Performance of Dual Header-Pulse Interval Modulation (DH-PIM) for
Optical Wireless Communication Systems
Nawras M. Aldibbiat* a, Z. Ghassemlooy **a, R. McLaughlin*** b
a
Optical Communications Research Group, School of Engineering, Sheffield Hallam University,
Pond Street, Sheffield S1 1WB UK.
b
School of Computing and Management Sciences, Sheffield Hallam University, Pond Street,
Sheffield S1 1WB UK.
ABSTRACT
In this paper, we present a study of dual header-pulse interval modulation (DH-PIM) scheme for optical wireless
communications. System theory and code properties of DH-PIM are discussed and expressions for the power spectral
density, slot and packet error rates and optical power requirements are presented. The problem of baseline wander is
also studied. The performance of DH-PIM is compared with other modulation schemes such as on-off keying (OOK),
pulse position modulation (PPM), differential pulse position modulation (DPPM) and digital pulse interval modulation
(PIM). We show that, DH-PIM offers higher bit rate and has a built-in frame synchronisation capability. For a simple
threshold detector receiver, it offers improved error performance compared with OOK, but marginally inferior
performance compared with PPM. The optimum system performance in terms of optical power and bandwidth
requirements is achieved at bit resolution of 5.
Keywords: Modulation, Wireless, Infrared, pulse modulation, optical modulation, OOK, PPM, DPPM, PIM, DH-PIM.
1. INTRODUCTION
Infrared wireless indoor communication offers many advantages over radio based systems such as, a huge unregulated
bandwidth, high data rates, immunity to electromagnetic interference, relative security since it does not pass through
walls, and the ability to reuse the same wavelength [1-2]. Optical networks increasingly require high data rates for
today’s and tomorrow’s applications particularly video, audio and graphics which users may exchange and download
from the Internet. Digital modulation techniques such as PPM and PIM have been suggested for optical communications
[2-5]. PPM delivers the same information as OOK, but gives a better performance by taking advantage of the optical
bandwidth, and it delivers a very low average power. PIM on the other hand not only solves the problem of frame
synchronisation, associated with PPM, by locating a short duration pulse at the start of each frame, but it also improves
the transmission capacity and data rate compared to PPM [3,6]. Dual header-pulse interval modulation (DH-PIM) which
was first proposed in 1999, offers even higher bit rate and requires less transmission bandwidth compared with PPM and
PIM, and it also has a built-in frame synchronisation capability [7,8]. In this paper we study the properties of DH-PIM
by presenting expressions for the pulse train, power spectral density, and slot and packet error probability. Also, the
optical power requirements are presented and compared with those of other modulation schemes.
2. FUNDAMENTAL PRINCIPLES
2.1 System theory
At the transmitter, an input symbol of M bits OOK signal is mapped into a frame which starts with a header which
represents the weight of the decimal value of the input binary word followed by number of time slots ( dTs )
*
Nawras M. Aldibbiat: e-mail: n.aldibbiat@shu.ac.uk; URL: http://www.shu.ac.uk/ocr; Tel.: +44 (0) 114 225 3254.
Z. Ghassemlooy: e-mail: z.f.ghassemlooy@shu.ac.uk; Tel.: +44 (0) 114 225 3274.
***
R. McLaughlin: e-mail: r.mclaughlin@shu.ac.uk; Tel.: +44 (0) 114 225 3284.
**
representing the information carried by the input frame. A frame is initiated with one of two possible headers.
Depending on the pulse width, each header starts with a pulse and ends with a guard band (space) of empty time slots to
cater for zero-input signals and multipath dispersion. The pulse duration for header one (H1) and header two (H2) are
α
Ts and αTs , respectively. Where, Ts is the slot duration, d n ∈ 0,1,..., (2 M −1 − 1) and α > 0 is a positive
2
{
}
integer, as shown in Fig. 1.
v
Header one
A
Guard
space
τ =αTs /2
Information slots
d nTs
Tn + (α + 1)Ts
Tn
Tn +1
t
Tn +1
t
th
n frame
v
Header two
A
τ = αTs
Guard
space
Information slots
d nTs
Tn
Tn + (α + 1)Ts
th
n frame
Fig. 1: The nth frame of DH-PIM with H1 (up), and with H2 (down).
If the most significant bit (MSB) of the binary input word is equal to 0, then H1 is used with d representing the decimal
value of the input binary word. However, if MSB = 1 then H2 is used with d being equal to the decimal value of the 1’s
complement of the input binary word [8]. The header pulse plays a dual role of frame initiation and time reference for
the preceding and succeeding frames as in the standard PIM [7,8]. DH-PIM not only removes the redundant time slots
following the pulse as in PPM frame, but it also reduces the average frame duration to around half that of PIM and
quarter that of PPM, thus resulting in a much higher bit rate as shown section 2.2.
2.2 Code properties
The DH-PIM frame shown in Fig. 1 can be expressed as a rectangular pulse that starts at
τ = (1 + hn )
t = Tn , and has duration of
αTs
, where hn ∈ {0,1} indicating H1 or H2 respectively, and n is the instantaneous-frame number.
2
DH-PIM pulse train can be expressed mathematically as [9]:
∞ 
 2(t − Tn ) 1 
 2(t − Tn ) 3  
x(t ) = A∑ rect 
−  + hn rect 
− 
2
2 
n =0 
 α Ts
 α Ts
where, A is the pulse amplitude, and the rectangular pulse function is defined as [10]:
(1)
1 ; − 0.5 < u < 0.5
rect (u ) = 
0 ; otherwise
The start of the nth frame is defined as:
n −1


