Terahertz Line-Of-Sight MIMO Communication: Theory and Practical Challenges

IEEE COMMUNICATIONS MAGAZINE, DRAFT 1

Heedong Do, Sungmin Cho, Jeonghun Park, Ho-Jin Song, Namyoon Lee, and Angel Lozano

Abstract—A relentless trend in wireless communica- this band is largely unexplored, the obstacles look tions is the hunger for bandwidth, and fresh bandwidth increasingly surmountable. First, signal sources is only to be found at ever higher frequencies. While 5G of adequate power and room-temperature detec- systems are seizing the mmWave band, the attention of researchers is shifting already to the terahertz range. tors of acceptable sensitivity have long been a In that distant land of tiny wavelengths, antenna arrays major challenge, but there is promising progress can serve for more than power-enhancing beamforming. on these fronts and recent experimental demon- Defying lower-frequency wisdom, spatial multiplexing strations with state-of-the-art solid-state electron- becomes feasible even in line-of-sight conditions. This ics have reached 100 Gb/s over 20 GHz of paper reviews the underpinnings of this phenomenon, bandwidth at 300 GHz [2]. Second, the THz band and it surveys recent results on the ensuing information- is challenging in terms of radio propagation. In theoretic capacity. Reconfigurable array architectures are put forth that can closely approach such capacity, particular, and owing to the lack of diffraction, practical challenges are discussed, and supporting ex- propagation is predominantly line-of-sight (LOS). perimental evidence is presented. This rules out wide-area coverage, yet it befits Index Terms—Terahertz (THz) communication, line- many emerging applications, both short-range of-sight (LOS), multiple-input multiple-output (MIMO) in nature (inter-chip communication, datacen- ter interconnections, indoor local-area networks, kiosk downloads) and also of longer range (wireless backhaul, unmanned aerial vehicle (UAV) I.INTRODUCTION communication, satellite interconnection). There The two mechanisms whereby wireless sys- are peaks of high atmospheric absorption that tems can increase their bit rates are augmenting should be avoided, but, interspersed with those, the bandwidth and improving the spectral effi- there are enormous windows—hundreds of GHz ciency, and both have progressed in tandem over altogether—where the absorption is below 10 the years. From 1G to 5G, the spectrum devoted dB/km [3]. to wireless communication has surged from a Despite this vast amount of potential spectrum, handful of MHz to multiple GHz, roughly three the bandwidth that could be made available to orders of magnitude, while system spectral effi- individual users is curbed because: ciencies have risen by about two orders of mag- • Power amplifiers are curtailed to about 10% nitude. For 5G, microwave spectrum allocations of the carrier frequency. no longer sufficed, and a first step is being taken • The energy efficiency of analog-to-digital beyond, into the mmWave realm (6–95 GHz). converters (ADCs) drops abruptly as the The spectral efficiency also continues to advance, sampling rate pushes past 100 MHz [4]. despite the exhaustion of many of its classical While, up to that point, the ADC power con- arXiv:2008.01482v1 [eess.SP] 4 Aug 2020 improvement strategies, by virtue of multiple- sumption grows linearly with the bandwidth, input multiple-output (MIMO) massification [1]. when moving from 100 MHz to 20 GHz the All in all, bit rates of about 20 Gb/s are within power consumption does not grow 200-fold reach in 5G. Further headway towards the Tb/s but rather 10000-fold. milestone will again require a leap forward in It follows from these limitations on the per-user both spectrum and spectral efficiency. bandwidth that, as anticipated, the spectral effi- Spectrum-wise, the next frontier is the terahertz ciency remains important—yet there is substantial (THz) band, broadly defined as 0.1–10 THz and downward pressure on it: sandwiched between the mmWave and the far- • The power of a signal source declines with infrared ranges. Although there are reasons why increasing frequency and, above 300 GHz, it is capped below 20 dBm; this restricts the H. Do, S.-M. Cho, H.-J. Song, and N. Lee are with POSTECH, Pohang, Korea (e-mail: {doheedong, sungmin.cho, hojin.song, signal-to-noise ratio (SNR) and, as a result, nylee}@postech.ac.kr). J. Park is with Kyungpook Nat’l Univer- the spectral efficiency. sity, Daegu, South Korea ([email protected]). A. Lozano • The pathloss for omnidirectional antennas is with Univ. Pompeu Fabra, 08018 Barcelona (e-mail: an- increases with frequency, further penalizing [email protected]). the SNR and the spectral efficiency. IEEE COMMUNICATIONS MAGAZINE, DRAFT 2

