Analyzing the Impact of Molecular Re-Radiation on the MIMO Capacity in High-Frequency Bands
11 Analyzing the Impact of Molecular Re-Radiation onthe MIMO Capacity in High-Frequency Bands
Sayed Amir Hoseini, Ming Ding,
Senior Member, IEEE , Mahbub Hassan,
Senior Member, IEEE and YoujiaChen,
Member, IEEE
Abstract —In this paper, we show how the absorption and re-radiation energy from molecules in the air can influence theMultiple Input Multiple Output (MIMO) performance in high-frequency bands, e.g., millimeter wave (mmWave) and terahertz.In more detail, some common atmosphere molecules, such asoxygen and water, can absorb and re-radiate energy in theirnatural resonance frequencies, such as 60 GHz, 180 GHz and320 GHz. Hence, when hit by electromagnetic waves, moleculeswill get excited and absorb energy, which leads to an extrapath loss and is known as molecular attenuation. Meanwhile,the absorbed energy will be re-radiated towards a randomdirection with a random phase. These re-radiated waves alsointerfere with the signal transmission. Although, the molecularre-radiation was mostly considered as noise in literature, recentworks show that it is correlated to the main signal and canbe viewed as a composition of multiple delayed or scatteredsignals. Such a phenomenon can provide non-line-of-sight (NLoS)paths in an environment that lacks scatterers, which increasesspatial multiplexing and thus greatly enhances the performanceof MIMO systems. Therefore in this paper, we explore thescattering model and noise models of molecular re-radiation tocharacterize the channel transfer function of the NLoS channelscreated by atmosphere molecules. Our simulation results showthat the re-radiation can increase MIMO capacity up to 3 foldsin mmWave and 6 folds in terahertz for a set of realistic transmitpower, distance, and antenna numbers. We also show that in thehigh SNR, the re-radiation makes the open-loop precoding viable,which is an alternative to beamforming to avoid beam alignmentsensitivity in high mobility applications.
Index Terms —Wireless Networks, Terahertz radiation, THz,Millimeter wave communication, MIMO, Spatial diversity, Ricianchannels, Molecular Absorption, Noise
I. I
NTRODUCTION
The relentless growth of data traffic is presenting significantchallenges for wireless network providers. Fixed WirelessAccess (FWA) connections are expected to increase three folds
Copyright (c) 2020 IEEE. Personal use of this material is permitted.However, permission to use this material for any other purposes must beobtained from the IEEE by sending a request to [email protected] Amir Hoseini (corresponding author) is with the School of Engi-neering and Information Technology (SEIT), University of New South Wales(UNSW) at Canberra, Northcott Drive, Campbell, ACT 2600, Australia. e-mail: [email protected] Ding is with Data61, CSIRO, Eveleigh, NSW 2015, Australia. e-mail:[email protected] Hassan is with the School of Computer Science and Engineering,University of New South Wales (UNSW), Sydney, Australia. E-mail: [email protected] chen is with the College of Physics and Information Engineering,Fuzhou University, China. e-mail: [email protected] work is supported by the Commonwealth Scientific and IndustrialResearch Organization (CSIRO) of Australia and the National Natural ScienceFoundation of China (NSFC Grant No. 61801119). by the end of 2025 while the total mobile data volume willgrow more than fourfold during the same period [1], requiringenormous capacity enhancements in wireless communicationsystems. 5G systems aim to provide a peak data rate of 10Gbps per user [2] while 6G is expected to enhance capacity10–100 times over 5G [3]. In addition to cellular networkcapacity demands, local wireless networks are expected tosupport Tbps data rates [4] to realize super bandwidth-hungryapplications such as wireless virtual reality (VR) [5].The major portion of the wireless communication trafficcurrently uses frequencies below 6 GHz. Unfortunately, thispart of the spectrum is currently highly saturated and willsoon become overloaded. Thus, in spite of the very efficientspectrum use in recent wireless standards, it is becomingnecessary to utilize the higher frequency bands above 6 GHzto realistically accommodate the future traffic growth. In par-ticular, largely unused parts of the spectrum in the range of 30-300 GHz, a.k.a. mmWave band, is currently being consideredfor use in 5G/6G systems [6]. To achieve extremely highbit rates, the terahertz band in the range of 0.1-10 THz isalso being considered by many research groups [7] for short-range applications such as nanoscale