Tn = T0 + Ts n(α + 1) + ∑ d k 
k =0


where,
(2)
T0 is the start time of the first pulse at n = 0 and d k ∈ {0,1,..., (2 M −1 − 1)} represents the number of
information time slots in the
k th frame.
The minimum, maximum and average frame lengths of DH-PIM are given as
(
Lmax = α + 2
M −1
)T
s
and
[
L = ( 2α + 1 + 2
M −1
]
Lmin = (α + 1)
Ts ,
) / 2 Ts respectively. The transmission bit rate is given as:
Rb = M / Ts L
(3)
Fig. 2 shows the bit rate versus M for DH-PIM ( α = 1 & α = 2 ), PIM, PPM normalised to that of OOK assuming that
all schemes have the same slot duration
Ts . At α = 1 , DH-PIM presents a slightly better bit rate than at α = 2
especially at high values of M. In both cases, DH-PIM offers higher bit rate than its counterparts, especially for high
values of M, e.g. for M > 8 the improvement is around 4 times that of PPM, which is required for infrared wireless
transmission, as shown in Fig. 2.
4
DH-PIM (alpha = 1)
Normalised transmission bit rate
3.5
DH-PIM (alpha = 2)
3
2.5
PIM
2
1.5
PPM
1
0.5
2
3
4
Fig. 2: Transmission bit rate of DH-PIM ( α
5
6
M [Bit]
7
8
9
10
= 1 & α = 2 ), PIM and PPM normalised to that of OOK.
3. SPECTRAL PROPERTIES AND BASELINE-WANDER
Fluorescent lighting not only contributes to the generation of background shot noise, but it also induces a nearly periodic
and deterministic interference, because the fluorescent light flickers at a constant rate determined by the lamp drive
frequency. This interference can contain harmonics up to around 50 kHz for lamps driven by the mains frequency and
up to 1 MHz when driven by high frequency electronic ballasts [11,12]. This interference can be reduced by employing
a high-pass filter, but this results in baseline wander, or inter-symbol interference (ISI) which is more severe in
modulation schemes that contain high power at DC and low frequencies [4,12].
The spectral analysis for DH-PIM has been studied thoroughly in [9]. The power spectral density profile contains a delta
function, slot component and its harmonics when α is odd and a continuos sinc envelope. The continuos part of the PSD
for DH-PIM is given as [9]:
Pc (ω) =
 αωTs
2 A 2 sin 2 
 4
 
