-VLC systems.

The rest of the paper is organized as follows. The definition and new construction of OZCZ code set pair are elaborated in Section 2, together with a specific example. Section 3 presents the system design and experiment setup. The results of simulation calculations and experiments for QS-CDMA-VLC system are addressed in Section 4. Finally, Section 5 draws the conclusions.

2. Optical zero correlation zone codes

2.1 Definition

Assuming two codes $\boldsymbol {x}_i=[x_{i,0},x_{i,1},\ldots ,x_{i,L-1}]$ and $\boldsymbol {y}_j =[y_{j,0},y_{j,1},\ldots ,y_{j,L-1}]$ with length $L$, their Periodic Cross-Correlation Function (PCCF) is defined as follows:

(1)$$\theta_{\boldsymbol{x}_i,\boldsymbol{y}_j}(\tau)={\sum_{l=0}^{L-1}x_{i,l}y_{j,(l+\tau)mod L} \forall\tau\geq0}$$

when $\boldsymbol {x}_i=\boldsymbol {y}_j$, it becomes the Periodic Auto-Correlation Function (PACF).

Definition 1: Let $\boldsymbol {X}=\left \{\boldsymbol {x}_i\right \}_{i=1}^{K}(x_{i,j}\in \{0,1\},0\leq j<L)$ denote a unipolar code set with $K$ codes, each has length $L$. And $\boldsymbol {Y}=\left \{\boldsymbol {y}_m\right \}_{m=1}^{K}(y_{m,n}\in \{-1,1\},0\leq n<L)$ denotes a bipolar code set with $K$ codes, each has length $L$. The combination of two code sets $\boldsymbol {X}$ and $\boldsymbol {Y}$ represented as $<\boldsymbol {X},\boldsymbol {Y}>$ can be called an OZCZ code set pair if the following correlation properties satisfy

(2)$$\theta_{\boldsymbol{x}_i,\boldsymbol{y}_m}(\tau)=\left\{\begin{matrix} \pm w & i=m,\tau=0\\ 0 & i\neq m,\tau=0\\ 0 & 0<\left | \tau \right | \leq Z_{cz} \end{matrix}\right.$$

where $w$ denotes the code weight, which is the number of ’1’ in the code and $Z_{cz}$ represents the length of zero correlation zone.

Definition 2: Let $\boldsymbol {A}=[a_{i,j}]_{0\leq i<M,0\leq j<N}$ be an $M\times N$ matrix and $\boldsymbol {B}$ be an arbitrary matrix, then $\boldsymbol {A}\times \boldsymbol {B}$ is defined as

(3)$$\boldsymbol{A}\times\boldsymbol{B}= \begin{bmatrix} a_{0,0}\boldsymbol{B} & a_{0,1}\boldsymbol{B} & \cdots\ & a_{0,N-1}\boldsymbol{B}\\ a_{1,0}\boldsymbol{B} & a_{1,1}\boldsymbol{B} & \cdots\ & a_{1,N-1}\boldsymbol{B}\\ \vdots & \vdots & \ddots & \vdots \\ a_{M-1,0}\boldsymbol{B} & a_{M-1,1}\boldsymbol{B} & \cdots\ & a_{M-1,N-1}\boldsymbol{B}\\ \end{bmatrix}$$

where $a_{i,j}\boldsymbol {B}$ is the scalar multiplication.

2.2 New construction of OZCZ code set pair

For the quasi-synchronous CDMA-VLC systems, we propose and construct a new OZCZ code set pair with parameters $(L,K,Z_{cz})=(4(K+1),K,2)$ as the following steps.

Step 1: Let $\boldsymbol {S}$ be an orthogonal matrix of order-4 written as

(4)$$\boldsymbol{S}=\begin{bmatrix} + & + & + & -\\ + & + & - & +\\ + & - & + & +\\ - & + & + & + \end{bmatrix}=\begin{bmatrix} \boldsymbol{s}_1\\ \boldsymbol{s}_2\\ \boldsymbol{s}_3\\ \boldsymbol{s}_4 \end{bmatrix}$$

where ’$+$’, ’$-$’ denote ’$+1$’ and ’$-1$’ respectively.

