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On the Performance of SC-FDE Schemes with w ith Decision Feedback Equalizer for Visible Light Communications 1,*
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Yasin Celik , Refik Caglar Kizilirmak , Niyazi Odabasioglu , and Murat Uysal 1 Department of Electrical and Electronics Engineering, Aksaray University, Aksaray, Turkey 2 Department of Electrical and Electronics Engineering, Nazarbayev University, Astana, Kazakhstan 3 Department of Electrical and Electronics Engineering, Istanbu l University, Istanbul, Turkey 4 Department of Electrical and Electronics Engineering, Ozyegin University, Istanbul, Turkey *Corresponding author:
[email protected] ABSTRACT In this paper, we investigate the two single carrier frequency domain equalization (SC-FDE) techniques, namely on-off keying single carrier frequency domain equalization (OOK-SC-FDE) and decomposed quadrature optical (DQO)-SC-FDE, under realistic channel conditions with a practical LED model for visible light communications (VLC). We first compare their performances under dynamic range constraints of the LEDs and observe lower peak-to-average power ratio (PAPR) for SC-FDE schemes as compared to orthogonal division multiplexing (OFDM) techniques. We further introduce decision feedback equalizer (DFE) for SC-FDE schemes and demonstrate performance improvement in multi-tap indoor VLC channels. Keywords: visible light communication, dynamic range constraint, on-off keying SC-FDE, decomposed quadrature optical SC-FDE, and decision feedback eq ualizer. 1. INTRODUCTION
In recent years, VLC has evolved as an alternative to several radio frequency (RF) short-range technologies [1]. It provides low cost and power efficient solution while ensuring high speed and secure transmission. Furthermore, it can use the already installed lighting infrastructure and it operates in an unregulated band. VLC systems employ intensity modulation and direct detection (IM/DD) technique which provides simple and low cost data transmission. Initial versions of VLC generally considered pulse modulation schemes where the data rate was limited mainly by the modulation bandwidth of the LEDs. Another concern with these schemes is that the reflected paths introduce intersymbol interference (ISI) which is another main limiting factor on the system performance [2]. Optical (O)-OFDM which was recently adopted for VLC systems, provides an effective solution to mitigate the detrimental effect of ISI. O-OFDM requires certain modifications to ensure that the information signal is non-negative and real-valued. There are number of different methods suggested in literature for O-OFDM [4] – [7]. However, all of these O-OFDM methods have large peak-to-average power ratio (PAPR) which leads to performance degradation due to the restricted dynamic range r ange of the LEDs [3]. As an alternative to O-OFDM, SC-FDE techniques which are also robust to ISI with low complexity and low PAPR have been proposed for optical wireless systems [8]. In [9], different SC-FDE schemes are proposed for VLC including ACO-SC-FDE, repetition and clipping optical (RCO)-SC-FDE and DQO-SC-FDE. Similarly, OOK-SC-FDE is proposed in [10] which has less complexity, low PAPR P APR and increased BER performance. In this study, we investigate the performances of OOK-SC-FDE and DQO-SC-FDE under realistic channel conditions with a practical LED model. We first co mpare the performances of OOK-SC-FDE and DQO-SC-FDE with asymmetrically clipped O-OFDM (ACO-OFDM [5]) under dynamic range constraints of LEDs and demonstrate the lower PAPR of SC-FDE schemes. Then, we introduce decision feedback equalizer (DFE) to SCFDE schemes under consideration to further enhance the system performance. The remainder of this paper is organized as follows: Section 2 summarizes the OOK-SC-FDE and DQO-SCFDE schemes. Section 3 introduces DFE. Numerical results are presented in Section 4. Finally, the paper is concluded in Section 5. 2. SIGNAL MODEL
In this section, we briefly review OOK-SC-FDE and DQO-SC-FDE modulation schemes. 2.1 OOK-SC-FDE
In OOK-SC-FDE scheme, input data is modulated by non-return-to-zero (NRZ) line code, so output of the modulator is real and positive which makes OOK-SC-FDE scheme simply implementable for IM/DD systems T [10]. After modulation, N length length input vector frame x = [ x0 , x1 , x2 , … x N-1] is obtained. Then, unique word (UW) with length N g is appended to the input vector frame which results in vector x . We denote the length of x by + N g . After the digital to analogue conversion, the intensity waveform x(t ) can be represented as L = N +
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L −1
x(t ) = ∑ x[ n] p (t − nT s ) ,
(1)
n=0
where p(t ) is the impulse response of the pulse shaping filter and T s is the sampling interval. The received electrical signal at the receiver can be written as
y (t ) = rg ( x (t ) ⊗ h(t ) ) + w(t ) ,
(2)
where r is the responsivity of the photodetector (A/W), g is the gain of the LED (W/A), and w(t ) is the additive white Gaussian noise (AWGN) term with (0,
2
) which includes the thermal noise and the shot noise due to
σ n
the ambient light. We assume rg = 1 for simplicity of the presentation. In (2), h(t) is the electrical channel impulse response (CIR) with unit energy and is defined as h(t ) = p(t )⊗c(t )⊗ p(-t ) where c(t ) is optical power delay profile. If the energy of the channel h(t ) is normalized to one, the average electrical SNR per symbol becomes
γ
= E / σ n where E = 2
∫ x(t )
2
.
