All-Optical Distributed MIMO for LiFi: Spatial Diversity Versus Spatial Multiplexing

LiFi or networked optical wireless communication is likely to play an important role in offloading mobile data traffic from radio into the optical spectrum. As the number of Internet of Things (IoT) devices is growing, the RF spectrum becomes a rare resource. Imaging IoT sensors like cameras, ultrasonic devices, and Lidars have real-time requirements, need a high-capacity uplink, and operate in environments that cause or are sensitive against electromagnetic interference. In this paper, for the first time, we present realtime communication over an all-optical fixed-wireless LiFi link based on the distributed multiple-input multiple-output concept. For distributing the wireless signals, plastic optical fibers are used as an analog front-haul. We study the operation of the distributed multiple-input multiple-output link in two modes, i.e., spatial diversity and spatial multiplexing. For the diversity mode, a new combiner is presented, which can support equal gain as well as selection combining. We demonstrate that selection combining is highly effective and enables a similar LiFi performance in up- and downlink, as it is desirable for industrial applications. For the spatial multiplexing mode, we observe that the channel rank and the achievable throughput depend strongly on the user location. As effective solutions, we study the benefits of angular diversity and multiple-input multiple-output mode switching together with multi-user multiplexing and conclude that a dynamic switching between spatial diversity and spatial multiplexing is a practical approach.

ronments, LiFi offers a practical solution, where additional 23 spectrum is needed. It is evident to complement mobile radio 24 with LiFi by offloading the wireless traffic from radio into 25 the optical spectrum [1], [2]. Moreover, light does not pene-26 trate through walls and it is robust against electromagnetic 27 The associate editor coordinating the review of this manuscript and approving it for publication was Liang Yang . interference and jamming [3]. LiFi is based on a network 28 of small cells, with only a few users per cell. This enables 29 frequent reuse of the optical spectrum, due to the confine-30 ment of optical wave propagation inside the light beam. 31 Distributed multiple-input multiple-output (D-MIMO) is a 32 modern wireless communication approach enabling seam-33 less mobility between distributed optical frontends that are 34 deployed as wireless infrastructure [4]. This approach can 35 support a higher network capacity, as well as lower latency. 36 Here mobility is supported by implementing MIMO algo-37 rithms at the lower physical and medium access layers in 38 the protocol stack, whereas conventional mobile networks 39 However, since only one transmitter is active at a particular 96 instant, spectral efficiency is limited. 97 Another method for increasing the capacity and spectral 98 efficiency is the SMUX technique, where independent data 99 streams are transmitted in parallel. The SMUX benefits from 100 inter-channel-interference (ICI). In [19], the authors proposed 101 a generalized SMUX technique by activating variable num-102 bers of LEDs to transmit multiple data streams. The authors 103 in [20] proposed a signal space diversity scheme incorporated 104 with SM for a 2 × 1 OWC MISO system. The results showed 105 that an adaptive MIMO is required for an OWC system. 106 In addition, performance evaluation has been presented using 107 a multi-directional receiver with different MIMO techniques 108 in [21]. Both studies rely on bit-error-rate (BER) and signal-109 to-noise ratio (SNR) as figures of merit. The authors in [20] 110 show that the RC is superior to SM, while SMUX was not 111 considered. The authors of [21] look at a large scale scenario, 112 which is interference-limited, in the SMUX mode at least. 113 The evaluation framework of [21] uses the required SNR 114 to reach a given BER, while we are using the achievable 115 throughput, which is considered more practical. The angular 116 diversity (AD) is shown to require less SNR in [21], and 117 reaches higher throughput in our work, compared to not using 118 it. Qualitatively, these results are consistent. Note that [20] 119 and [21] are based on simulation, while our work is based on 120 measurement in real-time. So far, the impacts of using SDIV 121 and SMUX have not been thoroughly investigated yet. 122 This paper investigates the application of distributed 123 MIMO for LiFi in the proposed system architecture, which 124 is composed of a wired fronthaul followed by distributed 125 wireless links, as shown in Fig. 1. Our first objective is to 126 develop a mathematical model of the distributed MIMO link 127 by using concatenated wired and wireless links, where either 128 SDIV or SMUX can be used. Next, we evaluate each method 129 to enable robust high-speed communication over the LiFi 130 link. Our second objective is to assess the proposed setup 131 through simulations and experiments to obtain quantitative 132 results. In the performance analysis, SNR versus frequency 133 and the achievable throughput are used as figures of merit. 134 VOLUME 10, 2022  The methodology of this article is illustrated in Fig. 2.

