1. NOC 2011 IT - 1
Optical Spatial Modulation with
Transmitter-Receiver Alignments
(Invited Paper)
Raed Mesleh Hany Elgala, Marwan Hammouda, and Irina Stefan Harald Haas
University of Tabuk Jacobs University Bremen The University of Edinburgh
47315/4031 Tabuk, Saudi Arabia 28759 Bremen, Germany Edinburgh, EH9 3JL, UK
Email:raed.mesleh@ieee.org Email:h.elgala,m.hammouda,&i.stefan}@jacobs-university.de Email:h.haas@ed.ac.uk
Abstract—Optical spatial modulation (OSM) is a pulsed modu- (LOS) paths. Imaging receivers can not collect light over
lation technique for indoor optical wireless (OW) communication a field of view (FOV) as wide as a non-imaging angle-
systems, proposed recently in [1]. In this paper, the performance diversity receivers, since the elements of the latter can be
of OSM is significantly enhanced by proper geometrical align-
ment of transmit and receive units. In OSM, multiple transmit oriented in any direction. Also, the size of the imaging lens
units are considered where only a single transmit unit is activated and the detector array depend on the location and is not
at a particular time instance and all others are turned off. The suitable for all applications. Another OW MIMO system with
incoming bits are grouped in blocks with length equivalent to subcarrier multiplexing (SCM) is proposed in [7] where a
the base-two logarithm of the number of transmit units. A block spatial multiplexing technique with zero forcing (ZF) detection
of bits forms a spatial symbol, and the actual transmit units are
considered as spatial constellation points. A 4x4 multiple-input is considered. The performance of the system depends on the
multiple-output (MIMO) model inside a room is considered to achievable signal to interference plus noise ratio (SINR) values
evaluate the performance of the proposed OSM system. It is for different configurations. It is shown that with transmitter
shown that the proposed scheme is very efficient in terms of semiangles (φ 1 ≥ 20◦ ), the separation between transmit and
2
power and bandwidth as compared to on-off keying (OOK), pulse receive units should be larger than 1.5 m to achieve a bit-
position modulation (PPM), and pulse amplitude modulation
(PAM). error-ratio (BER) lower than 10−4 . An alternative OW MIMO
system is the OSM system proposed in [1] to increase the data
I. I NTRODUCTION rate by adopting the SM concept [8]. OSM enhances the data
The key design challenge for OW is to increase the data rate by a factor of log2 Nt , where Nt is the number of transmit
rate while maintaining high power efficiency. For instance, units considered. However, the error performance depends on
PPM is a power efficient modulation technique, at the expense the locations and the directions of the transmit and receive
of an increased bandwidth to achieve higher data rate. The units. It is shown that when the transmit units are directed
data rate can be enhanced by considering PAM at the expense toward the floor and the receive units are directed toward the
of a significant power penalty. A compromise between power ceiling in a medium-sized room, the performance of the OSM
and bandwidth efficiencies can be achieved by considering system deteriorates due to the high optical channel correlation
OOK [2, 3]. and a BER of 10−3 requires signal to noise ratio (SNR) above
MIMO techniques for radio frequency (RF) systems have 20 dB. The same BER can be achieved at 5 dB and 8 dB SNR
been studied intensively over the last decade. As a result, the for PPM and OOK, respectively [2].
IEEE 802.11n amendment is proposed to significantly improve The performance of OSM can be significantly enhanced
network throughput over previous wireless local area network by de-correlating the MIMO channel matrix. In this paper,
(WLANs) standards by using MIMO [4]. The expected maxi- the optical MIMO channel matrix is de-correlated by properly
mum raw physical net bit rate is boosted from 54 Mbps to 130 aligning the transmit and the receive units. The aligned setup
Mbps for two parallel streams and 600 Mbps for four parallel creates a full rank MIMO channel matrix which significantly
streams. enhances the power efficiency of OSM. A gain of about 14 dB
A spatial multiplexing indoor MIMO technique for visible in SNR is reported. The SNR distribution for a practical
light communication (VLC) technology using orthogonal fre- aligned scenario supports 10−3 BER on a large area inside
quency division multiplexing (OFDM) is considered in [5]. a moderate size room. In addition, OSM performance is com-
It is shown that the channel is highly correlated which pared to OOK, PPM, and PAM in terms of power efficiency
significantly degrades the bit error performance at different as well as bandwidth efficiency.
locations inside the room. The performance can be enhanced The remainder of this paper is organized as follows: The
remarkably by considering the imaging diversity receivers OSM system model is presented in Section II. Performance
technique to de-correlate the MIMO channel matrix [6]. This analysis along with comparison to OOK, PPM, and PAM are
is achieved at the expense of placing a lens at proper locations presented in Section III. Finally, Section IV concludes the
between the transmitters and the receivers for line-of-sight paper.