Spherical wavefront model Planar wavefront model Validity region

Tx aperture

300 �, Spherical wavefront

Illustration � 30 Planar wavefront �

, [GHz] Frequency Carrier 3 �, 10 100 1000 Rx aperture Communication Range [m]

Fig. 1. Spherical and planar wavefront illustrations, and respective validity regions as a function of the communication range and carrier frequency when the aperture of the transmit and receive arrays is 50 cm.

• The noise power grows with the bandwidth, • Reconfigurable antenna architectures moti- compounding the SNR reduction. vated by these insights. • To harness the ADC power expenditure, a sacrifice in resolution may be inevitable; with a lower resolution comes, again, a lower A. Rethinking MIMO Channel Modeling for THz spectral efficiency. Frequencies Without a forceful countering of these effects, Unlike at microwave frequencies, multipath user bit rates may fall very short of the Tb/s mark. propagation is very weak in the THz band be- Besides, as in mmWave communication, the an- cause, compounding the lack of diffraction, the tidote to a low per-antenna spectral efficiency is roughness of most surfaces is comparable to the to increase the number of antennas, capitalizing wavelength. This leads to major scattering and re- on the tiny wavelength to pack massive arrays flection losses, leaving the LOS path as the dom- onto compact form factors. The most immediate inant means of propagation. Since microwave- use for such antenna arrays is SNR-enhancing frequency wisdom deems multipath richness as beamforming with a single baseband chain. This instrumental for spatial multiplexing while re- is the solution currently adopted for mmWave. garding LOS propagation as a roadblock to it, While this is a sound starting point for THz the possibility of spatial multiplexing would seem communication as well, per-antenna baseband compromised at THz frequencies. Understanding processing can already be envisioned. why this is not the case requires some careful The eventual conjunction of THz frequen- modeling of the inherent channel features. cies and per-antenna processing naturally invites The magnitude and phase of the channel con- MIMO transmission, which, while subsuming necting the mth transmit with the nth receive an- beamforming as a special case, broadens the tenna is governed by the corresponding distance, scope to spatial multiplexing [5]. Moreover, as we Dn,m. Under the reasonable proviso that the array move up in frequency, LOS goes from hampering apertures are small relative to their separation, spatial multiplexing to being an instrument for all these distances are similar enough for the it. This phenomenon is the thrust of the present magnitudes of those responses to be taken as paper, which expounds its theoretical foundations, identical. In contrast, the phase of the channel discusses the chief practical obstacles, presents responses cannot be deemed uniform, as even numerical and experimental evidence, and points minute distance variations may elicit pronounced to subsequent research. phase differences. Hence, an LOS channel repre- sentation adopts the form of a matrix containing II.THZ LOSMIMOCOMMUNICATION the phase of the responses for every transmit- Commencing on the theoretical front, this sec- receive antenna pair. tion addresses three key aspects: The time-honored model for this matrix rep- • The appropriate modeling of LOS MIMO resentation regards the wavefronts as locally flat channels at THz frequencies. over each array. Geometrically, this corresponds • Insights gleaned from applying information to factoring out a common distance D for all an- theory to such models. tenna pairs, as shown in Fig. 1; what remains are IEEE COMMUNICATIONS MAGAZINE, DRAFT 3 then the phase shifts corresponding to the residual should be such that a certain number of the singu- distances from each antenna to the wavefront, lar values—the gains along the matrix preferred and, as evidenced in the figure, these are linear. directions—are positive and identical while the Mathematically, the planar wavefront approxima- rest are zero; the rank is the number of positive tion amounts to a first-order series expansion singular values. The design objective is thus to of every Dn,m around D. As it turns out, the polarize the singular values of the channel matrix planar approximation is highly precise provided into two states, positive and zero, depending on that the product of the transmit and receive ar- the SNR. ray apertures is smaller than 4 λD, where λ is Three distinct regimes emerge: the wavelength [6]. Under this