Angel Lozano, Professor of Information and Communication Technologies, Univ. Pompeu Fabra
Published: 25 Aug 2021
CTN Issue: August 2021
A note from the editor:
Our colleague Angel Lozano takes on the challenge of explaining the line-of-sight MIMO concept without having to have a degree in EM theory. He explains why you don't always need a rich scattering environment for spatial multiplexing between a transmitter and a receiver. Indeed, as carrier frequencies reach the sub-terahertz range, where idle bandwidth abounds, small antenna arrays can appear electrically large relative to the distance between them. The MIMO effect that used to come from statistically independent fading in a multipath environment is now provided by deterministically distinct line-of-sight paths. Read on, and find out how you can enjoy the best of both the low-SNR and high-SNR worlds by juggling between beamforming and spatial multiplexing. A giveaway: after reading this, you'll probably understand why future transmitters and receivers may rotate their antennas like insects do when they see each other! As always, feedback and comments are most welcome.
Xiao Feng Qi, CTN Associate Editor
Miguel Dajer, CTN Editor-in-Chief
Harnessing the Radio Wavefront Curvature with Line-of-Sight MIMO
MIMO Prequel
Multiple-input multiple-output (MIMO) communication builds on a long pedigree of the application of antenna arrays to wireless communication. The earliest incarnation, back in the 1950s, was in the form of phased arrays, where the signal’s phase was adjusted at each antenna to create a beam towards an intended direction. This was followed by adaptive arrays, where both phase and magnitude could be adjusted, and by the 1980s by smart arrays, whose patterns could further null-out interference. An underlying attribute of these architectures is that each array acts as one degree-of-freedom (DOF): it launches or receives a single signal, appropriately weighted at each antenna, accepting the premise that the individual antenna transmissions from within an array cannot possibly be discerned by a distant receiver; from afar, only the overall signal is observed. Implicit in this premise is that the transmission range is long and the arrays are comparatively negligible in size.
Also, all of the above can all be viewed as spatial filters that rely on signal coherence across the arrays, an aspect that is disrupted by multipath propagation. Traditionally then, multipath propagation had been deemed undesirable, with countermeasures in place in the form of diversity. The preferred situation was line-of-sight (LOS) propagation, which assured coherence and the most received power.
Multipath Propagation: From Foe to Friend
Enter spatial multiplexing, which, starting in the 1990s, revolutionized wireless communications. While a broad understanding did not materialize until then, the seeds had been sowed well before that. Specifically, the coupling of multiple inputs into multiple outputs had been considered in a variety of works, ranging from abstract formulations to analyses motivated by coupled telephone lines [1, p. xix]. Crucially, this entailed the concurrent transmission of multiple signals, with the corresponding multiplicity of DOFs. By the late 1980s, the atmosphere was primed for the implementation of this idea on antenna arrays.
Although an earlier piece [2] had already featured multiantenna transmitters and receivers with many of the ingredients of contemporary MIMO communication, it was [3] that arguably served as the main catalyst. The authors of this seminal paper set out to design the perfect antenna from an information-theoretic standpoint; starting with an array and no preset conditions on how to use it, they found that, in a sufficiently rich scattering environment, spatially multiplexing multiple signals was not only feasible, but in fact the optimum strategy. Subsequent prototypes confirmed the practicality of this proposition and dispelled concerns that the concurrent signals would drown each other. Spatial multiplexing was radically novel in that it sought to exploit, rather than counter, the effects of multipath propagation. In fact, a multipath propagation environment was instrumental for the feasibility of spatial multiplexing, effectively acting as a lens that enabled distinguishing the signal emitted by each individual antenna within the transmit array at each antenna within the receiving array. By virtue of multipath propagation, the spatial resolution was no longer dictated by the size of the arrays themselves, but rather by the environment; precisely, by its supply of linearly independent relationships involving the signals radiated by the individual antennas (see Fig. 1).
