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An anti-noise modem for visible light communication systems using the improved M-ary position phase shift keying
Int. J. Electron. Commun. (AEÜ) 85 (2018) 126–133
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Regular paper
An anti-noise modem for visible light communication systems using the improved M-ary position phase shift keying
T
⁎
Pu Miaoa, , Lenan Wub, Zhimin Chenc a
Qingdao University, School of Electronic and Information Engineering, Ningxia Road, Qingdao 266071, China Southeast University, School of Information Science and Engineering, 2 Sipailou, Nanjing 210096, China c Shanghai Dianji University, School of Electronic Information, Olive Road, Shanghai 200240, China b
A R T I C L E I N F O
A B S T R A C T
Keywords: Visible light communication Anti-noise M-ary position phase shift keying Sampling offsets Soft decision
In this paper, we propose an anti-noise modem based on the improved M-ary position phase shift keying (MPPSK) for visible light communication (VLC) systems. The line spectral interferences in the original MPPSK are theoretically analyzed and approximately mitigated by adopting a set of improved waveform samples. Then, within one symbol duration, the peak envelopes of the received signals are captured at each of synchronization bit with a quantity of sampling offsets to improve the proportion of the reliable data tones. In addition, a novel demodulation scheme using an amplitude-position detector based on soft decision is proposed to recover the MPPSK symbols, which can minimize the contamination influence of channel noise on symbol decision. With this scheme, the false alarm error and wrong slot error caused by the multipath fading in VLC channel can be effectively corrected and the bit error rate (BER) performance of the system is significantly improved. Simulation results demonstrate that the proposed scheme reduce the required signal-to-noise ratio (SNR) at least by 2 dB for BER = 10−4, which show the feasibility and validity of this anti-noise modem.
1. Introduction Nowadays, the demand for wireless services has become so prevalent in everyday life, resulting in the shortage of available spectrum in wireless communications. With the rapid development of light emitting diode (LED) technology, these solid-state lighting devices are being widely used in many office buildings and traffic lights due to the advantage of high luminous efficiency, low power consumption, longevity and compact size [1–3]. Whereas it is possible to modulate the electrical information by LED in high frequencies such that the human eye can’t detect. Thus, the LED device can be exploited to provide illumination and communication simultaneously, usually referred to visible light communication (VLC) [4,5]. Due to the VLC owns the advantages such as worldwide available and unlicensed bandwidth, no electromagnetic interference and human security, it emerges as a promising technology for future wireless services accessing, which has attracted significant research in the last few years [6–8]. The data transmission in VLC is usually achieved by using the simple and low-cost intensity modulation and direct detection (IM/DD) structure [9], which means that it only deal with the real and positive signals. Conventional modulation schemes investigated in VLC include on-off keying (OOK), pulse-amplitude modulation (PAM) and multi-
⁎
level pulse position modulation (M-PPM). However, the spectrum efficiency is critical as the modulation bandwidth of LED is limited, which greatly reduces the transmission capacity [10,11]. Optical orthogonal frequency-division multiplexing (OFDM) or discrete multi-tone (DMT) modulation [12] have been employed in VLC to improve the system capacity due to they own high spectrum efficiency and resistance to inter symbol interference (ISI). However, OFDM (or DMT) suffers from high peak-to-average power ratio (PAPR) problem and is more susceptible to nonlinear distortions [13,14]. Similar to the power amplifier [15] in wireless communications, the LED also has a limited linear dynamic range. Therefore, the OFDM signals with high PAPR would drive the LED at the transmitter to saturation, resulting in more nonlinear distortions and the overall system performance degradation [16]. In addition, the complicated equalizer and synchronization device must be adopted at the receiver to maintain the demodulation performance. Fortunately, M-ary position phase shift keying (MPPSK) is a simple Sine-like modulation technology with low PAPR and owns high bandwidth efficiency [17]. However, the conventional MPPSK suffers from line spectral interference which degrades the spectral efficiency [18]. In addition, the original symbols are usually recovered by only a threshold detector which compares the sampling signals with different threshold levels, increasing the probability of interference by false alarm error
Corresponding author. E-mail addresses: [email protected] (P. Miao), [email protected] (L. Wu), [email protected] (Z. Chen).
https://doi.org/10.1016/j.aeue.2017.12.039 Received 23 August 2017; Accepted 31 December 2017 1434-8411/ © 2018 Elsevier GmbH. All rights reserved.
Int. J. Electron. Commun. (AEÜ) 85 (2018) 126–133
P. Miao et al.
and wrong slot error especially in the multipath optical diffuse channel [19,20]. Therefore, the anti-noise performance of the original MPPSK modem needs further improvement. In this paper, an improved modem with the modified MPPSK and the soft decision scheme is proposed in VLC transmission. The power spectral density (PSD) of the line spectra interferences in MPPSK is analyzed and the original waveform templates are modified to mitigate these spurious lines. A novel demodulation scheme with an amplitudeposition detector based on soft decision is proposed at the receiver to obtain the reliable observations which is less contaminated by channel noise in threshold comparator. The proposed scheme performs well and the modulated symbols can be recovered effectively in optical diffuse channel. In addition, it also offers more resilience to multipath distortion when compared to the conventional hard decoding. The rest of this paper is organized as follows. Section 2 briefly presents the VLC indoor model. In Section 3, an improved MPPSK waveform is adopted at the transmitter and a soft decision scheme is proposed at the receiver to overcome the sensitivity defect of channel noise in the conventional threshold comparator. Section 4 provides the simulation results and the discussions. Section 5 gives a conclusion of this paper.
A R (ϕ) T (ψ) g (ψ)cos(ψ)
h(0) (t ) =
f ⎧ R d2 ⎨ 0, ψ > ψ C ⎩
( ) d
δ t − c , 0 ⩽ ψ ⩽ ψC (2)
where δ (·) denotes the Dirac impulse, c denotes light speed in free space and R (ϕ) is the angular distribution of the radiation intensity pattern. Let m1 is the order of Lambertian emission [7], the R (ϕ) can be expressed by:
R (ϕ) =
m + 1 cosm1 ( ϕ ) π π ⎧( 1 ) , ϕ ∈ ⎡− 2 , 2 ⎤ 2π ⎣ ⎦ ⎨ 0, others ⎩
to overall h (t ) will decrease as the number The contribution of of reflections k v are increased. Although the signal power associated with more reflections is relatively small, the signal arrives at the receiver much later than that undergoing only one reflection. Therefore, (kv ) hNLOS (t ) cannot be ignored when considering high-speed diffuse links. (kv ) (t ) can be evaluated With the help of ray-tracing algorithm, the hNLOS after k v reflections by: NP (kv ) hNLOS (t ) =
∑
ρ ·h(kv − 1) (t ,dεr ,i ) ∗h(0) (t ,dεs,i )
i=1
Due to the movements of the receiver and the fact that the moving objects in the room are slower than the transmission rate of the system, the VLC channel can be regarded as a linear time invariant system as the room environment is determined [6]. Fig. 1 shows a typical VLC channel between a white LED as the transmitter, and a photo-detector (PD) as the receiver. The LED is located in the center of the room, ϕ denotes radiation angle (ϕ0 is related to the LED semi-angle at half power), d is the distance between the LED and the receiver, which is modeled as an active area AR collecting the radiation at angles ψ < ψc (ψc is the field-of-view). α and β are the angle of irradiance to a reflective point and the angle of irradiance to a receiver, respectively. The VLC channel h (t ) consists of line-of-sight (LOS) and diffuse non-LOS (NLOS) components undergoing exactly Kv reflections [7]:
kv = 1
N
(1) hNLOS (t ) =
(kv ) hNLOS (t ) =
∑
p m + 1 ρ ·A ΔA·cosm1 (ϕi) cos (αi)·cos (ψi) cos (βi) ∑ ⎧( 1 ) R · 2 2
⎨ ⎩ d + dri ⎞ ⎫ δ ⎛t − si c ⎝ ⎠⎬ ⎭ i=1
2πdsi dri
(5)
where dsi and dri are the propagation distance in a single reflection. 3. The improved MPPSK modem 3.1. The improved modulation scheme
Kv
Kv
∑
(4)
where ρ is the reflection coefficient, NP is the total reflecting elements of the entire space, dεr ,i and dεs,i denote the surface of the ith receiving element and the emitting element associated with the k v−1 reflection, respectively. The surfaces of the room are divided by many reflecting (1) (t ) can be approximately elements with an area of ΔA , then, the hNLOS expressed as:
2. The system model
h (t ) = hLOS (t ) +
(3)
(kv ) hNLOS (t )
h(kv) (t )
kv = 0
(1)
A MPPSK symbol consists a special sine wave occupying K slot duration within the total N0 time slots, whereas the remaining (N0−K ) slots are used to modulate other sine waves, which owns tiny difference between that of the former K slot duration. That’s to say, MPPSK employs small angle phase transition interval at different positions during a symbol period. The bit streams are modulated by both the phase transition and position together according to the M-ary modulated symbols. Let Xk (k = 0,1,…,M −1) denotes the (k + 1)th point of signal constellation, the waveform samples f (k ,t ) which have very tiny difference are modulated by Xk . For Xk = 0 , the waveform samples can be expressed as [19]:
Considering a receiver with an optical band-pass filter of transmission Tf (ψ) and a concentrator with gain g (ψ) [7], the impulse response of LOS channel can be calculated as [6]:
f (0,t ) = Asin(2πfc t ), 0 ⩽ t < T
(6)
For Xk = 1,2,…,M−1, the corresponding waveform samples are
f (k ,t ) =
0 ⩽ t < (k−1) τ ⎧ Asin(2πfc t ), ⎪ B sin(2πfc t + θ), (k−1) τ ⩽ t < kτ ⎨ kτ ⩽ t < T ⎪ Asin(2πfc t ), ⎩
(7)
where T = (2πN0/ ωc ) = N0 Tc is the symbol duration, Tc = 1/ fc is the carrier cycle, θ is the modulating angle, τ = KTc is the slots length of the phase transition, A and B are the amplitudes of the modulated waveforms, respectively. Hence, the modulated MPPSK signal can be expressed by
Fig. 1. The geometry of light propagation in VLC system.
