# BER Performance of Stratified ACO-OFDM for Optical Wireless Communications over Multipath Channel

Authors: Zelalem Hailu Gebeyehu; Philip Kibet Langat; Ciira Wa Maina
Journal: Journal of Computer Networks and Communications
 (2018)

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## Abstract

In intensity modulation/direct detection- (IM/DD-) based optical OFDM systems, the requirement of the input signal to be real and positive unipolar imposes a reduction of system performances. Among previously proposed unipolar optical OFDM schemes for optical wireless communications (OWC), asymmetrically clipped optical OFDM (ACO-OFDM) and direct current biased optical OFDM (DCO-OFDM) are the most accepted ones. But those proposed schemes experience either spectral efficiency loss or energy efficiency loss which is a big challenge to realize high speed OWC. To improve the spectral and energy efficiencies, we previously proposed a multistratum-based stratified asymmetrically clipped optical OFDM (STACO-OFDM), and its performance was analyzed for AWGN channel. STACO-OFDM utilizes even subcarriers on the first stratum and odd subcarriers on the rest of strata to transmit multiple ACO-OFDM frames simultaneously. STACO-OFDM provides equal spectral efficiency as DCO-OFDM and better spectral efficiency compared to ACO-OFDM. In this paper, we analyze the BER performance of STACO-OFDM under the effect of multipath fading. The theoretical bit error rate (BER) bound is derived and compared with the simulation results, and good agreement is achieved. Moreover, STACO-OFDM shows better BER performance compared to ACO-OFDM and DCO-OFDM.


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## Body

## 1. Introduction

Optical wireless communication is receiving more and more attentions from many researchers in recent years. Due to the high demand of wireless technologies, wireless data traffic in telecom network is tremendously increasing, and overutilization of the conventional RF spectrum is becoming a big challenge. To tackle the challenge of this RF spectrum crunch, utilizing the optical spectrum for wireless communication is popularly considered to be a potential remedy. The optical spectrum intended for this application can offer wide unregulated bandwidth compared to the conventional RF spectrum. Moreover, optical wireless communication (OWC) is not easily affected by electromagnetic interference and has excellent security features [1]. The advancement of cost-effective solid state lighting technologies creates a huge motivation towards visible light communication along with illumination purpose at the same time [2]. Intensity modulation and direct detection (IM/DD) technique is the best candidate for developing low-cost OWC using the shelf transmitters and receivers.Due to its potential of combating intersymbol interference (ISI), orthogonal frequency division multiplexing (OFDM) is confirmed as the best candidate for high speed OWC [3, 4]. The conventional complex bipolar OFDM scheme cannot be used directly for IM/DD-based OWC. Therefore, the conventional OFDM signal should be changed in to real and positive unipolar OFDM signal to make it suitable for the IM/DD system [4–9]. DCO-OFDM and ACO-OFDM are widely accepted unipolar OFDM schemes proposed for OWC on literatures [4–8]. Because of the imposed Hermitian symmetry in signal generation stage, both schemes waste 50% of the available bandwidth.DCO-OFDM [4–6] uses additional DC bias to obtain a positive unipolar signal. But, adding a DC bias on the information signal reduces energy efficiency of the system; hence, DCO-OFDM is an energy inefficient modulation scheme. On the contrary, ACO-OFDM [6–8] avoids a DC bias and generates a positive unipolar signal by utilizing only odd subcarriers. Since all of the even subcarriers and half of the odd subcarriers are wasted on the process, ACO-OFDM provides poor spectral efficiency compared to DCO-OFDM. In [10], we proposed STACO-OFDM to increase the data transmission rate along with the power efficiency of the OWC system. STACO-OFDM is intended to transmit multiple OFDM frames on both even and odd subcarriers simultaneously. It adopts a layered structure to use even subcarriers on the first stratum and several odd subcarriers on multiple strata. The indoor optical wireless channel has a low pass nature; therefore, utilizing both odd and even subcarriers becomes important to have more available subcarriers for data transmission in the low frequency region. STACO-OFDM has also an advantage of minimizing communication latency compared to eU-OFDM [11] which also uses a layered approach. In [10], the performance of STACO-OFDM has been analyzed and compared with the performance of ACO/DCO-OFDM in purely AWGN channel environment. The result presented on [10] reveals that STACO-OFDM can provide better BER performance compared to both ACO/DCO-OFDM on purely AWGN channel. In real world scenario, the information signal experiences multipath fading while propagating through optical wireless channel. Multipath fading is known for its challenge on the BER performance of wireless communication system during high speed communication. Due to the frequency selectivity property of the optical wireless channel, the BER performance of the overall system is degraded due to subcarriers having low channel gain. On this paper, the BER performance of STACO-OFDM is analyzed under the influence of multipath fading which is not done before. A diffused optical wireless channel configuration is considered, and ceiling bounce model is used to generate the channel impulse response (CIR).


## 2. System Model Descriptions

### 2.1. IM/DD System

Figure1 shows IM/DD-based indoor OWC system with its equivalent baseband model. Let xt, ht, zt, and yt represent transmitted electrical signal, the channel impulse response, the zero mean additive Gaussian noise, and the received electrical signal, respectively, and the relationship between the transmitted and the received signal can be written as follows [12]:(1)yt=xt×ht+zt.Figure 1
IM/DD system and its baseband representation.It is noted that the IM/DD system needsxt to be real and positive unipolar.


### 2.2. Diffused OWC Channel Model

In this paper, ceiling bounce model [1, 9, 13] is used to model the CIR of optical wireless channel. For diffused optical link configuration, ceiling bounce model uses a unit step function to model the CIR as follows:(2)ht=H06a6t+a7ut,where a=1211/13Drms and Drms and H0 are the channel delay spread and the DC optical gain of the channel, respectively.


### 2.3. DCO-OFDM

DCO-OFDM [4–6] utilizes both even and odd subcarriers for data transmission. It wastes half of the available subcarriers due to the involvement of Hermitian symmetry during the generation of real bipolar OFDM signal. For the system having N available subcarriers, the spectral efficiency SeDCO of DCO-OFDM can be written as follows:(3)SeDCO=log2⁡MN−22N+NCP,where M and NCP on (3) represent the level of QAM modulation used at each subcarriers and the number of cyclic prefix, respectively. In DCO-OFDM, DC bias is added on the bipolar signal to generate a positive unipolar OFDM signal. For k amount of added DC bias, the electrical power dissipation of DCO-OFDM is increased by BDC dB compared to the conventional bipolar OFDM [7]:(4)BDC=10⁡log10k2+1.


### 2.4. ACO-OFDM

The conventional ACO-OFDM [6–8] utilizes only odd subcarriers for data transmission. But it is also possible to utilize only even subcarriers by leaving odd subcarriers vacant; hence, ACO-OFDM wastes either even- or odd-indexed subcarriers. The wastage of either odd or even subcarriers makes ACO-OFDM spectrally inefficient scheme compared to DCO-OFDM. For conventional M-QAM, ACO-OFDM having N subcarriers and NCP cyclic prefix, the spectral efficiency is equal to(5)SeACOodd=log2⁡MN4N+NCP.The above equation is only for the case of odd subcarriers that are utilized for information transmission. If only even subcarriers are utilized instead of odd subcarriers, the spectral efficiency becomes(6)SeACOeven=log2⁡MN−44N+NCP.


### 2.5. eU-OFDM

The modulation concept of eU-OFDM can be considered as the modification of unipolar OFDM (U-OFDM) [11]. In eU-OFDM scheme, multiple U-OFDM frames are superimposed together to form single time domain OFDM frame as shown in Figure 2.Figure 2
Frame design of eU-OFDM.Successive demodulation technique is used to recover the signal carried by all layers. The demodulation process starts from the 1st layer and then continues towards the last layer. In eU-OFDM, the signal transmission is started after enough numbers of bits are received at the transmitter for the generation of one complete eU-OFDM frame. This introduces a significant latency for real time communication which is one practicality issue of eU-OFDM. The latency introduced at the transmitter increases with the available number of layer in the system. IfS is the total number of available layers in eU-OFDM, the latency of eU-OFDM at the transmitter is greater than the latency of DCO-OFDM by a factor of 2S−1 for the same M-QAM modulations used on both systems. Moreover, some latency is also experienced at the receiver of eU-OFDM during successive demodulation. To demodulate the information carried by lth layer, 2l frames should be received at the receiver. Hence, the latency is worse on higher level layers of eU-OFDM system. For enough number of available layers, the spectral efficiency, SeeU, offered by eU-OFDM is equivalent to the spectral efficiency of DCO-OFDM. For the eU-OFDM system having N subcarriers and S total layers, SeeU can be given by(7)SeeU=∑l=1Slog2MlN−22l+1N+NCP,where Ml and NCP are the level of QAM modulation at lth layer and the number of cyclic prefix, respectively.


