Indoor MIMO Optical Wireless Communication Using Spatial Modulation

Indoor MIMO Optical Wireless Communication Using Spatial Modulation Raed Mesleh‡ , Rashid Mehmood‡ , Hany Elgala‡ and Harald Haas‡∗ ‡ Jacobs

University Bremen, Campus Ring 1, 28759 Bremen, Germany, Email: {r.mesleh, h.elgala & r.mehmood} @jacobs-university.de ∗ Institute for Digital Communications, Joint Research Institute for Signal and Image Processing, The University of Edinburgh, Edinburgh EH9 3JL, UK, Email: [email protected] Abstract—In this paper, a multiple-input multiple-output (MIMO) technique for indoor optical wireless (OW) communication is proposed. The scheme is called optical spatial modulation (OSM). The key concept is based on spatial modulation (SM) technique. At each time instant, only one transmitter is active and the others are inactive. Each transmitter index corresponds to a spatial constellation point and the transmitters are switched on and off based on the incoming data bits. Hence, a data rate of the base two logarithm of the number of transmit units is achieved. The active transmitter radiates a certain intensity level at a particular time instant. At the receiver side, the optimal SM detector is slightly modified and used to estimate the active transmitter index. The estimated index is used to retrieve the original information bits. In this paper, the upper-bound bit-error-ratio (BER) of OSM is analyzed for a MIMO system consisting of four transmit units (light emitting diodes (LEDs)) and four receive units (photo diodes (PDs)) in a room. The BER versus electrical signal to noise-ratio (SNR) for different transmitter and receiver separation distances and different transmitter half power semiangles (φ 1 ) are numerically 2 calculated. Index Terms—Optical wireless communication, MIMO, SM, intensity modulation, direct detection.

I. I NTRODUCTION OW technology has the potential to serve as a viable complementary solution to the overcrowded spectrum of radio frequency (RF) transmission. OW offers almost limitless bandwidth to cope with the future demand of indoor wireless access to realtime bandwidth-intensive applications such as Voice over IP (VoIP), streaming video and music, and network attached storage (NAS) [1, 2]. It can offer infrared (IR) and visible light indoor links using commercially available LEDs and PDs. This fast-developing technology offers several benefits, among of which are the following: license-free operation, no interference caused to RF based systems, and vice versa, which fosters acceptance in airplanes and hospitals, and no health concerns as long as eye and skin safety regulations are fulfilled. For OW links utilizing LEDs, the most viable modulation is intensity modulation (IM) in which the desired waveform is modulated onto the instantaneous power of the optical carrier. The most practical down-conversion technique is direct detection (DD) in which a photo detector produces a current proportional to the received instantaneous power. DD is much simpler to implement than coherent detection. It detects only

the intensity of the optical wave (all frequency and phase information of the optical carrier is lost). Short-range indoor optical applications use IM/DD as a practical transmission to achieve simple and low-cost optical modulation and demodulation [3, 4]. The performance of OW systems depends on the propagation and type of system used. The basic system types fall into diffuse or line of sight (LOS) systems. In LOS systems, high data rates in the order of Gbit/s can be achieved [5], but the system is vulnerable to blockage/shadowing because of its directionality. In a diffuse OW system, several paths from source to receiver exist, which makes the system robust to blockage/shadwoing. However, the path losses are high and multipaths create inter-symbol interference (ISI) which limits the achievable data rate [3, 6]. A promising solution to boost the data rate without any bandwidth or power expansion is by using MIMO techniques. An OW MIMO system with subcarrier multiplexing (SCM) is proposed in [7] where spatial multiplexing technique with zero forcing (ZF) detection is considered. The performance of the system depends on the achievable SINR (signal to interference plus noise ratio) values for different configurations, which degrades with the use of ZF [8]. It is shown that with transmitter semiangles (φ 21 ≥ 20◦ ), the separation between the transmit units and the receive units should be larger than 2.5m for reasonable performance. OW MIMO schemes with repetition coding have been studied in [9– 11] assuming OOK (on-off keying) and PPM (pulse-position modulation). It is shown that unlike RF systems, OW systems are able to obtain spatial diversity gains from repetition coding. Another OW MIMO system in [12] proposes a modified version of Alamouti code which allows, in an interesting way, the use of unipolar pulsed modulation techniques for IM/DD links. The idea is generalized later for any number of transmit units in [13] and shows that repetition coding are more efficient techniques than space-time-coding (STC) for OW links employing IM/DD. In this paper, an indoor OW MIMO system, called OSM, is presented. Unlike other MIMO techniques, only one transmitter is active at a particular time instant. The active transmitter radiates a certain intensity level and all other transmitters are off for that particular time instant. Therefore, inter-channel