We construct a new matrix $\boldsymbol {S}^{'}$ with two codes $\boldsymbol {s}_{i}$ and $\boldsymbol {s}_{j}$ $(j=i+2, i\in \left \{{1,2}\right \})$ from $\boldsymbol {S}$ and separate it into two Hadamard matrices $\boldsymbol {A}$ and $\boldsymbol {B}$ of order-2 as follows

(5)$$\boldsymbol{S}^{'}=\begin{bmatrix} \boldsymbol{s}_{i}\\ \boldsymbol{s}_{j} \end{bmatrix}=\begin{bmatrix} \boldsymbol{A} & \boldsymbol{B} \end{bmatrix}$$

Step 2: An initial matrix $\boldsymbol {H}_0$ can be generated by

(6)$$\boldsymbol{H}_0=\begin{bmatrix} b\boldsymbol{B} & \boldsymbol{A} & \boldsymbol{B} & a\boldsymbol{A} \end{bmatrix}$$

where $ab=-1$ and $a+b=0$, it can be divided into four codes $\boldsymbol {C}_0=[c_{i}]_{0\leq i<4}$, $\boldsymbol {D}_0=[d_{i}]_{0\leq i<4}$, $\boldsymbol {E}_0=[e_{i}]_{0\leq i<4}$ and $\boldsymbol {F}_0=[f_{i}]_{0\leq i<4}$ with length $L=4$ as follows

(7)$$\boldsymbol{H}_0=\begin{bmatrix} \boldsymbol{C}_0 & \boldsymbol{D}_0\\ \boldsymbol{E}_0 & \boldsymbol{F}_0 \end{bmatrix}$$

Based on iterating method, a code set $\boldsymbol {H}_n$ with $2^{n+1}$ codes, each has length $2^{n+3}$, can be constructed as follows

(8)$$\boldsymbol{H}_n =\left\{\boldsymbol{h}_i\right\}_{i=1}^{2^{n+1}} =\begin{bmatrix} \boldsymbol{C}_n & \boldsymbol{D}_n\\ \boldsymbol{E}_n & \boldsymbol{F}_n \end{bmatrix} =\begin{bmatrix} \boldsymbol{X}\times\boldsymbol{C}_{n-1} & \boldsymbol{X}\times\boldsymbol{D}_{n-1}\\ \boldsymbol{Y}\times\boldsymbol{E}_{n-1} & \boldsymbol{Y}\times\boldsymbol{F}_{n-1} \end{bmatrix}n\geq 1$$

where $\boldsymbol {X}$ and $\boldsymbol {Y}$ are two Hadamard matrices of order-2, and $n$ is the iterating times. Also, the code set $\boldsymbol {H}_n$ consists of four codes $\boldsymbol {C}_n=[c_{i,j}]_{0\leq i< 2^{n}, 0\leq j< 2^{n+2}}$, $\boldsymbol {D}_n=[d_{i,j}]_{0\leq i< 2^{n}, 0\leq j< 2^{n+2}}$, $\boldsymbol {E}_n=[e_{i,j}]_{0\leq i< 2^{n}, 0\leq j< 2^{n+2}}$ and $\boldsymbol {F}_n=[f_{i,j}]_{0\leq i< 2^{n}, 0\leq j< 2^{n+2}}$. It has advantages in flexibility for generating initial matrix and possibility for constructions compared with our previous work [25].

Step 3: There is only one code in $\boldsymbol {H}_i$ with different number of ’$+1$’ and ’$-1$’, which needs to be discarded to ensure the weight $w=L/2$ and correlation properties.

Proof: Based on Step 1 and Step 2, a Hadamard matrix $\boldsymbol {U}_0$ can be obtained by

(9)$$\boldsymbol{U}_0=\frac{1}{2} \begin{bmatrix} \sum\limits_{i} c_i & \sum\limits_{i} d_i\\ \sum\limits_{i} e_i & \sum\limits_{i} f_i \end{bmatrix}$$

The Hadamard matrices $\boldsymbol {X}$ and $\boldsymbol {Y}$ are employed to extend the column and row of $\boldsymbol {H}_0$, so the matrix $\boldsymbol {U}_n(n\geq 1)$ calculated by (10) is also a Hadamard matrix.