sensor networks [8],wireless on-chip communications, and wireless personal areanetworks [9].Unfortunately, such high-frequency bands not only sufferfrom high path loss but also encounter severe frequency-selective molecular absorption, which is not observable insub-6 GHz frequencies. Recent studies have confirmed thatthe molecules in the communication medium can absorbsignificant amounts of wireless signal energy if excited intheir natural resonance frequencies [9–12]. For a normal atmo-sphere, oxygen and water molecules are the major players inmolecular absorption with their natural resonance frequenciesat around 60 GHz, 180 GHz, 320 GHz, and so on. Inter-estingly, according to fundamental physics, the atmosphericmolecules not only absorb the energy from the high-frequencyelectromagnetic waves but they also re-radiate some of theabsorbed energies at the same frequencies shortly after theirabsorption. Although this re-radiation is basically a source ofadditional noise [11, 13] for high-frequency bands, detailedtheoretical and experimental studies have revealed that it ishighly correlated to the main signal [14, 15] and hence can bemodeled as a scattered copy of the original signal [10].The absorption and re-radiation of the electromagnetic waveare not limited to oxygen and water. An experiment hasshown that nitrogen dioxide molecules absorb energy froma terahertz pulse and re-radiate a distorted copy of the pulse a r X i v : . [ c s . N I] F e b shortly after [15]. Molecules of carbon dioxide absorb photonenergy in infrared frequency and shortly re-radiate them in thesame band [12]. In the ultraviolet spectrum, ozone is the pri-mary constituent that absorbs and re-radiates electromagneticwaves [16]. The positive role of the molecular re-radiation,known as molecular scattering, in ultraviolet communication iswidely studied theoretically and experimentally where a prac-tical non-line-of-sight (NLoS) channel is created by moleculesand aerosols [16–18].Therefore, as a preliminary investigation into taking advan-tage of potential NLoS signal reception due to molecular re-radiation, we conduct a theoretical study on the performanceimpacts of the re-radiation behavior of oxygen and water vapormolecules on MIMO systems. In this paper, the molecular re-radiation is analyzed under two different approaches: (1) re-radiation is considered as random noise, or (2) re-radiationis treated as correlated scattering. As widely known, noise isharmful for both single antenna and multi-antenna channels,while scattering is viewed as a very important factor toprovide spatial multiplexing in MIMO. Since the molecularabsorption intensity depends on the resonance frequencies ofthe molecules in the atmosphere, the energy absorption and re-radiation are not flat in the mmWave/terahertz spectrum. Thus,the wireless channel experiences a frequency-selective noise orscattering along with the frequency-selective attenuation [19].Based on the aforementioned interpretation of molecularre-radiation, we propose the conjecture that the MIMO per-formance in the mmWave and terahertz bands would also befrequency-selective. We verify our conjecture via theoreticalstudies and computer simulations, which show that the MIMOcapacity increases dramatically in specific high-absorption fre-quency windows thanks to the ubiquitous existence of oxygenand water molecules. The intuition of our theoretical study isthat the channel molecules can radiate a distorted copy of thesignal with an additional random phase, which equivalentlycreates a richer scattering environment and consequently thepotential to improve the line-of-sight (LoS) MIMO capacity.Our discovery can fundamentally change our understand-ing of the relationship between the MIMO capacity andthe frequency spectrum. While the literature has extensivelystudied frequency selectivity of mmWave/terahertz commu-nications [20–23], our study provides a new perspective offrequency selectivity in the context of MIMO performancein these emerging spectrum bands. Importantly, our resultsreveal that several mmWave and terahertz frequency windowscan serve as valuable spectrum for high-efficiency MIMOcommunications, which may in turn shift the paradigm ofresearch, standardization, and implementation in the field ofhigh-frequency communications. In the future, it may be evenpossible to engineer mechanics at the transmitter/receiver sideto change the vapor and/or oxygen densities in the medium,which would in turn proactively change the mmWave/terahertzchannel environment to boost system capacity.We have published parts of the results in our