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The remainder of this paper is organized as follows.

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Distributing wireless APs is a well-known approach in cellu-157 lar radio networks to extend coverage and increase capacity.

158
The idea behind is frequency reuse, i.e. distant APs can reuse 159 the same spectrum [24]. However, the capacity is limited 160 by interference, when the nearer AP reuses the spectrum.

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In MIMO systems, the capacity is high if the channel vectors  In [25] it was demonstrated that, by using D-MIMO, the 175 performance is improved and a higher data rate is achievable 176 because the channel matrix is well-conditioned. In [5] implemented as a central unit (CU) and multiple APs, also 180 denoted as optical frontends (OFEs). In order to distribute 181 the OFEs, a fixed fronthaul link is required, forwarding the 182 signal from the CU to each OFE. Waveform transmission 183 over the fronthaul can be regarded as relaying, for which 184 Decode-and-forward (DF) as well as amplify-and-forward 185 (AF) are commonly used [25]. In the DF link, the received 186 signal is decoded first, then re-encoded and forwarded to 187 the user [28]. Even though DF is favored by the industry, 188 it is more complex and increases latency. In the AF link, 189 the received signal is amplified and forwarded by the relay. 190 The received signal contains additional noise, which after 191 amplification, can degrade the overall performance. This is 192 particularly important in the uplink, where the received wire-193 less signal can be very weak. To optimize the performance, 194 an automatic gain control (AGC) based on the received signal 195 strength indicator (RSSI) is required. In [29], a practical 196 method for D-MIMO using AF over plastic optical fiber 197 (POF) was presented, where the AGC is co-located with the 198 CU and the attenuation over the POF link is compensated by 199 electrical amplifiers. In the following, the functionality of each part is elabo-207 rated.

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The CU is providing a fundamental channel estimation and 210 feedback protocol with each MU to select the strongest 211 OFE signals, which can be used for joint transmission and 212 reception. Using the so-called Cloud Radio Access Network 213 (C-RAN) with centralized signal processing is a common 214 concept in cellular radio systems [30]. It is currently pro-215 posed in the IEEE P802.15.13 standard of LiFi for industrial 216 scenarios.

217
In this paper, we assume that the selection of the best 218 serving, i.e., nearby OFEs in the CU is already completed 219 and the signals from distant OFEs can be ignored. This 220 assumption is justified by the LOS-based light propagation, 221 which implies that the electrical signal reduces by a path-loss 222 exponent of four, even in indoor environments. 1 Coax cables are expensive and, besides satellite television 234 and Internet delivery, hardly used in indoor environments.

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Twisted-pair cables enable reliable transmission, which is 236 well known for phone lines and Ethernet cables, and have 237 been tested for LiFi [29]. However, proper shielding is needed 238 to avoid unwanted emissions and to make the link robust 239 against electromagnetic interference.

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An advantage of electrical media is that powering can be 241 supplied along with the fronthaul. Note that optical frontends 242 for LiFi will be co-located with the illumination infrastruc-   In this paper, we study MUs with one and two OFEs. When

285
In this section, we present the mathematical model of our dis-286 tributed MIMO link, which is a concatenation of the analog 287 fronthaul over POF and the wireless link [23]. We explain 288 the various MIMO modes of SDIV and SMUX, and how 289 to compute data rates. The model is used for quantitative 290 comparison, and the analysis of experimental results.