 αωTs  
 αωTs
5 − 4 sin 2 
 + 9 − 8 sin 2 
 
 4  
 4

2 M −1 − 1 

ω 2Ts 1 + α +
2 

   G 
 Re

   1 − G 
(4)
where, G is given by:
 1 − e − jωTs 2
G=
 1 − e − jωTs

M −1
e − jωTs ( α +1) 
⋅
2 M −1 
Fig. 3, shows a linear plot for the continuos part of the power spectral density for OOK, DPPM and DH-PIM (α=1 and
α = 2) for M = 4 assuming that a rectangular pulse shape is used and an equal average transmitted optical power in all
the systems. Unlike PPM [4], both DH-PIM and DPPM have a non-zero DC component, which is significantly small
compared to that of OOK. DH-PIM (α = 1) and DPPM contain less power at low frequencies compared with DH-PIM
(α = 2), but at the expense of increased bandwidth requirements. The bandwidth requirements for DPPM, DH-PIM (α =
1) and DH-PIM (α = 2) are 2.13, 2.75 and 1.63 times that of OOK, respectively as shown from the null positions of the
PSD curves in Fig. 3.
1
M=4
PSD (arbitrary linear units)
0.8
0.6
0.4
OOK-NRZ
DH-PIM (alpha=2)
DH-PIM (alpha=1)
0.2
DPPM
0
0
1
2
3
4
Normalised frequency (f / Rb)
5
6
Fig. 3: Continuos part of the power spectral density for DH-PIM (α=1 and α=2), DPPM and OOK.
4. ERROR PERFORMANCE AND OPTICAL POWER REQUIREMENTS
The block diagram of a typical DH-PIM system is shown in Fig. 4. The input signal is assumed to be composed of
binary independent, identically distributed (IID) bits of ‘1’s and ‘0’s. The DH-PIM signal plus noise is fed into a
matched filter, the output of which is sampled at the slot frequency f s = 1 / Ts , then followed by a decision circuit which
interprets every received slot into ‘1’ or ‘0’ according to the received optical power. The output of the decision circuit is
then fed into the DH-PIM demodulator in order to recover the original data signal.
Clock
recovery
t = Ts
M bits
data in
DH-PIM
Modulator
Optical
Channel
Matched
filter
Decision
circuit
DH-PIM
Demodulator
White
noise
M bits
data out
Fig. 4: Block diagram of a typical DH-PIM system.
In the following study we make the following assumptions: The channel is a distortion free channel, no bandwidth
limitations imposed by the transmitter and receiver, the dominant noise source is the background shot noise and no
interference due to artificial light. Assuming an average received optical power of
and an equal occurrence of H1 and H2, the peak photocurrent can be given by:
i peak =
4L
RP
3α
P , a photodetector responsivity of R,
(5)
The energy at the matched filter output is given by:
2
i peak
⋅ Ts ; "1" is sent
E=
0
; "0" is sent
Therefore, the energy of a pulse at the matched filter output is given by:
E=
16 R 2 P 2 ML
9α 2 Rb
(6)
Assuming that the threshold level is set at the mean of the expected ‘1’ and ‘0’, the slot error probability is given by:
 4 ML 2 R 2 P 2
Pe − slot = Q
 9α 2
No





(7)
where, N o = ηRb is the noise power spectrum and η/2 is the double-sided power spectral density of the white
Gaussian noise.
The concept of bit error rate has no meaning in anisochronous schemes such as DH-PIM and PIM, this is because the
frames have variable lengths, hence, any erroneous slot not only affects the bits associated with it but also shifts the bits
in the following frames. Alternatively, the concept of packet error rate ( Pe − pkt ) may be considered to analyse the DHPIM system and compare it with its counterparts.
Assuming that a packet of G bits (that is
GL
slots) is corrupted if one or more slots within the packet are in error, the
M
packet error rate can be given as [12]:
Pe − pkt = 1 − (1 − Pe − slot )
For very small values of
GL / M
(8)
Pe − slot , equation (8) may be approximated to:
Pe − pkt ≈
Therefore,
Pe − pkt ≈
GL
Pe − slot
M
GL  4 ML 2 R 2 P 2
Q
M  9α 2
No




(9)
The OOK electrical signal to noise ratio is given as:
SNROOK =
2R 2 P 2
No
(10)
Therefore, (9) can be rewritten as:
Pe − pkt ≈
GL  4 ML
Q
SNROOK
M  9α 2