Figure 1. Dual-antenna transmit and receive arrays. In LOS, individual antennas cannot be resolved for D ≫ d and there is only one DOF. With a multipath component, whose presence is tantamount to having mirror images of the arrays, the resolution becomes decoupled from D/d and is now dictated by the two paths; if these are sufficiently different to provide distinct signal mixings, two DOFs are possible. If additional, sufficiently different multipath components exist, extra antennas will yield further DOFs.
In the initial rush towards spatial multiplexing, then, it seemed as if LOS propagation was suddenly undesirable, yet a more nuanced understanding was ultimately reached: LOS propagation yields the most received power, but only one DOF, whereas multipath propagation yields a lower received power, but multiple DOFs. Depending on the signal-to-noise ratio (SNR), one or the other may be preferrable.
Privy to the benefits of spatial multiplexing, some inquisitive minds wondered, rather immediately, about the possibility of reaping those benefits in the absence of multipath propagation. Certain geometries were identified that did enable for a multiplicity of DOFs in LOS conditions, namely having the antennas of one of the arrays being spread out over large arcs or circles, or having the two arrays connected by a suitably sized urban canyon [5]. These are relevant scenarios, later generalized into multiuser and network MIMO settings, but for point-to-point MIMO they would entail arrays spread out over large distances. It became established that MIMO with compact transmit and receive arrays was not feasible in LOS channels.
New Times, New Rules
Fast-forward from the 1990s to today. Millimeter-wave frequencies, then deemed unusable because of their poor propagation characteristics, are now in commercial use and researchers have their eyes set on the sub-terahertz range. And, with the emergence of microcells, picocells, and femtocells—somehow nanocells got skipped—and the success of WiFi, the transmission range has shrunk from kms down to possibly a few meters. Altogether, these changes amount to a tidal transformation of the conditions in which wireless systems operate, and one of the consequences is a breakdown in some of the models under which previous wisdom had been established. In particular, a key modeling assumption underpinning that wisdom was the plane-wave model, which is the foundation of a vast literature on direction-of-arrival estimation, beamforming, and array theory.
The assumption of locally plane wavefronts over each array was soundly justified at sub-6 GHz frequencies and over sufficiently long transmission ranges. Consider the toy setting in Fig. 2, at 2 GHz and with a 1-km range. Basic trigonometry indicates that, for D and D' to differ by at least a quarter of a wavelength, leading to quadrature phases, the antenna spacing would have to be d>8.7 m. Over any array that could fit on a device or even a base station, the wavefronts are essentially flat and D≈D' in electrical terms. The channel matrix describing the channel is basically of unit rank; in the absence of multipath components, there is one DOF.
Now reconsider the example in Fig. 2 at 140 GHz and with a 20-m range. A spacing of d=14.6 cm suffices for D and D' to differ by a quarter of a wavelength, such that the 2x2 channel matrix has rank two and there are two DOFs, even without multipath components. The planar modeling assumption has broken down, as the curvature of the wave radiated by each transmit antenna is no longer negligible—relative to the wavelength—over the receive array. Taking it up another notch, at 300 GHz and with a 10-m range, 16 DOFs would be available via arrays of 15x15 cm. Indeed, at 300 GHz, 15 cm amount to 150 wavelengths, hence such a physically small array is electrically large enough to resolve 16 distinct transmissions from a similar array at 10 m.
For applications such as WiFi, kiosk information transfers, wireless interconnections within datacenters, ground-to-UAV and UAV-to-UAV communication, and even backhauling, this offers brand new opportunities for spatial multiplexing in situations with little or no scattering. Which is just as well because, as we move up in frequency, scattering dwindles. Experiments have confirmed the efficacy of spatial multiplexing in LOS channels [5] and, in conjunction with the enormous bandwidths available in the mmWave and sub-terahertz ranges, this could enable truly stupendous bit rates; think hundreds of Gb/s, possibly breaking through the Tb/s barrier.