292
In this section, the mathematical model for the distributed 293 MIMO link, including the channel matrix H(f), is presented. 294 This model describes the concatenation of POF and wireless 295 links in the frequency domain. The model is parallelized and 296 includes the crosstalk between the parallel wireless signals 297 over the air. In the model, DC-OFDM is used as a modulation 298 scheme. We assume that the CU is connected to N T OFEs all 299 working at the same optical wavelength. The received signal 300 vector at each MU for the f -th OFDM sub-carrier is described 301 by 302 where Z(f ) ∈ R N MU N R ×N T is the wireless MIMO channel 315 matrix and G(f ) ∈ R (N PD =N T )×N T describes the parallel POF 316 fronthaul links. Note that this model can potentially also 317 describe cross-talk in the POF link [23], which is not con-318 sidered in this paper. The coefficients of Z(f ) are computed 319 as where H LED j (f ) represents the frequency response of the 322 LED plus driver, g TX (φ j ) stands for the radiation pattern, d j,l 323 is the distance between j-th D-OFE and the l-th MU, φ j , φ l 324 are the angles of the link between transmitter and receiver, 325 respectively, g(d j,l ) denotes the path loss in the wireless link, 326 g RX(φ l ) and H PD l (f ) are is the photodiode sensitivity and the 327 frequency response of the photoreciver, respectively [11], 328 [33]. The POF is a color-dependent medium. However, in this 329 paper, we assume that all fronthaul signals are transmitted 330 via separate POF links at the same wavelength and there 331 is no crosstalk between them when distributing the signal 332   For the downlink, we consider two users k = 1, 2. The 357 received signal for user k is expressed as The CU signal is repeated over all distributed OFEs, yielding: where the elements of w amount all to 1 to indicate the spatial 362 repetition code used and d (k) is the data signal for the k (th) 363 MU.
In the uplink, the signal of each MU is received by all OFEs, 366 which is described for one of the users as where y l and n l are the received signal and the noise at the 369 distributed-OFE l = 1, . . . N T and x is the transmitted signal 370 of the one MU. In order to retrieve the transmitted data x, 371 we apply a weighted average of all received signals as:  (9), where each w i is given in (10).
The EGC technique weights all received signals equally for 394 diversity reception, i.e. w i = 1. Fig. 4    The weight matrix can be computed as Therefore, the retrieved signal after zero-forcing is obtained 435 as: where N 0 refers to the noise power and I is the identity 451 matrix. This method can overcome some implications of the 452 noise enhancement of ZF for ill-conditioned channel matrices 453 through regularization of the inverse matrix which is achieved 454 through the additional term N 0 I in equation 16 [36].

456
The singular value decomposition (SVD) is an effective math-457 ematical tool for evaluating the MIMO capacity [37], [38]. 458 In this section, we use the SVD and assume that the channel 459 state information is available at the D-OFEs and MUs.
where U and V are unitary matrices and D is a matrix, which 466 contains the singular values on the main diagonal and zeros 467 elsewhere. 468 (20) 471 VOLUME 10, 2022 Based on [39] and [40],  well as imperfect constellation shaping [42].

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When serving one user per time slot, the SNR for that user 487 can be estimated as follows

489
where n is the additive white Gaussian noise amplitude. has been developed and confirmed by measurements in [43].

507
To assess the properties of the communication link, 508 we have derived formulas for the SNR-versus-frequency, 509 including various combining techniques, the SVD and com-510 puted the achievable throughput. A 4 × 2 MIMO cell is 511 evaluated in SDIV mode, and a 2 × 4 MIMO LIFi cell 512 in SMUX mode, for selected user locations which were the 513 same like in our measurements. The simulation framework is 514 shown in Fig. 3.

516
In the experimental setups for both SDIV and SMUX, POF 517 was used to transmit the signals between CU and D-OFE 518 as shown in Figs. 5 and 6. In both setups, the front-haul 519 and the wireless units were similar as follows: The Avago 520 transceiver AFBR-59F3Z was used for the bidirectional fron-521 thaul transport over POF. At the transmission side, a 650 nm 522 LED was used together with an integrated driver to con-523 vert the electrical signal into an optical signal. An inte-524 grated fiber-optical receiver with a PIN photo-diode and a 525 trans-impedance amplifier (TIA) was used at the receiver. 526 In the wireless link, the OFEs were equipped with off-the-527 shelf high-power LEDs operating at 860nm (OSRAM-SFH 528 4715 AS) and large-area silicon PDs (Hamamatsu S6968) as 529 described in [44]. In the experiments, we employed the same 530 OFEs both in the wireless infrastructure and at the mobile 531 units.