previouspapers [24–26]. In [24], we simulated a simple MIMO systemin the mmWave band and showed the impact of re-radiationon the performance of the multiplexing technique. In thesecond step [25], we compared beamforming and multiplexing techniques in a massive MIMO system in the terahertz band.The main contributions of this paper can be summarized asfollows: • We analyze the theoretical upper bound and lower boundof MIMO capacity under the scattering model of molec-ular re-radiation. • For the scattering model of re-radiation, we re-define theRician K-factor with the absorption coefficient. • We investigate the extended multiplexing technique withthe optimal precoding matrix and power allocationscheme which owns beamforming and multiplexing bene-fits together. We show it can outperform the beamformingtechnique in the presence of molecular re-radiation.The rest of the paper is structured as follows. In Section II,a brief literature review is presented. In Section III, wefirstly present the molecular absorption model, and then thefundamental theory of MIMO capacity is reviewed. Section IVanalyzes MIMO capacity versus the molecular re-radiation,followed by simulation results and insightful discussions inSection V. The conclusion is presented in Section VI and thefuture research directions are discussed in Section VII.II. R
ELATED W ORK
Molecular absorption and re-radiation are well-known phe-nomena, which have been studied extensively in the literaturefor mmWave and Terahertz bands [13, 14, 27–29]. The ma-jority of these works have considered the re-radiated energyas a form of random noise. The molecular absorption noisehas been studied in the literature as early as 1986 when theauthors in [13] proposed a model for the sky atmosphericnoise for frequencies higher than 18GHz. However, theymostly investigated the sky noise where the magnitude is notinfluenced by the amplitude of the transmitted signal. Thistype of molecular noise has been referred to as brightnessnoise in ITU recommendation [30] where it is modeled asantenna noise. Moreover, in [13, 14, 31], it has been assumedthat the intensity of the transmitted power affects the molecularnoise, which is known as self-induced noise. Authors in [14]have proposed that the self-induced noise should be correlatedto the original signal, and modeled it as scattering frommultiple virtual NLoS paths [10]. However, the proposedmodel in [10] only characterized the power delay profile ofthe channel and did not include the phase information of re-radiated waves. Furthermore, authors in [10] have presenteda comprehensive discussion on alternative interpretations ofmolecular re-radiation as noise or scattering.An interesting experimental study has shown that themedium molecules can absorb and re-radiate a subpicosecondterahertz pulse [15]. More specifically, the authors have excitedN O molecules in a relatively short channel with a terahertzpulse and observed that a train of subpicosecond pulses wasre-radiated by channel molecules. The relative amplitude ofthe first re-radiated pulse was measured as one tenth of theexcitation pulse.Several studies have investigated the effect of atmosphericconditions on the mmWave channel [19, 32–35]. In particular,it was found that heavy rainfall would severely attenuate mmWave communications [36]. The rainfall was modeled andevaluated in [35] where the authors found that mild rainfallcould in fact have a positive effect on MIMO performance asthe raindrops were found to act as scatterers and improve theMIMO multiplexing gain. Interestingly, they also found thatwith increasing rain, the attenuation dominates the scatteringeffects of the raindrops, which results in capacity degradationunder heavy rain.In [16–18], authors have discussed the possibility of NLoScommunication in the Ultra-Violate (UV) spectrum thanks totropospheric molecular and aerosols scattering. In the UVspectrum, ozone is the primary constituent that absorbs andscatters the electromagnetic wave. All these works have con-ducted numerical and experimental analysis to show that theNLoS scattering by air can be an alternative to LoS commu-nication where UV LoS channel is vulnerable to blockage andshadowing. However, to the best of our knowledge, there isno previous work on studying the impact of the molecularabsorption and re-radiation on the MIMO capacity.III. C
HANNEL M ODEL AND
MIMO C
APACITY
In this section, we present the channel model that considersthe effect of molecular absorption and re-radiation on theelectromagnetic waves propagating through the channel. Later,MIMO capacity is analyzed for such channels.