### 2.6. STACO-OFDM Signal Model

STACO-OFDM [10] utilizes both even and odd subcarriers in stratified or layered architecture. At each stratum, ACO-OFDM modulators are used, and the time domain signals from each stratum are summed up for simultaneous transmission [10]. Only even subcarriers are utilized on the first stratum while odd subcarriers are used on the rest of the strata. Due to the low pass nature of optical wireless channel, subcarriers in the low frequency region are less attenuated and affected by the multipath effect of the channel. While utilizing both even and odd subcarriers, relatively good numbers of subcarriers can be available in the low frequency region for transmission of information bits. For theoretical analysis, we consider a system having a total of S strata on which even subcarriers are used on the 1st stratum while odd subcarriers are utilized on the rest of S−1 strata. As given on (5) and (6), utilizing odd subcarriers on multiple strata has an advantage of maximizing the spectral efficiency since the conventional ACO-OFDM offers one additional information carrying subcarrier per stratum in comparison to even subcarrier-based ACO-OFDM. It is also noted that approximately equivalent spectral efficiency to the STACO-OFDM scheme can be achieved by utilizing only odd subcarriers on all strata. But, utilizing even subcarriers on the 1st stratum of the STACO-OFDM scheme may add further advantage and flexibility for STACO-OFDM during cellular OWC. According to [14], a significant limitation on the performance of optical attocell OWC comes from cochannel interference coming from the nearby cells using the same optical wavelength. In communication scenarios which require deployment of variable bit rate system for different cells in optical attocell, a hybrid system which uses ACO-OFDM for low/medium data rate cells and STAC-OFDM for high data rate cells can be deployed since ACO-OFDM scheme is more economical and cost-effective for low/medium speed communications. If many superimposed symbols are loaded on odd subcarriers of STACO-OFDM in such hybrid optical attocell communication scenarios, the electrical power of those odd subcarriers will be high and will introduce a significant interference on odd subcarriers of the nearby ACO-OFDM based cells which use the same optical wavelength. Therefore, to reduce the power of each individual odd subcarriers of STACO-OFDM, significant numbers of symbols are loaded on even subcarriers at the 1st stratum to distribute the available electrical power over significantly large number of subcarriers. Hence, the interference on individual odd subcarriers of low/medium bit rate cells due to odd subcarriers of high bit rate cells will be significantly reduced. In the proposed STACO-OFDM, the length of OFDM signal is set to be Nl=N/2l−1 at lth stratum; hence, Nl-points IFFT/FFT module is used on that specific stratum. To equalize the length of OFDM frames to N, 2l−1 copies of the original OFDM signal are regenerated, and two subframes with length of N/2 samples are constructed at the lth stratum. To transmit the complete information carried by all strata, the superposition of signal from each stratum is performed based on subframes. On this paper, when we say the 1st and 2nd subframe, we are referring to N/2 samples on the 1st and 2nd half of the time domain OFDM signal, respectively. After adding cyclic prefix on each subframe, the 1st subframe from each stratum is combined together and transmitted in the first transmission session. Similarly, the 2nd subframes from each stratum will be combined together and transmitted in the second transmission session. The OFDM signal generation on all strata except the 1st stratum is based on conventional ACO-OFDM while flipping of the 2nd subframe is performed at the 1st stratum. On the first stratum, even subcarriers are loaded with the M-QAM symbol while odd subcarriers are loaded with zero. The vector of M-QAM symbols, Xs1, loaded on the subcarriers of the 1st stratum is given as follows (Figure 3):(8)Xs1=0,0,X2s1,0,X4s1,0,…,0,XN1−2s1,0,where N1=N.Figure 3
STACO-OFDM system model.The Hermitian symmetry is imposed on subcarriers to generate real OFDM signal by imposing the following relation on the loaded QAM symbols [9]:(9)Xks1=XN−ks1∗,0<k<N2.After IFFT operation is done on loaded QAM symbols on subcarriers, the output time domain OFDM signal can be obtained. Throughout this paper, unitary IFFT/FFT operations are used to conserve equal signal power both on time and frequency domain. Therefore, the output discrete time domain OFDM signalxs1n and the frequency domain QAM symbols at the 1st stratum are related as follows [15]:(10)xs1n=1N∑k=0N1−1Xks1exp2πknN,n=0,1,2,…,N−1,Xks1=1N∑n=0N−1xs1nexp−2πknN,l=1,2,3,4,…,S.The sample values in the above equation are related with each other as follows:(11)xs1n=xs1n+N2,0≤n≤N2−1.To ease the interframe interference cancelation at the receiver, the entire frame of the 1st stratum is divided into two subframes with the length ofN/2 samples each, and flipping of samples is performed on the 2nd subframe before clipping of negative samples is performed. Therefore, the two subframes xsf1s1n and xsf2s1n can be written as follows [10]:(12)xsf1s1n=xs1n,n=0,1,2,…,N2−1,xsf2s1n=−xs1n+N2,n=0,1,2,…,N2−1.Then, after clipping the negative samples from both subframes will have clipped signalsx¯sf1s1n and x¯sf2s1n as follows:(13)x¯sf1s1n=0,forxsf1s1n≤0,n=0,1,2,…,N2−1xsf1s1n,forxsf1s1>0,n=0,1,2,…,N2−1,x¯sf2s1n=0,forxsf2s1n≤0,n=0,1,2,…,N2−1xsf2s1n,forxsf2s1>0,n=0,1,2,…,N2−1.Now after adding cyclic prefix on each subframe, the two subframes of 1st stratum are ready to be combined with subframes from higher strata. In the rest of strata, only odd subcarriers are loaded with M-QAM symbols while even subcarriers are loaded with zero QAM symbols.For example, let us considerXsl is the frequency domain QAM symbols loaded on subcarriers at lth stratum where l≠1 (the superscripts sl stand for stratum−l or lth  stratum). Then, Xsl which is the vector of QAM symbols loaded on the lth stratum is given as follows:(14)Xsl=0,X1s2,0,X3s2,0,…,0,XNl−1s2,where Nl=N/2l−1,⁡l=2,3,4,…,S.From the above equation, it is noted that the even subcarriers are left empty while the odd subcarriers are loaded with QAM symbols. The Hermitian symmetry is introduced by imposing the following relations on the loaded QAM symbols for enabling the generation of real bipolar signal [9]:(15)Xksl=XNl−ksl∗,0<k<Nl2.After taking IFFT, the time domain OFDM signalxsln is obtained at the lth stratum as follows:(16)xsln=1Nl∑k=0Nl−1Xkslexp2πknNl,l=2,3,4,…,S.To equalize the length of time domain signal at each stratum toN, xsln is replicated to generate 2l−1 exact copies at the lth stratum. To conserve equal frame energy before and after the replication process, the original frame at the lth stratum should be scaled by a factor of 1/2l−1. The 2l−2 copies are then merged together to form xsf1sln and xsf2sln which are the 1st and 2nd subframes of the lth stratum, respectively. Clipping of negative samples and adding of cyclic prefixes are then done on the 1st and the 2nd subframes of all strata. Clipping of negative samples can be performed using the following operation:(17)x¯sf1sln=0,forxsf1sln≤0,n=0,1,2,…,N2−1,l=2,3,4,…,Sxsf1sln,forxsf1sl>0,n=0,1,2,…,N2−1,l=2,3,4,…,S,x¯sf2sln=0,forxsf2sln≤0,n=0,1,2,…,N2−1,l=2,3,4,…,Sxsf2sln,forxsf2sl>0,n=0,1,2,…,N2−1,l=2,3,4,…,S,where x¯sf1sln and x¯sf2sln are the 1st and the 2nd subframes, respectively, at the lth stratum after clipping of negative samples. The entire frame of STACO-OFDM is transmitted in two successive transmission sessions. The 1st subframes from each stratum are combined together to form xt1n to be transmitted in the 1st transmission session, and xt1n can be written as(18)xt1n=∑l=1Sx¯sf1sln.Similarly, for the second transmission session,xt2n is formed by summing the 2nd subframes of all strata as(19)xt2n=∑l=1Sx¯sf2sln.At the receiver of STAC-OFDM, there are two received signals,xr1n and xr2n, from two consecutive transmission sessions as follows [12]:(20)xr1n=xt1n×hn+z1n,xr2n=xt2n×hn+z2n,where hn and z1n and z2n are the channel impulse response and the AWGN signal added on the 1st and the 2nd subframes, respectively. The demodulation process is performed by adopting successive demodulation technique stratum by stratum [11, 16]. The 1st stratum information recovery is begun by subtracting xr2n from xr1n. After doing the subtraction, the output signal xrs1n becomes(21)xrs1n=xr1n−xr2n=xt1n−xt2n×hn+z1n−z2n=xsf1s1n−xsf2s1n×hn+zn=xdiffn×hn+zn.On the above equation,zn is the AWGN noise with single-sided noise spectral density N0 which is added in one complete OFDM frame, and xdiffn is the bipolar signal which is exactly equal to the 1st half of xs1n. In addition, the length of xdiffn is equal to N/2+NCP, and the length of hn is equal to L, where NCP≥L, hn is equal to zero for n>L. Therefore, the channel impulse response hl can be written in vector form as(22)hl=h0⁡h1⁡h2⋯hL−1⁡0⁡0⁡0⋯0︸N/2samples.But we can write (21) by using summation as [17](23)xrs1n=∑l=0L−1hlxdiffn−l+zn,n=0,1,2,…,N2+NCP.The matrix representation for the above (23) becomes [17, 18](24)xrs1=hxdiff+z,where xrs1, xdiff, and z are N/2+NCP×1 matrices while h is N/2+NCP×N/2+NCP matrix. To recover the information carried by the 1st stratum, xrs1 is given to N-point FFT module after removing the first NCP long samples from xrs1. But it is also noted that the N-point FFT module will pad N/2 zeros by default at the end of xrs1. After the default zero padding, xrs1, xdiff, and z become N×1 matrices and their last N/2 rows are zero valued. Similarly, h becomes an N×N matrix. But xdiff is exactly similar to xs1=xs1nT in which its last N/2 samples are clipped to zero. According to [8], the clipped signal can be given by(25)xdiff=Rxs1+d,where R is a constant which is equal to 0.5, and d is the clipping noise which is N×1 matrix, but we can write xs1 in terms of IFFT matrix F−1 and the frequency domain QAM symbol vector Xs1 as follows [18]:(26)xdiff=RF−1Xs1+d.Substituting (26) into (24), the result becomes(27)xrs1=RF−1hXs1+d+z.Taking FFT operation on the above signal by using FFT matrixF [18],(28)Fxrs1=RF−1hFXs1+Fd+Fz=RCXs1+Fd+Fz,where C=F−1hF is a diagonal matrix whose diagonal is equal to the Fourier transform of the channel impulse response hn as(29)Hk=Fhn,k,n=0,1,2,…,N−1.The received frequency domain signal at each subcarriers on the 1st stratum becomes(30)Yks1=RHkXks1+Dk+Zk,k=0,1,2,…,N−1.Introducing zero forcing equalization for reducing the channel effect [12, 19],(31)Yks1RHk=Xks1+DkRHk+ZkRHk,k=0,1,…,N−1.On the above equation, it is also noted that the clipping noise only affects the odd subcarriers [8, 10]. Since the even subcarriers are not affected by the clipping noise, we can write the received symbols on the even subcarriers at the 1st stratum as(32)Yks1RHk=Xks1+ZkRHk,k=2,4,6,…,N−2.The information bits carried by the 1st stratum can be recovered by demodulating the above symbols received on even subcarriers. To recover the information carried by the 2nd stratum, the recovered bits at the 1st stratum should be remodulated again and processed in the same way as it was done at the transmitter. The remodulated time domain subframes are then affected by the CIR of the channel and subtracted fromxr1n and xr2n to remove the contribution of the 1st stratum. By following similar mathematical analysis as it was done for the 1st stratum, the equalized QAM symbols received on odd subcarriers of the 2nd stratum will be in the following form:(33)Yks2RHk=Xks2+ZkRHk,k=1,3,5,…,N2−1.Then, by demodulating the above resulted symbols after subtraction by conventional ACO-OFDM demodulator, it is possible to recover the information signal from odd subcarriers. Similarly, by remodulating the bits recovered at the 2nd stratum and subtracting it from the received signal, the equalized QAM symbols received on the 3rd stratum can be written as(34)Yks3RHk=Xks3+ZkRHk,k=1,3,…,N4−1.Then, the bits stream carried by the 3rd stratum can be recovered by demodulating the above symbols using the QAM demodulator. The bits carried by the other strata can also be recovered by using the same strategy stratum by stratum.Due to its efficient signal generation and demodulation strategies, STACO-OFDM has lower system latency compared to eU-OFDM. For same M-QAM modulation used on all of the availableS strata of both eU-OFDM and STACO-OFDM schemes, the latency introduced at the transmitter of STACO-OFDM scheme is approximately less than the latency experienced at the transmitter of eU-OFDM by a factor of 2S−1. For example, if we consider S=3 for both schemes, 7log2⁡MN/2−1 bits should be received at the transmitter of eU-OFDM before transmission while log2⁡M7N/16−1 bits are enough for the case of STACO-OFDM. Furthermore, the latency introduced at the receiver of STACO-OFDM is also lower compared to eU-OFDM since the frame length of STACO-OFDM scheme is less than the frame length of eU-OFDM by a factor of 2S as shown in Figures 2 and 4. Therefore, STACO-OFDM scheme has better advantage over eU-OFDM for latency sensitive real-time communications.Figure 4
STACO-OFDM frame design.Furthermore, implementing one tap frequency domain channel equalization is easier in STACO-OFDM than in eU-OFDM. To perform frequency domain channel equalization on thelth layer of eU-OFDM, the CIR of the channel should be constant throughout 8 frames duration. On contrary, the channel effect can be equalized successfully in STACO-OFDM as long as the channel is invariant over one frame duration. Therefore, STACO-OFDM can be used on applications involving fast channel dynamics scenario.


