Research Archive. DOI:

Transcription

1 Researc Arcive Citation for publised version: Yufei Jiang, Yunlu Wang, Pan Cao, Majid Safari, Jon ompson, and Harald Haas, Robust and Low-Complexity iming Syncronization for DCO-OFDM LiFi Systems, IEEE Journal on Selected Areas in Communications, Vol. 36 (1):53-65, January DOI: ttps://doi.org/ /jsac Document Version: is is te Accepted Manuscript version. e version in te University of Hertfordsire Researc Arcive may differ from te final publised version. Copyrigt and Reuse: 2018 IEEE. Personal use of tis material is permitted. Permission from IEEE must be obtained for all oter uses, in any current or future media, including reprinting/republising tis material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrigted component of tis work in oter works. Enquiries If you believe tis document infringes copyrigt, please contact te Researc & Scolarly Communications eam at rsc@erts.ac.uk

2 1 Robust and Low-Complexity iming Syncronization for DCO-OFDM LiFi Systems Yufei Jiang, Member, IEEE, Yunlu Wang, Student Member, IEEE, Pan Cao, Member, IEEE, Majid Safari, Member, IEEE, Jon ompson, Fellow, IEEE, and Harald Haas, Senior Member, IEEE Abstract Ligt fidelity (LiFi), using ligt devices like ligt emitting diodes (LEDs) and visible ligt spectrum between 400 Hz and 800 Hz, provides a new layer of wireless connectivity witin existing eterogeneous radio frequency (RF) wireless networks. Link data rates of 10 Gbps from a single transmitter ave been demonstrated under ideal lab conditions. Syncronization is one of tese issues usually assumed to be ideal. However, in a practical deployment, tis is no longer a valid assumption. erefore, we propose for te first time a low-complexity maximum likeliood (ML) based timing syncronization process tat includes frame detection and sampling clock syncronization for direct current biased optical ortogonal frequency division multiplexing (DCO-OFDM) LiFi systems. e proposed timing syncronization structure can reduce te igcomplexity two-dimensional searc to two low-complexity onedimensional searces for frame detection and sampling clock syncronization. By employing a single training block, frame detection can be realized, and ten sampling clock offset (SCO) and cannels can be estimated jointly. We propose a number of tree frame detection approaces, robust against te combined effects of bot SCO and te low-pass caracteristic of LEDs. Furtermore, we derive te Cramér-Rao lower bounds (CRBs) of SCO and cannel estimations, respectively. In order to minimize te CRBs and improve syncronization performance, a single training block is designed based on te optimization of training sequences, te selection of training lengt and te selection of DC bias. erefore, te designed training block allows us to analyze te trade-offs between estimation accuracy, spectral efficiency, energy efficiency, and complexity. e proposed timing syncronization mecanism demonstrates low-complexity and robustness benefits, and provides performance significantly better tan existing metods. Index erms Ligt fidelity (LiFi), sampling clock offset (S- CO), frame detection, timing syncronization, DCO-OFDM I. INRODUCION A. Background and Motivation e exponentially increasing demand of mobile data traffic is saturating te spectral resources in te conventional radio frequency (RF) networks [1] [3]. A potential solution e work of Professor H. Haas was supported by te UK Engineering and Pysical Sciences Researc Council (EPSRC) under Grant EP/K008757/1. Y. Jiang is now wit Scool of Electronics and Information Engineering, te Harbin Institute of ecnology, Senzen, , Cina.( jiangyufei@it.edu.cn) Y. Wang, M. Safari, J. ompson and H. Haas are wit te Institute for Digital Communications, University of Edinburg, Edinburg, EH9 3JL, U.K. ( yunlu.wang@ed.ac.uk; majid.safari@ed.ac.uk; jon.tompson@ed.ac.uk;.aas@ed.ac.uk) P. Cao is now wit Scool of Engineering and ecnology at te University of Hertfordsire, U.K. ( p.cao@erts.ac.uk,). to tis spectral bottle-neck is to use ig carrier frequency for wireless communications, wit a large bandwidt utilized [4]. Ligt fidelity (LiFi) [5], wic uses an extremely wide visible ligt spectrum for ig speed communications, as recently been into te focus, and is considered as a promising tecnology for future networks. It as been sown in [6] tat LiFi can acieve data rates up to 14 Gbps using off-te-self ligt emitting diodes (LEDs). e intensity of te ligt at te output of LEDs can be rapidly canged/modulated to transmit data information and to provide illumination simultaneously. e main limitation on te data rate of LiFi systems is caused by te low bandwidt of pospor-coated LEDs, and can cause inter-symbol interference (ISI) wen using standard pulsed modulation tecniques suc as on-off keying (OOK). Ortogonal frequency division multiplexing (OFDM) in conjunction wit bit-and-power loading [7] is an effective solution, and as also been widely used for RF systems to combat multipat fading, due to ig spectrum efficiency and low-complexity cannel equalization. erefore, OFDM can be applied to solve te problem of ISI caused by LEDs for LiFi systems. OFDM allows transformation of signals between te frequency domain and te time domain by te use of inverse discrete Fourier transform (IDF) and discrete Fourier transform (DF). M-ary quadrature amplitude modulation (M- QAM) symbols can be mapped into a number of subcarriers for transmissions. However, complex-valued and bipolar signals are generated in te time domain, wic is not applicable for intensity modulation direct detection (IM/DD) LiFi sysems, as intensity modulation optical signals are real and nonnegative. is problem can partly be solved by imposing te constraint of Hermitian symmetry, resulting in real-valued signals in te time domain. However, te time-domain signals would be still negative and bipolar, wic requires oter tecniques to make tem unipolar before transmissions. So far, tere ave been a number of tecniques to generate unipolar OFDM signals. Direct current biased optical OFDM (DCO-OFDM) [7] [9] is one of common tecniques. A positive DC bias is introduced, and added to te time-domain signals. By clipping te negative parts of te DC biased signals, te resulting signals are non-negative and unipolar. In fact, te LED requires a level of DC bias for illumination, wic can also be used to generate unipolar OFDM signals for transmissions. Asymmetrically clipped optical OFDM (ACO- OFDM) [7], [8] is anoter modulation tecnique to generate unipolar signals by clipping entire negative signals. By te appropriate selection of subcarriers, te impairment from