condition, which • At low SNR, when the communication is virtually always holds at lower frequencies, the power-limited, the winning strategy is to LOS channel matrix is simply the outer product construct the channel matrix enabling the of the vectors of linear phase shifts induced highest possible power gain. There should by the plane wavefronts across the transmit and be a single positive and large singular value, receive arrays. And, being the outer product of and beamforming should take place along two vectors, the matrix is unit-rank, meaning that the corresponding direction. no spatial multiplexing (which requires a high- • At intermediate SNRs, a transition. The rank channel) is possible, but only beamforming number of positive singular values should (for which a unit-rank channel suffices). progress from one to the minimum number While perfectly appropriate for microwave fre- of antennas in the transmit/receive arrays as quencies, the planar wavefront approximation the SNR advances, and this number dictates becomes inadequate in THz territory. Because the order of the spatial multiplexing. Indeed, the wavelength is minute and the transmission as the SNR strengthens, multiple parallel distance tends to be short, the wave curvature signals can be sustained, multiplying the over the arrays ceases to be negligible. Rather, spectral efficiency. such curvature creates a richer pattern of phase • At high SNR, the singular values should all variations that endows the LOS channel matrix be positive and identical, and full spatial with a high rank. Representing this reality re- multiplexing of as many signals as antennas quires the matrix of absolute phases associated should take place. with the actual distances, Dn,m (see Fig. 1). While already noticeable at mmWave frequencies [7]– Besides being information-theoretically opti- [10], the effect of the wave curvature over the mum, the equality of the positive singular values arrays becomes categorical on the THz band. greatly simplifies the transmit and receive signal This offers the opportunity of customizing the processing [12]. Much of it amounts to applying channel matrix through a careful arrangement of unitary rotations, which are very amenable to im- the antennas within each array. Indeed, rather than plementation, and the allocation of power across by the vagaries of multipath propagation, here the the parallel transmit signals is trivially uniform. channel matrix is determined by sheer geometry. Before further exploring the possibilities asso- C. Reconfigurable Array Architectures ciated with custom antenna arrangements, it is instructive to view the problem at hand from the Having established the key design guideline for fundamental prism of information theory. the arrays, let us now put forth two specific architectures that, inspired by this guideline, polarize the singular values as a function of the SNR. B. Some Insights from Information Theory These are the reconfigurable array-of-subarrays For every channel and SNR, the information- (R-AOSA) and the rotating ULA. theoretic capacity is the highest possible spectral 1) R-AOSA: An AOSA consists of r subar- efficiency that can be achieved reliably. To in- rays, uniformly spaced. The antennas are divided corporate the newfound ability of modifying the evenly among these subarrays at, within each, channel matrix through antenna position adjust- they are tightly spaced relative to the wavelength. ments, we can introduce a broader capacity taken With AOSAs at both ends, the channel matrix over all possible antenna arrangements at a given features r positive and equal singular values. By SNR. Characterizing this broader capacity entails progressively increasing r as the SNR improves, identifying the best possible such arrangements i.e., by having more subarrays with fewer anten- at every SNR, a difficult task in general. nas each, an AOSA is rendered reconfigurable. At Fortunately, through a careful process of the low-SNR extreme, a linear R-AOSA reverts to bounding it can be determined that the key role a single array of tightly spaced antennas whereas, of the array geometries is to adjust the rank of at the high-SNR end, it becomes a ULA with the the channel matrix depending on the SNR [11], precise inter-antenna spacing that makes all the [12]. More precisely, the antenna dispositions singular values equal [13]. This is illustrated, for IEEE COMMUNICATIONS MAGAZINE, DRAFT 4

-3 3 SNR [dB] 8 Rotating ULAs R-AOSA 7 Upper bound z]

H 6

4 ficiency [bps /

High SNR Spectral E f 2

Low SNR 1

0 -5 -4 -3 -2 -1 0 1 2345 SNR [dB]