## 2.1. IM/DD System

Figure1 shows IM/DD-based indoor OWC system with its equivalent baseband model. Let xt, ht, zt, and yt represent transmitted electrical signal, the channel impulse response, the zero mean additive Gaussian noise, and the received electrical signal, respectively, and the relationship between the transmitted and the received signal can be written as follows [12]:(1)yt=xt×ht+zt.Figure 1
IM/DD system and its baseband representation.It is noted that the IM/DD system needsxt to be real and positive unipolar.


## 2.2. Diffused OWC Channel Model

In this paper, ceiling bounce model [1, 9, 13] is used to model the CIR of optical wireless channel. For diffused optical link configuration, ceiling bounce model uses a unit step function to model the CIR as follows:(2)ht=H06a6t+a7ut,where a=1211/13Drms and Drms and H0 are the channel delay spread and the DC optical gain of the channel, respectively.


## 2.3. DCO-OFDM

DCO-OFDM [4–6] utilizes both even and odd subcarriers for data transmission. It wastes half of the available subcarriers due to the involvement of Hermitian symmetry during the generation of real bipolar OFDM signal. For the system having N available subcarriers, the spectral efficiency SeDCO of DCO-OFDM can be written as follows:(3)SeDCO=log2⁡MN−22N+NCP,where M and NCP on (3) represent the level of QAM modulation used at each subcarriers and the number of cyclic prefix, respectively. In DCO-OFDM, DC bias is added on the bipolar signal to generate a positive unipolar OFDM signal. For k amount of added DC bias, the electrical power dissipation of DCO-OFDM is increased by BDC dB compared to the conventional bipolar OFDM [7]:(4)BDC=10⁡log10k2+1.


## 2.4. ACO-OFDM

The conventional ACO-OFDM [6–8] utilizes only odd subcarriers for data transmission. But it is also possible to utilize only even subcarriers by leaving odd subcarriers vacant; hence, ACO-OFDM wastes either even- or odd-indexed subcarriers. The wastage of either odd or even subcarriers makes ACO-OFDM spectrally inefficient scheme compared to DCO-OFDM. For conventional M-QAM, ACO-OFDM having N subcarriers and NCP cyclic prefix, the spectral efficiency is equal to(5)SeACOodd=log2⁡MN4N+NCP.The above equation is only for the case of odd subcarriers that are utilized for information transmission. If only even subcarriers are utilized instead of odd subcarriers, the spectral efficiency becomes(6)SeACOeven=log2⁡MN−44N+NCP.


## 2.5. eU-OFDM

The modulation concept of eU-OFDM can be considered as the modification of unipolar OFDM (U-OFDM) [11]. In eU-OFDM scheme, multiple U-OFDM frames are superimposed together to form single time domain OFDM frame as shown in Figure 2.Figure 2
Frame design of eU-OFDM.Successive demodulation technique is used to recover the signal carried by all layers. The demodulation process starts from the 1st layer and then continues towards the last layer. In eU-OFDM, the signal transmission is started after enough numbers of bits are received at the transmitter for the generation of one complete eU-OFDM frame. This introduces a significant latency for real time communication which is one practicality issue of eU-OFDM. The latency introduced at the transmitter increases with the available number of layer in the system. IfS is the total number of available layers in eU-OFDM, the latency of eU-OFDM at the transmitter is greater than the latency of DCO-OFDM by a factor of 2S−1 for the same M-QAM modulations used on both systems. Moreover, some latency is also experienced at the receiver of eU-OFDM during successive demodulation. To demodulate the information carried by lth layer, 2l frames should be received at the receiver. Hence, the latency is worse on higher level layers of eU-OFDM system. For enough number of available layers, the spectral efficiency, SeeU, offered by eU-OFDM is equivalent to the spectral efficiency of DCO-OFDM. For the eU-OFDM system having N subcarriers and S total layers, SeeU can be given by(7)SeeU=∑l=1Slog2MlN−22l+1N+NCP,where Ml and NCP are the level of QAM modulation at lth layer and the number of cyclic prefix, respectively.