3 2 clipping noise can be avoided. However, only a quarter of bandwidt in ACO-OFDM signals can be used to transmit data. us, it is not efficient in terms of bandwidt, compared to DCO-OFDM. However, OFDM based systems are vulnerable to syncronization errors [7], [10] [16]. As incoerent modulation, i.e., IM/DD, is used for LiFi systems, te frequency syncronization problem of carrier frequency offset (CFO) [17] is inerently absent. erefore, te remaining syncronization problems for optical OFDM systems are timing syncronization, i.e., frame detection and sampling clock syncronization. e frame detection is to find te starting point of data frame. An inaccurate detection could cause ISI tat degrades te system performance. e sampling clock syncronization is to estimate te sampling clock offset (SCO) witin a sampling period. is offset is equal to te fraction of te sampling period [13], and causes inter-carrier interference (ICI) [14] [16]. A number of frame detection metods are proposed in te literature using training sequences [10], [12], [13], [18]. In [10], Scmidl uses te correlation of repetition of codes for frame detection. However, te metod in [10] suffers from sallow gradient peaks, and te frame detection is not accurate. In [12], an improved metod is proposed by Park, were te starting point of data frame is detected by te strongest power at te receiver. However, tis metod requires cancellation of positive and negative parts in te time-domain signals, wic is not possible for LiFi systems wit non-negative and real signals. In [18], Park s frame detection metod is modified particularity for DCO-OFDM LiFi systems. However, tis metod is not robust against SCO. e sampling clock syncronization is anoter important issue for DCO-OFDM systems. In [13], te effect of SCO is simply analysed for ACO-OFDM systems. In [14], a resyncronization filter is proposed to compensate for te effect of SCO. In [15], [16], sampling clock syncronization metods are proposed. However, te frame detection is not considered. o te best of our knowledge, a general timing syncronization process including frame detection and SCO estimation as well as cannel estimation as not been investigated for DCO- OFDM LiFi systems. B. Contribution In tis paper, we provide a compreensive timing syncronization analysis for DCO-OFDM LiFi systems. Also, we propose a robust and low-complexity maximum likeliood (M- L) based timing syncronization process tat includes frame detection and SCO estimation as well as cannel estimation, using a single training mecanism wit respect to te optimization of training sequences, te selection of training sequence size and te selection of DC bias ratio. e contribution of tis work can be elaborated in te following: First, to te best of our knowledge, tis is te first work to apply ML to timing syncronization for DCO-OFDM LiFi systems. We propose a number of robust timing syncronization metods. us, a ig-complexity twodimensional searc for frame detection and sampling clock syncronization can be divided into two lowcomplexity one-dimensional searces. Second, we propose a minimization of negative cannel power (MNCP), a minimization of received signal power (MRSP) and a simplified minimization of received signal power (SMRSP) based frame detection approaces for LiFi systems, respectively. By exploring te non-negative property of LiFi systems, te MNCP frame detection is to minimize te sum power of negative cannel coefficients, wile te MRSP approac is to minimize te difference between te received and reconstructed signals. Bot approaces allow energy efficiency, as tey can perform well at low level of DC bias ratio. SMRSP, a special case of MRSP, is to minimize part of difference between te received and reconstructed signals for frame detection. e SMRSP approac provides low complexity, as fine frame detection is not required. e proposed frame detection approaces are sown to be robust against te combined effects of SCO and te low-pass caracteristic of LEDs. ird, by using te training block te same as tat for frame detection, SCO and cannel estimations are performed jointly. e Cramér-Rao lower bounds (CRBs) of SCO estimation and cannel estimation are derived te first time for DCO-OFDM LiFi systems. In order to minimize CRBs and improve frame detection accuracy, te training is designed wit respect to te optimization of training sequences, te selection of training sequence size and te selection of DC bias ratio. erefore, te proposed training design allows trade-offs between energy efficiency, performance, complexity and spectrum efficiency. Fourt, simulation results sow tat te proposed timing syncronization structure provides bit error rate (BER) performance close to te ideal case wit perfect cannel state information (CSI), no SCO and perfect frame detection. e proposed tree frame detection metods significantly outperform Scmidl s metod [10], [13] and Park s metod [12], [13], [18] in terms of probability of false frame detection. e proposed SCO estimation and cannel estimation metods can provide performance close to teir CRBs, respectively. e rest of te paper is organized as follows. e system model is presented in Section II. e optimum timing syncronization is proposed in Section III. e sub-optimum timing syncronization is proposed in Section IV. Performance analysis is described in Section V. Simulation results are presented in Section VI. Section VII draws te conclusion. C. Notations rougout te paper, we use bold symbols to represent vectors/matrices, and superscripts, and H to denote te complex conjugate, transpose, and complex conjugate transpose of a vector/matrix, respectively. I N and 1 N M represent an N N identity matrix and an N M all-one matrix, respectively. X(a : b, u : v) denotes a submatrix of X wit rows a to b and columns u to v. X(u : v) denotes a submatrix

4 3 of X wit all rows and columns u to v. [X] a,b denotes entry (a, b) of matrix X. [x] a denotes entry (a) of vector x. diag{x} represents a diagonal matrix wose diagonal elements are entries of vector x. 2 F is te Frobenius norm. E{ } denotes te expectation. trace{x} denotes te trace of matrix X. II. SYSEM MODEL Wireless optical communications perform best wit a strong line-of-sigt (LoS) cannel for transmissions [19], and can be described as te combination of a diffuse cannel and a LoS cannel. e optical wireless cannel impulse response LiFi (t) is written as follows [20]: LiFi (t) = η LoS δ(t) + diffuse (t t), (1) were η LoS is te LoS cannel component, δ(t) is te Dirac delta function, diffuse is te diffuse cannel component, and t is te delay between te LoS signal and te first arriving diffuse signal. e LoS cannel component η LoS is written as follows [21]: η LoS = { (m+1)arx 2πD 2 cos m (φ) cos(φ) (φ)g(ϕ), ϕ < Ψ 0, ϕ > Ψ, (2) were m = ln(2)/ ln[cos(φ 1/2 )] represents te Lambertian emission order, wit φ 1/2 denoting te alf-power semi-angle of LEDs, A rx is te detection area of te receiver, φ and ϕ are te ligt radiance angle of te transmitter and te corresponding ligt incidence angle of te receiver, respectively, D is te distance between transmitter and receiver, (φ) and G(ϕ) are te optical filter gain at te transmitter and concentrator gain at te receiver, respectively, and Ψ denotes te field of view (FOV) at te receiver. e diffuse cannel frequency response is written as follows [21]: H diffuse (f) = η diff e j2πf t 1 + j f f 0, (3) were f 0 is te 3 db cutoff frequency, and η diff is te diffuse signal gain, expressed as follows: η diff = A rx A room ρ 1 ρ, (4) were A room is te surface area of a room, and ρ is te average reflectivity of walls. Anoter effect of LiFi systems is te limited modulation bandwidt of LED, due to te low-pass caracteristic of te optical front-ends. is effect causes ISI for DCO-OFDM LiFi systems, and can be approximately modelled as follows [22]: LED (t) = e j2πf bt, (5) were f b is te cutoff bandwidt of LEDs. e equivalent cannel (t) can be expressed as follows [22] [24]: (t) = LiFi (t) LED (t), (6) were denotes linear convolution. e cannel impulse response in Eq. (6) is sample-spaced resulting in a number of L cannel pat delays as = [(0), (1),..., (L 1)], wit (l) denoting te l-t (l = 0, 1,..., L 1) cannel discretetime response. In te system, a single LED transmits M-QAM symbols to te receiver, were a number of N subcarriers are used in eac DCO-OFDM block. Define s(n) as te symbol on subcarrier n (n = 0,..., N 1). Complex baseband symbols are enforced to be real, by constraining te signals to ave Hermitian symmetry as s(n) = s (N n), n = 1, 2,..., N/2 1. Define s = [s(0), s(1),..., s(n 1)]. e resulting timedomain signals matrix X can be written as follows: X = F H diag{s}f(1 : L), (7) were F denotes te N N DF matrix, wit (u, v) entry [F] u,v = 1/ Nexp( j2πuv/n), (u, v = 0, 1,..., N 1). e time-domain symbol on te n-t subcarrier can also be N 1 N m=0 j2πmn s(m)e N expressed as x(n) = 1. A DC bias is added to x(n) to ensure tat most of negative signals become positive. e DC bias is calculated from x(n), defined as follows [25]: σ DC = K E{ x 2 (n)}, (8) were K is te DC bias ratio. By clipping te remaining negative signals, te resulting symbol x(n) is written as follows: x(n) = x(n) + σ DC + w clip (n), (9) were w clip (n) is te clipping noise, given by { 0, [ x(n) + σ DC ] > 0 w clip (n) = x(n) σ DC, [ x(n) + σ DC ] 0. (10) Using X in Eq. (6), te transmitted signals matrix X can also be written as follows: X = X + σ DC 1 N L + W clip, (11) were W clip = [wclip (0), w clip (1),..., w clip (L 1)], w clip (l) = [w clip (0, l), w clip (1, l),..., w clip (N 1, l)]. We define τ ( 0.5, 0.5) as te SCO, normalized by symbol duration. e received signal is oversampled by a oversampling ratio Q, and te sampling interval is s = /Q. In order to avoid inter-block interference (IBI) caused by te cannel and te low-pass caracteristic of te optical front-ends as sown in Eq. (6), eac DCO-OFDM block is prepended wit a cyclic prefix (CP) of lengt L cp L 1 before transmission. Assuming perfect frame detection, te oversampled signal vector y = [y(0), y(1),..., y(qn 1)] for eac DCO- OFDM block is written as follows [14], [16]: y = G(τ)X + w, (12) were G(τ) = [g(0), g(1),..., g(n 1)], g(n) = [g( n τ ), g( n + s τ ),..., g( n + (QN 1) s τ )], wit g(n) being te pulse saping filter; and w = [w(0), w(1),..., w(qn 1)], wit w(n) denoting te sot and termal noises, modelled as additive wite Gaussian noise (AWGN) wose entries are independent identically distributed (i.i.d.) Gaussian random variables wit zero mean and te summed variance σ 2 of sort noise and termal noise.