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P. Miao et al.
Fig. 2. The MPPSK waveforms (a) for time domain (b) for the PSD performance.
x (t ) =
∑
any discrete spectrum. Motivated by the previous analysis, the f (k ,t ) are modified by:
f (k ,t −nT ) (8)
n
The spectral performance of x (t ) are varied by changing the parameters such as N0 , τ and M . For a specific case such as fc = 100 MHz, N0 = 10 , K = 2 , θ = π and M = 4 , the MPPSK waveforms and the corresponding PSD are depicted in Fig. 2. As seen in the figure, there exists a large amount of line spectral components which may cause interference to other signals. To improve the spectral efficiency as well as the demodulation performance, these spurious components must be mitigated in VLC transmission. Let F (k ,ω) denotes the Fourier transform of f (k ,t ) . For Xk = 1,2,…,M−1, we have T 0
F (k ,ω) = ∫ f
ωc ⎡1 − 2exp ⎛ ⎢ ⎝ ⎣
T
f (k ,t )−
k=0
1 MT
M−1
∑
{F (k ,ωc ) e jωc t + F (k ,−ωc ) e−jωc t }
⎜
⎟
⎜
ω → ωc
⎟
F (0,ωc ) = lim F (0,ω) =
⎦
ω → ωc
(9)
j (2K −N0) π ,k = 1,2,…,M −1 ωc
(14)
Nπ ,k = 0 jωc
(15)
Then, the PSD of the improved MPPSK can be presented as
ωc [1−exp(−jωT )] ωc2−ω2
PŜ (ω) =
(10)
⎡ 1 F (k , mfc ) ⎤ fc |2 δ ⎛f − mfc ⎞ ⎢M ⎥ N0 ⎝ N0 ⎠ N0 ⎦ ⎣ ⎜
+∞
M−1
(
|
∑
−
⎟
∑ ∑
k=0
l=k+1
Pv (ω)
+
∑ k=0 M−2
−
f
· Nc
l=k+1
f
· Nc
0
where Fnew (k ,ω) is the Fourier transform of fnew (k ,t ) . As seen in (16), the first part of PŜ (ω) are the discrete components. However, as m ≠ ± N0 , we fortunately have the followings equations holding as
0
M−1
∑ ∑ k=0
M2
(16)
(M − 1) | F (M − 1,f ) − F (k ,f )|2 M2
)
mf f mf 1 ⎡ M Fnew (k , N c ) ⎤ Nc |2 δ f − N c 0 ⎦ 0 0 ⎣ m =−∞ k=0 M−2 (M − 1) | Fnew (M − 1,f ) − Fnew (k ,f )|2 fc + ·N M2 0 k=0 M−2 M−1 |Fnew (M − 1,f ) − Fnew (k ,f ) |·| Fnew (M − 1,f ) − Fnew (l,f )|
∑
∑
M−1
∑m =−∞ | ∑k =0 M−2
(13)
k=0
and ⎟
f (0,t ) e−jωt dt =
+∞
∑
F (k ,ωc ) = lim F (k ,ω) =
We assume that each transmitting symbol is modulated with equal probability as M−1. Therefore, the PSD of MPPSK can be presented as
PS (ω) =
M−1
where F (k ,ωc ) can be calculated by
−jω (k − 1) K ⎞ −jωK ⎞ −jωN0 ⎞ ⎤ + 2exp ⎛ − exp ⎛ ⎥ fc ⎠ ⎝ fc ⎠ ⎝ fc ⎠
ωc2 − ω2
∫0
1 M
q (t ) =
For Xk = 0 , F (0,ω) can be calculated by
F (0,ω) =
(12)
In addition, q (t ) is a waveform factor which can be designed as
(k ,t ) e−jωt dt ⎜
=
fnew (k ,t ) = f (k ,t )−q (t )
|F (M − 1,f ) − F (k ,f ) |·| F (M − 1,f ) − F (l,f )| M2
f
· Nc
0
(11)
mf mf F ⎛k , c ⎞ = Q ⎛ c ⎞ N 0 ⎝ ⎠ ⎝ N0 ⎠ ⎜
As seen in (11), the first part Pv (ω) is shown as discrete periodical Fourier components, which does not hold any useful information and may cause interference to other signals. As fc is a constant, the amplitude of Pv (ω) and the number of discrete components are determined by M and N0 . As N0 is a constant, the Pv (ω) is consisting of a series of pulses spaced at intervals of fc / N0 . Although the amplitude of the Pv (ω) is decreased as M is increased, the number of the discrete spectral components are also increased in quantity. If we could find some method to make the amplitude of Pv (ω) to be zeros, then the discrete spectral components will be suppressed consequently.As the discrete spectrum of MPPSK is induced by the special mapping between MPPSK symbols and the modulated waveform templates, we can modify the original f (k ,t ) so that the optimized PSD of the improved MPPSK doesn’t hold
⎟
⎜
⎟
(17)
and M−1
|
∑ k=0
⎡ 1 F ⎛k , mfc ⎞ ⎤ fc |2 = 0 ⎢ M new ⎝ N0 ⎠ ⎥ N0 ⎣ ⎦ ⎜
⎟
(18)
where Q (ω) is the Fourier transform of q (t ) . Then, the amplitude of
(
mf
δ f − Nc 0
) in (16) becomes zeros which mean that the discrete line
spectrum in PŜ (ω) are suppressed accordingly.The modified waveform samples is depicted in Fig. 3 based on the same modulation parameters as in Fig. 2. It should be noted that in this case the q (t ) can be calculated as 128
Int. J. Electron. Commun. (AEÜ) 85 (2018) 126–133
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Fig. 3. The improved MPPSK waveform: (a) for time domain (b) for the PSD performance.
q (t ) =
1 4
3
∑
f (k ,t )−0.7sin(ωc t )
k=0
decision decoder is proposed at the receiver and the corresponding demodulation procedure is demonstrated in Fig. 4. In addition, the details are also depicted in the subfigure. Generally speaking, the SIF can amplify the modulation characteristics of MPPSK as much as possible. After absolute operation, the signal envelop is extracted by a lowpass filter (LPF) and then fed into the soft decision module for recovering the original symbols. The transfer function of SIF can be represented as:
(19)
As seen in Fig. 3, the amplitude of the new waveforms have changed nearby the angle phase transition and the envelope of MPPSK signal is not a constant any more. In addition, the PSD is also depicted here. The figure clearly demonstrates that the PSD is smooth and the discrete periodical line spectrum is suppressed in the improved MPPSK by means of (12).
