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Abstract
In this paper, we propose a chaos-based visible light communication system, wherein multiple users can access the network via the multi-carrier code division multi-access (MC-CDMA). By utilizing the high security property of chaotic sequences being aperiodic and sensitive to initial values, secure access can be achieved. However, the multi-carrier transmission suffers from high peak to average power ratio (PAPR) due to the superposition of multiple carriers, which reduces the lifetime of the light-emitting diodes (LEDs). In order to suppress the PAPR, we propose a joint matrix transform and dual layered phase sequencing (MT-DLPS) scheme. By reducing the autocorrelations of signals, the PAPR can be reduced. Moreover, the computation complexity is analyzed. Simulations are then conducted to validate that the PAPR is effectively reduced while maintaining satisfactory bit error rate (BER) performances.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Growing customer demands for higher data rate have motivated recent interest in visible light communication (VLC), which has become a hot research field seen as a promising candidate for complementing the conventional radio frequency (RF) communications [1]. Compared to traditional RF communications, VLC systems have advantages such as no electromagnetic interference, energy conservation, brightness efficiency, and harmless to human [2].
In VLC systems, multiple users can access the network using the multi carrier code division multi-access (MC-CDMA) scheme by utilizing the high spectral efficiency of multi carrier transmissions and the orthogonal codes to identify each user. However, due to the superposition of multicarrier signals, the peak to average power ratio (PAPR) will be higher. Since the light emitting diodes, which are used as antennas to deliver the user data, are power constrained, the high PAPR of MC systems is required to be lowered.
A lot of research works have been conducted to reduce the PAPR of MC-CDMA based VLC systems [3]. One straightforward method is to premeditatedly clip the multi-carrier transmission signal before amplification. Although the clipping operation can improve the PAPR performances, this procedure is a nonlinear process that may induce momentous in-band distortions, which will deteriorate the BER performances and out-of-band noise. Then the spectral efficiency is reduced. Besides, other distortionless methods, such as linearly combining time-domain even and odd sequences with cyclic shift and phase rotation [4], the linear nonsymmetrical transform (ILNST) method [5], and the partial transmit sequences (PTS), are also proposed to suppress the PAPR. In the PTS method, the authors put efforts to find an optimal combination of phase-rotated signal subblocks to minimize the peak power of the transmitted signal. For continuous domain symbols, the PTS method uses the same phase weighting factors to scrambling, which reduces the complexity of the best scrambling sequences searching algorithm. Both methods can improve the PAPR performances, however, the side information is required to recover the original MC-CDMA signal at the receiver, and the computational complexity is high.
Recently, the authors in [6] proposed to reduce the PAPR by utilizing an amalgamation of discrete Fourier transform (DFT) precoding and Gaussian minimum shift keying (GMSK) pulse shaping. Besides, the concept of the group precoding is also introduced to deal with the increased complexity of the DFT precoding system.
In this paper, based on our previous research work on chaos-based MC-CDMA VLC system [7], we propose a joint matrix transform and dual layered phase sequencing (MT-DLPS) scheme to suppress the PAPR with low complexity. Our objective is to achieve better tradeoff among the security of multiple user access, the PAPR and the reliability performance.In this design, we apply chaotic sequences to facilitate multiple users to access the VLC network. Since a chaotic dynamical system is a deterministic system, its random-like behavior can be very helpful in disguising modulations as noise. In addition, a large number of uncorrelated, random-like, yet deterministic and reproducible signals can be generated via finite arithmetic machines. Thus chaos-based multiple user access system can accommodate multiple users. Moreover, the correlation properties of chaotic sequences are similar to those of random white noise. Therefore, chaotic waveforms, which are generated from chaotic non-linear dynamical systems, are inherently wide-band in nature and perfect candidates for spreading narrow-band signals.
In this chaos-based VLC system, we combine the matrix transform and the two-tier phase sequencing approaches, and propose an optimization method to search for the optimal phase weighting factor [8]. Then we analyze the complexity, and provide simulation results to validate that with the proposed design, the PAPR can be effectively suppressed, while maintaining the satisfactory BER performances.
Briefly, the major contributions of this paper are listed as follows.
- 1. We utilize the property being aperiodic and sensitive to initial values of chaotic sequences to achieve secure code division multiuser access for VLC networks.