978-1-86135-373-3/11/$25.00 ©2011 IEEE 1

2. NOC 2011 IT - 1
path gain between LED and PD i for the k th path given
∞
¯ (k)
by hi =
(k)
hi (t) dt. The notation n(t) indicates an Nr
−∞
dimensional noise vector. The noise is the sum of the receiver
thermal noise and shot noise due to ambient light which
can be modeled as independent and identically distributed
additive white Gaussian noise (AWGN) with double sided
power spectral density σ 2 [2, eqn.(21)]. For the analysis in
this paper, H(t) is an Nr × Nt × (K + 1) normalized indoor
optical MIMO channel tensor, defined as
Fig. 1: OSM communication system model. The LED mapper ⎡ ⎤
maps input bits to LED indices. Each sequence of log2 (Nt ) h11 (t) h12 (t) · · · h1Nt (t)
⎢ h21 (t) h22 (t) · · · h2Nt (t) ⎥
input bits correspond to a certain LED index. ⎢ ⎥
H (t) = ⎢ . . .. . ⎥ (3)
⎣ .
. .
. . .
. ⎦
II. OSM S YSTEM M ODEL hNr 1 (t) hNr 2 (t) · · · hNr Nt (t)
The system model of the OSM approach is depicted in
The channel paths are obtained numerically via ray tracing
Fig. 1. A MIMO system consisting of Nt transmit units (in
technique as discussed in details in [9, eqn.(13)].
particular, light emitting diodes (LEDs)) and Nr receive units
(in particular, photo diodes (PDs)) is illustrated. The bits At the receiver, the PD converts the optical signal to
electrical signal and applies the optimal SM detector [10] to
to be transmitted at each time instance, q(t), are grouped
detect the active transmit unit as follows,
as the row vectors of the matrix x(t). For illustration pur-
poses, the bits to be transmitted in three time instances are ˜ = s ¯
arg max py y|¯, H
q (t) = 1 0 0 1 1 1 . Assuming Nt = 4, each √
log2 (Nt ) bits are transmitted at one time instance and grouped = arg min ρ h s 2 − 2 yT h s , (4)
T
as follows, x (t) = 10 01 11 , where (·)T T
{t=1} {t=2} {t=3} K K K
denotes the transpose. The bits in this matrix are mapped to where h = ¯ (k)
h1 ¯ (k)
h2 ··· ¯ (k)
hN r is an
one of the transmitting LEDs. The selected LED ( ) transmits k=0 k=0 k=0
Nr dimensional vector containing the sum of the channel
a non-return to zero (NRZ) pulse with an optical power path gains from transmit unit to each receive unit, H = ¯
(intensity) s = Pt at a particular time instance while all other h1 h2 · · · hNt is the channel matrix after the optical
LEDs are off. The intensity level carries no information and to electrical conversion at the receiver, ¯ is the transmitted
s
can be utilized to optimize power consumption and range. In column vector from the matrix s(t) at this time instance, and
the considered example, assuming the mapping table in Fig. 1,
√ ¯ 2
the resultant matrix is given by, s ¯
py y|¯, H = π −Nt exp − y − ρH¯ F s (5)
⎡ ⎤
0 0 0
is the probability density function (pdf) of y conditioned on
⎢ 0 s 0 ⎥ ¯
⎢ ⎥ the transmitted vector ¯ and the channel H. The notation · F
s
s(t) = ⎢ 0 0 s ⎥. (1)
⎣ ⎦ stands for the Frobenius norm of a vector or a matrix.
s 0 0 The estimated transmit unit index ˜ is then used to decode
{t=1} {t=2} {t=3}
the original information bits by inverse mapping process using
Each column of the matrix s(t) is transmitted at a single the same mapping table as used at the transmitter.
time instance where each element in the column vector corre-
sponds to the respective transmit unit. As can be seen, at any III. P ERFORMANCE A NALYSIS
give time only one transmit unit is active, all others transmit For Monte Carlo simulations, the considered 4x4 MIMO
zero power. The transmission is made over the optical MIMO system inside a room is depicted in Fig. 2(a). The height of
channel H(t). the transmit units from the ground is given by z in meters and
The received signal can be written as, the transmitters half power angle is given by φ 1 in degrees.