5 4 III. OPIMUM IMING SYNCHRONIZAION A. iming Error Effects For LiFi DCO-OFDM systems, timing syncronization process consists of frame detection and sampling clock syncronization. e inaccurate frame detection leads to timing offset errors, wile SCO causes ICI between subcarriers of DCO- OFDM systems. 1) iming Offset: e equivalent cannel model in Eq. (6) could cause a cannel delay pat of L as interference to te next block. If te lengt of CP is long enoug, te CP contains a number of symbols tat are not affected by te previous block. If te starting point of data frame is in te ISI free range, te ortogonality of subcarriers is maintained. Let I m = { L cp,..., 0,..., N 1} be te index vector of symbols in eac DCO-OFDM block. Define ɛ = ˆθ ɛ θ ɛ as te timing offset, wit ˆθ ɛ and θ ɛ denoting te estimate and real starting points of data frame, respectively. If ɛ = 0, te starting point of data frame is te position of 0 in vector I m, and tere is no timing offset. If ɛ (, L + L cp ) and ɛ (0, ), ICI and interblock interference (IBI) are generated in te received samples. If ɛ [ L + L cp, 0), te symbol offset error causes a pase rotation of exp(j2πnɛ/n) on te n-t subcarrier symbol. is effect can be compensated for by cannel equalization. erefore, te CP sould be long enoug to protect te inaccurate frame detection. 2) Sampling Clock Offset: e SCO as two effects: sampling clock pase offset and sampling clock frequency offset. e sampling clock pase offset causes a pase sift, te same as te pase rotation caused by timing offsets, wic can also be corrected by cannel equalization. e clock frequency offset causes ICI and ISI, wic can degrade te system performance. B. Problem Formulation In tis paper, we first propose an optimum joint ML timing syncronization metod by a single block, performing frame detection, SCO estimation and cannel estimation for DCO- OFDM systems. For frame detection, te ML is performed in te time domain using a window of size QN on te received samples to move forward or backward. At te same time, te SCO and cannels can be estimated jointly alongside wit frame detection. Let θ ɛ and τ denote te trial index for te start position of te frame and te trial value of te SCO, respectively. Define y NQ ( θ ɛ ) = [y( θ ɛ ), y(1 + θ ɛ ),..., y(qn + θ ɛ 1)]. e optimum joint ML estimates of te start point θ ɛ, te SCO τ, and te cannel are performed by addressing te cost function as follows: ( ) Λ y NQ ( θ ɛ ); τ, θ ɛ, ( θ ɛ, τ) = { 1 (πσ 2 exp 1 ynq ) NQ σ 2 ( θ ɛ ) G( τ)x( θ ɛ, τ) 2 F }, (13) were ( θ ɛ, τ) is te estimate of cannel wit te effect of θ ɛ and τ. Remark 1: For OFDM RF systems wit complex-valued signals, te traditional solution to Problem (13) is to maximize te equation of y H NQ ( θ ɛ )Ψy NQ ( θ ɛ ) wit Ψ = ( 1 G( τ)x X H G ( τ)g( τ)x) H X H G H ( τ) [16]. However, te received signals in LiFi systems are real not complex, and unipolar not bipolar. Maximizing te RF based equation above wit complex-valued signals does not provide a correct solution to Problem (13) wit real-valued signals. Instead, we propose anoter solution by minimizing Problem (13) to perform te joint frame detection and sampling clock syncronization. Remark 2: e optimal solution to Problem (13) leads to extremely ig computational complexity, as a two-dimensional searc is required for joint frame detection and sampling clock syncronization. us, we propose a timing syncronization structure tat can reduce te ig-complexity two-dimensional searc to two low-complexity one-dimensional searces. IV. SUB-OPIMUM IMING SYNCHRONIZAION By exploring a number of properties of DCO-OFDM LiFi systems, a sub-optimum timing syncronization metod is proposed, dividing te wole process into a frame detection step and a sampling clock syncronization step, as sown in Fig. 1. us, te ig-complex two-dimensional searc can be divided into two low-complexity one-dimensional searces. In tis paper, all timing syncronization processes are performed using a single DCO-OFDM block, described as follows. First, a number of two coarse frame detection metods are proposed, respectively, to detect coarse timing indexes. Next, fine frame detection is used to provide an accurate start point of data frame. Furtermore, we propose a low-complexity frame detection metod, requiring no fine frame detection. en, by using te training block te same as tat for frame detection, te SCO and cannels are estimated jointly. Also, two CRBs are derived for te SCO estimation and te cannel estimation, respectively. In order to lower CRBs and improve estimation performance, a set of training sequences is designed. A. Frame Detection We propose a number of tree frame detection scemes designed particularly for DCO-OFDM LiFi systems: MRSP, SMRSP and MNCP. e MRSP frame detection is performed by minimizing te power between te received and reconstructed signals. SMRSP, a special case of MRSP, is to minimize part of difference between te received and reconstructed signals. is sceme provides low complexity, as fine frame detection is not required. e MNCP tecnique is to minimize te sum power of negative cannel coefficients, by exploring te non-negativity property of LiFi cannels. e proposed frame detection metods are robust against te combined effect of te SCO and te low bandwidt of pospor-coated LEDs. raditional RF frame detection metods [10], [12], require negative and positive parts of received signals to detect te start point of data frame. However, te received signals in

6 5 Data in Complex Signal Hermitian Symmetry IDF DC Bias + Clipping CP Addition Single raining block Fine Frame Detection MRSP Coarse Frame Detection Data out Equalization CP Removal & DF SCO Syncronization & Compensation Fine Frame Detection MNCP Coarse Frame Detection or CSI Estimate or SMRSP Frame Detection Frame Detection Fig. 1. Block diagram of te proposed timing syncronization for DCO-OFDM LiFi systems LiFi systems are real and non-negative, and are terefore not suitable for DCO-OFDM LiFi systems. Also, tese metods are not robust against te SCO and te low bandwidt of pospor-coated LEDs. 1) Coarse Frame Detection: a) Minimization of Received Signal Power: In order to acieve low complexity, we use a window size of N samples moving forward or backward one sample in te received signal sample vector, to searc for te start point of te frame. e received signals used for detection are equivalent to extracting a symbol by every Q samples from te oversampled signals in Eq. (13) to form a received signals vector N 1 as y N (θ ɛ ) = [y(q + θ ɛ ), y(2q + θ ɛ ),..., y(qn + Q + θ ɛ 1)]. Since te received optical signals are positive and real, we, assuming no SCO, propose to minimize te cost function, wit respect to te timing index θ ɛ, as J(θ ɛ ) = y N (θ ɛ ) X 2 F. (14) Define P as te lengt of training sequence used at te receiver. Using Eqs. (7) and (11), te training can be formulated as X P = X P + σ DC 1 N P + W clip, wit X P = F H diag{s}f(1 : P ). Using te training X P of size N P, te cannel ( θ ɛ ) at te trial timing index θ ɛ is written as ( θ ɛ ) = [ X P X P ] 1 X P y N ( θ ɛ ). (15) ( θ ɛ ) is used to reconstruct te received signal by substituting Eqs. (15) into (14). By minimizing te difference between te reconstructed signal and te received signal, te MRSP based coarse timing index ˆθ ɛmrsp is obtained as follows: yn ˆθ ɛmrsp = arg min ( θ ɛ ) X P ( θ ɛ ) 2. (16) θ F ɛ b) Simplified Minimization of Received Signal Power: Wen P = 1, te training matrix becomes a transmitted signal vector as x. Using Eq. (15), we ave ( θ ɛ ) = ( x x ) 1 x y N ( θ ɛ ). (17) Compared wit te MRSP metod, SMRSP is to minimize part of difference between te received and reconstructed signals to obtain te timing index ˆθ ɛsmrsp by yn ˆθ ɛsmrsp = arg min ( θ ɛ ) x( θ ɛ ) 2. (18) θ F ɛ Please note tat SMRSP is a special case of MRSP. SMRSP is robust against te effect of te SCO and te low-pass caracteristic of LEDs, requiring no fine frame detection, as te noise power is greatly reduced by te scalar of x x, as sown in Eq. (17). eorem 1: Given a fixed t in Eq. (5), iger cutoff bandwidt of te LED f b improves te SMRSP estimation performance. Wen te cutoff bandwidt of LED f b is as ig as possible, MRSP becomes SMRSP. Proof of eorem 1: See Appendix A. c) Minimization of Negative Cannel Power: Since te cannels are unipolar and non-negative for LiFi systems, ( θ ɛ ) in Eq. (15) contains non-negative cannel coefficients under a noiseless condition, if θ ɛ is correct, i.e., θ ɛ = θ ɛ. Wen noise is present, te sum power of negative cannel coefficients at te correct timing index is muc lower tan tat at incorrect timing index, i.e., θɛ θ ɛ. e MNCP tecnique aims to minimize te sum power of te negative cannel coefficients in ( θ ɛ ) to obtain te coarse timing index ˆθ ɛmncp as follows: ˆθ ɛmncp = arg min θ ɛ P 1 l=0 { ( θ ɛ ) < 0}. (19) l