(10)$$\boldsymbol{U}_n=\frac{1}{2^{n+1}} \begin{bmatrix} \sum\limits_{i,j} c_{i,j} & \sum\limits_{i,j} d_{i,j}\\ \sum\limits_{i,j} e_{i,j} & \sum\limits_{i,j} f_{i,j} \end{bmatrix}$$

According to the properties of Hadamard matrix, only one code with different number of ’+1’ and ’−1’ exsits in $\boldsymbol {H}_n$.

After discarding, a new code set $\boldsymbol {H}_{n}^{'}=\{\boldsymbol {h}_i^{'}\}_{i=0}^{2^{n+1}-1}\in \boldsymbol {H}_{n}$ is obtained to generate a pair of transmitting code set $\boldsymbol {T}$ and receiving code set $\boldsymbol {R}$ as follows

(11)$$\begin{aligned} &\boldsymbol{OZCZ}={<}\boldsymbol{R},\boldsymbol{T}>\\ &\left\{\begin{matrix} \boldsymbol{R}=\boldsymbol{H}_{n}^{'}=\left\{\boldsymbol{r}_k\right\}_{k=1}^{2^{n+1}-1}\\ \boldsymbol{T}=f(\boldsymbol{R})=\left\{\boldsymbol{t}_{k}^{d_k}\right\}_{k=1}^{2^{n+1}-1} \end{matrix}\right. \end{aligned}$$

where the $k$-th user original data $d_k\in \left \{ 0,1 \right \}$ and $f(\cdot )$ denotes the mapping relation between $\boldsymbol {T}$ and $\boldsymbol {R}$ given as

(12)$$\boldsymbol{t}_{k}^{d_k}=\frac{1+({-}1)^{d_{k}}\boldsymbol{r}_k}{2}$$

Based on above steps, the correlation properties between $\boldsymbol {r}_k$ and $\boldsymbol {t}_k^{d_t}$ can be given by

(13)$$\theta_{\boldsymbol{r}_i,\boldsymbol{t}_j^{d_k}}(\tau)=\left\{\begin{matrix} ({-}1)^{d_k}2^{n+2} & i=j,\tau=0\\ 0 & i\neq j,\tau=0\\ 0 & 0<\left | \tau \right | \leq 2 \end{matrix}\right.$$

where $w=L/2$ and $0\leq i,j<2^{n+1}-1$. Therefore, the above $\boldsymbol {OZCZ}$ is the OZCZ code set pair with $Z_{cz}=2$ and $K=2^{n+1}-1$. It includes two combinations due to different original user data $d_k$. With the same iterations, the new construction achieves a longer zero correlation zone than [25], and the length of zero correlation zone can also be extended by interleaving method.

Proof: By constructing the initial matrix and one iteration, the periodic correlation function of $\boldsymbol {H}_{1}^{'}=\{{\boldsymbol {h}_{i}^{'}}\}_{i=0}^{2}$ satisfy:

(14)$$\theta_{\boldsymbol{h}_i^{'},\boldsymbol{h}_j^{'}}(\tau)=\left\{\begin{matrix} 16 & i=j,\tau=0\\ 0 & i\neq j,\tau=0\\ 0 & 0<\left | \tau \right | \leq 2 \end{matrix}\right.$$

Because $\boldsymbol {X}$ and $\boldsymbol {Y}$ are both Hadamard matrices, the iterating method only changes the code length $L$ and the number of codes $K$ while $Z_{cz}$ keeping unchanged. The code set $\boldsymbol {H}_{n}^{'}(n\geq 1)$ generated by iterating can be used to generate the bipolar code set $\boldsymbol {R}$. As consequence, we have