## 2.6. STACO-OFDM Signal Model

STACO-OFDM [10] utilizes both even and odd subcarriers in stratified or layered architecture. At each stratum, ACO-OFDM modulators are used, and the time domain signals from each stratum are summed up for simultaneous transmission [10]. Only even subcarriers are utilized on the first stratum while odd subcarriers are used on the rest of the strata. Due to the low pass nature of optical wireless channel, subcarriers in the low frequency region are less attenuated and affected by the multipath effect of the channel. While utilizing both even and odd subcarriers, relatively good numbers of subcarriers can be available in the low frequency region for transmission of information bits. For theoretical analysis, we consider a system having a total of S strata on which even subcarriers are used on the 1st stratum while odd subcarriers are utilized on the rest of S−1 strata. As given on (5) and (6), utilizing odd subcarriers on multiple strata has an advantage of maximizing the spectral efficiency since the conventional ACO-OFDM offers one additional information carrying subcarrier per stratum in comparison to even subcarrier-based ACO-OFDM. It is also noted that approximately equivalent spectral efficiency to the STACO-OFDM scheme can be achieved by utilizing only odd subcarriers on all strata. But, utilizing even subcarriers on the 1st stratum of the STACO-OFDM scheme may add further advantage and flexibility for STACO-OFDM during cellular OWC. According to [14], a significant limitation on the performance of optical attocell OWC comes from cochannel interference coming from the nearby cells using the same optical wavelength. In communication scenarios which require deployment of variable bit rate system for different cells in optical attocell, a hybrid system which uses ACO-OFDM for low/medium data rate cells and STAC-OFDM for high data rate cells can be deployed since ACO-OFDM scheme is more economical and cost-effective for low/medium speed communications. If many superimposed symbols are loaded on odd subcarriers of STACO-OFDM in such hybrid optical attocell communication scenarios, the electrical power of those odd subcarriers will be high and will introduce a significant interference on odd subcarriers of the nearby ACO-OFDM based cells which use the same optical wavelength. Therefore, to reduce the power of each individual odd subcarriers of STACO-OFDM, significant numbers of symbols are loaded on even subcarriers at the 1st stratum to distribute the available electrical power over significantly large number of subcarriers. Hence, the interference on individual odd subcarriers of low/medium bit rate cells due to odd subcarriers of high bit rate cells will be significantly reduced. In the proposed STACO-OFDM, the length of OFDM signal is set to be Nl=N/2l−1 at lth stratum; hence, Nl-points IFFT/FFT module is used on that specific stratum. To equalize the length of OFDM frames to N, 2l−1 copies of the original OFDM signal are regenerated, and two subframes with length of N/2 samples are constructed at the lth stratum. To transmit the complete information carried by all strata, the superposition of signal from each stratum is performed based on subframes. On this paper, when we say the 1st and 2nd subframe, we are referring to N/2 samples on the 1st and 2nd half of the time domain OFDM signal, respectively. After adding cyclic prefix on each subframe, the 1st subframe from each stratum is combined together and transmitted in the first transmission session. Similarly, the 2nd subframes from each stratum will be combined together and transmitted in the second transmission session. The OFDM signal generation on all strata except the 1st stratum is based on conventional ACO-OFDM while flipping of the 2nd subframe is performed at the 1st stratum. On the first stratum, even subcarriers are loaded with the M-QAM symbol while odd subcarriers are loaded with zero. The vector of M-QAM symbols, Xs1, loaded on the subcarriers of the 1st stratum is given as follows (Figure 3):(8)Xs1=0,0,X2s1,0,X4s1,0,…,0,XN1−2s1,0,where N1=N.Figure 3
STACO-OFDM system model.The Hermitian symmetry is imposed on subcarriers to generate real OFDM signal by imposing the following relation on the loaded QAM symbols [9]:(9)Xks1=XN−ks1∗,0<k<N2.After IFFT operation is done on loaded QAM symbols on subcarriers, the output time domain OFDM signal can be obtained. Throughout this paper, unitary IFFT/FFT operations are used to conserve equal signal power both on time and frequency domain. Therefore, the output discrete time domain OFDM signalxs1n and the frequency domain QAM symbols at the 1st stratum are related as follows [15]:(10)xs1n=1N∑k=0N1−1Xks1exp2πknN,n=0,1,2,…,N−1,Xks1=1N∑n=0N−1xs1nexp−2πknN,l=1,2,3,4,…,S.The sample values in the above equation are related with each other as follows:(11)xs1n=xs1n+N2,0≤n≤N2−1.To ease the interframe interference cancelation at the receiver, the entire frame of the 1st stratum is divided into two subframes with the length ofN/2 samples each, and flipping of samples is performed on the 2nd subframe before clipping of negative samples is performed. Therefore, the two subframes xsf1s1n and xsf2s1n can be written as follows [10]:(12)xsf1s1n=xs1n,n=0,1,2,…,N2−1,xsf2s1n=−xs1n+N2,n=0,1,2,…,N2−1.Then, after clipping the negative samples from both subframes will have clipped signalsx¯sf1s1n and x¯sf2s1n as follows:(13)x¯sf1s1n=0,forxsf1s1n≤0,n=0,1,2,…,N2−1xsf1s1n,forxsf1s1>0,n=0,1,2,…,N2−1,x¯sf2s1n=0,forxsf2s1n≤0,n=0,1,2,…,N2−1xsf2s1n,forxsf2s1>0,n=0,1,2,…,N2−1.Now after adding cyclic prefix on each subframe, the two subframes of 1st stratum are ready to be combined with subframes from higher strata. In the rest of strata, only odd subcarriers are loaded with M-QAM symbols while even subcarriers are loaded with zero QAM symbols.For example, let us considerXsl is the frequency domain QAM symbols loaded on subcarriers at lth stratum where l≠1 (the superscripts sl stand for stratum−l or lth  stratum). Then, Xsl which is the vector of QAM symbols loaded on the lth stratum is given as follows:(14)Xsl=0,X1s2,0,X3s2,0,…,0,XNl−1s2,where Nl=N/2l−1,⁡l=2,3,4,…,S.From the above equation, it is noted that the even subcarriers are left empty while the odd subcarriers are loaded with QAM symbols. The Hermitian symmetry is introduced by imposing the following relations on the loaded QAM symbols for enabling the generation of real bipolar signal [9]:(15)Xksl=XNl−ksl∗,0<k<Nl2.After taking IFFT, the time domain OFDM signalxsln is obtained at the lth stratum as follows:(16)xsln=1Nl∑k=0Nl−1Xkslexp2πknNl,l=2,3,4,…,S.To equalize the length of time domain signal at each stratum toN, xsln is replicated to generate 2l−1 exact copies at the lth stratum. To conserve equal frame energy before and after the replication process, the original frame at the lth stratum should be scaled by a factor of 1/2l−1. The 2l−2 copies are then merged together to form xsf1sln and xsf2sln which are the 1st and 2nd subframes of the lth stratum, respectively. Clipping of negative samples and adding of cyclic prefixes are then done on the 1st and the 2nd subframes of all strata. Clipping of negative samples can be performed using the following operation:(17)x¯sf1sln=0,forxsf1sln≤0,n=0,1,2,…,N2−1,l=2,3,4,…,Sxsf1sln,forxsf1sl>0,n=0,1,2,…,N2−1,l=2,3,4,…,S,x¯sf2sln=0,forxsf2sln≤0,n=0,1,2,…,N2−1,l=2,3,4,…,Sxsf2sln,forxsf2sl>0,n=0,1,2,…,N2−1,l=2,3,4,…,S,where x¯sf1sln and x¯sf2sln are the 1st and the 2nd subframes, respectively, at the lth stratum after clipping of negative samples. The entire frame of STACO-OFDM is transmitted in two successive transmission sessions. The 1st subframes from each stratum are combined together to form xt1n to be transmitted in the 1st transmission session, and xt1n can be written as(18)xt1n=∑l=1Sx¯sf1sln.Similarly, for the second transmission session,xt2n is formed by summing the 2nd subframes of all strata as(19)xt2n=∑l=1Sx¯sf2sln.At the receiver of STAC-OFDM, there are two received signals,xr1n and xr2n, from two consecutive transmission sessions as follows [12]:(20)xr1n=xt1n×hn+z1n,xr2n=xt2n×hn+z2n,where hn and z1n and z2n are the channel impulse response and the AWGN signal added on the 1st and the 2nd subframes, respectively. The demodulation process is performed by adopting successive demodulation technique stratum by stratum [11, 16]. The 1st stratum information recovery is begun by subtracting xr2n from xr1n. After doing the subtraction, the output signal xrs1n becomes(21)xrs1n=xr1n−xr2n=xt1n−xt2n×hn+z1n−z2n=xsf1s1n−xsf2s1n×hn+zn=xdiffn×hn+zn.On the above equation,zn is the AWGN noise with single-sided noise spectral density N0 which is added in one complete OFDM frame, and xdiffn is the bipolar signal which is exactly equal to the 1st half of xs1n. In addition, the length of xdiffn is equal to N/2+NCP, and the length of hn is equal to L, where NCP≥L, hn is equal to zero for n>L. Therefore, the channel impulse response hl can be written in vector form as(22)hl=h0⁡h1⁡h2⋯hL−1⁡0⁡0⁡0⋯0︸N/2samples.But we can write (21) by using summation as [17](23)xrs1n=∑l=0L−1hlxdiffn−l+zn,n=0,1,2,…,N2+NCP.The matrix representation for the above (23) becomes [17, 18](24)xrs1=hxdiff+z,where xrs1, xdiff, and z are N/2+NCP×1 matrices while h is N/2+NCP×N/2+NCP matrix. To recover the information carried by the 1st stratum, xrs1 is given to N-point FFT module after removing the first NCP long samples from xrs1. But it is also noted that the N-point FFT module will pad N/2 zeros by default at the end of xrs1. After the default zero padding, xrs1, xdiff, and z become N×1 matrices and their last N/2 rows are zero valued. Similarly, h becomes an N×N matrix. But xdiff is exactly similar to xs1=xs1nT in which its last N/2 samples are clipped to zero. According to [8], the clipped signal can be given by(25)xdiff=Rxs1+d,where R is a constant which is equal to 0.5, and d is the clipping noise which is N×1 matrix, but we can write xs1 in terms of IFFT matrix F−1 and the frequency domain QAM symbol vector Xs1 as follows [18]:(26)xdiff=RF−1Xs1+d.Substituting (26) into (24), the result becomes(27)xrs1=RF−1hXs1+d+z.Taking FFT operation on the above signal by using FFT matrixF [18],(28)Fxrs1=RF−1hFXs1+Fd+Fz=RCXs1+Fd+Fz,where C=F−1hF is a diagonal matrix whose diagonal is equal to the Fourier transform of the channel impulse response hn as(29)Hk=Fhn,k,n=0,1,2,…,N−1.The received frequency domain signal at each subcarriers on the 1st stratum becomes(30)Yks1=RHkXks1+Dk+Zk,k=0,1,2,…,N−1.Introducing zero forcing equalization for reducing the channel effect [12, 19],(31)Yks1RHk=Xks1+DkRHk+ZkRHk,k=0,1,…,N−1.On the above equation, it is also noted that the clipping noise only affects the odd subcarriers [8, 10]. Since the even subcarriers are not affected by the clipping noise, we can write the received symbols on the even subcarriers at the 1st stratum as(32)Yks1RHk=Xks1+ZkRHk,k=2,4,6,…,N−2.The information bits carried by the 1st stratum can be recovered by demodulating the above symbols received on even subcarriers. To recover the information carried by the 2nd stratum, the recovered bits at the 1st stratum should be remodulated again and processed in the same way as it was done at the transmitter. The remodulated time domain subframes are then affected by the CIR of the channel and subtracted fromxr1n and xr2n to remove the contribution of the 1st stratum. By following similar mathematical analysis as it was done for the 1st stratum, the equalized QAM symbols received on odd subcarriers of the 2nd stratum will be in the following form:(33)Yks2RHk=Xks2+ZkRHk,k=1,3,5,…,N2−1.Then, by demodulating the above resulted symbols after subtraction by conventional ACO-OFDM demodulator, it is possible to recover the information signal from odd subcarriers. Similarly, by remodulating the bits recovered at the 2nd stratum and subtracting it from the received signal, the equalized QAM symbols received on the 3rd stratum can be written as(34)Yks3RHk=Xks3+ZkRHk,k=1,3,…,N4−1.Then, the bits stream carried by the 3rd stratum can be recovered by demodulating the above symbols using the QAM demodulator. The bits carried by the other strata can also be recovered by using the same strategy stratum by stratum.Due to its efficient signal generation and demodulation strategies, STACO-OFDM has lower system latency compared to eU-OFDM. For same M-QAM modulation used on all of the availableS strata of both eU-OFDM and STACO-OFDM schemes, the latency introduced at the transmitter of STACO-OFDM scheme is approximately less than the latency experienced at the transmitter of eU-OFDM by a factor of 2S−1. For example, if we consider S=3 for both schemes, 7log2⁡MN/2−1 bits should be received at the transmitter of eU-OFDM before transmission while log2⁡M7N/16−1 bits are enough for the case of STACO-OFDM. Furthermore, the latency introduced at the receiver of STACO-OFDM is also lower compared to eU-OFDM since the frame length of STACO-OFDM scheme is less than the frame length of eU-OFDM by a factor of 2S as shown in Figures 2 and 4. Therefore, STACO-OFDM scheme has better advantage over eU-OFDM for latency sensitive real-time communications.Figure 4
STACO-OFDM frame design.Furthermore, implementing one tap frequency domain channel equalization is easier in STACO-OFDM than in eU-OFDM. To perform frequency domain channel equalization on thelth layer of eU-OFDM, the CIR of the channel should be constant throughout 8 frames duration. On contrary, the channel effect can be equalized successfully in STACO-OFDM as long as the channel is invariant over one frame duration. Therefore, STACO-OFDM can be used on applications involving fast channel dynamics scenario.