532
The SDIV and SMUX modes were realized by using the 533 real-time digital signal processing in a chipset supporting 534 data transmission over several home networking media, i.e. 535 coaxial cable, phone-line, power line, and POF, according to 536 the ITU-T G.9960 home networking standard. The SDIV setup, as shown in Fig. 5, represents a 4×2 MIMO 539 link. At the CU, we have used the Wave-2 DCP962P modem 540 from Maxlinear in the coaxial cable mode. This modem is 541 based on two chips, the 88LX5153 yields the digital baseband 542 signals and the 88LX2730 provides the analog frontends out-543 put. We operated the CU as follows: In the downlink, the ana-544 log output CU signal of the digital baseband chip is replicated 545 N T times (number of OFEs) through Fanout buffers and sent 546 FIGURE 5. SDIV measurement setup. In the downlink, the CU distributes the signal equally and sends it via POF to D-OFEs. On the user side, there are two users with varying location. In the uplink, the CU combines the signals using either EGC or SC.  the POF link. In the combiner, we can use either EGC or SC 551 of all received signals. Both methods are implemented in the 552 analog domain and hence, act identically on all sub-carriers 553 of the DC-OFDM signal. Although this is theoretically sub-554 optimal, it works well in practice because optical propagation 555 has a flat frequency response due to the LOS link and all OFEs 556 have nearly identical responses. In SDIV mode, each MU has 557 one OFE. All MUs are equipped with the same OFE also used 558 in the D-OFE. 559

560
The experimental setup for the SMUX link is shown in Fig. 6. 561 The LiFi cell is defined as a 2×4 MIMO link, and the simula-562 tion emulates the same scenario as in the experiment. The CU 563 was connected to two D-OFEs via POF. Each mobile device 564 was equipped with two OFEs, which were either pointed into 565 the same or different directions, indicated by the angle α. 566 The CU was Maxlinear DCP962, operating in the phone-567 line mode, as defined in ITU-T recommendation G.9963 568 standard. The CU operated as a MIMO link with two channels 569 connected via POF to each D-OFE. At the MU side, the 570 OFEs were directly connected to the two channels of the same 571 modem. This setup was also considered for evaluating the 572 multi-user MIMO (MU-MIMO) performance. We observed 573    Fig. 7 (a,b). As mentioned before, 599 the diversity combining was performed only in the uplink, 600 while equal splitting was used in the downlink. Note that 601 the SNR for both users were identical in the simulation, due 602 to the symmetry in the scenarios and channel, accordingly. 603 We observe that the SNR of SC always outperforms EGC in 604 all scenarios. For instance, for user 1 in scenario I ( Fig. 7(a), 605 D 3 = 5cm, red line), where users were located close to 606 each other, at 100 MHz the SNR of the EGC method is 607 about 19 dB, while with SC it reaches approximately 27 dB. 608 In scenario II (D 3 = 90cm, green line), user 1, by using 609 EGC SNR at 100 MHz is about 18 dB, however, SC method 610 leads to 27 dB, which is 50% enhancement of SNR. By using 611 EGC, the received signals are summed with equal scaling, 612 which leads to lower SNR for each user in comparison to SC 613 method, where the received signals above a defined threshold 614 are selected and summed. SC avoids adding the noise from 615 the weak channel, which leads to a higher overall SNR. The 616 same inspection for scenario III (D 3 = 270cm blue-line) 617 was observed by using SC method. The simulation results 618 were principally confirmed by our experiments in the same 619 scenarios, as shown in Fig. 8 (a,b). In the measurement, the 620 SNR frequency spectrum was obtained with the monitoring 621 software provided by the digital signal processor manufac-622 turer [45]. SC improves only uplink SNR for both users, 623 especially in scenarios II and III, e.g., for user 1 leads to 624 40% and 36.3% improvement, as shown by the green and blue 625 dashed lines in Fig. 8 (a), respectively. SC is also effective in 626 scenario I (dashed red lines of Fig. 7 (a,b)), but for instance, 627 the SNR is only improved by about 3-5 dB, compared to full 628 red line in Fig. 7 (b).