⎛ H (Z ) = ⎜1 + ⎝
3.2. The proposed soft decision
I
∑ i=1
J
⎞ ⎞ ⎛ bi Z −i⎟/ 1− ∑ aj Z −j ⎜ ⎟ j=1 ⎠ ⎝ ⎠
(20)
where bi and aj are the coefficients associated with numerator and denominator, respectively, I and J are the number of zeros and poles. In this paper, three adjacent conjugate poles pj and one conjugate zeros z i are adopted in SIF designing. A quantum-based particle swarm optimization (QPSO) algorithm [21] is adopted for global searching the optimum parameters of bi and aj . After that, the optimum coefficients of SIF with oversampling factor of γ = 10 can be chosen as:
The fnew (k ,t ) have very tiny differences which increase the difficulty of symbols detections in the coherent demodulation procedure. Fortunately, the phase transition character can be distinguished with the help of the special impacting filter (SIF) and then converted to a series of amplitude impacting. However, the conventional threshold detector [18] recovers the original symbols by comparing the peak envelope of SIF outputting with fixed threshold level in a proper sequence, which will increase the probability of interference by false alarm error and wrong slot error, especially in multipath fading environment [2,9]. To improve the anti-interference ability, a soft
b = [1,−1.618092409933249,0.99990000250000044]
(21)
Fig. 4. Block diagram of the SIF based receiver for MPPSK scheme with soft decision decoding.
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Int. J. Electron. Commun. (AEÜ) 85 (2018) 126–133
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−2ωc ∏ (pj − z i)
6
yz (t ) =
∑
i=1 6
j = 1 (pj2 + ωc2)
·exp(pj (t −(k−1) τ )) ε [t −(k−1) τ ]
∏
(pj − pi )
j = 1,j ≠ i 2
6
+
2ωc ∏ (pj − z i)
∑
i=1
j = 1 (pj2 + ωc2)
exp(pj (t −kτ )) ε (t −kτ )
6
∏
(pj − pi )
(26)
j = 1,j ≠ i
where ε (·) is the step function. Therefore, as seen in (25) and (26), the SIF will produce a much higher amplitude impacting at the interval [(k−1) τ ,kτ ]. We assume that the total number of transmitting symbols is L . After the absolute processor and LPF, the signal envelope ∼ y ∈ NS × L of y (t ) is obtained, which can be expressed by
∼ y = [∼ y0,∼ y1,…,∼ yL − 1]
Fig. 5. Frequency response of the SIF.
a = [1,−4.5620074920961651,9.5862839416819483, −11.566980661101638,8.4523528839743243, −3.5467147693005732,0.6855154433139603]
v +ζ
i=1
y (t ) =
6
∏
+
z i2)
6
⎛ sin ωc t − ∑ φj + ⎜ j=1 ⎝ (ωc2 + pj2 )
2
∑ i=1
is
Δ
the
filter
gain,
⎛ φj = arccos ⎜ ⎝
T
(28)
(29)
Finally, we obtain the estimated symbol as
⎞ ϕi ⎟ ⎠
Xl ̂ = argmax(Cl ΛUl) k
j=1
where
+ζ
Kγ Kγ
Ul = {Sl ⩾ max (Sl)} (ωc2
v
In addition, the sampling offset ζ ∈ ⎡− 2 , 2 ⎤ is also adopted in (28). As ⎣ ⎦ smaller ζ is used, the acquisition of the effective envelopes can not fulfill the threshold requirement of signal demodulation. Similarly, the ζ should not be too large because excess samplings would induce more background noise, which will degrade the SNRs. Therefore, it is worth noting that appropriate ζ could improve the proportion of the effective data tones and the demodulation performance, which will be evaluated and discussed in Section 4. Then, Sl are sent to a comparator and we get a (M −1) × 1 logical vector as
2
∏
v +ζ
2 M−1 ⎡ 1 ⎤ Sl = [S1,l,S2,l,…,SM − 1,l]T = ⎢ ∑ yid,l , ∑ yid,l ,… , ∑ yid,l ⎥ id = v − ζ id = v − ζ id = v − ζ 1 2 M − 1 ⎣ ⎦
(22)
The corresponding frequency response is given in Fig. 5. As seen in the figure, there exists a large mutation of phase response in the steepest slope area associated with the magnitude response. Unlike other receiving filters, the fc can’t be placed in the center of SIF since the whole performance will be affected by the position of fc . In order to convert the phase transition of MPPSK into the amplitude impacting, the fc with the largest phase mutation point (as shown in Fig. 5) should be chosen in our system design. It should be note that the continuous time representations will be adopted in followings since such representations can easily provide analytical insights and give physical meaning to SIF processing. As Xk = 0 , the received signal after the SIF can be calculated as
Δ
(27)
yl = [y0,l ,y1,l ,…,yNS − 1,l ]T represents the received envelopes for the where ∼ th l (l = 0,1,…,L−1) symbols, NS = N0 γ denotes the total points of the corresponding sampling. For every received frame, the perfect synchronization is assumed. According to bit synchronization v = [v1,v2,…,vM − 1]T , the signal eny is sampled at every M −1 slot position and we could obtain the velope ∼ sampling matrix S = [S0,S1,…,SL − 1], where Sl ∈ (M − 1) × 1 can be presented as
pj ωc2 + pj2
⎞ ⎟ ⎠
(30)
(23)
where Λ = diag (1,2,…,M −1) , Cl is associated with the threshold level Γ at the sampling instant and can be calculated by
and
1, max (Sl) ⩾ Γ Cl = ⎧ ⎨ ⎩ 0, max (Sl) < Γ
z ϕi = arccos ⎛⎜ 2 i ⎟⎞. As Xk ≠ 0 , the output of SIF can be presented by ωc + zi2 ⎝ ⎠ y (t ) = ys (t ) + yz (t ) (24)
(31)
From the above analysis, it can be seen that the proposed demodulation scheme with a soft decision decoder recovers the modulated symbols with the help of the slot positions of phase transition, instead of the conventional threshold detecting.
where ys (t ) and yz (t ) are the steady state response and transient response, respectively. Therefore, ys (t ) and yz (t ) can be calculated as
4. Results and discussions 2
1
−2 ∏ (ωc2 + zi2) 2 i=1 6
ys (t ) =
1
6
2
sin(ωc t − ∑ φj +
∏ (ωc2 + pj2 ) 2
∑
j=1
In this section, Monte Carlo simulations are conducted to evaluate the system performance of the improved MPPSK with soft decision over VLC channel. In addition, the LED nonlinearity is not considered here due to the low PAPR advantage of MPPSK signals.
ϕi ){ε [t −(k−1) τ ]−ε [t −kτ ]}
i=1
j=1 2
1
Δ ∏ (ωc2 + zi2) 2 sin(ωc t −
+
i=1
6 j=1
6
2
∑ φj + ∑ ϕi) i=1
4.1. The simulation model
1
∏ (ωc2 + pj2 ) 2 j=1
For simplicity, an empty indoor room model with size of 5 × 5×3 m3 is considered and the coordinate set R = (lx,wy,hz) is adopted for numerical calculation, where −2.5 ⩽ l x ⩽ 2.5, −2.5 ⩽ wy ⩽ 2.5 and
(25) and 130
Int. J. Electron. Commun. (AEÜ) 85 (2018) 126–133
P. Miao et al.
position and amplitude impacting for different modulated signals are more obvious, and they are very easy to discriminate from each other without down-converting to a baseband.