(15)$$\theta_{\boldsymbol{r}_i,\boldsymbol{r}_j}(\tau)=\left\{\begin{matrix} 2^{n+3} & i=j,\tau=0\\ 0 & i\neq j,\tau=0\\ 0 & 0<\left | \tau \right | \leq 2 \end{matrix}\right.$$

where $0\leq i,j<2^{n+1}-1$. In the new construction, the weight of each code is $L/2$ and each transmitting code set satisfies $\boldsymbol {t}_{k}^{d_k}=\frac {1+(-1)^{d_{k}}\boldsymbol {r}_k}{2}$. The correlation function for the $\boldsymbol {OZCZ}$ can be simplified as follows

(16)$$\begin{aligned} \theta_{\boldsymbol{r}_i,\boldsymbol{t}_j^{d_k}}(\tau)&=r_{i,l}\sum_{l=0}^{L-1}(\frac{1+({-}1)^{d_k}r_{j,(l+\tau)mod L}}{2})\\ &=({-}1)^{d_k}\frac{\theta_{\boldsymbol{r}_i,\boldsymbol{r}_j}(\tau)}{2}\\ &=\left\{\begin{matrix} ({-}1)^{d_{k}}2^{n+2} & i=j,\tau=0\\ 0 & i\neq j,\tau=0\\ 0 & 0<\left | \tau \right | \leq 2 \end{matrix}\right. \end{aligned}$$

where $0\leq i,j<2^{n+1}-1$. Consequently, the combination of transmitting code set $\boldsymbol {T}$ and receiving code set $\boldsymbol {R}$ can be considered as OZCZ code set pair according to (2).

2.3 Example of the new construction

As an example, we generate an OZCZ code set pair with parameters $(L,K,Z_{cz})=(16,3,2)$ by one iteration. The generation steps and properties are given as follows.

Step 1: We construct a new matrix $\boldsymbol {S}^{'}$ with two codes $\boldsymbol {s}_{1}$ and $\boldsymbol {s}_{3}$ from $\boldsymbol {S}$ and separate it into two Hadamard matrices of order-2 as follows

(17)$$\boldsymbol{S}^{'}=\begin{bmatrix} \boldsymbol{s}_{i}\\ \boldsymbol{s}_{j} \end{bmatrix}=\left [ \begin{array}{c:c} \begin{matrix} + & +\\ + & - \end{matrix} & \begin{matrix} + & -\\ + & + \end{matrix} \end{array} \right ]$$

Step 2: When considering $a=1$ and $b=-1$ , an initial matrix $\boldsymbol {H}_{0}$ can be generated as follows

(18)$$\boldsymbol{H}_0 =\begin{bmatrix} -\boldsymbol{B} & \boldsymbol{A} & \boldsymbol{B} & \boldsymbol{A} \end{bmatrix} =\left [ \begin{array}{c:c:c:c} \begin{matrix} - & +\\ - & - \end{matrix} & \begin{matrix} + & +\\ + & - \end{matrix} & \begin{matrix} + & -\\ + & + \end{matrix} & \begin{matrix} + & +\\ + & - \end{matrix} \end{array} \right ]$$

which can be seen as four codes with length $L=4$,

(19)$$\left\{\begin{matrix} \boldsymbol{C}_{0}=\begin{bmatrix} - & + & + & + \end{bmatrix} \\ \boldsymbol{D}_{0}=\begin{bmatrix} + & - & + & + \end{bmatrix} \\ \boldsymbol{E}_{0}=\begin{bmatrix} - & - & + & - \end{bmatrix} \\ \boldsymbol{F}_{0}=\begin{bmatrix} + & + & + & - \end{bmatrix} \end{matrix}\right.$$

Then, we assume that two 2-order Hadamard matrices $\boldsymbol {X}=\begin {bmatrix}+ & -\\ + & +\end {bmatrix}$ and $\boldsymbol {Y}=\begin {bmatrix}+ & +\\ + & -\end {bmatrix}$. By iterating, a code set $\boldsymbol {H}_{1}$ can be constructed as follows