629
There are differences in the SNR values between the simu-630 lations and measurements. These differences are attributed to 631 the empirical gap factor introduced in (21). It mainly takes the 632 reduced modulation amplitude in real frontends into account 633 to avoid clipping and non-linear distortion. In addition, there 634 is always a penalty in real implementations, due to non-ideal 635 coding and transmit signal shaping, which reduce the per-636 formance. Moreover, potential NLOS contributions were not 637 included in our simulation analysis. Altogether, we observe 638 that SC outperforms EGC significantly in terms of SNR.

FIGURE 10.
Simulation results for singular values in the SMUX cell layout described in Section V-C for D 3 =5cm for two users without and with angular diversity for downlink (a) and uplink (b).

640
The estimated and measured throughput for SDIV are shown 641 in Fig. 9 (a,b). First of all, note that there is a differ-642 ence between uplink and downlink performance, particu-643 larly when using EGC. This is due to the accumulation of 644 noise when summing up four received signals. In addition, 645 there are scenario-dependent differences, due to the differ-646 ent geometrical path gains depending on the user positions.

647
In Fig. 9(a) the throughput is obtained by simulation from 648 the SNR using (21). In the downlink, there are no differences 649 between EGC and SC for each user, sequentially, as the signal 650 simply replicated and sent to each D-OFE. 651 We observe that the simulated uplink throughput for each 652 user is always higher when using SC compared to EGC. This 653 is also confirmed by the measured throughput of each user 654 obtained from the chipset software, as shown in Fig. 9 (b).  data streams that can be used in parallel for SMUX [46].   Scenario II is similar to scenario III for both with and 691 without AD. Therefore, we only show scenario III in Fig. 10. 692 In the downlink ( Fig. 10 (a)), there are two relatively equal 693 singular values, when there is no AD (purple and yellow 694 continuous line), indicating that the maximum capacity of the 695 channel can be almost realized since the users are located far 696 from each other and user have both OFEs pointing upwards. 697 Introducing AD when users are far from each other, leads to 698 unequal singular values, hence lower capacity. Considering 699 the downlink direction in Fig. 5, OFE 1 of user 1 is not 700 able to receive a strong signal, since it is looking away. 701 But OFE 2 of user 1 can capture the strong signal from 702 D-OFE 2. Therefore, λ 1 , (purple dashed-line) has a higher 703 value than λ 2 (yellow dashed-line). However, in the uplink 704 ( Fig. 10(b)), both singular values without and with AD have 705 strong values. Altogether, AD leads to a more consistent 706 behavior, specifically when users are close to each other, and 707 uplink direction. Therefore, AD provides less dependency on 708 the user positions in the cell. Despite being near to each other 709 (scenario I), multiple data streams can be transmitted, as a 710 benefit from AD. Throughput results for SMUX scenarios without and with 713 AD and by using MU-MIMO were measured and evaluated, 714 respectively. We consider MS transmission for each single 715 user (SU). Results are shown in Fig. 12. We observe that 716 the throughput is higher for all scenarios when using AD. 717 In the scenario I, the gain due to AD is reduced, compared 718 to other scenarios, because the link switched automatically to 719 VOLUME 10, 2022   signal model was developed, which allows for evaluating 757 the performance of the concatenated wired and wireless 758 links. The system was considered as a distributed multiple-759 input multiple-output link that can be operated in different 760 transmission modes: spatial diversity and spatial multiplex-761 ing. We investigated the performance of these modes by 762 means of simulation and measurements in different scenarios. 763 We observed that the performance of each transmission mode 764 highly depends on the channel condition, besides the received 765 power. Both are related to the spacing between the users 766 and the distance to the OFEs. Moreover, for closely-spaced 767 users, SDIV enables better performance than SMUX without 768 angular diversity. Selection combining provides impressive 769 diversity gains over equal gain combining, which is attributed 770 to the spatial selectivity of the optical wireless channel. 771 We have also considered SMUX in combination with angular 772 diversity, which improves the performance depending on 773 the user location. In low SNR scenarios, specifically in the 774 uplink, we observed that multi-user multiplexing can achieve 775 additional gains. As an outlook, future work need to con-776 sider dynamic switching between these spatial transmission 777 modes, i.e. single-and multi-stream transmission for single 778 and multiple users, to maximize the performance in each sce-779 nario. Channel estimation for distributed MIMO