Multiuser MISO Indoor Visible Light Communications Jie Lian, Mohammad Noshad and Maite Brandt-Pearce Charles L. Brown Department of Electrical and Computer Engineering University of Virginia, Charlottesville, VA 22904 Email: [email protected], [email protected], [email protected]

Abstract—Visible light communications is an energy efficient and cost effective solution for indoor wireless connectivity. In this paper we explore algorithms for supporting many users concurrently by optimizing the use of individual LEDs in each luminary. The directionality of LEDs is considered when assigning multiple LEDs to a user, forming a multiple input single output (MISO) system. Exploiting the spatial separation of detectors, MISO techniques using code division multiple access and minimum mean square error detection can offer high performance to simultaneous users while preserving the properties of the lighting system, such as spatially and temporally continuous dimmable illumination.

I. I NTRODUCTION In this age of fourth generation communications, higher speed data transmission is still demanded, especially indoors. Visible light communications (VLC) systems use white LEDs for communication, and can become the dominant indoor communication method because of their many advantages: LEDs can be simultaneously used for illumination and data transmission, they are efficient lighting sources, and they have long life expectancy; VLC systems have higher privacy than RF communication, and they are deemed safe for humans. Many researchers have proposed single-user indoor VLC designs, for instance [1]. The data-rate of such systems is fundamentally limited by the rise-time of the LEDs, which is not much faster than Wi-Fi systems. For VLC systems to compete with RF, other properties of VLC systems should be exploited. In this paper we explore using the spatial directionality of LEDs to increase the total data transmission for systems comprised of multiple users. Our approach can be considered a multiuser multiple input single output (MISO) system where multiple LEDs communicate with many users, each equipped with a single receiver. We also consider the lighting requirements within our design specifications, so that the dual-use system is jointly optimized. Multiuser VLC systems have received some attention in recent years. To provide data transmission for multiple users and to reduce the multiuser interference in VLC systems, some researchers proposed a precoding algorithm in [2]. They focus on maximizing the sum data rates, without concern for fairness of data-rate among users. Other researchers proposed a multiple input multiple output (MIMO) block diagonalization precoding algorithm for the multiuser scenario [3]. In our work, we aim to reduce the multiuser interference and maximize the quality of the transmission of all users to increase

throughput and fairness among users. We then compare the performance of our proposed algorithm with [3]. To reduce the multiuser interference, a power allocation joint optimization (PAJO) algorithm is proposed in this paper. Through the PAJO algorithm, the optimal power allocation for each user data and each LED is found, where the objective is to maximize the minimum signal to interference plus noise ratio (SINR) among all users. Code division multiple access (CDMA) is used to make the user signals separable. A minimum mean square error (MMSE) filter is used to reject residual multiple access interference at the receiver. We compare the bit error rate (BER) performance between the algorithm proposed in [3] and our PAJO algorithm. According to the simulation results, PAJO has a notably better BER performance than the block diagonalization precoding algorithm. We incorporate illumination requirements for the indoor space within the optimization formulation. The remainder of the paper is organized as follows. In Section II, the system model is described. In Section III we derive the PAJO algorithm with and without illumination constraints. In this section we also derive the design of the MMSE linear receiver for each user. Numerical results are discussed in Section IV. Finally, the paper is concluded in Section V. II. S YSTEM DESCRIPTION A. MISO Channel Model In this paper, we assume intensity-modulation and directdetection (IM/DD) because of the incoherence of the LED light. We consider two structures for the light fixtures: the 1LED lamp model with only one LED or an array of LEDs in the lamp all pointing in the same direction (towards the floor) and transmitting the same signal, as illustrated in Fig. 1, and a 25-LED lamp model, consisting of 25 LEDs with different inclination angles. The second structure is proposed to cover more illumination area and provide more power to the corner areas. The LEDs in this lamp are deployed in three layers with 1, 8 and 16 LEDs as shown in Fig. 2. Assuming an LED total power of P0 , the general formula for the line-of-sight (LOS) channel gain between the qth LED and the photodetector (PD) of the kth user can be written [1] − → → − A cosh− r→ qk , nk i hqk = P0 (m + 1) cosm h− r→ (1) qk , lq i 2 2πdqk

be defined as sk (t) =

L X

dk ck [l] · G(t − lTc ),

(4)

l=1

Fig. 1: 1-LED lamp

Fig. 2: 25-LED lamp structure, (a) side view, (b) bottom view

where dqk is the distance between the LED and the user, − r→ qk is the unit vector pointing from the LED towards the user, − − → is the kth receiver’s normal unit vector, and → n lq represents k the radiation unit direction vector for the qth LED. In (1), the notation hx, yi represents the angle between vectors x and y. Fig. 3 illustrates this notation. In addition, m is the Lambertian mode of the light source, which is related to the ln 2 LED’s semiangle Φ1/2 by m = ln(cos Φ1/2 ) .