interference (ICI) is completely avoided at the receiver side which simplifies the detection process. The incoming data bits control the active transmitter unit. Each transmitter index corresponds to a specific sequence of data bits. If, for instance, four transmit units exist, two bits are mapped to each transmitter index. This is the basic working mechanism of SM [14]. The overall spectral efficiency increases by the base two logarithm of the number of transmit units and the transmit units number must be a power of two. At the receiver, a hard decision optimum decoder is used to estimate the active transmit unit and retrieve the original information bits [15]. The performance of OSM is analyzed in this paper and the upper bound BER is derived. The BER performance versus electrical SNR for different transmitters-receivers separation distances and different values of φ 12 are numerically analyzed. In addition, an array of receivers are distributed throughout the room at certain hight from the ground and the achieved SNR at each receiver input for variable transmitters hight and φ 12 is computed through simulations. The remainder of this paper is organized as follows: Section II introduces the OSM. Performance analysis is presented in Section III. Numerical and simulation results are presented in Section IV. Finally, Section V concludes the paper. II. O PTICAL S PATIAL M ODULATION (OSM) SYSTEM MODEL

The system model of the proposed OSM idea is depicted in Fig. 1. A MIMO system consisting of four transmit units

resultant matrix is given by, 

0  0 s(t) =   I 0

0 0 0 I

 I 0  , 0  0

(1)

Each element in this matrix corresponds to the intensity level that is transmitted from the transmit units. The intensity carries no information and can be utilized to optimize SNR and power consumption. Each column from the matrix s(t) is transmitted from the existing transmit units over the optical MIMO channel H(t) at a specific time instant, i.e. each column represents a single time instant. For instance, at the first time instant, the elements of the first column are transmitted. Since, however, only one element is different from zero, only one transmitter emits a signal (intensity). This means, that only the third transmitter is active at this particular time instant while all other units are switched off. This guarantees no interference at the receiver side and simplifies the detection process. The transmitted data rate can be increased by increasing the number of transmit units. Also, the OSM idea can be combined with other modulation techniques, such as OOK, PPM, pulse amplitude modulation (PAM), etc. to increase the data rate. In such cases, depending on the incoming bits sequence, the time dependent characteristics of the optical pulse intensity is used to convey additional information. However, a complete analysis of such schemes, even though significant, falls beyond the scope of this paper and will be subject to future work.

The received signal can be written as, √ y(t) = ρrH(t)s(t) + n(t),

(2)

where ρ is the electrical SNR at each receive unit, r is the PD responsivity, H(t) is the Nr × Nt optical MIMO channel matrix, and n(t) is an Nr dimensional noise vector. The noise is the sum of the receiver thermal noise and the intense ambient shot light noise which can be modeled as independent and identically distributed additive white gaussian noise (AWGN) with double sided power spectral density σ 2 [3]. Fig. 1.

OSM communication system model

(Nt = 4) and four receive units (Nr = 4) is considered as an example. Different combination of transmit/receive units is possible, however, the number of transmit units must be a power of two. At each time instant, the transmitted bits are grouped based on the number of the transmit units. For illustration purposes, the incoming bit sequences to be transmitted at three time instants for the 4x4 MIMO system under investi£ ¤T gations are considered as follows, x (t) = 10 11 00 , where (·)T denotes the transpose. The bits in this vector are mapped to one of the transmitting units. The selected transmit unit (`) transmits the intensity s` = I at this particular time instant and all other units remain silent. In the considered example, assuming mapping of bits as depicted in Fig. 1, the

In this paper, LOS paths are assumed, hji (t) = Hji (t)δ(t), where Hji is defined as [3], ( A R (φ) Ts (ψ) g (ψ) cos ψ, 0 ≤ ψ ≤ ψc d2ji 0 Hji = (3) ψ > ψc 0, where A is the active area of the PD, dji is the distance between the ith transmitter and j th receiver, φ is the angle with respect to the transmitter, ψ is the angle with respect to the receiver (see Fig. 2 for more details), Ts (ψ) is the filter transmission, g (ψ) is the concentrator gain, ψc is the concentrator field of view (FOV) which is usually ψc ≤ π/2, R0 (φ) is the transmitter radiant intensity given by, R0 (φ) = [(m + 1) /2π] cosm φ,

(4)

and m is the mode number of radiation lope given by, m=

³

ln 2

ln cos φ 12

´.