(11)
Similarly, the packet error rate for OOK and PIM are given respectively as [13,4]:
(
Pe − pkt −OOK ≈ GQ SNROOK
Pe − pkt − PIM ≈
)
GLPIM  MLPIM
Q
SNROOK

M
4

(12)




(13)
where, the average PIM frame length is given by:
LPIM = (2 M + 3) / 2
Figs. 5 and 6, show the predicted slot error rate and packet error rate for DH-PIM ( α = 1 & α = 2 ), PIM, PPM and
OOK versus the SNROOK for M = 4 and a packet length of G = 1024 bits. DH-PIM and PIM offer improved error
performance compared with the benchmark scheme, i.e. OOK, but inferior to that of PPM. At slot error rate of 10-9 and
packet error rate of 10-6, PIM and DH-PIM ( α = 1 ) display an improvement of ~5 dB over DH-PIM ( α = 2 ).
L=16 slot (M=4 bits)
0
10
-2
10
OOK
PIM
Slot error rate
PPM
-4
10
-6
10
DH-PIM
(alpha=1)
DH-PIM
(alpha=2)
-8
10
-10
-8
-6
-4
-2
Fig. 5: Slot error rate for DH-PIM ( α
0
2
4
SNROOK [dB]
6
8
10
12
14
= 1 & α = 2 ), PIM, PPM and OOK versus the SNROOK.
L=16 slots (M=4bits)
0
10
-1
10
Packet error rate
OOK
PIM
PPM
-2
10
-3
10
DH-PIM (alpha=2)
-4
10
DH-PIM (alpha=1)
-5
10
-6
10
0
2
4
6
8
SNROOK [dB]
Fig. 6: Packet error rate for DH-PIM ( α
10
12
14
= 1 & α = 2 ), PIM, PPM and OOK versus the SNROOK.
From (10) and (11), the average optical power requirement for DH-PIM is given by:
Preq =
9α 2 N o
M

⋅Q −1 
Pe − pkt 
2
8ML R
 GL

(14)
Fig. 7 shows the average optical power requirements for OOK, PIM and DH-PIM ( α = 1 & α = 2 ) normalised to that
required by OOK-NRZ to send 1 KB packets at an average packet error rate of 10-6 versus the bandwidth requirements
normalised to that of OOK-NRZ. The numbers in Fig. 7 indicate L = 2 , the percentage values are the OOK duty
cycles and the bandwidth is defined as the span between the DC and the first zero crossing in the PSD curve in Fig. 3. In
Fig. 7, we may see that to minimise the optical power and bandwidth, the parameter combinations are: (L = 16, α = 1 )
and ( L = 64, α = 2 ) for DH-PIM and L = 16 for PIM.
M
4
DH-PIM (alpha=1)
DH-PIM (alpha=2)
PIM
OOK
Normalised optical-power requirement [dB]
L=2
2
4
0
2
2
100%
4 50%
4
8
-2
33.33%
16
25%
8
8
-4
32
16
16
64
32
-6
32
128
-8
64
256
64
-10
1
2
3
4
5
6
7
Normalised bandwidth requirements
8
Fig. 7: Optical power requirement versus normalised bandwidth requirement for DH-PIM ( α
9
= 1 & α = 2 ), PIM and OOK.
5. CONCLUSION
We have studied the fundamental properties of DH-PIM as a possible modulation scheme for optical wireless
communications where there is a need for higher transmission capacity and lower transmission bandwidth. The
theoretical error probability performance of DH-PIM has been given in terms of the slot and packet error rates, and
results have been compared with other schemes including OOK, PPM, DPPM and PIM. We have shown that, DH-PIM,
compared with other systems, offers a higher bit rate and requires less bandwidth. Frame synchronisation is built-in,
thus, yielding a simplified receiver structure for DH-PIM. However, results show that the error performance of DH-PIM
is inferior to that of PPM.
ACKNOWLEDGEMENT
Nawras M. Aldibbiat is financially assisted by the Aga Khan Foundation, Geneva.
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