where Tc is the chip duration time, ck is the CDMA code for user k, ck = (ck [1], ck [2] . . . ck [L])T . The length of the CDMA code is denoted as L. The pulseshape G(t) is considered rectangular in this work, i.e., ( 1 0 < t ≤ Tc G(t) = . (5) 0 otherwise The signal received by user k can be written as rk (t) =

hqk xq (t) + nk (t),

k = 1, . . . , K

(6)

q=1

where nk (t) is the white noise added to the received signal of user k. The noise is a combination of the thermal noise at the photodetector and shot noise due primarily to background light. After chip matched filtering and sampling the received signal, the discrete time signal received by user k can be written as rk [l] =

  rqk , lq

Q X

hqk xq [l] + nk [l],

k = 1, . . . , K

(7)

q=1

At the receiver we apply an MMSE filter, and the signal for user k at the symbol sampling instant becomes

Radiation Direction

  rqk , nk

Q X

yk = Fig. 3: Angle between the radiation direction and the path to user

L X l=1

rk [l]wk [l] +

L X

wk [l] nk [l] ,

(8)

l=1

where the MMSE filter for user k can be defined as wk = T (wk [1], wk [2], · · · wk [L]) .

B. Power Allocation Scheme We assume that the VLC network has Q LEDs with K users, and the VLC channel between LED q and user k is completely characterized by hqk in (1), i.e., there is no significant pulse broadening. Let sk (t) be the signal that is intended for user k at a given symbol time. The qth LED sends a linear combination of the users’ data as xq (t) =

K X

Pqk sk (t),

(2)

where Pqk ∈ [0, P0 ] is the power of the qth LED allocated to transmitting the data of user k. Assuming a total radiation power limit of P0 for each LED, which is the maximum optical power radiated from each LED, the constraint Pqk ≤ P0

yk =

Q L X K X X

hqk Pqj dj cj [l] wk [l] +

l=l j=1 q=1

L X

wk [l] nk [l] ,

l=1

(9) which can be written in matrix form as yk = dT Bk Cwk + nT k wk ,

(10) T

k=1

K X

Substituting (2), (4) and (7) into (8), we obtain

(3)

k=1

needs to be applied to the allocated powers. Since the power of light is nonnegative, we also require that Pqk ≥ 0, ∀q. The signal containing the intended data for user k, dk , can

where d is the data vector, d = (d1 , d2 , . . . , dK ) , and the T noise vector is nk = (nk [1], nk [2], · · · , nk [L]) . We assume the intended data for each user to be a binary data stream, i.e., dk ∈ {0, 1}. C represents the CDMA code matrix, which can be represented as   c1 [1] c1 [2] · · · c1 [L]  c2 [1] c2 [2] · · · c2 [L]    C= (11)  .. .. .. ..   . . . . cK [1] cK [2] · · · cK [L]
The matrix Bk = diag hTk · P , where hk =

(h1k , h2k , · · · , hQk )T . Thus,  P hkj P1j 0  j P  0 hkj P2j   j Bk =  .. ..   . .  0 0

···

0



···

0

    .   

.. .

..

. ···

P

hkj PKj

j

(12) III. J OINT O PTIMIZATION In this section we describe the PAJO algorithm to find the optimal power allocation that maximize the smallest SINR of the users. In the next two sections we consider the case that users need data transmission only and the case that users need both data transmission and illumination.

In this case, the MMSE receiver is independently designed for each user and the minimum SINR is maximized. To this end, we define the mean-squared error Jk for user k as 2

Jk = Ed,n {(yk − dk ) } 2

= Ed,n {(dBk Cwk + nk wk − dk ) },

(13)

where Ed,n represents expectation with respect to the data vector d and the noise nk . Solving for ∂Jk = 0, (14) ∂wk the MMSE liner receiver wk can be obtained as
−1 T wk = CT Bk Σd Bk C + σ 2 I C Bk qk ,

hqk Pqk dk ck [l] wk [l]

+

{z

Target

Q L X K X X

ck is defined as a matrix with a 1 in its where the matrix E (k, k)th element and zeros in all other places. Thus, the SINR for user k can be written as ck Σd E ck Bk T Cwk wk T CT Bk E SINRk = , ck Σd A ck Bk T Cwk + σ 2 wk T wk wk T CT Bk A (18) ck is defined as where A ck = I − E ck . A

max min SINRk P

min

+

L X

}

P

{z

Noise

β+1 β+1 SINR k k=1

for β large.