√ 2
The transmit units are placed on the ceilings with the exact
y(t) = ρH(t) ⊗ s(t) + n(t) (2)
locations shown in Fig. 2(b) and Fig. 2(c) for the unaligned
¯
r2 P 2
where ⊗ denotes time convolution, ρ = σ2r is the aver- and the aligned scenarios, respectively. The receive units are
age electrical SNR at each PD, r is the PD responsivity, placed on a desktop with height 1 m from the floor. The exact
Nr
¯ 1 (i) locations are shown in Fig. 2(b) and Fig. 2(c) for the unaligned
Pr = Nr Pr is the average received optical power at each
i=1 and the aligned scenarios, respectively.
K For the unaligned scenario, the transmit units are directed
PD with Pr
(i)
= ¯ (k)
hi Pt being the average received optical
k=0 toward the floor and the receive units are directed toward the
power at PD i when LED is active, K is the number of the ceiling. The receivers FOV is 90◦ . In Fig. 3, the average
¯ (k)
considered channel reflection paths, and hi is the channel BER is plotted versus the average electrical SNR at each
2

3. NOC 2011 IT - 1
0
10 0
10
−1 −1
10 10
−2 −2
10 10
BER
BER
−3 −3
10 10
−4 −4
10 10
φ1/2 = 35◦ simulation
z = 5m simulation
φ1/2 = 35◦ analytical z = 5m analytical
Fig. 2: (a) A 4x4 optical MIMO model inside a room. (b) Tx-
−5 −5
10 10
◦
φ1/2 = 40 analytical z = 6.5m analytical
φ1/2 = 60◦ analytical z = 8m analytical
Rx locations for the unaligned scenario. (c) Tx-Rx locations −6 −6
10 10
for the aligned scenario. Each Tx-Rx pair are directed toward 0 2 4 6
SNR (dB)
8 10 12 0 2 4 6
SNR (dB)
8 10 12
each other.
0
10 0
10
Fig. 4: Aligned OSM performance analysis.
−1
10 −1
10 1.00 at Rx1 1
Channel Impulse Response
0.55 at Rx2
1 0.53 at Rx3
Channel Impulse Response
0.55 at Rx4 0.8
−2
10 −2
10 0.8 LOS
First reflection
0.6
0.6
0.4
BER
BER
−3 −3
10 10
0.2
0.4
φ1/2 = 35◦ simulation z = 5m simulation
0
−4
10 φ1/2 = 35◦ analytical −4
10 z = 5m analytical 4
φ1/2 = 40◦ simulation z = 6.5m simulation 0.2
z = 6.5m analytical 2 Rx1 4
φ1/2 = 40◦ analytical
z = 8m simulation
−5 −5
10 10 2
φ1/2 = 60◦ simulation Y[m] 0
z = 8m analytical 0 0 X[m] 0 10 20 30 40
φ1/2 = 60◦ analytical Time (nsec)
−6 −6
10 10
0 5 10 15 20 25 30 0 5 10 15 20 25 30
SNR (dB) SNR (dB)
Fig. 5: Channel impulse response for the aligned scenario
between Tx2 and Rx1.
Fig. 3: Unaligned OSM performance analysis. In the left
subfigure, φ 1 values of 35◦ , 40◦ , and 60◦ are considered at
2 Compared to the results in Fig. 3, the aligned OSM sys-
z = 6 m. In the right subfigure, transmit units are considered tem performance enhances by at least 14 dB in SNR. This
at heights z =5, 6.5, and 8 m for φ 1 = 30◦ .