After sampling of y(t ) at T s, we get y = [ y0 , y1 ,..,y N-1]T . Then, we apply Discrete Fourier Transform (DFT) to the vector y and get (3) Y = ΛX + W , where Y = Fy, X = F x , W = Fw, w is the AWGN vector sampled from w(t) and F is DFT matrix [10]. Λ = Fh, h is the vector of channel coefficients and is obtained by sampling electrical CIR h(t) at a sampling rate T s. After minimum mean square error (MMSE) equalization of Y with V and the Inverse Fast Fourier Transform (IFFT) yield as
*
y = F VY ,
*
-1
-1
(4)
*
where V = (Λ Λ + γ I) Λ , I is the identity matrix, (.) * denotes complex conjugate, and y is the estimated symbols. 2.2 DQO-SC-FDE
In this scheme, complex data symbols are separated into four parts. First, its real and imaginary parts are separated and then each of them is separated further into positive and negative parts [9]. Hence, N length input vector frame x = [ x0 , x1 , x2 , … x N-1]T is turned into subframe vectors as x = [ x I+ , x I- , xQ+ , xQ-]T where the real (in phase) part of x is defined as xI = [ Re( x0) , Re( x1) ,… Re( x N-1)] and the imaginary (quadrature) part of x is defined as xQ = [ I m( x0) , I m( x1) ,… I m( x N-1)] [9]. The positive and negative parts of xI and xQ are separated. For instance, x I+ and x I- can be written as
x I ( n) x I + = 0
if
xI ( n) > 0,
if
x I ( n) ≤ 0,
if 0 x I − = − x I ( n) if
x I ( n) > 0,
(5)
xI ( n) ≤ 0.
xQ+ and xQ- can be constructed in a similar manner. Each subframe has a length of L which is the sum of N and appended UW length N g . Finally, transmitted vector x has a length of 4 L and is represented as x
= [ x I + , x I − , xQ+ , xQ− ]T ,
(6)
and the intensity waveform x(t) becomes 4 L −1
x (t ) =
∑ x[ n] p(t − nT ) .
(7)
s
n=0
As DQO-SC-FDE requires four time slots to transmit all real/imaginary and positive/negative parts, its spectral efficiency is four times less than OOK-SC-FDE. The DQO-SC-FDE receiver algorithm is similar to OOK-SC-FDE, but manipulations are done on every received subframe of DQO-SC-FDE symbols. After MMSE equalization estimated vector for each subframe is
obtained as S I + = VYI + , S I - = VYI - , S Q + = VYQ + , and S Q- = VYQ- . Then we get S I and S Q by subtracting
them as like S = S - S and S Q = S Q+ - SQ- . And finally, we obtain frequency domain estimated symbols as
S = SI
+
I
I+
I-
jS Q [9]. After, taking IFFT of S , we get the estimated symbols as
*
y=FS .