- 2. We propose to jointly utilize the matrix transform and the DLPS, and then the phase weighting factor is optimized for the PAPR suppressing.
- 3. We conduct the computational complexity analysis, and then simulations are provided to validate the proposed design.
The rest of the paper is organized as follows. In Section 2, The VLC system model for the MC-CDMA scheme is presented. Then we analyze the PAPR of real-valued MC-CDMA signals. In Section 3, we present the details of the proposed scheme. Simulation results are then provided in Section 4. Finally, we conclude this design in Section ??.
2. System model
In the considered VLC communication scenarios, the users distributed randomly in the office communicate with the LED in the center of the ceiling via the visible light channel which consists of the direct transmission and/or single/multiple reflections. The channel corresponding to the direct information transmission path is called the line-of-sight (LOS) channel, while the channel with reflections is called non-line-of-sight (NLOS) channel.
Multiple users access the VLC network via the MC-CDMA scheme and share the same bandwidth as well as the same time slots. With the aid of the chaos-based spreading, at the receiver, the user data can be identified securely with the known chaotic sequence chips.
Figure 1 illustrates the block diagram of the chaos-based MC-CDMA VLC system with the MT-DPLS PAPR suppressing design. In the proposed system, the intensity modulation and direct detection (IM/DD) scheme is employed, which is cost-effective compared to coherent ones. In IM/DD systems, no local oscillator is required, and the information bits are modulated onto the intensity, or power, of the light beam from a light-emitting diode (LED).
Fig. 1. Block diagram of MC-CDMA VLC system (DC: direct current, S/P: serial to parallel, P/S: parallel to serial, CP: cylix prefix, MT: matrix transform, IMT: inverse matrix transform)
To be explicit, at the transmitter, the data symbols from different users are first spread by chaotic sequences. After the serial to parallel (S/P) conversion, the matrix transform and the Hermitian symmetric mapping are conducted. Then the DPLS is carried out to suppress the PAPR. Subsequently, the inverse fast Fourier transform (IFFT) is performed. Notably, since the LED requires the real-valued signal, the input signals to the IFFT module should be Hermitian symmetric [2]. After adding the cyclic prefix (CP) and parallel to serial (P/S) conversion and the direct current, the electrical to optical (E/O) conversion, resultant optical signals are delivered via the VLC channels.
At the receiver, reverse operations are conducted. After the photo diodes conduct the detection and the optical to electrical (O/E) conversion is conducted, the S/P operation is carried out. Then the CP is removed, fast Fourier transform (FFT) and inverse matrix transform (IMT) are conducted. Next after the P/S and chaos-based de-spreading, the recovered data are delivered to the user equipments.
Note that the chaotic sequences are generated according to the following expression,
Then, the data from different users are added and modulated as a multiplexed MC-CDMA signal. MC-CDMA is an MC transmission scheme in which the original data payload is first modulated with the spreading sequence, and then the chips of the spread data are modulated onto orthogonal subcarriers. Here we define the MC-CDMA signal generated with a complex data symbol as of $a^{(h)}$, which is assigned to the user $h$. Besides, the user-specific spreading code is $b^{(h)} = \left [ b_{0}^{(h)}, b_{1}^{(h)},\ldots, b_{D-1}^{(h)} \right ]^{T}$, while the spread factor is $D$.
Let $x(t)$ represents the baseband signal in the time domain obtained after the IFFT transform, while $x^{(h)}(t)$ represent the signal for the $h_{th}$ user. For one MC-CDMA symbol, $0 \leqslant t \leqslant T_{s}$ can be expressed as
where $T_{s}$ is the MC-CDMA symbol period, $t$ is time, and $H$ is the total number of users.Then the PAPR for the MC-CDMA baseband signal in Eq. (2) is defined as the ratio of the maximum instantaneous peak power to the average power of the MC-CDMA signal [10], [11] and is given as follows
where $P_{av}$ is the average power, which can be calculated asConsidering that the user data are randomly distributed, naturally, we evaluate the statistical characteristics of the PAPR. The most classical approach for the analyses of PAPR is to use the complementary cumulative distribution function (CCDF), which is described as the probability of the PAPR exceeding a certain level $PAPR_0$ [5], that is,
where $prob(\cdot )$ refers to the probability of an event.As mentioned above, the chaos-based MC-CDMA baseband signal is the superposition of many independent signals modulated onto subchannels. Note that the chaotic sequences are real valued, which also have impacts on the PAPR. When the samples from all the subcarriers are in phase, the peak power of the signal becomes $N$ times that of the average power, i.e., $PAPR = 10 log(N)$. As a result, the PAPR increases. Since in a typical multicarrier transmission system, a high power amplifier (HPA) can be used to produce an output transmit power that is a multiple of the input transmit power. However, this type of amplifier has a limited linear region [12]. Thus, multicarrier transmission signals with a PAPR that is larger than the saturation point of the HPA will be clipped, resulting in deteriorations in both spectrum efficiency and energy efficiency [13]. To avoid this nonlinear distortion, either the linear range of HPA should be increased; that is, the value of input back off (IBO) should be greater than the PAPR, or the PAPR should be kept smaller than the IBO value. Nevertheless, the power consumption of HPA increases as the value of IBO increases, which leads to an inefficient HPA and results in expensive transmitters. In the following section, we will introduce how to suppress the PAPR to improve the performances.