Table 1 The simulation parameters of VLC channel. Channel Parameters
Values
Semi-angle ϕ0 (deg) Source optical power (mW) Reflection coefficients ρ Receiving panel d 0 LED number Lambert’s order m1 Active area AR (cm2) Field-of-view ψc (deg) Optical BPF Tf (ψ)
70 20 0.7 0.85 50 × 50 0.6461 1 60 1
Concentrator g (ψ) Refractive index Sampling frequency (GHz)
3 1.5 1
4.3. Performance of sampling offset In this study, several delivery tests employing the different sampling offset ζ are conducted to investigate the effect of ζ on the demodulation performance of the proposed soft decision scheme. Fig. 8a demonstrates the BER performance for the improved MPPSK at different sampling offset. The SNR is varied from 0 to 7 dB and the ζ is utilized from 0 to 5. As compared in the figure, besides the ζ = 0 and ζ = 1, most of the curves have an available demodulation performance which achieves an acceptable BER below 1 × 10−3 . It indicates that, as ζ = 0 and ζ = 1, the acquisition of the signal information can not sustain the SNR threshold requirement for the MPPSK demodulation. When ζ ⩾ 2 , the BER performance is improved due to the SNR gains by the sufficient valid data around the envelop peaks. However, as seen in Fig. 8b, the BER performance is degraded gradually when ζ increase beyond the optimum points, which indicates that the excess samplings offset would induce more background noise. Therefore, the optimum ζ can enhance the SNR and then improve the demodulation performance. In order to utilize the favorable envelope information, ζ = 3 is adopted in the following simulations.
−1.5 ⩽ hz ⩽ 1.5. In addition, the LED source is located at ceiling central with coordinate (0,0,1.5) . The parameters of the VLC channel model are designed based on Table 1. R 0 = (−0.625,−0.625,−0.65) Taking the coordinate and R1 = (2.083,2.083,−0.65) for an example. As only up to 5 times reflections are considered in VLC transmission, an approximation of the normalized channel impulse response (CIR) are calculated by (4) and depicted in Fig. 6. As shown in the figure, the first reflection dominates the total response for R 0 and the ratio of the reflected parts is very small. In addition, the channel delay spread is around 9 ns under the condition of 1 GHz sampling rate. Whereas for R1, the normalized CIR consists of LOS and NLOS component, the diffuse portion comes from the reflections of the walls and the NLOS components can’t be ignored when considering a high-speed transmission. Compared with the channel delay spread of the whole receiving panel, we can set the electrical MPPSK parameters as fc = 300 MHz, N0 = 10 , K = 1, θ = π , M = 8, A = 1 and B = 1, so as to obtain the appropriate symbol duration. Then, the corresponding waveform samples can be optimized by (12) and (13), respectively.
4.4. The BER performance Fig. 9 shows the BER performance of the modified MPPSK using both the proposed soft decision scheme and the conventional hard decision scheme at position R1. In addition, the BER of the original MPPSK are also depicted here. The conventional hard decision is easily disturbed by the multipath distortion, which will degrade the demodulation efficiency and restrict the communication areas. Conversely, results clearly demonstrate that the BER performance is significantly improved by the proposed soft decision since it owns excellent capability against false alarm error and wrong slot error. At BER = 1 × 10−4 , the required SNR are reduced at least by 2 dB for the modified MPPSK with the proposed demodulation scheme. In the case of low SNRs (e.g. SNR ⩽2 dB), the gap of the required SNR is very tiny because the channel noise are also contaminating the threshold level. While for the high SNRs (e.g. SNR ⩾3 dB), the SNR gap have gradually increased due to the decision error in (30) is minor and the advantage of the proposed scheme becomes more evident. In addition, the BER of the modified MPPSK performs approximately as the same as the original case, which indicates that the line spectral mitigation in (12) doesn’t affect the demodulation performance. Therefore, the proposed anti-noise modem can be used to improve the BER performance under multipath environment.
4.2. The SIF effect After the SIF and LPF processing, the received envelop of the improved MPPSK for position R1 is obtained and demonstrated in Fig. 7. Although there exists a certain amount of NLOS components at position R1, however, as seen in the figure, the SIF can still produce a much higher amplitude impacting, which has greatly improved the energy of the useful information. It is worthy noting that the characteristics of the
4.5. The complexity comparison The computational complexities of the proposed and the conventional schemes are discussed in this section. The elapsed time Telap , representing the total time consumed by signal demodulation, is adopted as a metric to measure the computational complexity. In this study, simulations with 200 MPPSK symbols are each performed with M = 4, 8 and 16, respectively. To provide a fair comparison, the other modulation parameters are fixed with same constants as fc = 300 MHz, N0 = 40 , K = 2 , θ = π , A = 1 and B = 1. For the proposed scheme, ζ = 0, 3 and 5 are adopted here. The Telap are measured and compared in Fig. 10. As seen in the figure, the Telap of these two schemes are increased dramatically with an increase of M . In addition, the proposed schemes require a little more time consumption than the hard decoding. However, the corresponding increments are not too much. The additional operations performed in the proposed scheme consist of (2M −1) adders and 2 multipliers, meaning that a lower extra computational
Fig. 6. The channel impulse response at position R0 and R1.
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Fig. 7. The received signal at position R1: (a) for SIF and (b) for LPF.
Fig. 8. The BER comparisons of the proposed soft decision scheme: (a) for different ζ (b) for SNR = 6 and 4 dB.
Fig. 10. The time consumption of signal demodulation in terms of hard decision and soft decision (200 symbols).
Fig. 9. The BER comparisons of MPPSK with hard decision and soft decision at position R1.
5. Conclusions complexity is consumed by soft decision. Moreover, the Telap of the proposed scheme changes very little as the number of ζ increases. In summary, the proposed scheme shows better BER performance and owns smaller complexity increments, which are beneficial to high-speed VLC communications.
In this paper, an improved modem using the modified MPPSK and soft decision detector has been proposed in VLC communications. The spurious components caused by original symbol mapping of MPPSK have been effectively suppressed and the probability of interference by false alarm error and wrong slot error is significantly reduced, which 132
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presents an effective solution for the improvement of anti-noise capability in VLC communications. Moreover, the proposed modem works well under multipath diffuse environment with moderate modulation parameters. It is easily applied in VLC system with low cost and offers better BER performance than the conventional hard decision, which validates the effectiveness of this scheme.
[7] Grubor Jelena, et al. Broadband information broadcasting using LED-based interior lighting. J Lightwave Technol 2008;26(24):3883–92. [8] Li X, et al. Wireless visible light communications employing feed-forward preequalization and PAM-4 modulation. J Lightwave Technol 2016;34(8):2049–55. [9] Barros Daniel JF, Wilson Sarah K, Kahn Joseph M. Comparison of orthogonal frequency-division multiplexing and pulse-amplitude modulation in indoor optical wireless links. IEEE Trans Commun 2012;60(1):153–63. [10] Neokosmidis Ioannis, et al. Impact of nonlinear LED transfer function on discrete multitone modulation: analytical approach. J Lightwave Technol 2009;27(22):4970–8. [11] Mesleh Raed, Elgala Hany, Haas Harald. On the performance of different OFDM based optical wireless communication systems. J Opt Commun Netw 2011;3(8):620–8. [12] Mossaad Mohammed SA, Hranilovic Steve, Lampe Lutz. Visible light communications using OFDM and multiple LEDs. IEEE Trans Commun 2015;63(11):4304–13. [13] Abdulrahman Ikram Siddiq. PAPR reduction in OFDM systems using peak insertion. AEU – Int J Electron Commun 2015;69(2):573–8. [14] Ling Xintong, et al. Offset and power optimization for DCO-OFDM in visible light communication systems. IEEE Trans Signal Process 2016;64(2):349–63. [15] Liu Haitao, Cong Wan, Wang Lei, Li Dongxia. Symbol error rate performance of nonlinear OFDM receiver with peak value threshold over frequency selective fading channel. AEU – Int J Electron Commun 2017;74:163–70. [16] Miao P, et al. RCLED optimization and nonlinearity compensation in a polymer optical fiber DMT system. Appl Sci 2016;6(9):260. [17] Miao P, Wu LN, Chen Z. A low-cost modem based on MPPSK in visible light communication for indoor accessing systems. 2017 International Conference on Wireless Communications, Signal Processing and Networking (WiSPNET). IEEE; 2017. p. 1862–6. [18] Wu LN, Qi C. Modulation and demodulation method for M-ary Pulse Position Shift Keying (MPPSK). CN Pat. No. 200710025202.1; 2007. [19] Wu LN. Advance in UNB high speed communications. Prog Nat Sci 2007;17:143–9. [in Chinese]. [20] Miao P, Wu LN, Jin Y. On power spectrum optimization of M-ary position PSK modulations. J Electron Inform Technol 2013;35:1687–93. [in Chinese]. [21] Yu J, Wu LN, Jin Y. QPSO-based auto-design of digital impacting filters. J Southeast Univ Nat Sci Ed 2012;42:224–8. [in Chinese].