7 6 B. Fine Frame Detection e presence of SCO results in a biased coarse timing index. erefore, furter fine frame detection is required to improve te accuracy. For LiFi systems, te first received signal is te strongest LoS component [19], [20], followed by a period of no signals until te first reflected signal reaces te receiver. is is because te signal propagation delay of te LoS pat is muc sorter tan te delay incurred by te reflected pats [19], [20]. is property is used in te fine frame detection to refine te coarse timing index. e residual timing error after coarse frame detection can be introduced into te cannel, wic causes te delay of te strongest pat. e proposed fine frame detection metod aims at finding te pat delay. is can be performed by searcing for te position of te strongest cannel pat. Plugging Eqs. (19) into (15) yields (ˆθ ɛmncp ) = [ X ] 1 P X P X P y N (ˆθ ɛmncp ). e proposed MNCP tecnique for fine frame detection can be described matematically as follows: ˆɛ MNCP = arg max l (ˆθ ɛmncp ). (20) l e estimated timing index ˆδ MNCP stemming from te MNCP based metod is defined as: ˆδ MNCP = ˆθ ɛmncp + ˆɛ MNCP. (21) Similarly, plugging Eqs. (16) into (15) yields (ˆθ ɛmrsp ) = X 1 P X P X P y N (ˆθ ɛmrsp ). Similar to MNCP, te delay of ˆɛ MRSP is obtained by searcing for te position of te strongest cannel pat as follows: ˆɛ MRSP = arg max l As a result and analog to Eq. (21), we obtain: (ˆθ ɛmrsp ). (22) l ˆδ MRSP = ˆθ ɛmrsp + ˆɛ MRSP. (23) Please note tat te LoS component η LoS is related to LoS cannel response gain, and tus affects fine frame detection. η LoS depends on te ligt radiance angle φ, and is inversely proportional to te distance D between te transmitter and receiver. Wen φ = 0, te LoS component η LoS acieves te maximum cannel power at te same distance. e SCO makes te inaccurate cannel estimation in te frame detection. us, we need to improve cannel estimation successively. In te next section, SCO and cannels are considered to be jointly estimated. C. Sampling Clock Syncronization e training sequences tat are used for frame detection can be employed again in tis section to perform joint ML SCO and cannel estimation. Wit correct timing index, te joint SCO and cannel estimations are performed by minimizing te cost function as follows: J(τ, ) = y G(τ)X 2 F. (24) As te SCO is between 0.5 and 0.5, we use te trial value of τ and te training sequences X P to estimate te cannel wit τ as follows: ( ) 1 ( τ) = X P G ( τ)g( τ)x P X P G ( τ)y. (25) By substituting Eqs. (25) into (24), te estimate of SCO ˆτ is to minimize te cost function as follows: ˆτ = arg min y G( τ)x P ( τ) 2 F. (26) τ ( 0.5, 0.5) By substituting Eqs. (26) into (25), te cannel estimation is performed as follows: ( ) 1 ĥ = X P G (ˆτ)G(ˆτ)X P X P G (ˆτ)y. (27) In a multiple input multiple output (MIMO) system, were tere are multiple transmitters and receivers, Eq. (13) is still applicable. However, using Eq. (13) leads to extremely ig computational complexity in te MIMO case. e proposed timing syncronization approac can divide te multi-dimensional problem into a number of one-dimensional problems, greatly reducing te complexity for MIMO systems. erefore, te proposed approac can easily be extended to MIMO systems. D. Cramér-Rao Lower Bound As te SCO estimation and te cannel estimation in Eqs. (26) and (27) are unbiased, CRBs [26] can be employed to provide a performance bencmark as lower bound. We derive te CRBs in terms of closed-form expression for te joint estimation of SCO τ and cannel. As te variance of any unbiased estimator is as ig as te inverse of te Fiser Information matrix, te CRB lower bound corresponds to te inverse of Fiser Information matrix. As τ and are real, te estimation vector θ can be expressed as θ = [τ, ]. (28) Using te received signals, te corresponding Fiser Information matrix for te estimate of vector can be written as follows: [26] F IM = 2 y y σ 2 θ θ. (29) In te Fiser Information matrix, we sould note tat, 1), te diagonal elements are non-negative; and 2), te diagonal elements of te inverse of Fiser Information matrix are te bounds for te joint estimates of τ and. e (u, v) component of Fiser Information matrix is expressed as [ [F IM ] u,v = 2 y σ 2 [θ] u y [θ] v ]. (30) Define A = G(τ) τ X P and B = G(τ)X P. Here, we ave 2 y τ = 2 H A H A, 2 y τ = H A H B, 2 y τ = BH A, and 2 y = 2 B H B. e Fiser Information matrix yields: F IM = 2 A A A B σ 2 B A B. (31) B Define α = ( A B A) 1 wit B = I B(B B) 1 B, β = (B B) 1 B A, and C = B B. e CRB of te joint