Fig. 2. Left-hand side: R-AOSA and rotating ULA with four antennas as a function of the SNR; right-hand side: spectral efficiencies achievable by R-AOSAs and by rotating ULAs, respectively, versus a capacity upper bound. a four-antenna linear R-AOSA, in Fig. 2. Up to an ture need not be embodied by a mechanically SNR of about −3 dB, the AOSA adopts the form turnable array. Instead, it can also be realized of a single compact array, subsequently morphing by electronically selecting among various ULAs to twin two-antenna arrays, and, beyond 3 dB, having a radial disposition. While additional an- to a four-antenna ULA. The spectral efficiencies tennas are needed to implement this solution, the achievable by these three configurations are also number of radio-frequency chains stays the same, depicted in Fig. 2, alongside a capacity upper meaning that the additional cost is marginal. bound. By switching to the correct configuration And, as it turns out, with as few as three fixed at every SNR, the bound is tracked rather closely. ULAs, properly angled, the performance is hardly This excellent performance, however, does come different from that of a freely rotating ULA [12]. at the cost of having to physically rearrange the antennas whenever the SNR changes, a drawback addressed by the next architecture. III.BEYOND ULAS:RECTANGULAR 2) Rotating ULA: As it turns out, the singular AND CIRCULAR ARRAYS values of the channel matrix can also be ma- While we have been invoking ULAs (and nipulated by simply rotating the transmit and/or AOSAs, which can be interpreted as two-tier receive arrays [12]. Moreover, provided the num- ULAs) as a running example, the ideas dis- ber of antennas is minimally large, an adequate cussed hitherto extend to any other array type. rotation can essentially polarize the singular val- In particular, a popular alternative to the ULA is ues in any desired fashion. (Asymptotically in the the uniform rectangular array (URA), which in numbers of antennas, the polarization is exact; for essence is the cartesian product of two ULAs, finite numbers thereof, it is approximate.) This is and the uniform circular array (UCA), which is again illustrated, for a four-antenna ULA, in Fig the preferred geometry for a sister communication 2. For SNRs below -3 dB, the ULA should be technique based on orbital angular momentum aligned with the direction of transmission, subse- [14]. Both the URA and the UCA feature more quently spinning towards a broadside disposition, compact form factors than the ULA for a given reached at about 3 dB.The exact rotation depends, number of antennas. To facilitate a comparison of not only of the SNR, but also on the number of these and other array types in LOS environments, antennas. The performance achievable on a set it is convenient to define the channel param- of angles is exemplified in Fig. 2 alongside the eter η = (Tx aperture)(Rx aperture)/(λDNmin), capacity upper bound; by effecting the correct which blends the array apertures, the wavelength, rotation at every SNR, the bound is virtually the transmission distance, and the minimum num- attained. ber of antennas in the transmit/receive arrays, Most interestingly, the rotating ULA architec- Nmin, into a single quantity; as it happens, the IEEE COMMUNICATIONS MAGAZINE, DRAFT 5

Aperture [m] need not correspond to a mere rotation. As of 0.2 0.4 0.6 0.8 1.0 1.2 UCAs, there is no conﬁguration for which they 250 do not exhibit a certain shortfall with respect to capacity, suggesting that the circular geometry is less favorable for the purpose of polarizing the 200 singular values. And, as a fallout of an incomplete polarization, the optimum allocation of powers across the parallel transmit signals is not uniform. In exchange, UCAs do simplify some of the 150 processing: rather than channel-dependent unitary rotations, here the transmitter and receiver reduce to channel-independent Fourier matrices. 100 IV. PRACTICAL CHALLENGES The implementation of THz MIMO transmis-