(5)

The receiver applies a slightly modified version of the optimal SM detector [15] to retrieve the active transmit unit index as follows, `˜ = arg max py (y|I, H) ` n o √ T = arg max (y − ρrh` I) h` ,

(6)

`

where `˜ is the estimated transmitter unit index, h` is the channel vector containing the channel path gains from transmit unit ` to all receive units, and ³ ´ √ 2 py (y|I, H) = π −Nr exp − ky − ρrHIkF (7) is the probability density function (pdf) of y conditioned on the transmitted intensity I from transmit index ` and the channel H. The notation k · kF stands for the Frobenius norm of a vector or a matrix. The estimated transmit unit index `˜ is then used to retrieve the original information bits by inverse mapping process using the same mapping table as used in the transmitter.

A significant observation is that the BER depends on the SNR and the correlation among the channel vectors from one transmit unit to all receiving units. In other words, the performance depends on the rank of the channel matrix. Full rank MIMO channel matrix enhances the performance as compared to rank deficient matrices, as expected. In LOS conditions, high SNR values are achieved at the receiver side but the correlation between the channel paths is also high. The correlation can be reduced by creating a diffused conditions at the expense of SNR reduction. Therefore, for each application and in different environments, an optimization of the channel parameters, transmit power, and PD responsivity is required to optimize the performance. IV. N UMERICAL AND S IMULATION R ESULTS In the numerical analysis, an optical MIMO system is considered for an indoor application as depicted in Fig. 2. The room dimensions in meters are 4 × 4 × 8m3 . Four transmit units are located at the corners of the ceilings and four receive units forming a square array of 30cm side length are placed at a desk-top height 1m from the floor. The receiver is assumed to have complete knowledge of the channel and Ts (ψ) = g (ψ) = 1. The PD responsivity is assumed to be r = 0.75A/W.

III. P ERFORMANCE A NALYSIS

z=4:0.5:8m

The upper bound BER performance of the proposed OSM system is similar to the derivation of the upper bound BER of SM with slight changes [15]. The changes consider that the channel and the noise are real valued. In addition, for specific placements of transmitters and receivers, the channel matrix is deterministic and not random as in RF communication. The derivation is based on the union bounding technique [16] and the average BER is given as,   ´ [ ¢ ³ ¡ M s ˜, s` Pr ` → `˜  BER = E`  `

˜ `6˜=` `,

=

³ ´ ˜` Nt X Nt 2M `, X ˜ `=1 `=1+1

Nt

³ ´ Pr ` → `˜ ,

Rx1(1,2.5,1) Rx2(1.3,2.5,1) Rx3(1,2.8,1) Rx4(1.3,2.8,1)

(8)

˜ `) is the number of bits in error between transmit where M (`, ³ ´ unit index `˜ and ` and Pr ` → `˜ is the pairwise error probability (PEP) denoting that `˜ is estimated given that ` was transmitted. Using eqn. (6), the PEP of the OSM scheme can be written as follows, ³ ´ ¡ ¢ ˜ Pr ` → `|H = Pr d`˜ > d` |H = Q(ν), (9) ´ ³ ° °2 √ where, d` = − °y − ρrh` I°F , R∞ 1 exp(−t2 /2)dt, and ν is defined as Q(x) = 2π x

ν = ρkh` − h`˜k2F .

Tx1(0.06,0.06,z) Tx2(0.06,3.94,z) Tx3(3.94,3.94,z) Tx4(3.94,0.06,z)

(10)

Fig. 2. 4x4 optical MIMO model in a room. The transmitters are located at the corners of the ceilings of the room and the receivers are located on a table in the office with a hight of 1m. The room dimensions in meters are 4 × 4 × 8m3 .

In the first results, shown in Fig. 3, the transmitters and receivers are assumed to be in the positioned shown in Fig. 2. The half power semiangle (φ 12 ) is assumed to be 30◦ and the transmitters are originally at hight z = 4m and moving in steps of 0.5m to 8m. For each step, the SNR is varied from 0dB to 30dB and the upper-bound BER is calculated as in (8). At each time instant, two bits are transmitted and only one transmitter unit is active as discussed previously. The performance degrades with increasing z. This, however, is not due to the higher path loss at higher distances as the

0

10

75.4 −2

10

75.2

75.5 −4

10

75 SNR in dB

75 −6

10

BER

z=4m −8

10

z=4.5m

74.8 74.5 74.6 74

74.4

z=5m −10

10

z=5.5m z=6m

−12

10

z=6.5m

3

2

z=8m

73.8

1 0

Room width

4 74

2

1

z=7.5m

10

74.2

Rx4 Rx1 Rx2

3

z=7m −14

Rx3

73.5 4

0

Room length

−16

10

15

20

25

30

SNR (dB)

Fig. 3. OSM upper-bound BER performance versus SNR for transmitter heights from 4m to 8m in 0.5m steps. The half power angle (φ 1 ) is set to 2 30◦ .