8 7 estimation of τ and is te inverse of te Fiser Information matrix, as sown in Appendix B, and tis leads to: C RB = σ2 α αβ 2 αβ +. (32) αββ C 1 As te diagonal elements of te C RB matrix are corresponding to te bounds for te estimations of τ and, te CRB of te SCO estimation C RB (τ) is te (1, 1) entry of C RB in Eq. (32), given as follows: C RB (τ) = σ2 2 α = σ2 2 ( ) 1 (33) A B A. e CRB of te cannel estimation C RB () is te (2, 2) entry of C RB in Eq. (32), given as follows: C RB () = σ2 2 ( C 1 + αββh). (34) It can be observed from Eqs. (33) and (34) tat te ig cannel gains and te strong power of training sequences can minimize te CRB of joint SCO and cannel estimations. E. raining Sequence Design e objective of training sequence design is to minimize te CRBs wit respect to te SCO and cannel estimations. It is observed in Eq. (32) tat C RB () is affected by C RB (τ). Minimizing C RB (τ) corresponds to minimizing C RB (). us, we design a set of training sequences ˆX P to minimize C RB (τ) as follows: ˆX P = σ2 arg min 2 X P { ( A B A) 1 }. (35) In oter words, te optimum set of training sequences can be found by maximizing te eigenvalue of A B A. As te cannel is unknown, it is not possible to find a set of optimal training sequences tat optimize Problem (35) wit general. In order to make Problem (35) tractable, we can simplify Problem (35) to σ2 ˆX P = 2 2 F { arg max trace X P { }} A B A. (36) Using Eqs. (7) and (11), X P can be expressed by te frequency-domain signal s. e optimization problem can be formulated to te design of te frequency-domain training sequences s. Let R(τ) = G(τ) τ. Using Eq. (7) and making some arrangements, considering te effect of A A in Problem (36), we can formulate te following problem to optimize training sequences as { { ŝ = arg max trace F H L diag{s H }FR (τ)r(τ)f H }} diag{s}f L, s subject to s H s = 1. (37) We only consider te dominate and significant component R (τ)r(τ) in (37) for te optimization of training sequences s. We can find te solution to (37) as te eigenvector of R (τ)r(τ) wit respect to te maximum eigenvalue [27]. Define λ max {R (τ)r(τ)} and v max {R (τ)r(τ)} as te largest eigenvalue and te associated eigenvector of R (τ)r(τ), respectively. en, we can find an optimization for Problem (37) as follows: ŝ = Fv max {R (τ)r(τ)}. (38) Altoug te solution is not an optimal solution to te original ard coupling Problem (35). However, we provide a tractable way to establis a solution wic is still meaningful in engineering applications. Note tat te training sequence design depends on R (τ)r(τ) wit respect to τ wic is not known in advance. However, R (τ)r(τ) is independent of τ, wit a large number of N and Q [28]. e variations of τ ave no significant impact on te performance [28]. us, we use te range wic sits at te center of te SCO between 0.5 and 0.5 to design te training sequences. A. Complexity Analysis V. PERFORMANCE ANALYSIS For frame detection, MNCP results in (N 2 P ) multiplication operations, wile MRSP leads to (N 2 P 2 ) multiplication operations. As can be seen, MNCP exibits a P -fold complexity reduction, compared to MRSP. is is because Eq. (16) is not required in MNCP. Wen P = 1, MRSP becomes SMR- SP, acieving (N 2 ) multiplication operations. e proposed sampling clock syncronization metod requires (N 4 Q 3 1 ) operations. Wit eac searc, te proposed optimum timing syncronization in Eq. (13) needs (N 6 Q 3 P 2 1 ) operations, wit denoting te step size of te searc for te SCO. Compared to te optimum metod, te proposed sub-optimal approac can acieve a reduction of at least approximately (N 2 P 2 ) multiplication operations. is is equal to about 589, 824 multiplication operations reduction wen N = 64 and P = 12. ese parameters are used in te simulation setup in Section VI. B. Performance Analysis for Frame Detection 1) Discussion of raining Lengt P : e proposed MRSP and MNCP frame detection metods can only work if te training matrix X P of size N P is singular. Wen P = N, X P is square. Eqs. (15) and (16) are independent of θ ɛ. MRSP and MNCP cannot work. Wen P N, te proposed MRSP and MNCP provide worse performance, verified in Fig. 4. Wen P 1, MNCP cannot perform, as sufficient training lengt P is required to generate te number of cannel pats L, i.e., P L, as sown in Fig. 4. Wen P = 1, MRSP becomes SMRSP. 2) Impact of DC Bias Ratio K: Wen DC bias ratio K is low, all frame detection metods provide poor performance, as less optical power is used, as sown in Eq. (40). Wen a ig level of te DC bias ratio is used, te DC power of training signals increases. e component of (X P X P ) 1 includes a number of stronger negative coefficients, wic is multiplied

9 8 to te noise in Eq. (15) for te MNCP and MRSP tecniques. e ig-valued negative coefficients do not reduce te noise power. e MNCP and MRSP tecniques cannot perform well. us, tere is a careful selection of DC bias ratio, as a too low or too ig level of DC bias ratio K makes te performance of te MRSP and MNCP tecniques become worse. For SMRSP, te noise is reduced by te scalar of x x K 2 E{ x 2 (n)} as sown in Eq. (17), wic is proportional to te DC bias ratio K. us, SMRSP provides performance improved wit iger value of K used. e impact of K on a number of frame detection metods is verified in Fig. 3. 3) Discussion of Noise Reduction: e MNCP tecnique reduces te noise by ( X P X P ) 1 X P, wile te MRSP tecnique does not reduce te noise power, as te component of X P ( X P X P ) 1 X P is multiplied to te noise. For tis reason, te MNCP tecnique provides better performance tan te MRSP tecnique. e SMRSP frame detection reduces te noise by a scalar of x x. However, some negative coefficients ave strong power in (X P X P ) 1 X P for te MNCP tecnique, wic does not reduce te noise power. us, te SMRSP frame detection provides better performance tan MNCP and MRSP tecniques, verified in Fig. 2. C. Performance Analysis for Sampling Clock Syncronization 1) Discussion of raining Lengt P : Let B = UΛV be te singular value decomposition (SVD), were Λ denotes te diagonal singular matrix of size QN P, U and V denote unitary matrices of sizes QN QN and P P, respectively. Let Ũ = U(1 : QN, 1 : P ). After some matematical simplification as sown in Appendix C, Eq. (36) can be rewritten as follows: σ2 ˆX P = 2 2 F { arg max trace X P { ( ) }} A I ŨŨ A. (39) Ũ is te QN P sub-matrix of an unitary matrix. Wen P N, ŨŨ tends towards an identity matrix, i.e., (I ŨŨ ) 0. Problem (39) cannot be optimized. Wen P 1, using Eqs. (26) and (27) does not generate a sufficient number of cannel pats. erefore, te training sequence lengt P sould be larger tan L, and muc less tan N. e impact of training sequence lengt P is verified in Fig. 7. 2) Impact of DC Bias Ratio K: Since C RB (τ) is a scalar, a ig DC bias ratio enances te power of training signals, and minimizes te C RB (τ) of te SCO estimation. For cannel estimation, te C RB () includes C 1 and αββ H, as sown in Eq. (34). Wit a large size of G(τ), it olds tat G (τ)g(τ) I. us, we ave C 1 (X P X P ) 1. Minimizing α, i.e., C RB (τ), results in αββ H 2 F (X P X P ) 1 2 F. us, te CRB of te cannel estimation depends on te component of C 1 or (X P X P ) 1 rater tan αββ H. If a low level of DC bias ratio K is used in training sequences, less optical power is used, as sown in Eq. (40). e proposed cannel estimation provides poor performance. However, a ig level of DC bias ratio does not minimize te CRB of te cannel estimation. is is because te ig DC bias makes te ig power of negative coefficients in (X P X P ) 1, resulting in te increased value of C RB (). us, te DC bias ratio K sould be carefully selected to trade off te SCO estimation and te cannel estimation. e impact of DC bias ratio K is verified in Fig. 8. VI. SIMULAION RESULS We use Monte-Carlo simulations to analyze te performance of te proposed timing syncronization metods for DCO- OFDM systems. Unless oterwise stated, te simulations assume tat a data frame contains 256 DCO-OFDM blocks of N = 64 subcarriers. e CP lengt is L CP = 16. An oversampling ratio of Q = 4 is used. A single DCO-OFDM block is used as training, resulting in a training overead of 1/256 = 0.39%. e DC bias ratio is set as K = 1. e training sequence lengt is P = 12 or P = 6. However, te optimum selection of K and P depends on metod used. able I sows te optimal selection of K and P for a number of frame detection and sampling clock syncronization metods. A raised cosine filter is employed, wit roll off factor of 0.2. e symbol rates are 500 Msymbols/s. A step size of = is used to searc for te SCO. e training sequences are generated using SCO τ = 0 or τ = 0.1. e mean squared error (MSE) between te true and estimated SCOs, is defined as MSE = E{(τ ˆτ) 2 }. e MSE of cannel estimation is defined as MSE = E{( ĥ) ( ĥ)}. Energy per bit for optical power is denoted by E b,opt, wile electrical power by E b,ele. e optical power is obtained from te electrical power as follows [8]: E b,opt N 0 = K2 1 + K 2 E b,ele N 0. (40) e 3-dB cutoff bandwidt of LED is f b = 81.5 MHz [19]. e room size is 5 m 5 m 3 m (lengt widt eigt) [23]. e LED is located on te ceiling, wit te coordinate (3 m, 3 m, 3 m). e receiver is on te desk of eigt 1 m facing upwards. A transmitter s ligt radiance angle of φ = 40 degrees is used, wile te receiver s corresponding ligt incidence angle is ϕ = 60 degrees [22] [24]. e receiver detection area is A rx = 1 cm 2 is used. e alf-power semiangle of LED is φ 1/2 = 60 degrees. e average reflectivity of walls is assumed to be ρ = 0.8. An optical filter gain of (φ) = 1 is considered at te transmitter, wile a concentrator gain of G(ϕ) = 1 is used at te receiver. A. Performance of Frame Detection In Fig. 2, te probability of false frame detection of te proposed MRSP, SMRSP and MNCP frame detection scemes is demonstrated, in comparison wit Scmidl s metod and Park s metod [10], [12], [13], [18], in te presence of SCO. e MRSP and MNCP frame detection scemes result in performance significantly better tan Scmidl s metod and Park s metod. MNCP outperforms MRSP in terms of 3 db gains. is is because MNCP can reduce noise power, as discussed in Subsection V-B-3). SMRSP is robust against te effect of SCO wen no fine frame detection is in place. It provides a better performance tan MRSP and MNCP at low E b,ele /N 0. is is because SMRSP can suppress noise