(20)$$\begin{aligned} \boldsymbol{H}_1 =\left\{\boldsymbol{h}_i\right\}_{i=1}^{4} =\begin{bmatrix} \boldsymbol{C}_1 & \boldsymbol{D}_1 \\ \boldsymbol{E}_1 & \boldsymbol{F}_1 \end{bmatrix} =\left[ \begin{array}{c:c} \begin{matrix} -++++---\\ -+++-+++ \end{matrix} & \begin{matrix} +-++-+--\\ +-+++-++ \end{matrix} \\ \hdashline \begin{matrix} --+---+-\\ --+-++-+ \end{matrix} & \begin{matrix} +++-+++-\\ +++----+ \end{matrix} \end{array} \right] \label{eq20}\end{aligned}$$

Step 3: The code $\boldsymbol {h}_{2}$ needs to be discarded. The new code set $\boldsymbol {H}_{n}^{'}=\{\boldsymbol {h}_i^{'}\}_{i=0}^{2}\in \boldsymbol {H}_{n}$ is obtained to generate a pair of transmitting code set $\boldsymbol {T}$ and receiving code set $\boldsymbol {R}$ as follows

(21)$$\begin{aligned} &\hspace{32pt}\boldsymbol{OZCZ}={<}\boldsymbol{R},\boldsymbol{T}>\\ &\left\{\begin{matrix} \boldsymbol{R}=\boldsymbol{H}_{1}^{'}=\left\{\boldsymbol{h}_1,\boldsymbol{h}_3,\boldsymbol{h}_4\right\}=\left\{\boldsymbol{r}_k\right\}_{k=1}^{3}\\ \boldsymbol{T}=f(\boldsymbol{R})=\left\{\boldsymbol{t}_{k}^{d_k}\right\}_{k=1}^{3}\\ =\left\{\begin{matrix} \begin{bmatrix} 0+{+}+{+}000+0+{+}0+00 \\ 00+000+0+{+}+0+{+}+0 \\ 00+0+{+}0+{+}+{+}0000+ \end{bmatrix} d_{k}=0\\ \begin{bmatrix} +0000+{+}+0+00+0+{+} \\ +{+}0+{+}+0+000+000+ \\ +{+}0+00+0000+{+}+{+}0 \end{bmatrix} d_{k}=1 \end{matrix}\right. \end{matrix}\right. \end{aligned}$$

The correlation properties between $\boldsymbol {r}_{k}$ and $\boldsymbol {t}_{k}^{d_k}$ can be calculated as follows

(22)$$\theta_{\boldsymbol{r}_i,\boldsymbol{t}_j^{d_k}}(\tau)=\left\{\begin{matrix} 8 & i=j,\tau=0,d_k=0\\ -8 & i=j,\tau=0,d_k=1\\ 0 & i\neq j,\tau=0\\ 0 & 0<\left | \tau \right | \leq 2 \end{matrix}\right.$$

Consequently, the $\boldsymbol {OZCZ}$ is the OZCZ code set pair with $Z_{cz}=2$, $L=16$ and $K=3$. The transmitting code set $\boldsymbol {T}$ and the receiving code set $\boldsymbol {R}$ can be respectively applied to transmitter and receiver in the 3 users’ QS-CDMA-VLC system.

3. The QS-CDMA-VLC system design and experiment setup

3.1 System design

Figure 1(a) gives the QS-CDMA-VLC system design for LOS (Line-of-sight) case. The multi-user system contains two optical channels introducing MAI and time delay among users practically. Two experiment setups are designed to generate different signals with different user numbers. There are two users in experiment setup 1, each transmitted signal has two levels for On-Off keying (OOK) modulation. In experiment setup 2, each optical channel contains multi-level signals from multiple users with same number. We adopt setup 2 to evaluate the effects of user numbers with different code sets in the QS-CDMA-VLC system. We investigate and compare four different constructions of optical code sets shown in Table 1, which are all suitable for quasi-synchronous system.

Fig. 1. (a) Block diagram of QS-CDMA-VLC system (b) Experiment setup of the QS-CDMA-VLC system.

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Table 1. Comparison among the proposed code set pair and some existing code sets for the QS-CDMA-VLC system.

