Design of a Cyclic Shifted LACO-OFDM for Optical Wireless Communication

This paper proposes a cyclic shifted layer asymmetrically clipped optical orthogonal frequency division multiplexing system (CS-LACO-OFDM) for optical wireless communications. The transmitted signal in CS-LACO-OFDM is generated by combining the signal of the first layer and signals of the remaining <inline-formula> <tex-math notation="LaTeX">$L$ </tex-math></inline-formula>-1 layers with cyclic shift equivalents, where <inline-formula> <tex-math notation="LaTeX">$L$ </tex-math></inline-formula> is the number of the CS-LACO-OFDM layers. In particular, the sets of cyclic shift value in CS-LACO-OFDM are modulated on the odd subcarriers of the first layer with complex-valued symbols. Information on cyclic shift sets can be easily detected with the help of modulated symbols conveyed in the first layer without increasing the receiver complexity. Simulation results show that the CS-LACO-OFDM has a similar peak-to-average power ratio performance as LACO-OFDM with separate selective mapping scheme when the number of candidate signals is the same but at remarkably low computational complexity. Furthermore, the average bit error rate of CS-LACO-OFDM over all layers is minimized by the proposed optimal optical power allocation.


I. INTRODUCTION
Compared with conventional radio frequency wireless communication system, orthogonal frequency division multiplexing (OFDM) based optical wireless communication (OWC) system is perceived as a promising technology that has numerous advantages, such as no electromagnetic interference, license-free spectrum, and high privacy protection [1]. The transmitted signals of OWC have to be real and unipolar owing to the inherent nature of an optical light emitting diode (LED) transmitter. To meet this criterion, pulse amplitude modulated discrete multitone (PAM-DMT), asymmetrically clipped optical OFDM (ACO-OFDM), flip OFDM, direct current-biased optical OFDM (DCO-OFDM) have been extensively discussed in the literature [2]- [6]. However, these schemes have some drawbacks. DCO-OFDM increases the transmitted optical power because of the introduction of DC-bias. Although PAM-DMT and ACO-OFDM achieve higher optical power efficiency than DCO-OFDM, the spectral efficiency is sacrificed by half. Moreover, flip OFDM transmits the positive and negative components of real bipolar OFDM signals over two frame durations at the cost of an additional transmission delay.
The associate editor coordinating the review of this manuscript and approving it for publication was Jie Tang .
Layer ACO-OFDM (LACO-OFDM) has been recently proposed for OWC systems, which combine different layers of conventional ACO-OFDM with different subcarriers [7]- [12]. Although LACO-OFDM enhances the spectral efficiency without adding DC-bias, LACO-OFDM continues to suffer from the non-linear signal distortion of LED because of the presence of a high peak-to-average power ratio (PAPR). The high PAPR problems have been addressed by numerous PAPR reduction schemes for OFDM-based OWC systems [13]- [20]. However, these PAPR reduction schemes may be unsuitable for LACO-OFDM because of the specific superimposed properties of transmitted signals. The majority of these methods also require high computational complexity. To the best of the author's knowledge, the design of the low-PAPR transmitter with low complexity for LACO-OFDM has yet to be addressed sufficiently.
Inspired by the joint design of low-PAPR and lowcomplexity in a LACO-OFDM system, a cyclic shifted LACO-OFDM (CS-LACO-OFDM) is proposed for OWC. At the transmitter side of the CS-LACO-OFDM, the signal with the lowest PAPR is chosen to be transmitted from the combination of the signal of the first layer and the signals of the remaining L-1 layers with cyclic shift equivalents. In particular, the sets of cyclic shift value in CS-LACO-OFDM are encoded into binary bits and modulated on the odd subcarriers of the first layer with complex-valued symbols. At the receiver, the CS-LACO-OFDM symbols on the first layer are first demodulated as in LACO-OFDM, and the information on cyclic shift sets can also be detected with the assistance of the modulated symbols transmitted in the first layer. Thereafter, the CS-LACO-OFDM symbols on the remaining high L-1 layers can be demodulated layer-by-layer without increasing the receiver complexity. The main contributions of the CS-LACO-OFDM system are listed as follows.
1) In terms of the optical modulation for OWC systems, this is the first joint design of the low-PAPR and low-complexity in a LACO-OFDM system.
2) Compared with the SLM-based scheme that was applied to each layer of LACO-OFDM, CS-LACO-OFDM achieves considerable PAPR reduction performance, but at substantially low computational complexity. Furthermore, the CS-LACO-OFDM system has the same receiver complexity as that of LACO-OFDM.
3) We also propose the optimal optical power allocation to improve the detection performance of the sets of cyclic shift and minimize the average bit error rate of CS-LACO-OFDM over all the layers.