A. Molecular Absorption Coefficient
The absorption of a given molecule is characterized byabsorption coefficient k i ( f ) at frequency f , which varies withpressure and temperature of the environment. The molecularabsorption coefficients of many chemical species for differentpressure and temperature are available from the publicly acces-sible databases such as HITRAN [37] and
NIST Atomic Spec-tra [38]. To model molecular absorption of a communicationchannel, let us assume that the wireless channel is a mediumconsisting of N chemical species where m , m , ..., m N arethe mole fraction per volume of spices. The medium ab-sorption coefficient , i.e., k ( f ) , at frequency f is, therefore,a weighted sum of the molecular absorption coefficients inthe medium [11], which can be formulated as k ( f ) = N (cid:88) i =1 m i k i ( f ) , (1)where k i ( f ) is the molecular absorption coefficient of species i . It should be noted that climate conditions, such assummer versus winter, or even the weather changes dur-ing the day would affect the absorption coefficients in themmWave/terahertz band [19]. In this work, we extract k i ( f ) from HITRAN [37] for some predefined standard atmosphericconditions as shown in Table II. B. Attenuation of Radio Signal
The attenuation of the electromagnetic signal at themmWave/terahertz frequencies is due to free space path loss(FSPL) and molecular absorption [39]. The total attenuation at frequency f at a distance of d from the radio transmittercan be written as A ( f, d ) = A FSPL ( f, d ) × A a ( f, d ) , (2)where A FSPL ( f, d ) and A a ( f, d ) denote the attenuation due toFSPL and molecular absorption, respectively. In more detail,the FSPL attenuation is given by A FSPL ( f, d ) = (cid:18) πf dc (cid:19) , (3)where c is the speed of light. The attenuation due to molecularabsorption is characterized as [39] A a ( f, d ) = e k ( f ) × d , (4)where k ( f ) is the absorption coefficient of the medium atfrequency f . Thus, the received power for LoS path is obtainedas P r , LoS ( f, d ) = P t ( f ) A ( f, d )= P t ( f ) × (cid:18) c πf d (cid:19) × e − k ( f ) × d . (5) C. Molecular Re-radiation
The absorbed energy excites the channel molecules byincreasing their vibrational-rotational energy levels [12]. Theexcitement is temporary and the vibrational-rotational energyreturns to a steady state where the absorbed energy is re-radiated in the same frequency. In the literature, the re-radiatedenergy is commonly assumed as an additional source of noise,often referred to as the molecular noise [9]. As differentmolecule species exhibit different resonance frequencies, thepower spectral density of the molecular noise, N a , is not flatover its spectrum. Generally speaking, both the atmosphericnoise, N atm , and the self-induced noise, N si , contribute to themolecular noise as investigated in [11, 13]: N a ( f, d ) = N atm ( f, d ) + N si ( f, d ) , (6) N atm ( f, d ) = lim d →∞ ( k B T (1 − e − k ( f ) d )) (cid:16) c √ πf (cid:17) , (7) N si ( f, d ) = P t ( f )(1 − e − k ( f ) d ) (cid:16) c πf d (cid:17) , (8)where T is the reference temperature ( K ) , k B is theBoltzmann constant, P t ( f ) is the power spectral density of thetransmitted signal and c is the speed of light. The first termin (6), which is also called sky noise (7), is independent ofthe signal wave. However, the self-induced noise (8) is highlycorrelated with the signal wave [14], and can be considered asa distorted copy of the signal wave. Thus, the received powerof the signal re-radiated by the molecules can be expressed asfollows: P r , a ( f, d ) = P t ( f )(1 − e − k ( f ) d ) (cid:16) c πf d (cid:17) . (9)Since the phase of the re-radiated wave depends on thephase of molecular vibration, which varies from moleculesto molecules [40], the received power is actually affected by alarge number of phase-independent re-radiated photons. Thus,the phase for the received signal, β , is assumed to be uniformlydistributed in the range [0 , π ) , with its power given by (9). D. Channel Transfer Function
The channel transfer function of an LoS channel is givenby h LoS ( f, d ) = (cid:115)(cid:18) c πf d (cid:19) e − k ( f ) × d × e j π dλ = (cid:18) c πf d (cid:19) e − k ( f ) × d × e j π dλ . (10)Then, the partial channel transfer function resulting fromthe molecular absorption and excluding the LoS componentcan be represented by h a ( f, d ) = (cid:115) (1 − e − k ( f ) d ) (cid:16) c πf d (cid:17) × e j πβ = (1 − e − k ( f ) d ) (cid:16) c πf d (cid:17) × e j πβ . (11)Hence, the total channel transfer function is the superposi-tion of the partial channel transfer functions, which is writtenas h ( f, d ) = h LoS ( f, d ) + h a ( f, d )= (cid:18) c πf d (cid:19) e − k ( f ) × d × e j π dλ +(1 − e − k ( f ) d ) (cid:16) c πf d (cid:17) × e j πβ . (12) E. MIMO Channel Model and Capacity