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In the transmitter, the $k$-th user original data $d_k(t)$ is first through spread module. The total optical signal $s(t)$ can be written as

(23)$$s(t)=CH1(t)+CH2(t)=\sum_{k=1}^{K}s_{k}(t)$$

where $s_{k}(t)$ is the $k$-th user transmitted signal, $T_{c}$ is the chip time interval and $T=LT_{c}$ is the symbol period. According to different constructions, the waveform $s_{k}(t)$ for $k$-th user transmitting one symbol $d_{k}(t)$ can be given by

(24)$$s_{k}(t)=\left\{\begin{matrix} \mathop{\sum}\limits_{i=0}^{L-1}\frac{1+({-}1)^{d_k(t)}r_k(i)}{2}P_{T_c}(t-iT_c) & case1 \\ \mathop{\sum}\limits_{i=0}^{L-1}r_k(i)P_{T_c}(t-iT_c) & case2 \end{matrix}\right.$$

where $r_k(i)=r_k(i+L)$ , and $P_{T_c}(t)$ is a unit rectangular pulse. And case1 and case2 represent two situations of the system. The system adopts the proposed construction or OZCZ [20] as spreading code set in case1 and adopts OZCZ [16] or ZCC [21] in case2.

At the receiver, the received signals $r(t)=s(t)+n(t)$ from the photodetector (PD) contain the active users’ signals and the additive white Gaussian noise (AWGN). Transmission time is influenced by signal transmission rate and transmission distance. The difference of free-space transmission distance among users would introduce time delay. In zero correlation zone, the OZCZ code set pairs have excellent correlation properties of each code. When the time delay does not exceed zero correlation zone length, the desired user data can be easily recovered by de-spreading and decision [25].

3.2 Experimental setup

Figure 1(b) shows the experimental setup used for the QS-CDMA-VLC experimental system. The $K$-user system is based on different code sets for different transmission rates and free-space transmission distance. The transmitted signals $CH1(t)$ and $CH2(t)$ for two optical channels are generated by an arbitrary waveform generator (AWG 70002A) and then amplified by amplifiers (ZHL-6A-S+). The red LEDs as the light sources are driven by two Bias-Tee (ZFBT-6GW+). And the two LEDs for the two channels emit the same power. In the optical channel, lenses are adopted to enhance the received optical power. At the receiver, a PD (APD AD500) is used to detect the optical signals, which can be recorded by a mixed signal oscilloscope (MSO 70604C) for offline signal processing. The free-space transmission distance of one optical channel is set to 1 m. All the experiments are conducted under normal ambient light ($\sim$200 lux).

4. Results and discussion

In this section, we investigate and analyze the QS-CDMA-VLC system illumination and communication performance when the proposed construction and existing optical code sets are used, respectively. The LEDs are optimally biased at 2.45V to ensure that received optical signals have little nonlinear distortion. The sampling rate of MSO is set as 625 MS/s. In all the result figures, the 7% FEC threshold of 3.8$\times$10$^{-3}$ is shown by a horizontal line. We rename OZCZ code set [16,20] and ZCC code set [21] as code sets OZCZ I, OZCZ II and ZCC, respectively.

By simulation calculations, we obtain the dimming values in terms of different active user numbers and input ratios of original user data. The dimming value defined by the ratio of ’1’s in the transmitted signals has an effect on the illumination performance of the system [26,27]. Figure 2 shows the dimming values of optical CDMA system adopting code sets OZCZ I, OZCZ II, ZCC and the proposed OZCZ code set pair. As shown in Fig. 2(a), the increasing active user numbers will lead to decline of the performance of effective illumination using code sets OZCZ I and ZCC. The new construction in this work and code set OZCZ II can always maintain constant illuminance, regardless of the number of users. The reason is that the dimming values of the system with the proposed OZCZ, OZCZ II, OZCZ I and ZCC are $0.5$, $0.5$, $1/3K$ and $1/K$, respectively. With the increasing number of users, the proposed and OZCZ II can constant dimming value at $0.5$ which have a reduced value when using OZCZ I and ZCC. It is indicated from Fig. 2(b) that input ratio of ’0’s and ’1’s of original user data makes no difference to the system dimming value system with the new construction, but the dimming values would reduce rapidly with the increase of ’0’s when the system using code sets OZCZ I and ZCC. The reason is that, the input data ’0’ is mapped to the proposed OZCZ and OZCZ II code with $L/2$ zeros but mapped to the proposed OZCZ I and ZCC code with $L$ zeros. Therefore, the proposed construction is superior to other constructions regarding dimming value, which is beneficial to the illumination performance.