The LOS MIMO Paradigm
The most striking feature of LOS MIMO is that it allows one to have one’s cake and eat it: maximum received power over the direct LOS path and a multiplicity of DOFs. Both at once. In fact, if the antenna spacings can be suitably set, the channel matrix can be made to be both optimum from an information-theoretic standpoint (all the DOFs are equally strong) and convenient from a signal processing perspective (simple transmit and receive structures).
Now, while the spotlight has understandably been on spatial multiplexing and on driving each antenna as a separate DOF, it must be borne in mind that this is a high-SNR strategy. At low SNR, it continues to be better to concentrate the power on a single DOF via beamforming. Therefore, suitably curved wavefronts are desirable at high SNR whereas planar wavefronts are preferable at low SNR. At intermediate SNRs, we would want a combination of both—which is actually possible by arranging each array into subarrays of tightly spaced antennas, with those subarrays appropriately spaced [6]. As shown in Fig. 3, the available antennas should ideally be split, depending on the SNR, into subarrays over which wavefronts are essentially flat; the number of subarrays determines the DOF. Alternatively, a single array structure can be retained, but with the antenna spacing adjusted as a function of the SNR (see again Fig. 3). Of course, both these solutions present the conundrum of requiring mechanically reconfigurable arrays in applications where the SNR is not fixed.
Fortunately, there is a way in which a variable antenna spacing can be mimicked without actually changing the physical spacing, namely by controlling the relative orientation of the transmit and receive arrays [7]. Indeed, if the arrays are linear, then what matters is the projection of one on the direction of the other, and the antenna spacings on that projection shrink with the cosine of their relative angle. As shown in Fig. 4, this enables reconfiguration via a simple rotation, or else via selection among a few radially arranged arrays: at low SNR, the arrays should be almost orthogonal (so each one appears collapsed from the vantage of the other) while, at high SNR, they should essentially be colinear (so each appears fully extended to the other). For nonlinear arrays, reconfigurability is also possible.
Thus, another characteristic of LOS MIMO is that, in contrast with multipath-based MIMO at lower frequencies, geometry is king. There is a strong interplay among the SNR, the topology and orientation of the arrays, and the optimum mixture of spatial multiplexing and beamforming, so perhaps future generations of smartphones will be showing us on their screens how we should rotate them for better performance, or hovering UAVs will orient themselves optimally while they download contents.
Also, LOS MIMO may only be the tip of the iceberg of new advances as we stretch time-honored operating conditions in terms of frequency, bandwidth, numbers of antennas, and range, and as metamaterials with funky properties are concocted. There is a flurry of research activity at the intersection of information theory and electromagnetics, with the promise of concepts such as holographic MIMO, super-directivity, or orbital angular momentum, and there is seismic wave of excitement on the topic of reflecting intelligent surfaces, with the ultimate dream of creating smart radio environments. But this is a topic for another day. One thing is for sure: exciting times are ahead!
References
- R. W. Heath Jr and A. Lozano, Foundations of MIMO Communication, Cambridge University Press, 2019.
- J. Winters, “On the capacity of radio communication systems with diversity in a Rayleigh fading environment,” IEEE J. Sel. Areas Commun., vol. 5, no. 5, pp. 871–878, 1987.
- G. J. Foschini and M. Gans, “On limits of wireless communications in a fading environment when using multiple antennas,” Wireless Personal Communications, vol. 6, no, 3, 311-335, 1998.
- P. Driessen and G. J. Foschini, “On the capacity formula for multiple input-multiple output wireless channels: a geometric interpretation,” IEEE Trans. Commun., vol. 47, no. 2, pp. 173-176, 1999.
- C. Sheldon, M. Seo, E. Torkildson, M. Rodwell and U. Madhow, “Four-channel spatial multiplexing over a millimeter-wave line-of-sight link,” IEEE MTT-S Int’l Microwave Symp., pp. 389-392, 2009.
- C. Lin and G. Li, “Terahertz communications: An array-of-subarrays solution,” IEEE Commun. Mag., vol. 54, no. 12, pp. 124–131, Dec. 2016.