Spectral Efficiency [bps/Hz] Efficiency Spectral ULAs 50 sion is not without challenges, some of which are URAs sketched next. UCAs 1) Misalignments: Maintaining a perfect Upper bound alignment between transmitter and receiver 0 may be impossible in some of the envisioned 0 0.5 1 1.5 2 2.5 3 applications. Analyses of the sensitivity to Channel Parameter unwanted tilts and rotations are necessary to guide the designs and to establish the accuracy Fig. 3. Spectral efficiency as a function of the channel parameter to which the ideal orientations must be tracked for ULAs, URAs, and UCAs, with 64 transmit and receive in the face of motion or disturbances, say wind antennas at SNR = 10 dB. Also shown is the capacity upper bound at this SNR. The array apertures—equal at transmitter turbulence in the case of UAVs. and receiver—corresponding to the channel parameter are also 2) Frequency Variations: The optimum con- indicated for a transmission distance of 10 m. figuration at some wavelength need no longer be optimum at some other wavelength, everything else being the same. A meaningful objective is thus to identify arrangements that are robust LOS MIMO capacity depends only on this quan- across the broadest possible swaths of spectrum. tity [12]. For a ULA, the array aperture in the 3) Intersymbol Interference: In stark contrast above relationship is the length, for a URA it is with lower frequencies, where LOS channels are the side of the square, and for a UCA it is the devoid of intersymbol interference, at THz fre- diameter of the circle on which the antennas are quencies it may arise on account of the short placed; in all cases, the aperture is measured with transmission distance. Precisely, back-and-forth the arrays broadside to the transmission. reflections may occur when the arrays face each Equipped with the aforedefined channel param- other at close range, leading to a rather distinct eter, we can contrast the spectral efficiencies of form of distance-dependent intersymbol interfer- ULA, URA, and UCA architectures over a broad ence. This issue needs to be characterized, and assortment of configurations. A comparison is mitigating solutions developed. presented in Fig. 3 for 64 antennas at each end 4) Low-Resolution ADCs: Lowering the res- of the link and SNR = 10 dB, with the chan- olution of the ADCs and of the mirror digital- nel parameter sweeping the interval [0, 3]. This to-analog converters ameliorates the cost and the corresponds to varying either the transmission power consumption, but at the expense of a distance, the wavelength, the number of antennas, surge in quantization noise. While some results or the apertures (say by reconfiguring the arrays, are available on the capacity of MIMO channels if they are embodied by R-AOSAS, or by rotating with one-bit ADCs the understanding is far from them, thereby modifying their broadside projec- complete [15]. Substantial progress might be pos- tion). With ULAs, the capacity upper bound is sible for LOS MIMO specifically, given its rather essentially achieved for specific parameter values. unique nature. Applying the ideas in the previous section, any 5) Array Apertures: Having reduced array ULA can be reconfigured to operate at these footprints is a desirable trait for certain applica- points through a simple rotation—with the small- tions, say portable devices or UAVs. At a given est such operating point being the most attractive SNR, the optimum channel parameter maps to a from the vantage of a small array footprint. URAs product of the transmit and receive apertures that also attain the upper bound for specific configura- grows with the transmission distance, meaning tions, although in this case the reconfigurability that long-range transmissions are in principle IEEE COMMUNICATIONS MAGAZINE, DRAFT 6