Fig. 2. Comparison of dimming value versus (a) the number of active users and (b) the input ratio of original user data for the QS-CDMA-VLC system.

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An overall bit rate $R$ for multi-user system can be obtained by $R=SK/L$ , where $S$ is the sample rate of AWG. Figure 3 compares the overall bit rate of the CDMA-VLC system with different active user numbers using the proposed construction, code sets OZCZ I, OZCZ II and ZCC when $S$=100 MS/s. For a fair comparison, we assume that the length of zero correlation zone remains the same for the proposed construction, OZCZ I and OZCZ II. And the code weight equals $2(K+1)$ in numerical calculations for different code construction. For the proposed construction and OZCZ II, with the increasing number of active users, the overall bit rate of the system increases and the riding speed gradually becomes gentle as shown in Fig. 3. However, the overall bit rate decreases obviously for the OZCZ I and ZCC code set. It is because when the code weight and number of different codes are certain, OZCZ I and ZCC need to extend the length of code. Besides, too many ’0’s will degrade the BER performance of the VLC system, which would be discussed in the subsequent analysis.

Fig. 3. Overall bit rate versus the number of active users for the QS-CDMA-VLC system adopting different code sets when the sample rate of AWG is 100 MS/s.

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Figure 4 compares the BER performance versus sample rate of AWG of the 2-user QS-CDMA-VLC experimental system adopting different code sets in the case of experiment setup 1. The transmission distance difference is set as 0 m and 1 m in Figs. 4(a) and (b) respectively, for the different time delay difference between the two optical channels. The results from Fig. 4 indicate that compared with the other code sets, the proposed construction can effectively improve the system BER performance and can be applied to the system with higher transmission rate. This reason is that the proposed construction has better correlation properties and greater weight than unipolar code sets OZCZ I and ZCC, which can better overcome the interference among users. Meanwhile, the proposed construction has longer zero correlation zone length than OZCZ II. It can more effectively suppress the impact of time delay on BER performance for the QS system. As a result, the system using the proposed OZCZ has higher overall bit rate than that using OZCZ II under the 7% FEC limit as shown in Fig. 4. Time delay caused by transmission distance difference has less impact on the BER performance for OZCZ I and ZCC code set, this is because the longer symbol cycle for lower sample rate of AWG is less sensitive to the time delay. Besides, the BER performance of the 2-user system is degraded as the sample rate of AWG increases, which is similar with above discussion about system performance with different user numbers.

Fig. 4. Comparison of BER performance of the experimental QS-CDMA-VLC system versus sample rate of AWG in case of experiment setup 1 taking (a) 0 m and (b) 1 m as transmission distance difference.

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The communication performances of the QS-CDMA-VLC system varying as the user numbers, free-space transmission distance differences and sample rates of AWG are further investigated. Figure 5 firstly gives the BER performance of the CDMA-VLC system using the proposed OZCZ code set pair with different free-space transmission difference between the two optical channels. Two experimental setups with different number of active users $K$=2 and $K$=14 have been used in evaluation. In the experiment, the free-space transmission distance difference is adjusted from 0 m to 1 m to introduce different time delay. As shown in Fig. 5, the BER can still satisfy 7% FEC limit when time delay exists and the transmission distance difference is 0.5 m. With the increase of free-space transmission distance difference, the BER performance of different system has a similar degradation trend. Because extending transmission distance of one optical channel would cause lower received power, which also has impact on BER performance. Further, it is demonstrated that due to the influence of high-frequency fading characteristics of LEDs, the transmitted signals with the higher transmission rate have lower power, leading to the decrease of system performance. The results also show that for the 2-user and 14-user CDMA-VLC system, about 32.5 Mb/s and 24.1 Mb/s overall bit rate can achieve for 7$\%$ FEC limit, when the transmission distance difference is 1 m. The further improvement of BER performance can be realized by channel equalization technology.