Acknowledgments This work is supported in part by the National Natural Science Foundation of China (61601281) and by the Shandong Provincial Natural Science Foundation, China (ZR2017BF028). The authors would like to express gratitude to Prof. Wu, Dr. Chen and Dr. Song for constructive suggestions and assistance to this article. References [1] Hany Elgala, Mesleh Raed, Haas Harald. Indoor optical wireless communication: potential and state-of-the-art. IEEE Commun Mag 2011;49(9). [2] Ozgur Ergul, Dinc Ergin, Akan Ozgur B. Communicate to illuminate: state-of-the-art and research challenges for visible light communications. Phys Commun 2015;17:72–85. [3] Hua Qian, et al. On the benefit of DMT modulation in nonlinear VLC systems. Opt Express 2015;23(3):2618–32. [4] Barroso Alberto Rui Frutuoso, Johnson Julia. Optical wireless communications omnidirectional receivers for vehicular communications. AEU – Int J Electron Commun 2017;79:102–9. [5] Liane Grobe, et al. High-speed visible light communication systems. IEEE Commun Mag 2013;51(12):60–6. [6] Komine T, Nakagawa M. Fundamental analysis for visible-light communication system using LED lights. IEEE Trans Consum Electron 2004;50(1):100–7.
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Int. J. Electron. Commun. (AEÜ) journal homepage: www.elsevier.com/locate/aeue
Regular paper
An anti-noise modem for visible light communication systems using the improved M-ary position phase shift keying
T
⁎
Pu Miaoa, , Lenan Wub, Zhimin Chenc a
Qingdao University, School of Electronic and Information Engineering, Ningxia Road, Qingdao 266071, China Southeast University, School of Information Science and Engineering, 2 Sipailou, Nanjing 210096, China c Shanghai Dianji University, School of Electronic Information, Olive Road, Shanghai 200240, China b
A R T I C L E I N F O
A B S T R A C T
Keywords: Visible light communication Anti-noise M-ary position phase shift keying Sampling offsets Soft decision
In this paper, we propose an anti-noise modem based on the improved M-ary position phase shift keying (MPPSK) for visible light communication (VLC) systems. The line spectral interferences in the original MPPSK are theoretically analyzed and approximately mitigated by adopting a set of improved waveform samples. Then, within one symbol duration, the peak envelopes of the received signals are captured at each of synchronization bit with a quantity of sampling offsets to improve the proportion of the reliable data tones. In addition, a novel demodulation scheme using an amplitude-position detector based on soft decision is proposed to recover the MPPSK symbols, which can minimize the contamination influence of channel noise on symbol decision. With this scheme, the false alarm error and wrong slot error caused by the multipath fading in VLC channel can be effectively corrected and the bit error rate (BER) performance of the system is significantly improved. Simulation results demonstrate that the proposed scheme reduce the required signal-to-noise ratio (SNR) at least by 2 dB for BER = 10−4, which show the feasibility and validity of this anti-noise modem.
1. Introduction Nowadays, the demand for wireless services has become so prevalent in everyday life, resulting in the shortage of available spectrum in wireless communications. With the rapid development of light emitting diode (LED) technology, these solid-state lighting devices are being widely used in many office buildings and traffic lights due to the advantage of high luminous efficiency, low power consumption, longevity and compact size [1–3]. Whereas it is possible to modulate the electrical information by LED in high frequencies such that the human eye can’t detect. Thus, the LED device can be exploited to provide illumination and communication simultaneously, usually referred to visible light communication (VLC) [4,5]. Due to the VLC owns the advantages such as worldwide available and unlicensed bandwidth, no electromagnetic interference and human security, it emerges as a promising technology for future wireless services accessing, which has attracted significant research in the last few years [6–8]. The data transmission in VLC is usually achieved by using the simple and low-cost intensity modulation and direct detection (IM/DD) structure [9], which means that it only deal with the real and positive signals. Conventional modulation schemes investigated in VLC include on-off keying (OOK), pulse-amplitude modulation (PAM) and multi-
⁎
level pulse position modulation (M-PPM). However, the spectrum efficiency is critical as the modulation bandwidth of LED is limited, which greatly reduces the transmission capacity [10,11]. Optical orthogonal frequency-division multiplexing (OFDM) or discrete multi-tone (DMT) modulation [12] have been employed in VLC to improve the system capacity due to they own high spectrum efficiency and resistance to inter symbol interference (ISI). However, OFDM (or DMT) suffers from high peak-to-average power ratio (PAPR) problem and is more susceptible to nonlinear distortions [13,14]. Similar to the power amplifier [15] in wireless communications, the LED also has a limited linear dynamic range. Therefore, the OFDM signals with high PAPR would drive the LED at the transmitter to saturation, resulting in more nonlinear distortions and the overall system performance degradation [16]. In addition, the complicated equalizer and synchronization device must be adopted at the receiver to maintain the demodulation performance. Fortunately, M-ary position phase shift keying (MPPSK) is a simple Sine-like modulation technology with low PAPR and owns high bandwidth efficiency [17]. However, the conventional MPPSK suffers from line spectral interference which degrades the spectral efficiency [18]. In addition, the original symbols are usually recovered by only a threshold detector which compares the sampling signals with different threshold levels, increasing the probability of interference by false alarm error
Corresponding author. E-mail addresses: [email protected] (P. Miao), [email protected] (L. Wu), [email protected] (Z. Chen).
https://doi.org/10.1016/j.aeue.2017.12.039 Received 23 August 2017; Accepted 31 December 2017 1434-8411/ © 2018 Elsevier GmbH. All rights reserved.
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and wrong slot error especially in the multipath optical diffuse channel [19,20]. Therefore, the anti-noise performance of the original MPPSK modem needs further improvement. In this paper, an improved modem with the modified MPPSK and the soft decision scheme is proposed in VLC transmission. The power spectral density (PSD) of the line spectra interferences in MPPSK is analyzed and the original waveform templates are modified to mitigate these spurious lines. A novel demodulation scheme with an amplitudeposition detector based on soft decision is proposed at the receiver to obtain the reliable observations which is less contaminated by channel noise in threshold comparator. The proposed scheme performs well and the modulated symbols can be recovered effectively in optical diffuse channel. In addition, it also offers more resilience to multipath distortion when compared to the conventional hard decoding. The rest of this paper is organized as follows. Section 2 briefly presents the VLC indoor model. In Section 3, an improved MPPSK waveform is adopted at the transmitter and a soft decision scheme is proposed at the receiver to overcome the sensitivity defect of channel noise in the conventional threshold comparator. Section 4 provides the simulation results and the discussions. Section 5 gives a conclusion of this paper.