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(8)
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3. DECISION FEEDBACK EQUALIZER
DFE schemes are used to cancel out the ISI and avoid the infinite noise enhancement. In these schemes, ISI from earlier symbols can be removed in a feedback manner. Feedback part can be implemented in time domain (TD) or frequency domain (FD). TD-DFE schemes have a good performance/complexity trade-offs as long as the CIR is not too long [13]. TD-DFE equalizer is expected to give good performance with low complexity for indoor VLC systems since the CIR is not long due to the limited scattering and reflections in the environment. The SC-FD-DFE scheme in Fig. 1 contains a feedforward part in the frequency domain and a feedback part in the time domain. In this scheme, x is the transmitted vector, h is the channel vector, w is the noise, and y represents the received time domain signal vector. After applying FFT, Y is obtained in the frequency domain
and equalized with W which is feedforward filter coefficient vector. The signal Y is transform to the time domain and again equalized with coefficient vector b and the output data vector a in the feedback filter. We use UW for training sequence, which can start the feedback process. Finally, equalized signal z just before the slicer is obtained as [13]
zn =
1
N −1
∑W Y e N l
l
j 2 π nl / N
*
− b an − k .
(9)
l = 0
Figure 1. Single carrier scheme with FD-DFE. 4. SIMULATION RESULTS
In this section, we present Monte Carlo simulation results to show the BER performances of VLC system under consideration. In the simulations, the number of subcarriers N is 64, the number of UW N g is 4. Signal power is varied from 0 dBm to 25 dBm and AWGN power is set to -10 dBm. In order to have fair comparison with OOKSC-FDE, we considered 16 QAM for both DQO-SC-FDE and ACO-OFDM schemes. We consider a white LED (Golden DRAGON, LW W5SM) from OSRAM [12] which has linear voltage-current characteristics in the region of 3.25 V – 3.55 V. Amplitude levels of the intensity waveforms exceeding this range are clipped. We consider a typical office space with dimensions of 5×5×3 m. The light source which is at the ceiling provides ambient light and emits information to the receiver. We follow the optical power delay profile c(t ) for this channel model presented in [11, Fig. 4(b)] and obtain 3-tap indoor channel with sampling rate T s of 50 ns. In Fig. 2, the BER curves are presented for the OOK-SC-FDE, DQO-SC-FDE and ACO-OFDM modulation schemes under the dynamic range constraint of the LEDs. It is observed that S C-FDE schemes outperform ACOOFDM due to their lower PAPR. ACO-OFDM is exposed to clipping distortion at nearly 10 dBm signal power and above the BER of 10 -2. DQO-SC-FDE is clipped at nearly 14 dBm signal power and the BER of 5×10 -6. For OOK-SC-FDE, there is no clipping in the figure, when transmitted signal power exceeds the maximum allowed voltage of LED, BER is fixed at a value which is very small. In Fig. 3, we compare the performances of OOK-SC-FDE and DQO-SC-FDE modulation schemes with DFE. For OOK-SC-FDE nearly 2 dB improvement is achieved with two tap feedback filter. BER performance of DQO-SC-FDE also improves with two tap DFE equalizer. However, after the signal power of 26 dBm, its performance is worse than the case without DFE due to the feedback errors. 5. CONCLUSIONS
In this paper, we have investigated the performances of SC-FDE modulation schemes under dynamic range constraint of the LEDs for indoor VLC systems. DQO-SC-FDE has a lower PAPR than ACO-OFDM and has a better BER performance than ACO-OFDM. OOK-SC-FDE has the lowest PAPR and gives the best BER performance, therefore minimally affected from the d ynamic range constraints. We have implemented DFE with low complexity for SC-FDE modulation schemes and demonstrated a performance improvement of up to 2 dB with only two tap feedback filter size.
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Figure 2. BER performances of OOK-SC-FDE, DQOSC-FDE and ACO-OFDM under the dynamic range constraint of LED in 3 tap VLC channel.
Figure 3. BER performances of OOK-SC-FDE-DFE, DQO-SC-FDE-DFE under dynamic range constraint of LED in 3 tap VLC channel.
ACKNOWLEDGEMENTS
This work was supported by Scientific Research Projects Coordination Unit of Istanbul University. Project number is 51094. REFERENCES
[1] [2] [3] [4] [5] [6] [7] [8] [9]
[10] [11] [12] [13]
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