(21)

Using (21) we minimize the sum of the function instead of performing a minmax search, resulting in the same solution for a sufficiently large β. B. With Both Data Transmission and Illumination Requirements For applications that need both data transmission and illumination requirements, we can use our PAJO algorithm to find the optimal power allocation scheme and the MMSE receivers. Usually, users in the room need data transmission as well as illumination. Considering the total radiation power limit and the illumination requirements of the users, the constraints can be represented as Pqk ≤ Po

Pqk ≥ 0 Q K X X (r) h P η − P qk qj k ≤∆ q=1 j=1 (r)

wk [l] nk [l]

l=1

|

(20)

k=1

(16) Interference

k

K X

K X

hqk Pqj dj cj [l] wk [l] {z

(19)

We use the β-fair cost function [4] to simplify the optimization and reduce the computational burden, since the matrix P can be quite large if there are many LEDS and/or many users. For our problem the β-fair cost function can be written as

}

l=1 j=1 q=1 j6=k

|

(17)

Noise

l=1 q=1

|

Interference

+ nk wk . | {z }

(15)

where Σd is the covariance matrix for the data, Σd = E{dT d}, qk = E{d · dk }, I is the identity matrix of size L × L and σ 2 is the discrete-time equivalent noise variance. From (9), the signal after the receiver consists of three parts: the target (intended data) for user k, the multiple interference, and the noise. Thus, the signal after the receiver can be represented as Q L X X

Target

Now, we aim to maximize the minimum SINR for each user. Here, we define the cost function as

A. Without Illumination Constraints

yk =

  ck Bk T Cwk ck Bk T Cwk + d I − E yk = dE {z } | | {z }

}

The received signal yk here can also be rewritten using matrix notation as

k = 1, 2, . . . K,

(22)

where Pk is the required received power for illumination of user k, and ∆ is the illumination tolerance. This constraint is used to make sure that the illumination level at these users is not too dark or bright. η represents the CDMA code weight to CDMA code length ratio, which decides the illumination level per LED.

TABLE I: Parameters Used in Numerical Results

User locations Radiation power of each lamp OOC code index Length of CDMA code Code power efficiency η Semiangles of LEDs

5m×5m×3m (1.25, 1.25, 3) (1.25, 3.75, 3) (3.75, 1.25, 3) (3.25, 3.75, 3) (1.2, 2.0, 0) (2.0, 3.5, 0) (1.2, 1.2, 0) (1.5, 2.0, 0) 300 mW {1, 2, 4} {2, 3, 5} {3, 4, 6} {4, 5, 7} 7 42% 20o

−1

10

BER

Size of the room LED lamp placement

0

10

−2

10

−3

10

To illuminate the room uniformly in space, we also define virtual users that must have a fixed illumination, but no data transmission. These V virtual users are distributed uniformly in the room. For these virtual users that require just illumination, we use the constraint X V Q X (r) hq` Pqj η − P` ≤ ∆ ` = 1, 2, . . . V, (23) q=1 j=1

−4

10

30

JO−Two users JO−Three users JO−Four users BD−Two users BD−Three users BD−Four users 35

40 45 50 55 Total radiation power to noise power ratio (dB)

60

65

Fig. 4: BD algorithm vs PAJO for 4, 3 and 2 users with 1-LED lamp case, no illumination requirements 0

10

where hq` is the channel between the qth transmitter to the `th (r) virtual user, P` is the required received power illumination for user `.

1−LED with constraints 1−LED no constraints 25−LED with constraints 25−LED no constraints −1

10

IV. N UMERICAL R ESULTS

The illumination requirement for a standard office environment, determined by the Illuminating Engineering Society of North America [5], should be around 400 lx. Since a detector with 1 cm2 effective area collects 10−4 mW under 1 lx illumination, we set up the required received power by (r) (r) users as Pk = P` = 0.04 mW assuming the standard illumination level of 400 lx. We consider the illumination constraints to compare the BER performance of the 1-LED and 25-LED cases, where the total transmitted power of a 25LED lamp is assumed to be the same as that of a 1-LED lamp. We assume V = 16 virtual users needing just illumination,

−2

BER

The parameters used to obtain the numerical results are shown in Table I. The CDMA code used is an optical orthogonal code (OOC). The BER performance of the proposed PAJO technique compared with the block diagonalization algorithm precoding MISO system proposed in [3] is shown in Fig. 4 for the case of no illumination requirement. The results are plotted for VLC systems with 2, 3 and 4 users, using BD and JO algorithms, where “BD” represents the block diagonalization, and “JO” represents PAJO. According to the results in Fig. 4, the BER of PAJO proposed in this paper is better than the algorithm in [3]. Since the algorithm proposed in [3] adds a DC bias to the precoded transmitted signals, the distance between the constellation points of the transmitted signal is compressed by the total radiation power limit. But for PAJO, the transmitted power is allocated optimally; there is no need to add a DC bias. Therefore, the PAJO algorithm has a better BER performance.