A R (ϕ) T (ψ) g (ψ)cos(ψ)
h(0) (t ) =
f ⎧ R d2 ⎨ 0, ψ > ψ C ⎩
( ) d
δ t − c , 0 ⩽ ψ ⩽ ψC (2)
where δ (·) denotes the Dirac impulse, c denotes light speed in free space and R (ϕ) is the angular distribution of the radiation intensity pattern. Let m1 is the order of Lambertian emission [7], the R (ϕ) can be expressed by:
R (ϕ) =
m + 1 cosm1 ( ϕ ) π π ⎧( 1 ) , ϕ ∈ ⎡− 2 , 2 ⎤ 2π ⎣ ⎦ ⎨ 0, others ⎩
to overall h (t ) will decrease as the number The contribution of of reflections k v are increased. Although the signal power associated with more reflections is relatively small, the signal arrives at the receiver much later than that undergoing only one reflection. Therefore, (kv ) hNLOS (t ) cannot be ignored when considering high-speed diffuse links. (kv ) (t ) can be evaluated With the help of ray-tracing algorithm, the hNLOS after k v reflections by: NP (kv ) hNLOS (t ) =
∑
ρ ·h(kv − 1) (t ,dεr ,i ) ∗h(0) (t ,dεs,i )
i=1
Due to the movements of the receiver and the fact that the moving objects in the room are slower than the transmission rate of the system, the VLC channel can be regarded as a linear time invariant system as the room environment is determined [6]. Fig. 1 shows a typical VLC channel between a white LED as the transmitter, and a photo-detector (PD) as the receiver. The LED is located in the center of the room, ϕ denotes radiation angle (ϕ0 is related to the LED semi-angle at half power), d is the distance between the LED and the receiver, which is modeled as an active area AR collecting the radiation at angles ψ < ψc (ψc is the field-of-view). α and β are the angle of irradiance to a reflective point and the angle of irradiance to a receiver, respectively. The VLC channel h (t ) consists of line-of-sight (LOS) and diffuse non-LOS (NLOS) components undergoing exactly Kv reflections [7]:
kv = 1
N
(1) hNLOS (t ) =
(kv ) hNLOS (t ) =
∑
p m + 1 ρ ·A ΔA·cosm1 (ϕi) cos (αi)·cos (ψi) cos (βi) ∑ ⎧( 1 ) R · 2 2
⎨ ⎩ d + dri ⎞ ⎫ δ ⎛t − si c ⎝ ⎠⎬ ⎭ i=1
2πdsi dri
(5)
where dsi and dri are the propagation distance in a single reflection. 3. The improved MPPSK modem 3.1. The improved modulation scheme
Kv
Kv
∑
(4)
where ρ is the reflection coefficient, NP is the total reflecting elements of the entire space, dεr ,i and dεs,i denote the surface of the ith receiving element and the emitting element associated with the k v−1 reflection, respectively. The surfaces of the room are divided by many reflecting (1) (t ) can be approximately elements with an area of ΔA , then, the hNLOS expressed as:
2. The system model
h (t ) = hLOS (t ) +
(3)
(kv ) hNLOS (t )
h(kv) (t )
kv = 0
(1)
A MPPSK symbol consists a special sine wave occupying K slot duration within the total N0 time slots, whereas the remaining (N0−K ) slots are used to modulate other sine waves, which owns tiny difference between that of the former K slot duration. That’s to say, MPPSK employs small angle phase transition interval at different positions during a symbol period. The bit streams are modulated by both the phase transition and position together according to the M-ary modulated symbols. Let Xk (k = 0,1,…,M −1) denotes the (k + 1)th point of signal constellation, the waveform samples f (k ,t ) which have very tiny difference are modulated by Xk . For Xk = 0 , the waveform samples can be expressed as [19]:
Considering a receiver with an optical band-pass filter of transmission Tf (ψ) and a concentrator with gain g (ψ) [7], the impulse response of LOS channel can be calculated as [6]:
f (0,t ) = Asin(2πfc t ), 0 ⩽ t < T
(6)
For Xk = 1,2,…,M−1, the corresponding waveform samples are
f (k ,t ) =
0 ⩽ t < (k−1) τ ⎧ Asin(2πfc t ), ⎪ B sin(2πfc t + θ), (k−1) τ ⩽ t < kτ ⎨ kτ ⩽ t < T ⎪ Asin(2πfc t ), ⎩
(7)
where T = (2πN0/ ωc ) = N0 Tc is the symbol duration, Tc = 1/ fc is the carrier cycle, θ is the modulating angle, τ = KTc is the slots length of the phase transition, A and B are the amplitudes of the modulated waveforms, respectively. Hence, the modulated MPPSK signal can be expressed by
Fig. 1. The geometry of light propagation in VLC system.
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P. Miao et al.
Fig. 2. The MPPSK waveforms (a) for time domain (b) for the PSD performance.
x (t ) =
∑
any discrete spectrum. Motivated by the previous analysis, the f (k ,t ) are modified by:
f (k ,t −nT ) (8)
n
The spectral performance of x (t ) are varied by changing the parameters such as N0 , τ and M . For a specific case such as fc = 100 MHz, N0 = 10 , K = 2 , θ = π and M = 4 , the MPPSK waveforms and the corresponding PSD are depicted in Fig. 2. As seen in the figure, there exists a large amount of line spectral components which may cause interference to other signals. To improve the spectral efficiency as well as the demodulation performance, these spurious components must be mitigated in VLC transmission. Let F (k ,ω) denotes the Fourier transform of f (k ,t ) . For Xk = 1,2,…,M−1, we have T 0
F (k ,ω) = ∫ f
ωc ⎡1 − 2exp ⎛ ⎢ ⎝ ⎣
T
f (k ,t )−
k=0
1 MT
M−1
∑
{F (k ,ωc ) e jωc t + F (k ,−ωc ) e−jωc t }
⎜
⎟
⎜
ω → ωc
⎟
F (0,ωc ) = lim F (0,ω) =
⎦
ω → ωc
(9)
j (2K −N0) π ,k = 1,2,…,M −1 ωc
(14)
Nπ ,k = 0 jωc
(15)
Then, the PSD of the improved MPPSK can be presented as
ωc [1−exp(−jωT )] ωc2−ω2
PŜ (ω) =
(10)
⎡ 1 F (k , mfc ) ⎤ fc |2 δ ⎛f − mfc ⎞ ⎢M ⎥ N0 ⎝ N0 ⎠ N0 ⎦ ⎣ ⎜
+∞
M−1
(
|
∑
−
⎟
∑ ∑
k=0
l=k+1
Pv (ω)
+
∑ k=0 M−2
−
f
· Nc
l=k+1
f
· Nc
0
where Fnew (k ,ω) is the Fourier transform of fnew (k ,t ) . As seen in (16), the first part of PŜ (ω) are the discrete components. However, as m ≠ ± N0 , we fortunately have the followings equations holding as
0
M−1
∑ ∑ k=0
M2
(16)
(M − 1) | F (M − 1,f ) − F (k ,f )|2 M2
)
mf f mf 1 ⎡ M Fnew (k , N c ) ⎤ Nc |2 δ f − N c 0 ⎦ 0 0 ⎣ m =−∞ k=0 M−2 (M − 1) | Fnew (M − 1,f ) − Fnew (k ,f )|2 fc + ·N M2 0 k=0 M−2 M−1 |Fnew (M − 1,f ) − Fnew (k ,f ) |·| Fnew (M − 1,f ) − Fnew (l,f )|
∑
∑
M−1
∑m =−∞ | ∑k =0 M−2
(13)
k=0
and ⎟
f (0,t ) e−jωt dt =
+∞
∑
F (k ,ωc ) = lim F (k ,ω) =
We assume that each transmitting symbol is modulated with equal probability as M−1. Therefore, the PSD of MPPSK can be presented as
PS (ω) =
M−1
where F (k ,ωc ) can be calculated by
−jω (k − 1) K ⎞ −jωK ⎞ −jωN0 ⎞ ⎤ + 2exp ⎛ − exp ⎛ ⎥ fc ⎠ ⎝ fc ⎠ ⎝ fc ⎠
ωc2 − ω2
∫0
1 M
q (t ) =
For Xk = 0 , F (0,ω) can be calculated by
F (0,ω) =
(12)
In addition, q (t ) is a waveform factor which can be designed as
(k ,t ) e−jωt dt ⎜
=
fnew (k ,t ) = f (k ,t )−q (t )
|F (M − 1,f ) − F (k ,f ) |·| F (M − 1,f ) − F (l,f )| M2
f
· Nc
0
(11)
mf mf F ⎛k , c ⎞ = Q ⎛ c ⎞ N 0 ⎝ ⎠ ⎝ N0 ⎠ ⎜
As seen in (11), the first part Pv (ω) is shown as discrete periodical Fourier components, which does not hold any useful information and may cause interference to other signals. As fc is a constant, the amplitude of Pv (ω) and the number of discrete components are determined by M and N0 . As N0 is a constant, the Pv (ω) is consisting of a series of pulses spaced at intervals of fc / N0 . Although the amplitude of the Pv (ω) is decreased as M is increased, the number of the discrete spectral components are also increased in quantity. If we could find some method to make the amplitude of Pv (ω) to be zeros, then the discrete spectral components will be suppressed consequently.As the discrete spectrum of MPPSK is induced by the special mapping between MPPSK symbols and the modulated waveform templates, we can modify the original f (k ,t ) so that the optimized PSD of the improved MPPSK doesn’t hold
⎟
⎜
⎟
(17)
and M−1
|
∑ k=0
⎡ 1 F ⎛k , mfc ⎞ ⎤ fc |2 = 0 ⎢ M new ⎝ N0 ⎠ ⎥ N0 ⎣ ⎦ ⎜
⎟
(18)
where Q (ω) is the Fourier transform of q (t ) . Then, the amplitude of
(
mf
δ f − Nc 0
) in (16) becomes zeros which mean that the discrete line
spectrum in PŜ (ω) are suppressed accordingly.The modified waveform samples is depicted in Fig. 3 based on the same modulation parameters as in Fig. 2. It should be noted that in this case the q (t ) can be calculated as 128
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P. Miao et al.