10 9 ABLE I ESIMAORS WIH ANALYICAL PARAMEERS (SYN.: SYNCHRONIZAION, ES.: ESIMAION, CS: CHANNEL ESIMAION ) Item Frame Detection Sampling Clock Syn. MRSP SMRSP MNCP SCO est. CS DC bias ratio K raining sequence lengt P Probability of False Detection Scmidl's metod [10] [13] Park's metod [12] [13] [18] MRSP coarse detection + fine frame detection MNCP coarse detection + fine frame detection SMRSP frame detection Probability of False Detection Coarse Detection Coarse + fine frame detection Eb,ele/N0 (db) Fig. 2. Probability of false frame detection performance of te proposed MRSP, SMRSP and MNCP based frame detection metods, wit P = 12 training sequence lengt and K = 1 DC bias ratio, in te presence of SCO SMRSP frame detection MNCP frame detection MRSP frame detection raining Lengt P Fig. 4. Impact of training sequence lengt P on te probability of false frame detection performance of te proposed MRSP, SMRSP, MNCP based frame detection metods, wit K = 1 DC bias ratio and E b,ele /N 0 = 10 db, in te presence of SCO. Probability of False Detection 10 0 Scmidl's metod [10] [13] Park's metod [12][13][18] MRSP coarse detection + fine frame detection MNCP coarse detection + fine frame detection SMRSP frame detection DC Bias Ratio Fig. 3. Impact of DC bias ratio K on te probability of false frame detection performance of te proposed MRSP, SMRSP and MNCP based frame detection metods, wit P = 12 training sequence lengt and E b,ele /N 0 = 10 db, in te presence of SCO. power, more tan MNCP, as discussed in Subsection V-B- 3). Scmidl s and Park s metods are not robust against te combined effect of SCO and te low-pass caracteristic of LED. Fig. 3 demonstrates te impact of DC bias ratio on te false frame detection probability performance wen using MRSP, SMRSP and MNCP, in te presence of SCO, wit E b,ele /N 0 = 10 db and P = 12. MRSP and MNCP frame detection approaces demonstrate a concave wit te variations of DC bias ratio, and acieve te best performance at K = 1 DC bias ratio. ere is significant improvement using SMRSP wen a iger DC bias ratio used. is is because te noise is reduced by te scalar of x x K 2 E{ x 2 (n)}, wic is proportional to te DC bias ratio K, as discussed in Subsection V-B-2). In Fig. 4, te impact of training sequence lengt P on te performance of false frame detection probability for te proposed metods is demonstrated, in te presence of SCO, wit E b,ele /N 0 = 10 db and K = 1. SMRSP is sown wit P = 1 training sequence lengt, as a special case of MRSP. Wit sort training sequence lengt, MRSP provides better performance tan MNCP. is is because MNCP requires sufficient training lengt to generate te total number of cannel pats for frame detection. SMRSP can minimize part of difference between te received and reconstructed signals to perform frame detection. Wen P becomes large and close to N, te proposed metods provide worse performance, because te training matrix is close to square. is is consistent wit te discussion in Subsection V-B-1). B. Performances of Sampling Clock syncronization Figs. 5 and 6 demonstrate te MSE performance of te proposed SCO estimation and cannel estimation metods, respectively, wit K = 1 DC bias ratio and P = 6 training

11 10 MSE MSE MRSP frame detection + proposed SCO estimation MNCP frame detection + proposed SCO estimation SMRSP frame detection + proposed SCO estimation CRB of SCO estimation Eb,ele/N0 (db) Proposed cannel estimation Proposed SCO estimation CRB raining Lengt P Fig. 5. MSE performance of te proposed SCO estimation, in comparison to te CRB of SCO estimation, wit K = 1 DC bias ratio and P = 6 training sequence lengt. Fig. 7. Impact of te training sequence lengt P on te MSE performance of te proposed SCO and cannel estimation metods, wit K = 1 DC bias ratio and E b,ele /N 0 = 20 db MRSP frame detection + proposed CS MNCP frame detection + proposed CS SMRSP frame detection + proposed CS CRB of CS Proposed cannel estimation Proposed SCO estimation CRB MSE MSE Eb,ele/N0 (db) DC Bias Ratio K Fig. 6. MSE performance of te proposed cannel estimation, in comparison to te CRB for cannel estimation, wit K = 1 DC bias ratio and P = 6 training sequence lengt. CS refers to cannel estimation in te legend. Fig. 8. Impact of te DC bias ratio K on te MSE performance of te proposed SCO and cannel estimation metods, wit P = 6 training sequence lengt and E b,ele /N 0 = 20 db. sequence lengt. From E b,ele /N 0 s = 0 db to 15 db, tere is a big performance gap. is is due to te false frame detection, affecting te MSE performance of te proposed SCO estimation and cannel estimation metods. From E b,ele /N 0 s = 15 db to 30 db, te proposed SCO estimation and cannel estimation scemes alongside te proposed frame detection can provide MSE performance, close to teir CRBs. Fig. 7 demonstrates te impact of training sequence lengt P on te MSE performance of te proposed SCO and cannel estimation scemes, wit E b,ele /N 0 = 20 db and K = 1 DC bias ratio. e proposed SCO and cannel estimation scemes sow te best performance at training sequence lengt P = 6. is is because te sufficient training lengt P is required to generate te total number of cannel pats. Wen P is too large, we ave (I ŨŨ ) 0 in Eq. (39). Problem (39) cannot be optimized. e proposed SCO and cannel estimation scemes cannot work. is is consistent wit te discussion in Subsection V-C-1). Fig. 8 sowcases te impact of DC bias ratio K on te MSE performance of te proposed SCO and cannel estimation scemes, wit E b,ele /N 0 = 20 db and P = 6. e proposed SCO estimation sceme provides performance improvements wen te DC bias ratio increases. is is due to two reasons: One reason is tat greater optical power is used wit a iger level of DC bias ratio. e oter reason is tat at te same time wit te addition of a larger DC bias, te DC signal power can be enanced, minimizing te C RB (τ) of te SCO estimation. us, te proposed SCO estimation metod improves. is is consistent wit te discussion in Subsection V-C-2). Also, it is sown tat te proposed SCO estimation