II. PROPOSED CS-LACO-OFDM
This section illustrates the transmitter architecture, receiver architecture, optimal optical power allocation, and complexity analysis in detail. In general, we assume that the ACO-OFDM symbols of the lth layer are independently chosen from the QAM constellation M (l) with zero mean and variance of σ 2 . Therefore, the time-domain ACO-OFDM signals of the lth layer is provided as follows: is the kth subcarrier in the lth layer. In CS-LACO-OFDM, the modulated subcarriers for the lth layer are provided as follows: where l = 2 l−1 , 3 × 2 l−1 , 5 × 2 l−1 , . . . , N − 2 l−1 denotes the sets of Layer l subcarriers carrying data. As shown in [10], x (l) ACO,n is a real-valued bipolar signal that has an anti-symmetry as follows: In addition, the variance of x (l) ACO,n for the lth layer is provided as follows: Thereafter, the negative amplitude of x (l) ACO,n has to be clipped to produce unipolar signals, which are suitable for transmission in optical wireless channel. The generated unipolar signals for the lth layer are denoted as follows: Compared with LACO-OFDM, the transmitted signal in the CS-LACO-OFDM is obtained by combining the clipped Layer 1 ACO-OFDM signal and the cyclic shift version of the clipped Layer l (l ≥ 2) ACO-OFDM signal. Therefore, the vth combined CS-LACO-OFDM signal can be obtained as follows: v is defined as follows: ]. (7) The current study denotes as a cyclic shift set for the vth transmitted signal. The CS-LACO-OFDM signal with the lowest PAPR among the V alternative cyclic shift sets is determined and transmitted as follows:v where PAPR of t v,n in CS-LACO-OFDM is defined as follows: Lastly, the transmitted signal suffers from the double-sided clipping of LED, where the resultant signal is provided as follows: where v upper and v ton denote the maximum permissible and turn-on voltages, respectively. In a CS-LACO-OFDM system, the V cyclic shift sets have to be modulated to complex-valued symbols based on the selected constellation and assigned thereafter on the odd subcarriers of the first layer. The number of required odd subcarriers is calculated as , where κ is the ceiling function that gives the smallest integer ≥ κ, and M (1) is the constellation set of the first layer. Evidently, CS-LACO-OFDM only requires the N cyclic subcarriers of the first layer to indicate the selected signal without losing considerable spectrum efficiency. Accordingly, the modulated subcarriers of the first layer are modified as follows:

B. RECEIVER ARCHITECTURE OF CS-LACO-OFDM
The proposed receiver architecture of CS-LACO-OFDM is illustrated in the bottom part of Fig. 1. The received electrical signal is obtained from the output of photodiode and is expressed as r v,n = h n ⊗ tˆv ,n + w n , where h n is the channel impulse frequency, ⊗ denotes the circular convolution, and w n is time-domain AWGN noise with a zero mean and a variance of σ 2 w . After removing the cyclic prefix and applying N -point FFT on the received electrical signal, the resulting frequency-domain symbols are obtained as R v,k = H k T v,k + W k , where H k is the channel frequency response of the kth subcarrier. Based on the fact that the clipping noise of Layer 1 ACO-OFDM only impacts even subcarriers, the Layer 1 ACO-OFDM symbols could be first estimated using the odd subcarriers of R v,k : where M (1) is the constellation set of the Layer 1 ACO-OFDM symbols. As shown in (12), before demodulating ACO-OFDM symbols in the high layer, we should compensate the cyclic shift of each layer based on the estimated symbolŜ (1) ACO,k . It means that information on cyclic shift sets can be easily detected with the help of modulated symbols conveyed in the first layer without increasing the receiver complexity. Subsequently, the time-domain regenerated Layer 1 ACO-OFDM signalsx (1),c ACO,n are obtained using equations (1) and (5). The channel frequency response could be obtained through channel estimation and is assumed to be a perfect estimation in this paper. Accordingly, the estimated Layer 2 ACO-OFDM signals can be obtained by subtracting the time-domain regenerated Layer 1 ACO-OFDM signals from the received signals with the channel compensation: where c  (13), we could obtain the frequency-domain Layer 2 ACO-OFDM symbols as follows: ACO,k e j2πk l / N + where I ACO,k , U (l) ACO,k , C 1 ACO,k , W ACO,k denote the clipping noise of the Layer 2 ACO-OFDM symbol, frequency-domain interference from the high layer of the ACO-OFDM symbols, estimation error of the Layer 1 ACO-OFDM symbol, and AWGN noises, respectively, which are provided as follows: At high SNR, c ACO,n ≈ 0 and l = 0, Equation (14) could be further simplified as follows: where U (l) ACO,k = 0 depends on the fact that the carriers used in each ACO-OFDM layer do not overlap, and the demodulation of the low layer is unaffected by the high layers. Therefore, the Layer 2 ACO-OFDM symbols could be estimated as follows: where k ∈ 2 = {2, 6, . . . , N − 2} and M (2) is the constellation set of the Layer 2 ACO-OFDM symbols. Thereafter, the ACO-OFDM symbols in the high layers could be estimated successively in similar fashion as follows:

C. OPTIMIZATION OF THE OPTICAL POWER ALLOCATION
In CS-LACO-OFDM systems, each layer can modulate different subcarriers with different optical power allocation. Without loss of generality, we assume that each layer uses the same modulation schemes, the constellation sets of which are denoted as M (l) = M , 1 ≤ l ≤ L. As derived in [12], BER of the Layer 1 ACO-OFDM symbols is given as follows: where E s,1 N o is the electrical energy-per-bit to noise power spectral density of the Layer 1 ACO-OFDM symbols. Thus, BER of the Layer 2 ACO-OFDM symbols could be derived as follows: where B 2|1 and B 2|1 denote the conditional probability of the Layer 2 ACO-OFDM signals error, given that Layer 1 ACO-OFDM signals have been demodulated successfully and wrongly, respectively. In general, B 2|1 and B 2|1 could be small under high SNR. Thus, Equation (22) is approximately obtained as follows: BER of the high layer ACO-OFDM symbols relies on the estimation of the low layers. Thus, the BER performance of the lth layer ACO-OFDM is obtained as follows: Given the Hermitian symmetry on the lth ACO-OFDM, only the N 2 l+1 subcarriers are used to modulate the ACO-OFDM symbols. Thus, the overall average BER for the L layers is expressed as follows: The object of this study is to find the optimal optical power allocation on each layer to minimize the average BER performance as follows: ρ (1) , ρ (2) , . . . , ρ (L) = arg min The average BER performance is highly relevant to optical power allocation, side information detection, and adopted modulation constellation set. The electrical power of the Layer l clipped ACO-OFDM signals has been verified and calculated as follows: Moreover, the optical power of the Layer l ACO-OFDM signals is also easily proven as follows: The minimal average BER performance can be achieved on the bases of these observations, in which each subcarrier of the lth layer should have equal electrical power. Thus, the optical power allocation to the lth layer ACO-OFDM signals can be derived as follows: (29)

D. ANALYSIS OF COMPUTATIONAL COMPLEXITY
On the basis of Equation (6) We can easily obtain CCRR regarding real multiplications and real additions, denoted by CCRR rm and CCRR ra , respectively, as follows: CCRR ra Evidently, equations (31) and (32) show that CS-LACO-OFDM can achieve the high CCRR in real multiplications and real additions when V increases. The numerical analysis provided in Table 1 is consistent with the mentioned above.

III. SIMULATION RESULTS
This section evaluates the performance of the CS-LACO-OFDM system in terms of the average BER and complementary cumulative distribution function (CCDF) of PAPR by simulations. We consider the 6-Layer ACO-OFDM with 128 subcarriers (N = 128 and L = 6), where the symbols are modulated with 16-QAM in all layers and the optical power allocation for each layer is obtained from equation (29). The indicators of cyclic shift sets in the CS-LACO-OFDM system are modulated on the odd subcarriers of the first layer with the complex-valued symbols. Thus, we should first decode the Layer 1 ACO-OFDM signal to extract the information of the cyclic shift sets. Fig. 2 shows the detection error rate of cyclic shift sets with the proposed optical power allocation and the equal optical power allocation when the adopted subcarriers N cyclic are QPSK and 16QAM modulation, respectively. In this figure, 16 candidate signals are adopted leading to the required subcarriers of two and one for QPSK and 16QAM, respectively. Evidently, the proposed power allocation outperforms the equal power allocation by a SNR reduction of 7dB and 5dB for QPSK and 16QAM, respectively, at a target of detection error rate of 10 −3 . Fig. 3 shows CCDF of PAPR for the CS-LACO-OFDM, 6-Layer ACO-OFDM with SLM scheme, and 6-Layer ACO-OFDM without PAPR reduction. In this figure, the optimal power allocation is used in all schemes. CS-LACO-OFDM has a similar PAPR performance as 6-Layer ACO-OFDM with the SLM scheme when the   number of candidate signals is the same, but at a remarkably lower computational complexity as shown in Table 1. Fig. 4 shows the average BER of the 16-QAM modulation 6-Layer CS-LACO-OFDM system using equal power allocation and the proposed power allocation. The BER performance of LACO-OFDM with conventional SLM schemes and perfect side information is also shown in this figure as the benchmark. Note that from the simulation results that the average BER performance of CS-LACO-OFDM is close to the LACO-OFDM with SLM when the optimal optical power allocation is used. However, a marginal gap exists in the average BER performance of CS-LACO-OFDM and LACO-OFDM with SLM under the equal power allocation. The reason is that the detection error rate of the cyclic shift sets with the equal power allocation is worse than that of the proposed optical power allocation.

IV. CONCLUSION
This study proposed a cyclic shifted layer asymmetrically clipped optical orthogonal frequency division multiplexing system for optical wireless communications. The proposed system has a similar PAPR performance as LACO-OFDM with separate SLM scheme when the number of candidate signals is the same, but at a remarkably lower computational complexity. Compared with equal power allocation scheme, the proposed optimal optical power allocation could achieve an improved performance in terms of the detection of cyclic shift sets and average BER over all layers.