3. MT-DLPS scheme
In this section, we present the details of the joint MT-DLPS PAPR suppressing scheme, as shown in Fig. 2.
3.1 Matrix transform
In OFDM systems, PAPR of OFDM signal is closely linked with the auto correlation function of input signal, which can be represented by
where $N$ is the number of subcarriers, and $R_{k}$ is the auto correlation function of signal which is expressed as where $X$ is the input signal. We can see from the Eq. (7) that the PAPR of the signal will be smaller when the $\sum _{k=1}^{N}\left | R_{k} \right |$ becomes smaller. Thus, we can use the matrix tansform method to reduce the autocorrelation in MC-CDMA VLC systems.In addition, the matrix transform method has a low computational complexity because the system only needs to complete only one matrix transformation. Besides, there is no need to carry out IFFT operation many times. The transform matrix used by the transceiver usually is preset , and no additional information is needed for demodulation. The PAPR suppressing performances of the matrix transformation is related to the selected transform matrix, and two typical transformation matrices are presented as below.
3.1.1 Hadamard matrix transform
The Hadamard matrix [14] can be generated by
3.1.2 Discrete cosine transform
Discrete cosine matrix is also an orthogonal matrix. Since the DCT meets the it makes use of the Passevel theorem [15], the energy of the signal before and after transformation remains the same. Thus, with the aid of the DCT processing, the PAPR of MC-CDMA VLC systems can be reduced. The discrete cosine matrix is generated by
3.2 Dual layered phase sequencing method
Dual layered phase sequencing (DLPS) is proposed to reduce the computational complexity of PTS. The layers are classified as micro- and macro-optimization layers. In micro-optimization, the $M$ subblocks are grouped into $M/2$ divisions. Within each division all possible combinations of phase rotation factors are optimized to obtain a combination with minimum PAPR. In the second layer, a macro-optimization occurs, in which each individually optimized division is considered as a block for reducing the PAPR.
Assuming the signal after the matrix transform operation is expressed as $X=[X_{0},X_{1},\ldots,X_{N-1}]$, let $x$ denote the weighted output signal obtained from an exhaustive search, then we have,
Similar to the PTS method, the key of the DLPS approach is optimize the sequence $\left \{ \varphi _{m} \right \}_{m=0}^{M-1}$, which enable the PAPR of the time domain output signal to be optimized, can be represented by
It is worth mentioning that we can apply the exhaustive searching algorithm or suboptimal optimization algorithms such as the Newton iteration algorithms to find the solution.
4. Simulation details and results
In this section, the LoS and NLoS model developed in [16] is chosen as the channel model. The simulation parameters are listed in Table 1. In the simulations, without loss of the generality, we assume that the channel state information is known at the receiver, and the inter symbol interference (ISI) can be perfectly removed with the aid of the CP. Without loss of generality, we assume that the LED operates under the perfect condition.
Table 1. The simulation parameters.
Note that the PAPR issue is mainly induced by the superposition of signals in the electrical domain. Since for VLC systems, the LED in fact acts as the antenna for delivery of the optical signals. Hence the nonlinearity of the LED in the optical domain is neglected for the discussion of the BER in the electrical domain. Namely, the imperfect condition of the LED needs not be considered for the BER evaluations of electrical signals with the aide of the PAPR suppressing.