Lorem ipsum

Vector Network Analyzer Rx Antenna Tx Antenna

Fig. 4. Left-hand side: experimental setup; right-hand side: phase vs receive antenna displacement. problematic from the standpoint of keeping the 4. It is seen that the phase exhibits a quadratic apertures small. However, there is relief in that variation over the synthetic ULA, in validation the dependence is on the product of the apertures, of the spherical wavefront model; under a planar making it possible to keep one end of the link wavefront model, instead, it would be linear. compact at the expense of the other end. Depend- ing on the setting, then, the correct balance of transmit and receive apertures would have to be VI.SUMMARY determined. The vast amount of spectrum available on the THz band dwarfs what is currently being conquered at mmWave frequencies—even with V. EXPERIMENTAL EVIDENCE all the intervals of high atmospheric attenuation Shown in Fig. 4 is an experimental setup discounted. However, this enormous bandwidth designed to verify some of the underlying ideas. can only be assigned in moderate doses to in- A narrowband signal is transmitted over a link dividual users, and thus the spectral efficiency distance D ranging from 0.5 m to 5.4 m at 300 remains a relevant figure of merit vis-a-vis bit GHz. Both transmitter and receiver are equipped rates. As an assortment of factors pressure the with a single horn antenna, fairly directive (25 spectral efficiency down at these frequencies, a dBi antenna gain for 18 degrees of half-power mechanism to boost it becomes imperative, and beamwidth). This directivity ensures that no sig- MIMO emerges as a welcome opportunity. nificant ground bounce is present while radiation- Contrary to the lower-frequency wisdom that absorbent material prevents back-and-forth re- only beamforming is possible in the LOS con- flections. The measurements rest on a through- ditions that are prevalent in THz channels, the reflect-line calibration kit and a vector network combination of a tiny wavelength and a short analyzer, with a minimum SNR of 30 dB at all transmission distance opens the door to spatially times. resolving each antenna, and hence to spatial mul- Through a mechanical displacement of the re- tiplexing, even in LOS situations.Transcending ceive antenna in 1-mm steps, with a dwell time the classic planar wavefront approximation and of 5 ms, a 300-antenna synthetic ULA receiver embracing the actual spherical nature of the wave is produced while the transmitter is held fixed. propagation, it is possible to tightly bound the Despite the directivity of the physical antennas, information-theoretic capacity of LOS MIMO it is verified that the magnitude of the channel settings and observe that the optimum trans- response varies but little over the synthetic array; mission strategy polarizes the channel’s singular in most deployments, the antennas would be values depending on the SNR. Several ways to go far less directive, reinforcing this aspect. With about this have been put forth, chiefly the SNR- the premise that the channel behavior depends dependent rotation (either mechanic or electronic) only on the phase fluctuations being therefore of a ULA. satisfied, the phase of the channel response at The rollout of MIMO transmission at THz each displacement, i.e., for each virtual receive frequencies is not without challenges, and the antenna when D = 1.8 m, is depicted in Fig. main practical hurdles have been outlined. Fi- IEEE COMMUNICATIONS MAGAZINE, DRAFT 7 nally, experimental evidence has been provided [15] Y. Nam, H. Do, Y.-S. Jeon, and N. Lee, “On the capacity to support some of the theoretical underpinnings. of MISO channels with one-bit ADCs and DACs,” IEEE J. Sel. Areas Commun., vol. 37, no. 9, pp. 2132–2145, 2019. Heedong Do (S’20) received a B.S. in mathematics and a M.S. CKNOWLEDGMENTS in electrical engineering from Pohang University of Science & A Technology (POSTECH), Pohang, Korea, in 2018 and 2020, This work was supported by the Samsung respectively. He is currently a Ph.D. candidate. Research Funding and Incubation Center of Sam- sung Electronics under Project SRFC-IT1702- 04, by the Basic Science Research Programs under the National Research Foundation of Korea Sungmin Cho (S’19) received a B.S. from Kyungpook Nat’l (NRF) through the Ministry of Science and ICT University, Daegu, Korea in 2017 and a M.S degree in 2019 from under NRF2020R1C1C1013381, and by the Eu- Pohang University of Science & Technology (POSTECH), where ropean Research Council under the H2020/ERC he is currently pursuing the Ph.D. degree. grant agreement 694974.