## 3. Spectral Efficiency of STACO-OFDM

The spectral efficiency of STACO-OFDM can be calculated as the summation of the spectral efficiencies delivered by all available strata. The spectral efficiencySel offered by the lth stratum is given by [10](35)Sel=log2⁡MlN−44N+NCP,l=1log2⁡M1N2l+1N+NCP,l≠1.Then, the total spectral efficiencySe of STACO-OFDM can be calculated as follows:(36)Se=∑l=1SSel.STACO-OFDM has equivalent spectral efficiency with eU-OFDM and DCO-OFDM schemes, and it can offer better spectral efficiency compared to ACO OFDM.


## 4. Theoretical BER Bound of STACO-OFDM

### 4.1. BER Interms of Electrical SNR

It is known that the real bipolar time domain OFDM signal at each stratum has a Gaussian distribution for enough number of available subcarriers [20]. The average electrical power of the OFDM signal at the lth stratum is equal to σl2 which is the variance of the signal samples distribution. Therefore, the average transmitted electrical power Pl of the bipolar signal at the lth stratum is given by(37)Pl=σl2=∫−∞∞m2flmdm,where flm is the probability density function (PDF) of the signal at the lth stratum and given by [20](38)flm=12πσle−m2/2σl2,l=1,2,3,…,S.Letxln is the complete frame signal at lth stratum after clipping and scaling of the signal for conserving the symbol energy, so xln can be written by merging the two subframes as(39)xln=x¯sf1sl⁡x¯sf2sl,l=1,2,3,…,S.The clipping of negative samples reduces the average electrical power by a factor of1/2 compared to the bipolar signal. The average electrical power Pl′ of the time domain signal xln at the lth stratum becomes:(40)Pl′=Exl2n=12Pl2l−1=σl22l,l=1,2,…,S.In (40), the factors 1/2 and 1/2l−1 come from the clipping of negative samples and the scaling of signal, respectively. Considering xTn is the aggregate OFDM signal after combining the OFDM signals from all strata as(41)xTn=∑l=1Sxln.The average electrical powerPelavg of the combined OFDM signal xTn becomes [11, 20, 21](42)Pelavg=ExT2n=E∑l=1Sxln2=∑l=1SExl2n+∑l1=1S∑l2=1l1≠l2SExl1nExl2n=∑l=1Sσl22l+∑l1=1S∑l2=1l1≠l2Sσl12l1πσl22l2π=∑l=1Sσl22l+1π∑l1=1S∑l2=1l1≠l2Sσl1σl22l1+l2.The average achieved SNR per bit at thekth subcarrier of the entire combined system is given by [11, 16](43)γk=Hk2PelavgBN0Se.But the SNR per bit at thekth subcarrier has different values at different strata; the SNR per bit at the kth subcarrier of the lth stratum can be given by(44)γl,k=Hk2Pl′BN0Sel,where Pl′ is the electrical power of the clipped signal at the lth stratum which is equal to σl2/2. The theoretical BER at the kth subcarrier of the lth stratum can be given by the BER formula of M-QAM modulation as follows [22]:(45)BERl,k=4log2⁡Ml1−1Ml∑i=1Ml/2Q2i−13⁡log2⁡Mlγl,kMl−1.From the above equation, the overall BER at thelth stratum can be calculated as(46)BERl=1Nlinfo∑k=1Nl/2−1BERl,k,l=1,2,3,…,S,where Nlinfo is the number of information-carrying subcarriers at the lth stratum. For the 1st stratum (i.e., l=1), k is even as k=2,4,6,…,N/2−2 since only even subcarriers are carrying information. For the rest of the strata, k is odd as k=1,3,5,…,Nl/2−1.The theoretical BER bound of STACO-OFDM on multipath channel can be derived from the theoretical BER bound achieved at the available strata. LetS and Nlbits stand for the total number of used strata and the total number of bits transmitted at the lth stratum in one complete OFDM frame transmission, respectively, the BER of the overall STACO-OFDM system is then given by [10](47)BERtot=total  number  of  erroneous  bits  per  STACO-OFDM  frametotal  number  of  transmitted  bits  per  STACO-OFDM  frame=∑l=1SBERl⁡Nlbits∑s=1SNlbits.


### 4.2. BER Interms of Optical Power of Transmitted Signal

Percival’s theorem can be applied at each stratum since unitary IFFT/FFT is used on each stratum [15]. Therefore, at any lth stratum, the electrical power is equal in time and frequency domain as(48)E∑k=0N−1Xksl2=E∑n=0N−1xsln2=∑n=0N−1Exsln2.According to the above equation, the average electrical power of the bipolar signal at thelth stratum can be calculated as(49)Pl=1Nl∑n=0Nl−1Exsln2=2l−1N∑n=0N/2l−1−1Exsln2=σl2,where l=1,2,3,…,S.But from (48) and (49), we have(50)2l−1N∑n=0N/2l−1−1Exsln2=2l−1NE∑k=0N/2l−1−1Xksl2=σl2,where l=1,2,3,…,S.Then, after clipping the negative samples of the signal, the average electrical powerPl′ of the unipolar signal at the lth stratum will equal to the average symbol power of the clipped symbol X¯kl as(51)Pl′=2l−1NE∑k=0N/2l−1−1X¯ksl2=σl22,where l=1,2,…,S.Similarly, the average optical power of the transmitted signal on thelth stratum can be calculated as mean of truncated random variables [11, 21]:(52)Plo=Exln=σlπ2l,l=1,2,3,…,S.But using (51) and (52), we can write Pl′ as(53)Pl′=π2l−1Plo2,l=1,2,3,…,S.Then, it is possible to writePl′ as(54)Pl′=2l−1NE∑k=0N/2l−1−1X¯ksl2=π2l−1Plo2,where l=1,2,3,…,S.If we assume all the clipped version of QAM symbols on subcarriers at thelth stratum have equal average electrical power, we will have(55)EX¯ksl2=π2l−1Plo2.Then, at the receiver, the transmitted clipped QAM symbol at thekth subcarrier of lth stratum is further attenuated by the channel gain Hk; hence, the received QAM symbol Yksl at the kth subcarrier of the lth stratum will have average electrical power of(56)EYksl2=⁡Hk2EX¯ksl2=π2l−1Plo2Hk2.To calculate the effective SNR of the QAM symbol received at thekth subcarrier, the AWGN noise power at kth the subcarrier should be known. Let N0 be the single-sided noise spectral density; the noise variance σz2 at each subcarriers is given by [15](57)σz2=EZk2=N0Bsc2N2l−1,l=1,2,…,S,where Bsc is the bandwidth of subcarrier, and N/2l−1 term comes from the definition of the unitary IFFT/FFT algorithm. The SNR of the symbol received at the kth subcarrier is then given by [7, 15](58)SNRk=EYksl2σz2=22l−1πPlo2Hk2N0BscN,l=1,2,…,S.But for more simplicity, writingSNRk in terms of the total average optical power of the combined signal is vital. The average optical power Poavg of the combined signal xTt can be given by [11, 21](59)Poavg=ExTn=E∑l=1Sxln=∑l=1Sσlπ2l.The optical power penalty of the combined system with respect to the optical power at thelth stratum can be written as follows:(60)αlo=Poavg2Plo2,l=1,2,…,S.Therefore,SNRk can be written in terms of the overall transmitted optical power of STACO-OFDM system as follows:(61)SNRk=22l−1πPoavg2Hk2N0BscNαlo,l=1,2,…,S.The SNR per bitγl,k can also be calculated as(62)γl,k=SNRl,klog2⁡Ml=22l−1πPoavg2Hk2N0BscNαlolog2⁡Ml,l=1,2,…,S.Then, the BER at thekth subcarrier of the lth stratum becomes [22](63)BERl,k=4log2⁡Ml1−1Ml∑i=1Ml/2Q2i−1322l−1πPoavg2Hk2Ml−1BscN0Nαlo.The total theoretical BER bound of thelth stratum is then calculated by using the same formula as (46):(64)BERl=1Nlinfo∑k=1Nl/2−1BERl,k,l=1,2,3,…,S.The overall theoretical BER bound of STACO-ODM can be calculated by using similar formula defined on (47).