Fig. 3. The improved MPPSK waveform: (a) for time domain (b) for the PSD performance.
q (t ) =
1 4
3
∑
f (k ,t )−0.7sin(ωc t )
k=0
decision decoder is proposed at the receiver and the corresponding demodulation procedure is demonstrated in Fig. 4. In addition, the details are also depicted in the subfigure. Generally speaking, the SIF can amplify the modulation characteristics of MPPSK as much as possible. After absolute operation, the signal envelop is extracted by a lowpass filter (LPF) and then fed into the soft decision module for recovering the original symbols. The transfer function of SIF can be represented as:
(19)
As seen in Fig. 3, the amplitude of the new waveforms have changed nearby the angle phase transition and the envelope of MPPSK signal is not a constant any more. In addition, the PSD is also depicted here. The figure clearly demonstrates that the PSD is smooth and the discrete periodical line spectrum is suppressed in the improved MPPSK by means of (12).
⎛ H (Z ) = ⎜1 + ⎝
3.2. The proposed soft decision
I
∑ i=1
J
⎞ ⎞ ⎛ bi Z −i⎟/ 1− ∑ aj Z −j ⎜ ⎟ j=1 ⎠ ⎝ ⎠
(20)
where bi and aj are the coefficients associated with numerator and denominator, respectively, I and J are the number of zeros and poles. In this paper, three adjacent conjugate poles pj and one conjugate zeros z i are adopted in SIF designing. A quantum-based particle swarm optimization (QPSO) algorithm [21] is adopted for global searching the optimum parameters of bi and aj . After that, the optimum coefficients of SIF with oversampling factor of γ = 10 can be chosen as:
The fnew (k ,t ) have very tiny differences which increase the difficulty of symbols detections in the coherent demodulation procedure. Fortunately, the phase transition character can be distinguished with the help of the special impacting filter (SIF) and then converted to a series of amplitude impacting. However, the conventional threshold detector [18] recovers the original symbols by comparing the peak envelope of SIF outputting with fixed threshold level in a proper sequence, which will increase the probability of interference by false alarm error and wrong slot error, especially in multipath fading environment [2,9]. To improve the anti-interference ability, a soft
b = [1,−1.618092409933249,0.99990000250000044]
(21)
Fig. 4. Block diagram of the SIF based receiver for MPPSK scheme with soft decision decoding.
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P. Miao et al. 2
−2ωc ∏ (pj − z i)
6
yz (t ) =
∑
i=1 6
j = 1 (pj2 + ωc2)
·exp(pj (t −(k−1) τ )) ε [t −(k−1) τ ]
∏
(pj − pi )
j = 1,j ≠ i 2
6
+
2ωc ∏ (pj − z i)
∑
i=1
j = 1 (pj2 + ωc2)
exp(pj (t −kτ )) ε (t −kτ )
6
∏
(pj − pi )
(26)
j = 1,j ≠ i
where ε (·) is the step function. Therefore, as seen in (25) and (26), the SIF will produce a much higher amplitude impacting at the interval [(k−1) τ ,kτ ]. We assume that the total number of transmitting symbols is L . After the absolute processor and LPF, the signal envelope ∼ y ∈ NS × L of y (t ) is obtained, which can be expressed by
∼ y = [∼ y0,∼ y1,…,∼ yL − 1]
Fig. 5. Frequency response of the SIF.
a = [1,−4.5620074920961651,9.5862839416819483, −11.566980661101638,8.4523528839743243, −3.5467147693005732,0.6855154433139603]
v +ζ
i=1
y (t ) =
6
∏
+
z i2)
6
⎛ sin ωc t − ∑ φj + ⎜ j=1 ⎝ (ωc2 + pj2 )
2
∑ i=1
is
Δ
the
filter
gain,
⎛ φj = arccos ⎜ ⎝
T
(28)
(29)
Finally, we obtain the estimated symbol as
⎞ ϕi ⎟ ⎠
Xl ̂ = argmax(Cl ΛUl) k
j=1
where
+ζ
Kγ Kγ
Ul = {Sl ⩾ max (Sl)} (ωc2
v
In addition, the sampling offset ζ ∈ ⎡− 2 , 2 ⎤ is also adopted in (28). As ⎣ ⎦ smaller ζ is used, the acquisition of the effective envelopes can not fulfill the threshold requirement of signal demodulation. Similarly, the ζ should not be too large because excess samplings would induce more background noise, which will degrade the SNRs. Therefore, it is worth noting that appropriate ζ could improve the proportion of the effective data tones and the demodulation performance, which will be evaluated and discussed in Section 4. Then, Sl are sent to a comparator and we get a (M −1) × 1 logical vector as
2
∏
v +ζ
2 M−1 ⎡ 1 ⎤ Sl = [S1,l,S2,l,…,SM − 1,l]T = ⎢ ∑ yid,l , ∑ yid,l ,… , ∑ yid,l ⎥ id = v − ζ id = v − ζ id = v − ζ 1 2 M − 1 ⎣ ⎦
(22)
The corresponding frequency response is given in Fig. 5. As seen in the figure, there exists a large mutation of phase response in the steepest slope area associated with the magnitude response. Unlike other receiving filters, the fc can’t be placed in the center of SIF since the whole performance will be affected by the position of fc . In order to convert the phase transition of MPPSK into the amplitude impacting, the fc with the largest phase mutation point (as shown in Fig. 5) should be chosen in our system design. It should be note that the continuous time representations will be adopted in followings since such representations can easily provide analytical insights and give physical meaning to SIF processing. As Xk = 0 , the received signal after the SIF can be calculated as
Δ
(27)
yl = [y0,l ,y1,l ,…,yNS − 1,l ]T represents the received envelopes for the where ∼ th l (l = 0,1,…,L−1) symbols, NS = N0 γ denotes the total points of the corresponding sampling. For every received frame, the perfect synchronization is assumed. According to bit synchronization v = [v1,v2,…,vM − 1]T , the signal eny is sampled at every M −1 slot position and we could obtain the velope ∼ sampling matrix S = [S0,S1,…,SL − 1], where Sl ∈ (M − 1) × 1 can be presented as
pj ωc2 + pj2
⎞ ⎟ ⎠
(30)
(23)
where Λ = diag (1,2,…,M −1) , Cl is associated with the threshold level Γ at the sampling instant and can be calculated by
and
1, max (Sl) ⩾ Γ Cl = ⎧ ⎨ ⎩ 0, max (Sl) < Γ
z ϕi = arccos ⎛⎜ 2 i ⎟⎞. As Xk ≠ 0 , the output of SIF can be presented by ωc + zi2 ⎝ ⎠ y (t ) = ys (t ) + yz (t ) (24)
(31)
From the above analysis, it can be seen that the proposed demodulation scheme with a soft decision decoder recovers the modulated symbols with the help of the slot positions of phase transition, instead of the conventional threshold detecting.
where ys (t ) and yz (t ) are the steady state response and transient response, respectively. Therefore, ys (t ) and yz (t ) can be calculated as
4. Results and discussions 2
1
−2 ∏ (ωc2 + zi2) 2 i=1 6
ys (t ) =
1
6
2
sin(ωc t − ∑ φj +
∏ (ωc2 + pj2 ) 2
∑
j=1
In this section, Monte Carlo simulations are conducted to evaluate the system performance of the improved MPPSK with soft decision over VLC channel. In addition, the LED nonlinearity is not considered here due to the low PAPR advantage of MPPSK signals.