In this work, a point to point wireless communicationssystem is considered with multiple antennas where the numberof antennas at the receiver and transmitter equals to n r and n t ,respectively. A generic wireless channel is considered wherethe up-link and down-link directions are outside the scopeof the study. The received signal vector y at n r receivingantennas can be formulated as [41] y = Hx + n , (13)where x is the transmitted signal vector form n t transmittingantennas, and n is an n r × vector with zero-mean indepen-dent noises with variance σ . The channel matrix H is definedby H (cid:44) h h . . . h n t h h . . . h n t ... ... . . . ... h n r h n r . . . h n r n t , (14)where h ij is a complex value denoting the transfer coefficientbetween the i th receiving antenna and the j th transmittingantenna. Note that h ij can be obtained from (12) for frequency f and distance d ij . The channel coefficients of a MIMOsystem consisting of antennas at both the transmitter andthe receiver is presented in Fig. 1.For a MIMO system with equally distributed power amongthe transmitting antennas, the capacity can be written as C = log det( I n r + Pn t σ HH † ) , (15)where P is the total transmit power, H † is the Hermitiantranspose of H and I is the identity matrix [41]. Fig. 1: A 3x3 MIMO system, the channel transfer coefficient h ij of each antenna pair between transmitters and receivers isshown.The singular value decomposition (SVD) of the channeltransfer matrix H can be given by: H = UΣV † , (16)where U and V , respectively, are n r × n r and n t × n t unitarymatrices, Σ is a rectangular diagonal n r × n t matrix and V † isthe Hermitian transpose of V . The non-negative real diagonalelements of matrix Σ , λ ≥ λ ≥ ... ≥ λ m , are the orderedsingular values of matrix H . Hence, the squared singularvalues λ i denote the eigenvalues of the matrix HH † . TheSVD decomposition describes an equivalent MIMO systemwith parallel independent channels where i th channel is avirtual single-input-single-output (SISO) with a gain λ i andthe allocated power P i . Therefore, the capacity of the MIMOsystem is equal to the cumulative capacity of the independentSISO channels [42] C = m (cid:88) i =1 log (1 + P i λ i σ ) , (17)where m is the number of non-zero λ i , m ≤ min( n r , n t ) ,which is also called the rank of H . P i λ i σ is the associatedreceived signal-to-noise ratio (SNR) to each SISO channel.Furthermore, the SNR of the equivalent channel should meeta minimum threshold to be reliably detectable by the receiver.In this paper, we assume 0 dB as the SNR threshold. F. SVD-Based Precoding
Precoding technology assigns different precoder weights toindependent data streams transmitted by multiple antennas,aiming to enhance the transmission rate or the transmissionreliability by exploiting the spatial dimension [43]. We assumethat the transmitter has z independent data streams to transmitsimultaneously, denoted by s = [ s , ..., s z ] T , z ≤ min( n r , n t ) .With the linear precoding scheme, a precoding matrix W isused to generate the precoded signal vector x , x = Ws . (18)We assume the precoder matrix is orthonormal i.e., W † W = I z [43].The optimal linear precoder in term of capacity can beobtained by choosing W = V z Q , where the V z is an n t × z matrix constructed by the first z columns of V in (16) and Q is a diagonal matrix for power allocation [43, 44]. If P is thetotal power constraint, Q = diag { (cid:112) P i , ..., (cid:112) P z } , where (cid:32) z (cid:88) i =1 P i (cid:33) ≤ P. (19)
1) Optimal Beamforming:
In the absence of multipathchannel, a single stream beamforming (BF) is used to focusenergy in one direction and improve the SNR. In this approach,the same copy of data is sent to all transmitter antennas to forma directional beam and exploit the high single power gain [45].Therefore, z = 1 and the optimal precoder vector is W = √ P V , (20)where V is the first column of V [46]. This technique alsois known as Closed-loop rank-1 precoding and is optimal forthe LoS channel where the rank of the channel transfer matrixis one [45].
2) Closed-Loop Spatial Multiplexing:
As mentioned above,multiplexing aims to exploit spatial multiplexing to increasechannel throughput. Hence, it is optimal when exploiting allthe parallel sub-channels to maximize the channel capacity.But the number of parallel channels depends on the channelrank, the so-called degree-of-freedom, i.e., the number ofnon-zero singular values in Σ . The channel is full rank ifthe channel matrix H is sufficiently random. In presenceof Channel State Information (CSI) at the transmitter, theoptimal multiplexing is to send an independent data streamon each sub-channel which is known as Closed-Loop SpatialMultiplexing . In other words, if we consider a full rankchannel, z = min( n r , n t ) and W = VQ . (21)The optimal power allocation Q can be obtained by thewater-filling scheme. In this way, the equivalent virtual SISOchannel with a larger channel gain, λ i , will be allocated witha larger transmit power, P i . That is, P i = (cid:18) µ − σ λ i (cid:19) , (22)where µ is chosen to satisfy the overall power constraint.Hence, the transmitter needs to know all the elements of thematrices V and Σ for precoding and adopting the water-filling.Note that for a pure LoS channel with rank 1, there is onlyone independent sub-channel. Therefore, both multiplexingand beamforming use the precoding matrix, W = √ P V ,which results in the same capacity.