## 4.1. BER Interms of Electrical SNR

It is known that the real bipolar time domain OFDM signal at each stratum has a Gaussian distribution for enough number of available subcarriers [20]. The average electrical power of the OFDM signal at the lth stratum is equal to σl2 which is the variance of the signal samples distribution. Therefore, the average transmitted electrical power Pl of the bipolar signal at the lth stratum is given by(37)Pl=σl2=∫−∞∞m2flmdm,where flm is the probability density function (PDF) of the signal at the lth stratum and given by [20](38)flm=12πσle−m2/2σl2,l=1,2,3,…,S.Letxln is the complete frame signal at lth stratum after clipping and scaling of the signal for conserving the symbol energy, so xln can be written by merging the two subframes as(39)xln=x¯sf1sl⁡x¯sf2sl,l=1,2,3,…,S.The clipping of negative samples reduces the average electrical power by a factor of1/2 compared to the bipolar signal. The average electrical power Pl′ of the time domain signal xln at the lth stratum becomes:(40)Pl′=Exl2n=12Pl2l−1=σl22l,l=1,2,…,S.In (40), the factors 1/2 and 1/2l−1 come from the clipping of negative samples and the scaling of signal, respectively. Considering xTn is the aggregate OFDM signal after combining the OFDM signals from all strata as(41)xTn=∑l=1Sxln.The average electrical powerPelavg of the combined OFDM signal xTn becomes [11, 20, 21](42)Pelavg=ExT2n=E∑l=1Sxln2=∑l=1SExl2n+∑l1=1S∑l2=1l1≠l2SExl1nExl2n=∑l=1Sσl22l+∑l1=1S∑l2=1l1≠l2Sσl12l1πσl22l2π=∑l=1Sσl22l+1π∑l1=1S∑l2=1l1≠l2Sσl1σl22l1+l2.The average achieved SNR per bit at thekth subcarrier of the entire combined system is given by [11, 16](43)γk=Hk2PelavgBN0Se.But the SNR per bit at thekth subcarrier has different values at different strata; the SNR per bit at the kth subcarrier of the lth stratum can be given by(44)γl,k=Hk2Pl′BN0Sel,where Pl′ is the electrical power of the clipped signal at the lth stratum which is equal to σl2/2. The theoretical BER at the kth subcarrier of the lth stratum can be given by the BER formula of M-QAM modulation as follows [22]:(45)BERl,k=4log2⁡Ml1−1Ml∑i=1Ml/2Q2i−13⁡log2⁡Mlγl,kMl−1.From the above equation, the overall BER at thelth stratum can be calculated as(46)BERl=1Nlinfo∑k=1Nl/2−1BERl,k,l=1,2,3,…,S,where Nlinfo is the number of information-carrying subcarriers at the lth stratum. For the 1st stratum (i.e., l=1), k is even as k=2,4,6,…,N/2−2 since only even subcarriers are carrying information. For the rest of the strata, k is odd as k=1,3,5,…,Nl/2−1.The theoretical BER bound of STACO-OFDM on multipath channel can be derived from the theoretical BER bound achieved at the available strata. LetS and Nlbits stand for the total number of used strata and the total number of bits transmitted at the lth stratum in one complete OFDM frame transmission, respectively, the BER of the overall STACO-OFDM system is then given by [10](47)BERtot=total  number  of  erroneous  bits  per  STACO-OFDM  frametotal  number  of  transmitted  bits  per  STACO-OFDM  frame=∑l=1SBERl⁡Nlbits∑s=1SNlbits.


## 4.2. BER Interms of Optical Power of Transmitted Signal

Percival’s theorem can be applied at each stratum since unitary IFFT/FFT is used on each stratum [15]. Therefore, at any lth stratum, the electrical power is equal in time and frequency domain as(48)E∑k=0N−1Xksl2=E∑n=0N−1xsln2=∑n=0N−1Exsln2.According to the above equation, the average electrical power of the bipolar signal at thelth stratum can be calculated as(49)Pl=1Nl∑n=0Nl−1Exsln2=2l−1N∑n=0N/2l−1−1Exsln2=σl2,where l=1,2,3,…,S.But from (48) and (49), we have(50)2l−1N∑n=0N/2l−1−1Exsln2=2l−1NE∑k=0N/2l−1−1Xksl2=σl2,where l=1,2,3,…,S.Then, after clipping the negative samples of the signal, the average electrical powerPl′ of the unipolar signal at the lth stratum will equal to the average symbol power of the clipped symbol X¯kl as(51)Pl′=2l−1NE∑k=0N/2l−1−1X¯ksl2=σl22,where l=1,2,…,S.Similarly, the average optical power of the transmitted signal on thelth stratum can be calculated as mean of truncated random variables [11, 21]:(52)Plo=Exln=σlπ2l,l=1,2,3,…,S.But using (51) and (52), we can write Pl′ as(53)Pl′=π2l−1Plo2,l=1,2,3,…,S.Then, it is possible to writePl′ as(54)Pl′=2l−1NE∑k=0N/2l−1−1X¯ksl2=π2l−1Plo2,where l=1,2,3,…,S.If we assume all the clipped version of QAM symbols on subcarriers at thelth stratum have equal average electrical power, we will have(55)EX¯ksl2=π2l−1Plo2.Then, at the receiver, the transmitted clipped QAM symbol at thekth subcarrier of lth stratum is further attenuated by the channel gain Hk; hence, the received QAM symbol Yksl at the kth subcarrier of the lth stratum will have average electrical power of(56)EYksl2=⁡Hk2EX¯ksl2=π2l−1Plo2Hk2.To calculate the effective SNR of the QAM symbol received at thekth subcarrier, the AWGN noise power at kth the subcarrier should be known. Let N0 be the single-sided noise spectral density; the noise variance σz2 at each subcarriers is given by [15](57)σz2=EZk2=N0Bsc2N2l−1,l=1,2,…,S,where Bsc is the bandwidth of subcarrier, and N/2l−1 term comes from the definition of the unitary IFFT/FFT algorithm. The SNR of the symbol received at the kth subcarrier is then given by [7, 15](58)SNRk=EYksl2σz2=22l−1πPlo2Hk2N0BscN,l=1,2,…,S.But for more simplicity, writingSNRk in terms of the total average optical power of the combined signal is vital. The average optical power Poavg of the combined signal xTt can be given by [11, 21](59)Poavg=ExTn=E∑l=1Sxln=∑l=1Sσlπ2l.The optical power penalty of the combined system with respect to the optical power at thelth stratum can be written as follows:(60)αlo=Poavg2Plo2,l=1,2,…,S.Therefore,SNRk can be written in terms of the overall transmitted optical power of STACO-OFDM system as follows:(61)SNRk=22l−1πPoavg2Hk2N0BscNαlo,l=1,2,…,S.The SNR per bitγl,k can also be calculated as(62)γl,k=SNRl,klog2⁡Ml=22l−1πPoavg2Hk2N0BscNαlolog2⁡Ml,l=1,2,…,S.Then, the BER at thekth subcarrier of the lth stratum becomes [22](63)BERl,k=4log2⁡Ml1−1Ml∑i=1Ml/2Q2i−1322l−1πPoavg2Hk2Ml−1BscN0Nαlo.The total theoretical BER bound of thelth stratum is then calculated by using the same formula as (46):(64)BERl=1Nlinfo∑k=1Nl/2−1BERl,k,l=1,2,3,…,S.The overall theoretical BER bound of STACO-ODM can be calculated by using similar formula defined on (47).


## 5. Simulation Results

The performance of the developed stratified ACO-OFDM (STACO-OFDM) is analyzed and compared with the performance of ACO-OFDM, DCO-OFDM, and eU-OFDM schemes for nonflat dispersive diffused optical wireless channel. Zero-forcing equalizer is used in all cases. The performance comparison is based on energy efficiency and BER performance over channels having different amount of delay spread and normalized channel impulse response (CIR). The simulation models used for comparisons (ACO/DCO-OFDM) are verified by simulation results presented in [12, 23] for the same parameters. The major simulation parameters are listed out in Table 1.Table 1
Major simulation parameters.
OFDM parameters
IFFT/FFT size
2048
Cyclic prefix length
64
Sampling frequency (fs)
100 MHz
Channel delay spread (Drms)
10 ns, 20 ns
Modulation techniques
STACO-OFDM/eU-OFDM
Stratum-1
Stratum-2
Stratum-3
16-QAM
8-QAM
4-QAM
32-QAM
16-QAM
16-QAM
64-QAM
64-QAM
16-QAM
ACO-OFDM
64, 256, 1024-QAM
DCO-OFDM
8, 16, 32-QAM
Spectral efficiency
≈1.5, 2, and 2.5 bits/s/Hz
Bit rate
145 Mbs, 194 Mbs, 242 MbsIn the proposed STACO-OFDM and eU-OFDM schemes, the length of the cyclic prefix is set to be 32 for each subframes which are transmitted into two consecutive sessions. To achieve similar spectral efficiency for the three schemes and for fair comparison, 64 samples long cyclic prefix is used for ACO-OFDM and DCO-OFDM.