REFERENCES Jeonghun Park (S’13–M’17) is an Assistant Professor at Kyung- [1] F. Boccardi, R. Heath, A. Lozano, T. Marzetta, and pook Nat’l University, Daegu, Korea. Before that, he worked at P. Popovski, “Five disruptive technology directions for 5G,” Qualcomm wireless R&D, San Diego, USA. He received a Ph.D. IEEE Commun. Mag., vol. 52, no. 2, pp. 74–80, 2014. degree in electrical and computer engineering at The University [2] H. Hamada, T. Tsutsumi, H. Matsuzaki, T. Fujimura, of Texas at Austin, USA, in 2017. I. Abdo, A. Shirane, K. Okada, G. Itami, H. Song, H. Sugiyama, and H. Nosaka, “300-GHz-band 120-Gb/s wireless front-end based on InP-HEMT PAs and mixers,” IEEE Journal of Solid-State Circuits, pp. 1–1, 2020. [3] I. F. Akyildiz, J. Jornet, and C. Han, “Terahertz band: Next frontier for wireless communications,” Physical Commun., Ho-Jin Song (S’02-M’06-SM’13) received a Ph.D. degree from vol. 12, pp. 16–32, 2014. Gwangju Institute of Science & Technology (GIST), Gwangju, [4] B. Murmann, “ADC performance survey 1997-2016,” Korea, 2005. He was with the Nippon Telegraph and Telephone http://www.stanford.edu/murmann/adcsurvey.html, 2016. (NTT) Laboratories, Kanagawa, Japan, in 2006 - 2016. Since [5] R. W. Heath, Jr. and A. Lozano, Foundations of MIMO 2016, he has been an Associate Professor at POSTECH, Pohang, Communication. Cambridge University Press, 2018. Gyeongbuk, Korea. Prof. Song was awarded the Best Thesis [6] J.-S. Jiang and M. A. Ingram, “Spherical-wave model for Award from the Gwangju Institute of Science and Technology short-range MIMO,” IEEE Trans. Commun., vol. 53, no. 9, (2005), the Young Scientist Award of the Spectroscopical Society pp. 1534–1541, 2005. of Japan (2010), the IEEE MTT-S Tatsuo Itoh Prize (2014), and [7] F. Bohagen, P. Orten, and G. Oien, “Construction and ca- the Best Industrial Paper Award at IEEE MTT-S-IMS2016 (2016). pacity analysis of high-rank line-of-sight MIMO channels,” in Proc. IEEE Wireless Commun. Netw. Conf., Mar. 2005, pp. 432–437. [8] C. Sheldon, E. Torkildson, M. Seo, C. Yue, U. Madhow, and M. Rodwell, “A 60 GHz line-of-sight 2x2 MIMO link Namyoon Lee (S’11–M’14–SM’20) received a Ph.D. degree operating at 1.2 Gbps,” in IEEE AP-S Int. Symp., Jul. 2008. from The University of Texas at Austin, in 2014. He was with [9] L. Bao and B.-E. Olsson, “Methods and measurements of Communications and Network Research Group, Samsung Ad- channel phase difference in 2x2 microwave LOS-MIMO vanced Institute of Technology (SAIT), Korea, in 2008-2011 and systems,” in Proc. IEEE Int. Conf. Commun., Jun. 2015, also with Wireless Communications Research (WCR), Intel Labs, pp. 1358–1363. Santa Clara, USA, in 2015-2016. He is currently an Associate [10] T. Halsig, D. Cvetkovski, E. Grass, and B. Lankl, “Mea- Professor at POSTECH, Pohang, Gyeongbuk, Korea. He was a surement results for millimeter wave pure LOS MIMO recipient of the 2016 IEEE ComSoc Asia–Paciﬁc Outstanding channels,” in Proc. IEEE Wireless Commun. Netw. Conf., Young Researcher Award. He is currently an Editor for both Mar. 2017. the IEEE Trans. on Wireless Communications and the IEEE [11] H. Do, N. Lee, and A. Lozano, “Capacity of line-of-sight Communications Letters. MIMO channels,” in Int’l Symp. Inform. Theory (ISIT’20), 2020. [12] ——, “Reconﬁgurable ULAs for line-of-sight MIMO transmission,” 2020, arXiv:2004.12039 [cs.IT]. Available: https://arxiv.org/abs/2004.12039. [13] P. F. Driessen and G. Foschini, “On the capacity formula Angel Lozano (S’90 – M’99– SM’01 - F’14) received a Ph.D. for multiple input-multiple output wireless channels: A from Stanford University in 1998. From 1999 to 2008 he was geometric interpretation,” IEEE Trans. Commun., vol. 47, with joined Bell Labs (Lucent Technologies, now Nokia). He is no. 2, pp. 173–176, Feb. 1999. currently a Professor at Univ. Pompeu Fabra (UPF), Barcelona, [14] O. Edfors and A. J. Johansson, “Is orbital angular mo- and the co-author of the textbook “Foundations of MIMO Com- mentum (OAM) based radio communication an unexploited munication” (Cambridge University Press, 2019). He serves as area?” IEEE Trans. Antennas Propag., vol. 60, no. 2, pp. Area Editor for the IEEE Trans. on Wireless Communications. 1126–1131, 2012. He received the 2009 Stephen O. Rice Prize, the 2016 Fred W. Ellersick prize, and the 2016 Communications Society & Information Theory Society joint paper award. He holds an Advanced Grant from the European Research Council and was a 2017 Clarivate Analytics Highly Cited Researcher.