12 SCO and te low-pass caracteristic of te optical front-ends. e proposed SCO estimation and cannel estimation metods result in performance close to CRBs. e proposed timing syncronization mecanism allows arnessing of trade-offs between estimation accuracy, spectral efficiency, energy efficiency, and complexity. In future work, we consider extending te timing syncronization to MIMO systems. BER APPENDIX A PROOF OF HEOREM Scmidl's frame detection [10] [13] + ZF EQ Park's frame detection [12] [13][18]+ ZF EQ MRSP frame detection + SCO est. & CS + ZF EQ SMRSP frame detection + SCO est. & CS + ZF EQ MNCP frame detection + SCO est. & CS + ZF EQ ZF EQ (perfect frame detection + no SCO + perfect CSI ) Eb,ele/N0 (db) Fig. 9. BER performance of te proposed timing syncronizing sceme. EQ refers to equalization; CE refers to cannel estimation and est. refers to estimation. sceme yield performance tat is close to te CRB. For te proposed cannel estimation metod, a ig level of DC bias ratio does not improve te performance. is is because te ig DC bias makes te ig power of negative coefficients in (X P X P ) 1, resulting in te increased value of C RB (), as discussed in Subsection V-C-2). us, te performance of te proposed cannel estimation is sown to be concave. e best performance can be acieved at K = 1. C. BER Performance of Proposed iming Syncronization In Fig. 9, te BER performance of te proposed timing syncronization process is demonstrated wit 16 QAM modulation. e zero forcing (ZF) based equalization metod wit perfect frame detection, no SCO and perfect CSI is used as bencmark. e proposed timing syncronization process includes tree frame detection metods, i.e., MRSP, SMRSP and NMCP, and te proposed SCO and cannel estimation metods. Wit a training overead of 0.39%, a number of proposed timing syncronization scemes provide BER performance significantly better tan Scmidl s and Park s metods [10], [12], [13], [18], and performance close to te ZF equalization based case wit perfect CSI, no SCO and perfect frame detection. VII. CONCLUSION In tis paper, we ave proposed a timing syncronization mecanism for DCO-OFDM LiFi systems. By using a single training DCO-OFDM block, frame detection and SCO estimation can be performed togeter jointly wit cannel estimation. e proposed timing syncronization tecniques provide BER performance close to te ideal case wit perfect CSI, no SCO and perfect frame detection. e proposed new frame detection metods significantly outperform Scmidl s metod and Park s metod in terms of probability of false frame detection, and demonstrate te robustness against te Let x(n, l) denote te transmitted symbol on te n-t row and l-t column of X. Let X = [x(0), x(1),..., x(n 1)], wit x(n) = [x(n, 0), x(n, 1),..., x(n, L 1)]. e transmitted signal vector can be written as x = [x(0, 0), x(1, 0),..., x(n 1, 0)]. Eq. (17) can be re-written as follows: ( θ ɛ ) = ( x x ) 1 {r(0)(0) + r(1)(1) +... r(l 1)(L 1)} (41) were r(0) = x 2 (0, 0) + x 2 (1, 0) x 2 (N 1, 0), r(1) = x(0, 0)x(0, 1) +... x(n 1, 0)x(N 1, 1),..., r(l 1) = x(0, 0)x(0, L 1) +... x(n 1, 0)x(N 1, L 1). Since x x = r(0), te reconstructed signal in Eq. (18) is given as follows: ( θ ɛ )x = (0)x + ( x x ) 1 {r(1)(1) +... r(l 1)(L 1)} x. (42) e first term of Eq. (42) is te part of received signals y N ( θ ɛ ), wile te second term is te difference. e SMRSP based frame detection is to cancel te first term, by treating te second term as noise. If f b1 < f b2, from Eq. (5), we can obtain LED (t, f b2 ) LED (t, f b1 ) = ej2πt(f b 1 f b2 ) < 1. (43) We can see LED (t, f b2 ) < LED (t, f b1 ) wit a fixed t and t 0. us, te iger cutoff bandwidt leads to lower cannel response of (1),..., (L 1). e power of te second term of Eq. (42) is reduced. e difference between te received and reconstructed signals is minimized. e SMRSP frame detection improves. Wen te cutoff bandwidt is as ig as possible, we ave e j2πf bt 0 wit a fixed t and t 0, resulting in (1),..., (L 1) 0. MRSP becomes SMRSP. is proves eorem 1. APPENDIX B MAHEMAICAL DERIVAIONS OF C RB e Fiser Information matrix in Eq. (31) can be rewritten as follows: F IM = 2 Cτ Υ σ 2 (44) Υ C

13 12 were C τ = H A H A, C = B H B and Υ = B H A. According to te matrix inverse lemma [29], we can obtain te inverse of Fiser Information matrix: ] [ 2 σ 2 F 1 IM = 01 L I L L [ 1 + C 1 Υ = [ L 0 L 1 C 1 C 1 [0 L 1, I L L ] ] (Cτ Υ C 1 ] is proves Eq. (39) from Eq. (36). Υ) 1 [ 1 Υ C 1 + ( C τ Υ C 1 Υ) 1 ] ] (45) REFERENCES [1] Cisco Visual Networking Index, Global mobile data traffic forecast update, , Cisco, San Jose, U.S.A., Wite Paper, Feb [2] H. Burcardt, N. Serafimovski, D. sonev, S. Videv, and H. Haas, VLC: Beyond point-to-point communication, IEEE Communications Magazine, vol. 52, no. 7, pp , Jul [3] H. Elgala, R. Mesle, and H. Haas, Indoor optical wireless communication: Potential and state-of-te-art, IEEE Communications Magazine, vol. 49, no. 9, pp , Sep [4] GBI Researc, Visible ligt communication (VLC) - Apotential solution to te global wireless spectrum sortage, GBISC017MR, ecnical Report, Mar [5] S. Dimitrov and H. Haas, Principles of LED Ligt Communications: owards Networked Li-Fi. Cambridge, U.K.: Cambridge University [ 1 Υ C 1 Press, [6] K. D. Langer, J. Grubor, O. Boucet, M. E. abac, J. W. Walewski, C 1 Υ C 1 ΥΥ C 1 S. Randel, M. Franke, S. Nerreter, D. C. O Brien, G. E. Faulkner, I. Neokosmidis, G. Ntogari, and M. Wolf, Optical wireless communications for broadband access in ome area networks, in International Let α = ( ( ) C τ Υ C 1 Υ) 1 1 = H A H Conference on ransparent Optical Networks, vol. 4, Jun. 2008, pp. B A wit B = I B(B B) 1 B and β = C 1 Υ = [7] J. Armstrong, OFDM for optical communications, Journal of Ligtwave ecnology, vol. 27, no. 3, pp , Feb (B H B) 1 B H A. Eq. (45) can be rewritten: [8] J. Armstrong and B. J. C. Scmidt, Comparison of asymmetrically [ ] clipped optical OFDM and DC-biased optical OFDM in AWGN, IEEE 2 σ 2 F 1 IM = K 1 β H Communications Letters, vol. 12, no. 5, pp , May K 1 C 1 + α β ββ H. (46) [9] D. J. F. Barros, S. K. Wilson, and J. M. Kan, Comparison of ortogonal frequency-division multiplexing and pulse-amplitude modulation in indoor optical wireless links, IEEE ransaction on Communications, us, te joint CRB of te SCO estimation and cannel vol. 60, no. 1, pp , Jan [10]. M. Scmidl and D. C. Cox, Robust frequency and timing syncronization for OFDM, IEEE ransaction on Communications, vol. 45, estimation is expressed: no. 12, pp , Dec C RB = σ2 α αβ H [11] M. Spet, S. A. Fectel, G. Fock, and H. Meyr, Optimum receiver 2 αβ C 1 +. (47) αββh design for OFDM-based wireless broadband transmission- part ii: a case study, IEEE ransactions on Wireless Communications, vol. 49, no. 4, Apr is proves Eq. (32). [12] B. Park, H. Ceon, C. Kang, and D. Hong, A novel timing estimation metod for OFDM systems, IEEE Communications Letters, vol. 7, no. 5, pp , May [13] S. ian, K. Panta, H. A. Suraweera, B. J. C. Scmidt, S. McLauglin, APPENDIX C and J. Armstrong, A novel timing syncronization metod for ACO- PROOF OF EQ. (39) OFDM-based optical wireless communications, IEEE ransactions on Wireless Communications, vol. 7, no. 12, pp , Dec It olds tat [14] X. Li, Y. C. Wu, and E. Serpedin, iming syncronization in decodeand-forward cooperative communication systems, IEEE ransaction on (B B) 1 = ( VΛ U UΛV ) 1 ( = VΛ 2 V ) 1 Signal Processing, vol. 57, no. 4, pp , Apr (48) [15] B. Gimire, I. Stefan, H. Elgala, and H. Haas, ime and frequency = VΛ 2 V. syncronisation in optical wireless OFDM networks, in Proc. IEEE International Symposium on Personal, Indoor and Mobile Radio Communications, Sep us, [16] A. A. Nasir, H. Merpouyan, S. D. Blostein, S. Durrani, and R. A. B(B B) 1 B = UΛV VΛ 2 V VΛ U Kennedy, iming and carrier syncronization wit cannel estimation in multi-relay cooperative networks, IEEE ransactions on Signal = UΛΛ 2 Λ U (49). Processing, vol. 60, no. 2, pp , Feb [17] Y. Jiang, X. Zu, E. Lim, Y. Huang, and H. Lin, Low-complexity Define Λ semi-blind multi-cfo estimation and ICA based equalization for CoMP = Λ(1 : L, 1 : L) as te diagonal matrix wit diagonal elements being te eigenvalue of B. Since Λ = [ Λ, OFDM systems, IEEE ransactions on Veicular ecnology, vol. 63, 0], no. 4, pp , May we ave Λ 2 = Λ 2 and Λ = [ Λ, [18] M. F. G. Medina, O. Gonzlez, S. Rodrłguez, and I. R. Martłn, iming 0]. Also, we can obtain syncronization for OFDM-based visible ligt communication system, in Wireless elecommunications Symposium (WS), Apr. 2016, pp Λ ΛΛ 2 Λ = Λ 2 [ Λ, IL L 0 [19] C. Cen, D. A. Basnayaka, and H. Haas, Downlink performance of 0] =. (50) optical attocell networks, Journal of Ligtware ecnology, vol. 34, no. 1, pp , Jan [20] V. Jungnickel, V. Pol, S. Nonnig, and C. V. Helmolt, A pysical Plugging Eq. (50) into Eq. (49) results in: model of te wireless infrared communication cannel, IEEE Journal on Selected Areas in Communications, vol. 20, no. 3, pp , Aug B = I B(B B) 1 B IL L 0 = I U U = I ŨŨ.[21] J. M. Kan and J. R. Barry, Wireless infrared communications, 0 0 (51) Proceedings of te IEEE, vol. 85, no. 2, pp , Feb [22] L. Zeng, D. Obrien, H. Le-Min, K. Lee, D. Jung, and Y. O, Improvement of date rate by using equalization in an indoor visible ligt communication system, in Proc. IEEE International Circuits System Communication, May 2008.