4.1 PAPR performance
We first evaluate the PAPR of the MT-DLPS scheme scrambled MC-CDMA signals with different grouping methods, namely adjacent group, cross group, random group and random cross group. It can be seen from Fig. 3 that the PAPR performance of the 4QAM-based MC-CDMA signals with random group outperforms that of the system with other grouping methods. At $CCDF = 10^{-3}$, the random group method can reduce the PAPR by approximately 6dB compared with the original signal. In addition, the performances of the random cross group and adjacent group are similar, with the gain of PAPR at $CCDF = 10^{-3}$ being almost 5.6dB.
Subsequently, we evaluate the PAPR performances of the chaos-based MC-CDMA VLC system using different PAPR suppressing schemes. We can see from the Fig. 4 that with the proposed joint MT-DLPS scheme, the VLC systems achieves better PAPR performances than those of benchmark MT or PTS approach. The gain of PAPR at $CCDF = 10^{-3}$ is more than 5dB. It is also noticeable that the DCT-based system outperforms the VLC system using the walsh hadamard transform (WHT) based PAPR suppressing method.
Fig. 3. PAPR performances of MA-CDMA VLC systems adopting MT-DLPS scheme with different grouping method
4.2 BER performance
Figure 5 illustrates the BER performances and compare them among the proposed MT-DLPS scheme, conventional PTS-based system and the original MC-CDMA VLC system over a multipath wireless optical channel. It can be seen from Fig. 5 that the VLC systems with PTS scheme outperform the original system and the proposed chaos-based MC-CDMA VLC system using the proposed MT-DLPS scheme. The reason is that the matrix transform method decrease the correlation of signals of different users, thus larger interferences are induced to degrade the BER performances. Moreover, we can observe that when the SNR increases, thanks to smaller interferences between users, the BER performances of the chaos-based VLC system using the MT-DLPS scheme are improved and approach those of benchmark system with no PAPR suppressing scheme. Besides, it is also noticeable that the performance gap between the proposed system and the benchmark PTS system become larger due to interferences induced by the real-valued chaotic sequences.
4.3 Computational complexity
Finally, we compare the complexity of the proposed design and benchmark schemes as shown in Table 2. Considering that the optimization involved in Eq. (12) might use suboptimal method, for fairness of comparisons, we neglect the complexity induced by the optimization given in Algorithm 1. In the complexity analysis, $W$ means the number of phase weighting factor, $M$ denotes the number of grouping. Thus, the sequences $\left \{ \varphi _{m} \right \}_{m=0}^{M-1}$ has $W^{M}$ kinds of values. One PTS operation corresponds to $W$ times N-point IFFT, then a total of $MW^{M}$ times N-point IFFT need to be calculated. Each N-point IFFT requires to conduct the computation of the complex multiplication and the complex addition, which is represented as,
Fig. 5. BER performances of the proposed joint MT-DLPS aided chaotic VLC system and benchmark PTS-based VLC systems.
Table 2. Complexity comparison of different precoding schemes.
When the number of grouping $M = 4$, the phase weighting factor set number $W = 4$, PTS scheme needs to take $2^{10}$ times IFFT, while the proposed MT-LDPS scheme requires only 520 times IFFT. Thus the complexity of the proposed design is much smaller than that of the PTS scheme.
5. Conclusion
conclusion In this paper, we propose a chaos-based MC-CDMA VLC system and the PAPR suppressing scheme. In this design, we utilize the aperiodic and high security property of chaotic sequences to realize secure multiple user access, and then we propose the joint MT-DLPS scheme to suppress the PAPR with lower computational complexity. By utilizing the matrix transform and the optimized DLPS method, the PAPR performance can be effectively suppressed. Moreover, we conduct the simulations over the VLC channels to validate our design. The results demonstrate that the proposed system achieves better PAPR performances than benchmark systems, while maintaining satisfactory BER performances. Furthermore, we provide the computational complexity analysis to show that the complexity of the proposed design is lower than that of benchmark systems. Therefore, the proposed PAPR suppression chaos-based MC-CDMA VLC design can effectively lower the PAPR and extend the lifetime of LEDs and will be potentially applied in practical systems for multiple users.
Funding
National Natural Science Foundation of China (61872254, U20A2016); Key Research & Development and Transformation Plan of Science and Technology Program for Tibet Autonomous Region (XZ201901-GB-16); Guangdong Basic and Applied Basic Research Foundation (2020A1515010703).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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