ϕi ){ε [t −(k−1) τ ]−ε [t −kτ ]}
i=1
j=1 2
1
Δ ∏ (ωc2 + zi2) 2 sin(ωc t −
+
i=1
6 j=1
6
2
∑ φj + ∑ ϕi) i=1
4.1. The simulation model
1
∏ (ωc2 + pj2 ) 2 j=1
For simplicity, an empty indoor room model with size of 5 × 5×3 m3 is considered and the coordinate set R = (lx,wy,hz) is adopted for numerical calculation, where −2.5 ⩽ l x ⩽ 2.5, −2.5 ⩽ wy ⩽ 2.5 and
(25) and 130
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position and amplitude impacting for different modulated signals are more obvious, and they are very easy to discriminate from each other without down-converting to a baseband.
Table 1 The simulation parameters of VLC channel. Channel Parameters
Values
Semi-angle ϕ0 (deg) Source optical power (mW) Reflection coefficients ρ Receiving panel d 0 LED number Lambert’s order m1 Active area AR (cm2) Field-of-view ψc (deg) Optical BPF Tf (ψ)
70 20 0.7 0.85 50 × 50 0.6461 1 60 1
Concentrator g (ψ) Refractive index Sampling frequency (GHz)
3 1.5 1
4.3. Performance of sampling offset In this study, several delivery tests employing the different sampling offset ζ are conducted to investigate the effect of ζ on the demodulation performance of the proposed soft decision scheme. Fig. 8a demonstrates the BER performance for the improved MPPSK at different sampling offset. The SNR is varied from 0 to 7 dB and the ζ is utilized from 0 to 5. As compared in the figure, besides the ζ = 0 and ζ = 1, most of the curves have an available demodulation performance which achieves an acceptable BER below 1 × 10−3 . It indicates that, as ζ = 0 and ζ = 1, the acquisition of the signal information can not sustain the SNR threshold requirement for the MPPSK demodulation. When ζ ⩾ 2 , the BER performance is improved due to the SNR gains by the sufficient valid data around the envelop peaks. However, as seen in Fig. 8b, the BER performance is degraded gradually when ζ increase beyond the optimum points, which indicates that the excess samplings offset would induce more background noise. Therefore, the optimum ζ can enhance the SNR and then improve the demodulation performance. In order to utilize the favorable envelope information, ζ = 3 is adopted in the following simulations.
−1.5 ⩽ hz ⩽ 1.5. In addition, the LED source is located at ceiling central with coordinate (0,0,1.5) . The parameters of the VLC channel model are designed based on Table 1. R 0 = (−0.625,−0.625,−0.65) Taking the coordinate and R1 = (2.083,2.083,−0.65) for an example. As only up to 5 times reflections are considered in VLC transmission, an approximation of the normalized channel impulse response (CIR) are calculated by (4) and depicted in Fig. 6. As shown in the figure, the first reflection dominates the total response for R 0 and the ratio of the reflected parts is very small. In addition, the channel delay spread is around 9 ns under the condition of 1 GHz sampling rate. Whereas for R1, the normalized CIR consists of LOS and NLOS component, the diffuse portion comes from the reflections of the walls and the NLOS components can’t be ignored when considering a high-speed transmission. Compared with the channel delay spread of the whole receiving panel, we can set the electrical MPPSK parameters as fc = 300 MHz, N0 = 10 , K = 1, θ = π , M = 8, A = 1 and B = 1, so as to obtain the appropriate symbol duration. Then, the corresponding waveform samples can be optimized by (12) and (13), respectively.
4.4. The BER performance Fig. 9 shows the BER performance of the modified MPPSK using both the proposed soft decision scheme and the conventional hard decision scheme at position R1. In addition, the BER of the original MPPSK are also depicted here. The conventional hard decision is easily disturbed by the multipath distortion, which will degrade the demodulation efficiency and restrict the communication areas. Conversely, results clearly demonstrate that the BER performance is significantly improved by the proposed soft decision since it owns excellent capability against false alarm error and wrong slot error. At BER = 1 × 10−4 , the required SNR are reduced at least by 2 dB for the modified MPPSK with the proposed demodulation scheme. In the case of low SNRs (e.g. SNR ⩽2 dB), the gap of the required SNR is very tiny because the channel noise are also contaminating the threshold level. While for the high SNRs (e.g. SNR ⩾3 dB), the SNR gap have gradually increased due to the decision error in (30) is minor and the advantage of the proposed scheme becomes more evident. In addition, the BER of the modified MPPSK performs approximately as the same as the original case, which indicates that the line spectral mitigation in (12) doesn’t affect the demodulation performance. Therefore, the proposed anti-noise modem can be used to improve the BER performance under multipath environment.
4.2. The SIF effect After the SIF and LPF processing, the received envelop of the improved MPPSK for position R1 is obtained and demonstrated in Fig. 7. Although there exists a certain amount of NLOS components at position R1, however, as seen in the figure, the SIF can still produce a much higher amplitude impacting, which has greatly improved the energy of the useful information. It is worthy noting that the characteristics of the
4.5. The complexity comparison The computational complexities of the proposed and the conventional schemes are discussed in this section. The elapsed time Telap , representing the total time consumed by signal demodulation, is adopted as a metric to measure the computational complexity. In this study, simulations with 200 MPPSK symbols are each performed with M = 4, 8 and 16, respectively. To provide a fair comparison, the other modulation parameters are fixed with same constants as fc = 300 MHz, N0 = 40 , K = 2 , θ = π , A = 1 and B = 1. For the proposed scheme, ζ = 0, 3 and 5 are adopted here. The Telap are measured and compared in Fig. 10. As seen in the figure, the Telap of these two schemes are increased dramatically with an increase of M . In addition, the proposed schemes require a little more time consumption than the hard decoding. However, the corresponding increments are not too much. The additional operations performed in the proposed scheme consist of (2M −1) adders and 2 multipliers, meaning that a lower extra computational
Fig. 6. The channel impulse response at position R0 and R1.
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Fig. 7. The received signal at position R1: (a) for SIF and (b) for LPF.
Fig. 8. The BER comparisons of the proposed soft decision scheme: (a) for different ζ (b) for SNR = 6 and 4 dB.
Fig. 10. The time consumption of signal demodulation in terms of hard decision and soft decision (200 symbols).
Fig. 9. The BER comparisons of MPPSK with hard decision and soft decision at position R1.
5. Conclusions complexity is consumed by soft decision. Moreover, the Telap of the proposed scheme changes very little as the number of ζ increases. In summary, the proposed scheme shows better BER performance and owns smaller complexity increments, which are beneficial to high-speed VLC communications.
In this paper, an improved modem using the modified MPPSK and soft decision detector has been proposed in VLC communications. The spurious components caused by original symbol mapping of MPPSK have been effectively suppressed and the probability of interference by false alarm error and wrong slot error is significantly reduced, which 132
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presents an effective solution for the improvement of anti-noise capability in VLC communications. Moreover, the proposed modem works well under multipath diffuse environment with moderate modulation parameters. It is easily applied in VLC system with low cost and offers better BER performance than the conventional hard decision, which validates the effectiveness of this scheme.
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Acknowledgments This work is supported in part by the National Natural Science Foundation of China (61601281) and by the Shandong Provincial Natural Science Foundation, China (ZR2017BF028). The authors would like to express gratitude to Prof. Wu, Dr. Chen and Dr. Song for constructive suggestions and assistance to this article. References [1] Hany Elgala, Mesleh Raed, Haas Harald. Indoor optical wireless communication: potential and state-of-the-art. IEEE Commun Mag 2011;49(9). [2] Ozgur Ergul, Dinc Ergin, Akan Ozgur B. Communicate to illuminate: state-of-the-art and research challenges for visible light communications. Phys Commun 2015;17:72–85. [3] Hua Qian, et al. On the benefit of DMT modulation in nonlinear VLC systems. Opt Express 2015;23(3):2618–32. [4] Barroso Alberto Rui Frutuoso, Johnson Julia. Optical wireless communications omnidirectional receivers for vehicular communications. AEU – Int J Electron Commun 2017;79:102–9. [5] Liane Grobe, et al. High-speed visible light communication systems. IEEE Commun Mag 2013;51(12):60–6. [6] Komine T, Nakagawa M. Fundamental analysis for visible-light communication system using LED lights. IEEE Trans Consum Electron 2004;50(1):100–7.
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