3) Open-Loop Spatial Multiplexing:
When the channelinformation is unknown, an Open-loop spatial multiplexingscheme can be used to maximize the spatial multiplexingcapacity [44, 45], where the equal power allocation and theidentity matrix, I n t , are used to adapt the precoding matrix.That is, W = √ P I n t . (23)Also, due to the unknown channel information, data can bedecoded using maximum-ratio combining (MRC) method [42].IV. MIMO C APACITY WITH M OLECULAR R E - RADIATION M ODELED AS S CATTERING
In this section, we analyze MIMO capacity when molecularre-radiation is assumed to be scattering. To quantitativelycharacterize the scattering richness of the channel, we firstlydecompose and normalize the channel transfer function, H , as ˆ H ( f, d ) = (cid:114) KK + 1 ˆ H LoS ( f, d ) + (cid:114) K + 1 ˆ H a ( f, d ) , (24)where ˆ H , ˆ H LoS and ˆ H a are normalized matrices of H , H LoS and H a , respectively. Because of the uniformly distributedrandom phase of the large number of re-radiated signals, theelements of ˆ H a are approximately independent and identicallydistributed (i.i.d) complex Gaussian random variables [47]with zero mean and unit magnitude variance. Denoted by K , the ratio of powers of the LoS signal and the re-radiatedcomponents under the assumption that the channel distance ismuch larger than the antenna array size, can be obtained by K = P r , LoS ( f, d ) P r , a ( f, d ) = e − k ( f ) d − e − k ( f ) d . (25)This is also known as the Rician K-factor in Rician fadingmodel. Equivalently, K-factor represents the channel richnessin terms of scattering and multipath rays. Equation (25)shows that K is a decreasing function of both the absorptioncoefficient k ( f ) and the distance between the transmitter andreceiver d . Fig. 2 illustrates how K-factor changes with theabsorption coefficient in the atmosphere for a distance of 1-100m. The MIMO capacity in relation to the Rician K-factorhas been well studied in the literature [48], [49] and [50].Obtaining a closed-form expression of the MIMO capacityas a function of k ( f ) is very complicated. Hence, we statethe lower and upper bounds of the expected capacity of theMIMO channel as a function of k ( f ) in two lemmas. Lowerbound expression is stated as Lemma 1 based on [50] whereauthors showed the lower bound of the expected capacity ofa Rician channel. Lemma 1.
When the transmitter does not have CSI and the power is allocated equally to all transmitter antennas, the capacitylower bound of a Rician channel is the capacity contributed by the NLoS component: E ( C ( ˆ H ) , ρ ) ≥ E ( C ( ˆ H a ) , (cid:114) K + 1 ρ ) , (26) = ⇒ E ( C ( ˆ H ) , ρ ) ≥ E ( C ( ˆ H a ) , (cid:112) − e − k ( f ) d ρ ) , (27) where E ( . ) denotes the expectation, ρ is the received SNR for equivalent single channel and E ( C ( ˆ H , ρ ) is the average capacityof a channel with normalized channel transfer matrix ˆ H and a reception SNR ρ . It is clear that the lower bound is an increasingfunction of the absorption coefficient.Proof. See [50].On the other hand, the capacity upper bound of a Rician MIMO channel with perfect CSI at receiver and transmitter wherethe power is optimally distributed among antennas with a water-filling algorithm is also presented in [48]: E ( C ( ˆ H ) , ρ ) ≤ log (cid:32) n r (1 + n t K ) K + 1 (cid:16) min (cid:26) ρn t , K (1 + K ) n r (1 + n t K ) (cid:27) n t + (cid:20) ρn t − K (1 + K ) n r (1 + n t K ) (cid:21) + (cid:17)(cid:33) +( n t − (cid:32) n r K (cid:20) ρn t − K (1 + K ) n r (1 + n t K ) (cid:21) + (cid:33) , (28)where [ x ] + = max( x, .To obtain a simpler expression, let us consider a specific scenario where n r = n t = n : Lemma 2.