10

−3

10

−4

10

30

35

40 45 50 55 Total radiation power to noise power ratio (dB)

60

Fig. 5: BER of 4 users for 1-LED lamp and 25-LED lamp cases with and without illumination requirements; the illumination is 400 lx with 10% tolerance

uniformly distributed in a rectangular grid around the room. The BER for the 1-LED lamp and 25-LED lamp cases with and without illumination constraints can be seen in Fig. 5 for the PAJO method. According to the results in Fig. 5, the BER with illumination requirements for the 1-LED and 25-LED lamp cases are always worse than no-illumination requirement cases, as expected. Furthermore, the 25-LED lamp outperform the 1-LED lamp since 25-LED lamps have more flexibility in controlling their illumination distribution compared to 1-LED lamps. The illumination tolerance ∆ affects the BER performance (r) in multiuser indoor VLC systems. The tolerance of P` and

−1

−2

BER

10

width of the room

No constraints 60% tolerance 30% tolerance 20% tolerance 15% tolerance 13% tolerance 12% tolerance 9% tolerance

45

45

40

40

35

35 width of the room

10

30 25 20

400lx

350lx

30 25

300lx

20

15

15

10

10

250lx

5

5

200lx 10

−3

10

20 length of the room (a)

30

40

10

20

30

40

length of the room (b)

Fig. 7: Illumination distribution comparison of (a) data transmission case and (b) no data transmission case. The red dots identify the real users, and the blue dots represent the virtual users, with 10% tolerance, and the 25-LED model.

−4

10

48

48.5

49 49.5 50 50.5 51 51.5 Total radiation power to noise power ratio (dB)

52

52.5

Fig. 6: BER comparison with different lighting tolerances, with 4 users and 16 virtual users for the 25-LED lamp case, 400 lx illumination requirements (r)

Pk is assumed to be in the range of 9% to 60%. From the simulation results, we observe that if the tolerance of illumination increases, the BER performance curve converges to the no-illumination-constraint case. Simulations are shown for 4 users with data and illumination requirements and 16 virtual users with only illumination requirement in Fig. 6. From these results, the BER with 60% tolerance is quite close to the BER without constraints. Note that this variation in the room lighting may be unpleasant for a human eye. The evaluation of this aspect of the design is beyond the scope of this paper. Fig. 7-(a) shows a contour plot of the illumination distribution for 4 users with both data transmission and illumination requirements, plus 16 virtual users with illumination requirements only. Fig. 7-(b) shows the illumination distribution without data transmission requirements. Comparing these two figures, the illumination distribution in (a) is still smooth and flat. That is to say, setting illumination constraints prevents the lighting system from creating too dark and too bright spots in the room, and the illumination requirements at all the user locations are satisfied. V. C ONCLUSION In this paper, we present an optimization algorithm we call PAJO to find the optimal transmitted power allocation for each LED to different users. The multiple access interference rejection is accomplished using an MMSE receiver for each

user in the VLC MISO system. For our proposed algorithm, our objective is to maximize the minimum SINR over all users. We compare the 25-LED and 1-LED lamp models, finding that the 25-LED lamp case has better BER performance than the 1-LED lamp case with the same transmitted power. We also compare our proposed algorithm with the block diagonalization algorithm in [3]. From the results in Fig. 4, our proposed PAJO algorithm has better BER performance than the block diagonalization algorithm in VLC systems. In addition, our algorithm takes the illumination requirements into account. From the simulation results in Fig. 7, our proposed algorithm satisfies the illumination requirements of real and virtual users, providing a constant illumination level close to the target lighting level established by the desired dimming. In future work we plan to design a distributed version of the optimization algorithm. In large indoor environments, the centralized approach presented here would be computationally too expensive. We will also consider the LED nonlinear response. R EFERENCES [1] T. Komine and M. Nakagawa, “Adaptive detector arrays for optical communication receivers,” IEEE Trans. Consum. Electron., vol. 50, no. 1, pp. 100–107, 2004. [2] Z. Yu, R. Baxley, and G. Zhou, “Multi-user miso broadcasting for indoor visible light communication,” IEEE International Conf. Acoustics, Speech and Signal Processing (ICASSP) 2013, pp. 4849–4853, 2013. [3] Y. Hong, J. Chen, Z. Wang, and C. Yu, “Performance of a precoding mimo system for decentralized multiuser indoor visible light communications,” IEEE Photon. J., vol. 5, no. 4, 2013. [4] X. Wang, D. Wang, and H. Zhuang, “Fair energy-efficient resource allocation in wireless sensor networks over fading tdma channels,” IEEE J. Sel. Areas Commun., vol. 28, no. 7, pp. 1063–1072, 2010. [5] M. Noshad and M. Brandt-Pearce, “Application of expurgated ppm to indoor visible light communications part i: Single-user systems,” J. Lightw. Technol., vol. 32, no. 5, pp. 875–882, 2014.