SNR for all curves is the same; rather due to the correlation between the channel paths which is worse at higher values of z. At higher values of z, the relative geometry differences between the transmitters and receivers decreases which creates high correlation environment. At very high distance z, the correlation is very high and the transmitters can be considered as point source in the geometry. This behavior can be further explained by considering Figs. 4 and 5. In both figures, the SNR is simulated for the similar room shown in Fig. 2 and considering an array of receivers placed horizontally in the room at z = 1m. Each transmit unit consists of 60 × 60 array of LEDs [17]. The simulation considers a sphere model and calculate the SNR similar to [17, eqns.(4)–(13)]. The simulation parameters are also similar to [17, Table 1], except that the PD responsivity is r = 0.75A/W.

SNR in dB

81 82

80

80

79

78

78

76

77

74

76

72 4

Rx3 Rx4 Rx1 Rx2

3

3

2

2

1

1 0

Room width

75 4 74

0

Room length

Fig. 4. Simulated SNR values for a receiver array placed horizontally in the room at hight of 1m from the ground. The transmit units are located at z = 4m and the value of φ 1 is set to 30◦ . 2


The effect of the transmit unit height on the SNR values inside the room is evident from Figs. 4 and 5 and explains the behavior of the BER results in Fig. 3. For high values of z, the correlation between the channel paths increases and distinguishing the active transmit unit is more difficult, which degrades the OSM performance. However, for z = 4m (Fig. 4), and at the positions of the receivers in Fig. 2, the SNR variation is higher. Therefore, low correlation between the channel paths is expected which enhances the OSM performance. Another parameter that affects the correlation between the channel paths is φ 12 . The upper-bounded BER performance versus SNR for different φ 12 angles and with the transmitters located at z = 6m distance is depicted in Fig. 6. Again, the performance degrades with increasing φ 21 . This could be also attributed to the increase in channel paths correlation with increasing φ 12 . The SNR values inside the room for the receiver array for φ 12 =20◦ and 60◦ are depicted in Figs. 7 and 8, respectively. The performance of the MIMO system can be optimized by proper selection of z, φ 12 , and the azimuth and elevation of transmitters and receivers. The optimization should target maximum SNR with the possible lowest correlation between the channel paths. V. C ONCLUSIONS This paper proposes a MIMO technique for OW communication. The technique avoids interference at the receiver side by adopting the SM approach. At each time instant, only one transmitter is active and transmitting certain intensity level. The intensity level is a design parameter that can be set to optimize SNR and power consumption. The upper bound analyzes demonstrate that low BER can be achieved at moderate SNR values. By reducing both the distance z and the angle φ 12 , lower correlation between the channel paths is achieved which leads to better performance for certain SNR value. Reducing the correlation between the channel paths by considering a diffuse link and proper placements of transmitters and receivers will be considered in future works.

0

10

69.9 70

69.8

69.8

69.7

69.6

69.6

69.4

69.5

69.2

69.4

69 4

69.3

−5

10

φ1/2 = 15◦

SNR in dB

φ1/2 = 20◦ φ1/2 = 25◦

−10

10

BER

φ1/2 = 30◦ φ1/2 = 35◦ −15

φ1/2 = 40◦

10

φ1/2 = 45◦

3

φ1/2 = 50◦ −20

10

φ1/2 = 55

4 3

2

◦

2

1

φ1/2 = 60◦

1 0

Room width

0

69.2 69.1

Room length

−25

10

14

16

18

20 SNR (dB)

22

24

26

Fig. 8. Simulated SNR values for a receiver array placed horizontally in the room at hight of 1m from the ground. The transmit units are located at z = 6m and the value of φ 1 is set to 60◦ .

Fig. 6. OSM upper-bounded BER performance versus SNR for different φ 1 2 angles. φ 1 values are set from 15◦ to 60◦ in steps of 5◦ .