### 5.1. Channel Impulse Response (CIR)

Figure5 shows the discrete time simulation result of normalized time domain CIR of the diffused optical channel hn for channel delay spread of 10 ns and 20 ns. The time duration between two discrete points is used to generate the channel samples with consideration of no blocking object which blocks the reflected light from arriving at the receiver. The result in Figure 5 confirms that 32 samples long cyclic prefix is enough to avoid ISI since the magnitude of hn is almost zero for samples beyond the 12th sample. Figure 6 shows the plot of frequency domain subcarrier gain of the optical wireless channel for the normalized CIR with Drms of (10 ns, 20 ns). As presented in Figure 5, the optical wireless channel has low pass nature and is becoming more frequency selective when the quantity of Drms is increased. The subcarriers near to the zero frequency are relatively in better condition to achieve relatively better SNR since they have relatively higher channel gain. Moreover, while the channel delay spread is increasing, the channel gains of the subcarriers are decreasing; hence, it is difficult to achieve enough SNR for better BER performance while the quantity of the channel delay becomes large.Figure 5
The normalized time domain CIR from ceiling bounce model forDrms=10,20ns.Figure 6
Frequency domain subcarrier gain for CIR withDrms=10,20ns.


### 5.2. BER versus Electrical SNR per Bit

To compare the electrical energy efficiencies of the four schemes, the BER performances versus electricalEb/N0 are analyzed for all modulation schemes having similar spectral efficiencies and bit rates. As shown in Figure 7, the simulation result and the theoretical BER bound have shown good agreement apart from the inclusion of the residual error introduced by the successive demodulation on the simulated BER. The result in Figure 8 presented the comparison of the four schemes in terms of electrical energy efficiency for the system providing 1.5 bits/s/Hz and bit rate of 145 Mb/s over diffused optical channel. As the simulation result shows, to achieve a BER of 10−5 over multipath channel having delay spread of 10 and 20 ns, respectively, the proposed STACO-OFDM delivers electrical energy savings of about 1.7 and 1.6 dB compared to ACO-OFDM, about 4.8 and 5.5 dB electrical energy savings compared to DCO-OFDM, and about 1.2 and 1.6 dB electrical energy savings compared to eU-OFDM.Figure 7
Theoretical and simulated BER of STACO-OFDM for spectral efficiency of 2 bits/s/Hz.Figure 8
BER versus electrical SNR performance of STACO-OFDM, ACO-OFDM, and DCO-OFDM with spectral efficiency of 1.5 bits/s/Hz over multipath channel withDrms=10,20ns.In Figure9, the BER performance with respect to electrical SNR is presented for the four schemes providing spectral efficiency of 2 bits/s/Hz and a bit rate of 194 Mb/s. As the simulation result confirms, the performance of proposed STACO-OFDM scheme outsmarts the performances of ACO-OFDM, DCO-OFDM, and eU-OFDM for nonflat multipath channel with the given channel delay spreads. To achieve a BER of 10−5 over multipath channel having Drms of 10 ns, STACO-OFDM provides electrical energy savings of about 4.3, 1.3, and 4.3 dB, respectively, compared to ACO-OFDM, eU-OFDM, and DCO-OFDM. To achieve the same BER (10−5) on channel with Drms of 20 ns, STACO-OFDM offers 4.1, 1.6, and 4.1 dB electrical energy savings compared to ACO-OFDM, eU-OFDM, and DCO-OFDM, respectively. The BER performances of the four schemes over multipath channel for system having spectral efficiency of 2.5 bits/s/Hz and bit rate of 242 Mb/s are presented in Figure 10. For the channel with Drms of 10 ns, STACO-OFDM achieves BER of 10−5 with 6.1, 5, and 3.1 dB lower electrical energy consumption compared to ACO-OFDM, DCO-OFDM, and eU-OFDM, respectively. Similarly, for the second channel scenario (Drms=20ns), the energy consumption of STACO-OFDM is lower by 5.9, 5.7, and 3.7 dB compared to ACO-OFDM, DCO-OFDM, and eU-OFDM, respectively.Figure 9
BER versus electrical SNR performance of STACO-OFDM, ACO-OFDM, and DCO-OFDM with spectral efficiency of 2 bits/s/Hz over multipath channel withDrms=10,20ns.Figure 10
BER versus electrical SNR performance of STACO-OFDM, ACO-OFDM, and DCO-OFDM with spectral efficiency of 2.5 bits/s/Hz over multipath channel withDrms=10,20ns.The overall presented simulation results also show that when the spectral efficiency increases the SNR penalty of ACO-OFDM in comparison to STACO-OFDM is increased since higher order QAM modulations are used in ACO-OFDM to fill the spectral efficiency gap.It is noted that higher order QAM modulation are not energy efficient. To achieve a better BER over multipath channel having relatively larger channel delay spread, the electrical power of the transmitted signal should be high to achieve enough SNR. But while increasing the electrical power of the transmitted signal, the peak of the negative samples also increase in the negative region, and this will introduce large clipping noise for the case of DCO-OFDM since most peaks are left in the negative region even after adding a DC bias. Thus, the presented simulation results show that DCO-OFDM is more affected by multipath fading due to the presence of unavoidable clipping noise. The presented results also revealed that the residual noise propagating from stratum to stratum during successive demodulation affects the energy efficiencies of STACO-OFDM and eU-OFDM for large channel delay spreads.According to the results given on previous literatures [10, 16], both STACO-OFDM and eU-OFDM schemes have shown equivalent BER performances as a function of electrical SNR for a linear AWGN channel. Nevertheless, the results presented on this paper have shown that STACO-OFDM can offer somehow better BER performance compared to eU-OFDM on frequency selective multipath channel. As given in Figure 6, the optical wireless channel has low pass nature and the subcarriers on the high frequency region are more attenuated by the effect of the channel. eU-OFDM utilizes those subcarriers in the low and high frequency region at each layer for transmission of information bits. On the other hand, STACO-OFDM avoids utilizing those high frequency subcarriers on higher depth strata. Therefore, the usages of high frequency region subcarriers on all layers reduce the BER performance of eU-OFDM.


### 5.3. BER versus Optical Power

To evaluate the BER performance of STACO-OFDM scheme in terms of transmitted optical power, the parameters listed in Table2 are used in addition to the main parameters listed in Table 1.Table 2
Simulation parameters for BER versus optical power.
Simulation parameters
DC channel gain (H0)
10
−
6
Noise spectral density (N0)
3.05
×
10
−
23
Transmitted optical power (Po)
25
−
40
dBmThe channel parameters (Drms, H0, and N0) in Table 2 for simulation are consistent with channel parameters presented on literature [1]. The results from numerical simulation and the theoretical BER bound given at (64) and (47) have shown good agreement as shown in Figure 11.Figure 11
Theoretical and simulated BER of STACO-OFDM in terms of transmitted optical power for a system with spectral efficiency of 1.5 bits/s/Hz over multipath channel withDrms of 10 ns.The BER versusPo (transmitted optical power) performances of the three optical OFDM schemes over multipath channel having a delay spread of 10ns are presented in Figures 12–14 for spectral efficiencies of 1.5, 2, and 2.5 bits/s/Hz, respectively. For a system delivering spectral efficiency of 1.5 bits/s/Hz, STACO-OFDM shows better performance with around 0.6 dB and 2.6 dB optical energy savings to achieve a BER of 10−5 compared to ACO-OFDM and DCO-OFDM, respectively, as shown in Figure 12. The simulation results in Figure 13 revealed that STACO-OFDM saves about 1.5 dB optical energy compared to ACO-OFDM and 2.5 dB optical energy compared to DCO-OFDM for the system offering spectral efficiency of 2 bits/s/Hz with a BER of 10−5. The optical power penalty of ACO-OFDM with respect to STACO-OFDM is increased because of higher level QAM (256-QAM) usage to equalize the spectral efficiency of ACO-OFDM to 2 bits/s/Hz. Due to the energy inefficient properties of higher level QAM modulations, the power penalty of ACO-OFDM has become large. Similarly, as the results in Figure 14 confirmed, the performance of STACO-OFDM outsmarts the performance of both ACO-OFDM and DCO-OFDM for the system providing a spectral efficiency of 2.5 bits/s/Hz.Figure 12
BER versus optical power performance of STACO-OFDM, ACO-OFDM, and DCO-OFDM with spectral efficiency of 1.5 bits/s/Hz over multipath channel withDrms=10ns.Figure 13
BER versus optical power performance of STACO-OFDM, ACO-OFDM, and DCO-OFDM with spectral efficiency of 2 bits/s/Hz over multipath channel withDrms=10ns.Figure 14
BER versus optical power performance of STACO-OFDM, ACO-OFDM, and DCO-OFDM with spectral efficiency of 2.5 bits/s/Hz over multipath channel withDrms=10ns.To achieve a BER of10−5, STACO-OFDM requires 35.3 dBm optical power while DCO-OFDM and ACO-OFDM schemes require optical power of 37.6 dBm and 37.8 dBm, respectively. Therefore, compared to ACO/DCO-OFDM schemes, the overall presented results have shown that STACO-OFDM provides better optical power efficiency which has huge significance for solving drawbacks of optical power constraints to meet eye and skin safety regulations in indoor optical wireless communications.