2 enhancement is not due to lower path loss for the aligned
scenario since the SNR is the same for all compared systems.
receiver. The results for at least 106 channel realizations are The improvement is rather due to de-correlating the MIMO
considered. Analytical and simulation results are presented for channel matrix by direct alignment of the transmit and receive
Nt = Nr = 4, z = 6 m for different values of φ 1 , and for
2
units. Further reduction in the FOV creates a diagonal channel
φ 1 = 30◦ for different values of z. The analytical results are
2
matrix and further enhances the performance.
upper bounds and calculated as discussed in [1, Section III, For the aligned scenario as in Fig. 2(c), the channel impulse
eqns. (5) and (6)]. The analytical BER equation is also shown response (LOS) when a single transmitter Tx2 is on and is
in Table I, where N (κ, ν) is the number of bit errors when aligned to the location of Rx1 is shown in the left-subplot of
choosing κ instead of ν as transmit unit index. Fig. 5 (φ 1 is 60◦ , FOV is 45◦ , z = 6 m). Rx1 is aligned to
2
The performance of the unaligned system is poor and for the location of Tx2 and the other receive units are directed
all considered φ 1 angles, see the left sub-plot in Fig. 3,
2
toward the ceiling. The de-correlation is clearly noticed from
SNR values above 20 dB are required to achieve 10−2 BER. the obtained amplitudes at the different locations of the four
According to the right sub-plot in Fig. 3, at 20 dB SNR, a transmit units. For the same aligned scenario, the channel
BER ≤ 10−3 can not be achieved regardless of the considered impulse response (LOS and first reflection path) between Tx2
height, z. and Rx1 is shown in the right-subplot of Fig. 5. It can be
The performance can be significantly enhanced by aligning found that the 3 dB bandwidth for this path is 30 MHz and
the transmit and receive units as depicted in Fig. 2(c) and that the channel delay spread is approximately 33 ns. At this
reducing the receivers FOV to 45◦ . Performance results for delay spread, 96% from the overall power is captured.
this scenario are shown in Fig. 4. It can be observed that The SNR distributions on a horizontal plan at 1 m from
neither changing the angles, nor changing the heights affect the floor for the unaligned and the aligned scenarios (a single
the simulated BER performance. However, slight differences transmit unit, Tx2, is turned on and an AWGN model intro-
are noticeable between analytical and simulation results which duced in [2, eqn.(21)] is considered) are shown in Fig. 6(a) and
can be attributed to numerical errors caused by the small Fig. 6(b), respectively. For the unaligned scenario, it can be
variation between the channel path gains with different heights seen that the maximum achieved SNR is 11 dB. The achieved
and angles. maximum SNR would not allow a useful BER as can be found
3

4. NOC 2011 IT - 1
TABLE I: OSM, OOK, PPM, and PAM performance
Scheme BER Data rate
√
OOK Q ρ B
L Llog2 L log2 L
L-PPM 2
Q 2
ρ L
B
2(L−1) log 2 L
L-PAM Llog2 L
Q (L−1)2
ρ Blog2 L
Nt Nt
1 ρ 2
OSM Nt
N (κ, ν)Q 4
hk − hν Blog2 Nt
κ=1 ν=1
ν=κ
(a) (b)
IV. C ONCLUSIONS
Fig. 6: SNR distribution. A single transmitter Tx2 is on (15 W OSM performance can significantly be enhanced by a proper
optical power), φ 1 is 60◦ , and the receiver is directed toward
2 alignment of transmit and receive units. The resultant scheme
the ceiling. (a) unaligned scenario. Tx2 directed toward the is shown to be very efficient in terms of power and band-
floor and FOV is 90◦ . (b) aligned scenario. Tx2 is aligned to width efficiency as compared to the existing OW modulation
the location of Rx1 and FOV is 45◦ . techniques. The simplicity of the scheme makes it a strong
candidate for practical implementations. The considered OSM
−1
10
4−PPM, 10 Mbps
OSM, 40 Mbps
system is shown to achieve a BER slightly better than OOK
OOK, 20 Mbps
−2
4−PAM, 40 Mbps and a data rate that is twice that of OOK. The power efficiency
10
of OSM is expected to be significantly enhanced by increasing
−3
the number of receive units and/or considering channel coding
BER
10
−4
10 techniques. In addition, the bandwidth efficiency of OSM
−5
can be boosted by increasing the number of transmit units.
10
These will be addressed in detail in future publications and in
−6
10
0 5 10
SNR (dB)
15 20 experimental demonstrations.
Fig. 7: Performance comparison between aligned OSM, OOK, R EFERENCES
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2
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4