2

2

84

83

86

SNR in dB

84

82

82 81 80 80

78 76 4

79 3

4 3

2 1 0

Room width

78

2

1 0

Room length


ACKNOWLEDGEMENT We gratefully acknowledge support for this work from Airbus Germany. In addition, we acknowledge the support from the German Federal Ministry of Economics and Technology (BMWi) as part of the Lufo 2nd Call project SINTEG. R EFERENCES [1] M. Kavehrad and S. Jivkova, “Indoor Broadband Optical Wireless Communications: Optical Subsystems Designs and their Impact on Channel Characteristics,” IEEE Wireless Communications Magazine, vol. 10, no. 2, pp. 30–35, 2003. [2] C. Singh, J. John, Y. N. Singh, and K. K. Tripathi, “A Review of Indoor Optical Wireless Systems,” IETE Technical Review, vol. 19, pp. 3–17, Jan.–Apr. 2002. [3] J. M. Kahn and J. R. Barry, “Wireless Infrared Communications,” Proceedings of the IEEE, vol. 85, no. 2, pp. 265–298, Feb. 1997. [4] O. Bouchet, H. Sizun, C. Boisrobert, F. de Fornel, and P.-N. Favennec, Free-Space Optics: Propagation and Communication, P.-N. Favennec, Ed. ISTE Ltd, 2006.

[5] M. Akbulut, C. Chen, M. Hargis, A. Weiner, M. Melloch, and J. Woodall, “Digital Communications Above 1 Gb/s Using 890-nm Surface-Emitting Light-Emitting Diodes,” IEEE Photonics Technology Letters, vol. 13, no. 1, pp. 85–87, Jan. 2001. [6] S. Dimitrov, R. Mesleh, H. Haas, M. Cappitelliz, M. Olbertz, and E. Bassow, “Path Loss Simulation of an Infrared Optical Wireless System for Aircraft,” IEEE Journal on Selected Areas in Communications (JSAC), to be published. [7] D. Takase and T. Ohtsuki, “Optical Wireless MIMO Communications (OMIMO),” in Proc. IEEE Global Telecommunications Conference GLOBECOM ’04, vol. 2, Texas, USA, 29 Nov.–3 Dec. 2004, pp. 928– 932. [8] D. C. O’Brien, Q. Shabnam, Z. Sasha, and G. E. Faulkner, “Multiple Input Multiple Output Systems for Optical Wireless; Challenges and Possibilities,” in Proceedings of SPIE, San Diego, California, USA, Aug. 15–17 2006. [9] E. J. Lee and V. W. S. Chan, “Part 1: Optical Communication Over the Clear Turbulent Atmospheric Channel Using Diversity,” IEEE Journal on Selected Areas in Communications, vol. 22, no. 9, pp. 1896–1906, Nov. 2004. [10] S. G. Wilson, M. Brandt-Pearce, Q. Cao, and M. Baedke, “Optical Repetition MIMO Transmission with Multipulse PPM,” IEEE Journal on Selected Areas in Communications, vol. 23, no. 9, pp. 1901–1910, Sep. 2005. [11] S. M. Navidpour, M. Uysal, and M. Kavehrad, “BER Performance of Free-Space Optical Transmission with Spatial Diversity,” IEEE Transactions on Wireless Communications, vol. 6, no. 8, pp. 2813–2819, Aug. 2007. [12] M. K. Simon and V. A. Vilnrotter, “Alamouti-Type SpaceTime Coding for Free-Space Optical Communication With Direct Detection,” IEEE Transactions on Wireless Communications, vol. 4, no. 1, pp. 35–39, Jan. 2005. [13] M. Safari and M. Uysal, “Do We Really Need OSTBCs for Free-Space Optical Communication with Direct Detection?” IEEE Transactions on Wireless Communications, vol. 7, no. 11, pp. 4445–4448, Nov. 2008. [14] R. Mesleh, H. Haas, S. Sinanovi´c, C. W. Ahn, and S. Yun, “Spatial Modulation,” IEEE Transactions on Vehicular Technology, vol. 57, no. 4, pp. 2228 – 2241, Jul. 2008. [15] J. Jeganathan, A. Ghrayeb, and L. Szczecinski, “Spatial Modulation: Optimal Detection and Performance Analysis,” IEEE Communication Letters, vol. 12, no. 8, pp. 545–547, 2008. [16] J. G. Proakis, Digital Communications. McGraw–Hill, 1995. [17] L. Zeng, D. O’Brien, H. Le-Minh, K. Lee, D. Jung, and Y. Oh, “Improvement of Date Rate by using Equalization in an Indoor Visible Light Communication System,” in 4th IEEE International Conference on Circuits and Systems for Communications ICCSC 2008, Shanghai, China, 26–28 May 2008, pp. 678–682.