IEEE COMMUNICATIONS MAGAZINE, DRAFT 1 Terahertz Line-Of-Sight MIMO Communication: Theory and Practical Challenges 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 (wire- less 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: fdoheedong, sungmin.cho, hojin.song, signal-to-noise ratio (SNR) and, as a result, [email protected]). 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 LOS MIMO COMMUNICATION 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