## 5.1. Channel Impulse Response (CIR)

Figure5 shows the discrete time simulation result of normalized time domain CIR of the diffused optical channel hn for channel delay spread of 10 ns and 20 ns. The time duration between two discrete points is used to generate the channel samples with consideration of no blocking object which blocks the reflected light from arriving at the receiver. The result in Figure 5 confirms that 32 samples long cyclic prefix is enough to avoid ISI since the magnitude of hn is almost zero for samples beyond the 12th sample. Figure 6 shows the plot of frequency domain subcarrier gain of the optical wireless channel for the normalized CIR with Drms of (10 ns, 20 ns). As presented in Figure 5, the optical wireless channel has low pass nature and is becoming more frequency selective when the quantity of Drms is increased. The subcarriers near to the zero frequency are relatively in better condition to achieve relatively better SNR since they have relatively higher channel gain. Moreover, while the channel delay spread is increasing, the channel gains of the subcarriers are decreasing; hence, it is difficult to achieve enough SNR for better BER performance while the quantity of the channel delay becomes large.Figure 5
The normalized time domain CIR from ceiling bounce model forDrms=10,20ns.Figure 6
Frequency domain subcarrier gain for CIR withDrms=10,20ns.


## 5.2. BER versus Electrical SNR per Bit

To compare the electrical energy efficiencies of the four schemes, the BER performances versus electricalEb/N0 are analyzed for all modulation schemes having similar spectral efficiencies and bit rates. As shown in Figure 7, the simulation result and the theoretical BER bound have shown good agreement apart from the inclusion of the residual error introduced by the successive demodulation on the simulated BER. The result in Figure 8 presented the comparison of the four schemes in terms of electrical energy efficiency for the system providing 1.5 bits/s/Hz and bit rate of 145 Mb/s over diffused optical channel. As the simulation result shows, to achieve a BER of 10−5 over multipath channel having delay spread of 10 and 20 ns, respectively, the proposed STACO-OFDM delivers electrical energy savings of about 1.7 and 1.6 dB compared to ACO-OFDM, about 4.8 and 5.5 dB electrical energy savings compared to DCO-OFDM, and about 1.2 and 1.6 dB electrical energy savings compared to eU-OFDM.Figure 7
Theoretical and simulated BER of STACO-OFDM for spectral efficiency of 2 bits/s/Hz.Figure 8
BER versus electrical SNR performance of STACO-OFDM, ACO-OFDM, and DCO-OFDM with spectral efficiency of 1.5 bits/s/Hz over multipath channel withDrms=10,20ns.In Figure9, the BER performance with respect to electrical SNR is presented for the four schemes providing spectral efficiency of 2 bits/s/Hz and a bit rate of 194 Mb/s. As the simulation result confirms, the performance of proposed STACO-OFDM scheme outsmarts the performances of ACO-OFDM, DCO-OFDM, and eU-OFDM for nonflat multipath channel with the given channel delay spreads. To achieve a BER of 10−5 over multipath channel having Drms of 10 ns, STACO-OFDM provides electrical energy savings of about 4.3, 1.3, and 4.3 dB, respectively, compared to ACO-OFDM, eU-OFDM, and DCO-OFDM. To achieve the same BER (10−5) on channel with Drms of 20 ns, STACO-OFDM offers 4.1, 1.6, and 4.1 dB electrical energy savings compared to ACO-OFDM, eU-OFDM, and DCO-OFDM, respectively. The BER performances of the four schemes over multipath channel for system having spectral efficiency of 2.5 bits/s/Hz and bit rate of 242 Mb/s are presented in Figure 10. For the channel with Drms of 10 ns, STACO-OFDM achieves BER of 10−5 with 6.1, 5, and 3.1 dB lower electrical energy consumption compared to ACO-OFDM, DCO-OFDM, and eU-OFDM, respectively. Similarly, for the second channel scenario (Drms=20ns), the energy consumption of STACO-OFDM is lower by 5.9, 5.7, and 3.7 dB compared to ACO-OFDM, DCO-OFDM, and eU-OFDM, respectively.Figure 9
BER versus electrical SNR performance of STACO-OFDM, ACO-OFDM, and DCO-OFDM with spectral efficiency of 2 bits/s/Hz over multipath channel withDrms=10,20ns.Figure 10
BER versus electrical SNR performance of STACO-OFDM, ACO-OFDM, and DCO-OFDM with spectral efficiency of 2.5 bits/s/Hz over multipath channel withDrms=10,20ns.The overall presented simulation results also show that when the spectral efficiency increases the SNR penalty of ACO-OFDM in comparison to STACO-OFDM is increased since higher order QAM modulations are used in ACO-OFDM to fill the spectral efficiency gap.It is noted that higher order QAM modulation are not energy efficient. To achieve a better BER over multipath channel having relatively larger channel delay spread, the electrical power of the transmitted signal should be high to achieve enough SNR. But while increasing the electrical power of the transmitted signal, the peak of the negative samples also increase in the negative region, and this will introduce large clipping noise for the case of DCO-OFDM since most peaks are left in the negative region even after adding a DC bias. Thus, the presented simulation results show that DCO-OFDM is more affected by multipath fading due to the presence of unavoidable clipping noise. The presented results also revealed that the residual noise propagating from stratum to stratum during successive demodulation affects the energy efficiencies of STACO-OFDM and eU-OFDM for large channel delay spreads.According to the results given on previous literatures [10, 16], both STACO-OFDM and eU-OFDM schemes have shown equivalent BER performances as a function of electrical SNR for a linear AWGN channel. Nevertheless, the results presented on this paper have shown that STACO-OFDM can offer somehow better BER performance compared to eU-OFDM on frequency selective multipath channel. As given in Figure 6, the optical wireless channel has low pass nature and the subcarriers on the high frequency region are more attenuated by the effect of the channel. eU-OFDM utilizes those subcarriers in the low and high frequency region at each layer for transmission of information bits. On the other hand, STACO-OFDM avoids utilizing those high frequency subcarriers on higher depth strata. Therefore, the usages of high frequency region subcarriers on all layers reduce the BER performance of eU-OFDM.


## 5.3. BER versus Optical Power

To evaluate the BER performance of STACO-OFDM scheme in terms of transmitted optical power, the parameters listed in Table2 are used in addition to the main parameters listed in Table 1.Table 2
Simulation parameters for BER versus optical power.
Simulation parameters
DC channel gain (H0)
10
−
6
Noise spectral density (N0)
3.05
×
10
−
23
Transmitted optical power (Po)
25
−
40
dBmThe channel parameters (Drms, H0, and N0) in Table 2 for simulation are consistent with channel parameters presented on literature [1]. The results from numerical simulation and the theoretical BER bound given at (64) and (47) have shown good agreement as shown in Figure 11.Figure 11
Theoretical and simulated BER of STACO-OFDM in terms of transmitted optical power for a system with spectral efficiency of 1.5 bits/s/Hz over multipath channel withDrms of 10 ns.The BER versusPo (transmitted optical power) performances of the three optical OFDM schemes over multipath channel having a delay spread of 10ns are presented in Figures 12–14 for spectral efficiencies of 1.5, 2, and 2.5 bits/s/Hz, respectively. For a system delivering spectral efficiency of 1.5 bits/s/Hz, STACO-OFDM shows better performance with around 0.6 dB and 2.6 dB optical energy savings to achieve a BER of 10−5 compared to ACO-OFDM and DCO-OFDM, respectively, as shown in Figure 12. The simulation results in Figure 13 revealed that STACO-OFDM saves about 1.5 dB optical energy compared to ACO-OFDM and 2.5 dB optical energy compared to DCO-OFDM for the system offering spectral efficiency of 2 bits/s/Hz with a BER of 10−5. The optical power penalty of ACO-OFDM with respect to STACO-OFDM is increased because of higher level QAM (256-QAM) usage to equalize the spectral efficiency of ACO-OFDM to 2 bits/s/Hz. Due to the energy inefficient properties of higher level QAM modulations, the power penalty of ACO-OFDM has become large. Similarly, as the results in Figure 14 confirmed, the performance of STACO-OFDM outsmarts the performance of both ACO-OFDM and DCO-OFDM for the system providing a spectral efficiency of 2.5 bits/s/Hz.Figure 12
BER versus optical power performance of STACO-OFDM, ACO-OFDM, and DCO-OFDM with spectral efficiency of 1.5 bits/s/Hz over multipath channel withDrms=10ns.Figure 13
BER versus optical power performance of STACO-OFDM, ACO-OFDM, and DCO-OFDM with spectral efficiency of 2 bits/s/Hz over multipath channel withDrms=10ns.Figure 14
BER versus optical power performance of STACO-OFDM, ACO-OFDM, and DCO-OFDM with spectral efficiency of 2.5 bits/s/Hz over multipath channel withDrms=10ns.To achieve a BER of10−5, STACO-OFDM requires 35.3 dBm optical power while DCO-OFDM and ACO-OFDM schemes require optical power of 37.6 dBm and 37.8 dBm, respectively. Therefore, compared to ACO/DCO-OFDM schemes, the overall presented results have shown that STACO-OFDM provides better optical power efficiency which has huge significance for solving drawbacks of optical power constraints to meet eye and skin safety regulations in indoor optical wireless communications.


## 6. Conclusions

The BER performance of the proposed STACO-OFDM is evaluated under the influence of multipath fading. Performance comparisons based on BER have been also made with ACO-OFDM, DCO-OFDM, and eU-OFDM. For systems providing similar bit rates, the results from simulation have confirmed that STACO-OFDM provides better energy efficiency and BER performances compared to ACO-OFDM, DCO-OFDM, and eU-OFDM over multipath channel. Moreover, STACO-OFDM has reduced communication latency compared to eU-OFDM scheme. The future research will focus on improving the performance of STACO-OFDM on frequency selective optical wireless channel by incorporating bit and power loading adaptive capabilities.



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*Source: 9575281-2018-04-01.xml*