- H. Do, N. Lee and A. Lozano, “Reconfigurable ULAs for line-of-sight MIMO transmission,” IEEE Trans. Wireless Commun., vol. 20. No. 5, pp. 2933-2947, 2020.
Statements and opinions given in a work published by the IEEE or the IEEE Communications Society are the expressions of the author(s). Responsibility for the content of published articles rests upon the authors(s), not IEEE nor the IEEE Communications Society.
Comments
A very interesting discourse, I gained more knowledge than reading a 30 page long IEEE Transactions paper. I also highly recommend such articles to PhD students who are starting their career and they need clear directions. I first listened to Prof. Lozano in ISWCS 2018 in Lisbon. Looking forward to read more from the author.
While working on space shift keying (SSK), a variant of spatial multiplexing, solely dependent on the richness of the scattering environment, we found that they are unable to provide SNR diversity. When we tried combinations of SSK with other traditional space diversity combining techniques, the results are still not very encouraging. Any ideas on why these combinations don't work or how to make combinations useful?
Submitted by aniruddha_chan… on 27 August 2021
Are the array elements assumed to be isotropic radiators? [7] seems to be based on array factors sans any specific array element characterisation. Typically, in these bands, directive elements are employed for various reasons, e.g., packaging, conformity, etc. With reference to the medium SNR case on the right hand side of Fig. 3, as the element spacing is increased beyond the half-wavelength, spatial aliasing will manifest as grating lobes. This will restrict the field of view (FoV), which in turn may limit the multi-path richness of the channel. A quick skimming of the referred literature on mmWave LoS MIMO links appears to indicate the reliance on horn antennae. Would a medium SNR hybrid solution depicted in Fig. 3 right side be optimal for omni-directional antennae, say the half wavelength printed dipoles on a mobile/UAV in view of the restricted FoV with ULA spacing spacings beyond the half-wavelength at the centre frequency?
Also, the spatial aliasing will become increasingly more prominent towards the higher frequency sub-carriers in the broadband mmWave/THz communications.
The left hand side of Fig. 3 basically uses the sub-array to realise the directive radiation or the beamforming power gain similar to the horn antennae in [5] and the references therein.
Submitted by krishan.tiwari… on 28 August 2021
Are the array elements assumed to be isotropic radiators? [7] seems to be based on array factors sans any specific array element characterisation. Typically, in these bands, directive elements are employed for various reasons, e.g., packaging, conformity, etc. With reference to the medium SNR case on the right hand side of Fig. 3, as the element spacing is increased beyond the half-wavelength, spatial aliasing will manifest as grating lobes. This will restrict the field of view (FoV), which in turn may limit the multi-path attribute of the channel. A quick skimming of the referred literature on mmWave LoS MIMO links appears to indicate the reliance on horn antennae. Would a medium SNR hybrid solution depicted in Fig. 3 right side be optimal for omni-directional antennae, say the half wavelength printed dipoles on a mobile/UAV in view of the restricted FoV with ULA spacing spacings beyond the half-wavelength at the centre frequency? Also, the spatial aliasing will become increasingly more prominent towards the higher frequency sub-carriers in the broadband mmWave/THz communications. The left hand side of Fig. 3 basically uses the sub-array to realise the directive radiation or the beamforming power gain similar to the horn antennae in [5] and the references therein.
From Angel Lozano: Excellent observation. For the sake of explaining the basic idea, isotropic elements were indeed (implicitly) considered. Indeed, as the reader indicates, in practice one will often want to use directive elements, and this restricts the number of array rotation options because some rotations end up causing a loss in directivity, and hence in SNR. Fortunately, the rotation illustrated in the article preserves the antenna gains, so it is possible to optimize the number of DoF without a loss in SNR. Things become more complicated if the arrays are not ULAs, and a paper addressing that will be presented at Globecom this year. So a very timely question indeed!
Submitted by krishan.tiwari… on 28 August 2021
Very nice article, Dr. Lozano! Well written and interesting. Thank you.
Submitted by jandrews@ece.u… on 26 August 2021