Fig. 5. BER performance of the experimental QS-CDMA-VLC system versus free-space transmission distance difference with two experimental setups (a) $K$=2 and (b) $K$=14

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The BER performance of the QS-CDMA-VLC system varying with transmission distance difference for the proposed OZCZ construction and OZCZ II is further given in Fig. 6. The experiment is in case of experiment setup 2, each LED transmits multi-level signals with the same number of levels. Two-level and multi-level signals have different transmission characteristics in the optical channel, so there is no comparison with OZCZ I and ZCC. The experimental results show that, the BER performance of the system is degraded as the user numbers increase. The reason is that with the increase of active user numbers, a single user cannot effectively suppress MAI, which would limit the capacity of the system. It is similar to the above analysis that the increase of free-space transmission distance difference also leads to reduction of received power and degradation of BER performance. Meanwhile, for the new construction, the longer zero zone correlation can effectively overcome small time delay among users induced by the difference of channel. It is revealed that when the transmission distance difference is 0.5 m, the system with the proposed OZCZ can support 14 users when the overall bit rate is 26.3 Mb/s, but only support 6 user with 16.9 Mb/s overall bit rate using OZCZ II as shown in Fig. 6. Furthermore, we can extend the length of zero zone correlation for the OZCZ construction by interleaving method [25]. It is necessary to make a trade-off between overall bit rate and BER performance according to the system requirement.

Fig. 6. Comparison of BER performance of the QS-CDMA-VLC system in case of experiment setup 2 adopting the proposed construction and OZCZ II.

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5. Conclusion

In this paper, we present a new construction of OZCZ code set pair with $(L,K,Z_{cz})=(4(K+1),K,2)$ and $w=2(K+1)$ based on iterating method. The proposed construction has ideal zero correlation zone properties and can be more suitable for the QS VLC system. We investigate and compare the dimming value, overall bit rate and BER performance of the QS-CDMA-VLC system employing the proposed OZCZ codes and other existing optical codes. The results show that the proposed construction can always maintain a specific dimming value at 50% without considering the number of users and the input ratio of original user data, which is beneficial to the improvement of the illumination performance. Furthermore, it is reveal that the BER performance in the QS-CDMA-VLC system using the proposed construction can suppress MAI and time delay impact effectively with different user numbers, sample rates and transmission distance difference. The results show that the system with the proposed OZCZ construction can support 2 users with 32.5 Mb/s overall bit rate and 14 users with 24.1 Mb/s overall bit rate. In a word, the proposed OZCZ code set pairs can be considered as a potential and appropriate candidate for multiple access in VLC system, which can significantly enhance the illumination and communication performance.

Funding

National Natural Science Foundation of China (61671055).

References

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Construction	Parameters $(L, K, Z_{c z})$	Weight $(w)$	Polarity (Transmitter-Receiver)
Proposed	(4( $K$ +1), $K$ ,2)	2( $K$ +1)	Unipolar-Bipolar
Ref. [16]	(3 $K w$ , $K$ ,2)	Arbitrarily	Unipolar-Unipolar
Ref. [20]	(4( $K$ +1), $K$ ,1)	2( $K$ +1)	Unipolar-Bipolar
Ref. [21]	( $K w$ , $K$ ) without $Z_{c z}$	Arbitrarily	Unipolar-Unipolar

On the study of a quasi-synchronous CDMA-VLC system with two channels

Abstract

1. Introduction

2. Optical zero correlation zone codes

2.1 Definition

2.2 New construction of OZCZ code set pair

2.3 Example of the new construction

3. The QS-CDMA-VLC system design and experiment setup

3.1 System design

3.2 Experimental setup

4. Results and discussion

5. Conclusion

Funding

References

Cited By

Figures (6)

Tables (1)

Equations (24)

Optics Express