14 13 [23] L. Wu, Z. Zang, J. Dang, and H. Liu, Adaptive modulation scemes for visible ligt communications, Journal of Ligtwave ecnology, vol. 33, no. 1, pp , Jan [24] D. Obrien, Visible ligt communications: Callenges and potential, in Proc. IEEE Potonics Conference, Oct [25] D. sonev, S. Videv, and H. Haas, Unlocking spectral efficiency in intensity modulation and direct detection systems, IEEE Journal on Selected Areas in Communications, vol. 33, no. 9, pp , Sep [26] H. L. V. rees and K. L. Bell, Bayesian Bounds for Parameter Estimation and Nonlinear Filtering/racking. Wiley-IEEE Press, [27] S. Boyd and L. Vandenberge, Convex Optimization. Cambridge University Press, [28] Y. Wu and E. Serpedin, raining sequences design for symbol timing estimation in MIMO correlated fading cannels, in Proc. IEEE Global eleommunications, Nov [29]. Soderstrom and P. Stoica, System Identification. London, U.K.: Prentice Hall, Majid Safari (S 08-M 11) received B.Sc. in Electrical and Computer Engineering from te University of eran, Iran, in 2003, M.Sc. in Electrical Engineering from Sarif University of ecnology, Iran, in 2005 and P.D. in Electrical and Computer Engineering from te University of Waterloo, Canada in He is currently an assistant professor in te Institute for Digital Communications at te University of Edinburg. Before joining Edinburg in 2013, He eld te prestigious MIACS elevate strategic fellowsip at McMaster University, Canada. Dr. Safari is currently an associate editor of IEEE Communication letters He also served as a guest Editor for a special issue of IEEE Access journal on Optical Wireless ecnologies for 5G Communications and beyond and was te PC co-cair of te 4t International Worksop on Optical Wireless Communication in His researc interests include optical fibre and optical wireless communications, and signal processing for optical communication systems. Yufei Jiang (S 12-M 14) received te P.D. degree from te University of Liverpool, Liverpool, U.K, in From 2014 to 2015, e was wit te Department of Electrical and Electronic Engineering, te University of Liverpool, as a Postdoctoral Researcer. From 2015 to 2017, e ave worked as a Researc Associate in te Institutes for Digital Communications at te University of Edinburg, U.K. Currently, e is an assistant professor at te Harbin Institute of ecnology, Senzen, Cina. His researc interests include LiFi, DCO-OFDM, syncronization, full-duplex and blind source separation. Jon ompson (M 94-SM 13-F 16) currently olds a personal cair in Signal Processing and Communications in University of Edinburg, UK. His main researc interests are in wireless communications, sensor signal processing and energy efficient communications networks and smart grids. He as publised around 300 papers in tese topics and was recognised by omson Reuters as a igly cited researcer in 2015 and He also currently leads te European Marie Curie raining Network ADVANAGE wic trains 13 PD students in Smart Grids. He was a distinguised lecturer on green topics for ComSoc in He is also currently an editor of te Green Series of IEEE Communications Magazine and an associate editor for IEEE ransactions on Green Communications and Networks. Yunlu Wang (S 14) received te B.Eng. degree in elecommunication Engineering in 2011 from te Beijing University of Post and elecommunications, Cina, and te double M.Sc. degrees in Digital Communication and Signal Processing in 2013 from te University of Edinburg, UK, and in Electronic and Electrical Engineering in 2014 from Beiang University, Cina, respectively. Currently, e is pursuing a P.D. degree in Electrical Engineering at te University of Edinburg. His researc focus is on visible ligt communication (VLC) and radio frequency (RF) ybrid networking. Pan Cao (S 12-M 15) received te B.Eng. degree in Mecano-Electronic Engineering and te M.Eng. degree in Information and Signal Processing from Xidian University, Xian, P. R. Cina in 2008 and 2011, respectively, and te Dr.-Ing (P.D.) degree in Electrical Engineering from U Dresden, Germany in From Marc 2015 to September 2017, e worked as a postdoctoral researc associate in te Institutes for Digital Communications at te University of Edinburg, UK, supported by te EPSRC project SERAN (Seamless and Efficient Wireless Access for Future Radio Networks). He was also a visiting postdoctoral researc associate at Princeton University during te first tree mont of Since September 2017, e as been a Senior Lecturer at Scool of Engineering and ecnology at te University of Hertfordsire, UK. His current researc interests include millimeter-wave communication, signal processing for radar and communications, and non-convex optimization. He received te Best Student Paper Award of te 13t IEEE International Worksop on Signal Processing Advances in Wireless Communications (SPAWC), Cesme, urkey in 2012, and te Qualcomm Innovation Fellowsip (QInF) Award in Harald Haas received te PD degree from te University of Edinburg in He currently olds te Cair of Mobile Communications at te University of Edinburg, and is te initiator, co-founder and Cief Scientific Officer of purelifi Ltd as well as te Director of te LiFi Researc and Development Center at te University of Edinburg. His main researc interests are in optical wireless communications, ybrid optical wireless and RF communications, spatial modulation, and interference coordination in wireless networks. He first introduced and coined spatial modulation and LiFi. LiFi was listed among te 50 best inventions in IME Magazine Prof. Haas was an invited speaker at ED Global 2011, and is talk: Wireless Data from Every Ligt Bulb as been watced online more tan 2.4 million times. He gave a second ED Global lecture in 2015 on te use of solar cells as LiFi data detectors and energy arvesters. is as been viewed online more tan 1.8 million times. He as publised 400 conference and journal papers including a paper in Science. He co-autors a book entitled: Principles of LED Ligt Communications owards Networked Li-Fi publised wit Cambridge University Press in Prof. Haas is editor of IEEE ransactions on Communications and IEEE Journal of Ligtwave ecnologies. He was co-recipient of recent best paper awards at VC-Fall, 2013, VC-Spring 2015, ICC 2016 and ICC He was co-recipient of te EURASIP Best Paper Award for te Journal on Wireless Communications and Networking in 2015, and co-recipient of te Jack Neubauer Memorial Award of te IEEE Veicular ecnology Society. In 2012 and 2017, e was te recipient of te prestigious Establised Career Fellowsip from te EPSRC (Engineering and Pysical Sciences Researc Council) witin Information and Communications ecnology in te UK. In 2014, e was selected by EPSRC as one of ten RISE (Recognising Inspirational Scientists and Engineers) Leaders in te UK. In 2016, e received te outstanding acievement award from te International Solid State Ligting Alliance. He was elected a Fellow of te Royal Society of Edinburg in 2017.