When there is perfect CSI at receiver and transmitter and the power is allocated optimally to transmitter antennas,the capacity upper bound of a Rician channel is E ( C ( ˆ H ) , ρ ) ≤ log n − e − k ( f ) d ) (cid:16) min ρ, e − k ( f ) d − e − k ( f ) d (1 + ( n − e − k ( f ) d ) n + ρ − e − k ( f ) d − e − k ( f ) d (1 + ( n − e − k ( f ) d ) + (cid:17) + ( n − − e − k ( f ) d ) ρ, e − k ( f ) d − e − k ( f ) d (1 + ( n − e − k ( f ) d ) + . (29) Proof.
See [48].Fig. 2: Rician K-factor varies with the absorption coefficientand distance.We can see two extreme cases: the low absorption k ( f ) = 0 and the high absorption k ( f ) = ∞ . Hence, the capacity of aRician channel for MIMO will limit to lim k ( f ) →∞ C = n log(1 + ρ ) , (30) lim k ( f ) → C = log(1 + n ρ ) . (31)Note that from (25), k ( f ) = ∞ means an extremely highre-radiation channel, which provides a pure Rayleigh channel.In contrast, k ( f ) = 0 implies no re-radiation, i.e., a pure LoSchannel. V. S IMULATION
In this section, simulation results of MIMO in the presenceof molecular absorption and re-radiation are presented.
A. Simulation Set-up -0.01-0.008-0.006-0.0040.01-0.00200.0020.0040.0060.0080.01 0.005 0 0.12-0.005 0.10.080.060.040.02-0.01 0-0.02 s s d
Fig. 3: Illustration of a MIMO system with uniform squarearrays.To evaluate the performance impact of the molecular ab-sorption on the MIMO capacity in the mmWave/terahertzband, we consider an n × n MIMO system with two squareuniform arrays as illustrated in Fig. 3. The inter-elementspacing, s , is equal to half of the wavelength while the channeldistance, d , represents the distance between the transmitter and TABLE I: Simulation parameters
Transmitter and receiver distance ( d ) ∼ mInter-element spacing ( s ) . λ (wave length)Transmitter array angle randomReceiver array angle randomNumber of antennas on each side ( n ) in mmWave, in terahertzSNR (in fixed SNR configurations) , dBNon-molecular noise − dBmTransmit power mW in mmWave and mW, mW in terahertz -5 Absorption Coefficient (m -1 )0100200300400 C apa c i t y ( bp s / H z ) SNR = 15dB, d = 15m
Analytical upper boundSimulation - CL-MPSimulation - OL-MPAnalytical lower bound -5 Absorption Coefficient (m -1 )050100150 C apa c i t y ( bp s / H z ) SNR = 5dB, d = 50m
Analytical upper boundSimulation - CL-MPSimulation - OL-MPAnalytical lower bound -5 Absorption Coefficient (m -1 )0100200300400 C apa c i t y ( bp s / H z ) SNR = 15dB, d = 50m
Analytical upper boundSimulation - CL-MPSimulation - OL-MPAnalytical lower bound -5 Absorption Coefficient (m -1 )050100150 C apa c i t y ( bp s / H z ) SNR = 5dB, d = 15m
Analytical upper boundSimulation - CL-MPSimulation - OL-MPAnalytical lower bound
Fig. 4: Analytical bounds and simulation results of 64x64MIMO capacity versus absorption coefficient for differentSNR and distance. The re-radiation is assumed as scattering.the receiver. All simulations parameters are defined in Table I.Some of these parameter values are varied to achieve a morecomprehensive evaluation of the MIMO system under differentconditions. Given that molecular re-radiation produces randomphases, a large number (5000) of test cases are evaluated andaveraged to obtain the result for each parameter value.The absorption coefficients are obtained from HITRAN [37]for some predefined standard gas mixtures of the atmosphere atsea level, which is accessible online . The related informationof the predefined gas mixtures is shown in Table II. Recallthat the oxygen and water molecules are the main absorp-tion players in the normal atmosphere at mmWave/terahertzbands [19]. While the oxygen ratio is invariant, the amountof water molecules in the air is variable. We use the highestand lowest water ratio in Table II, i.e., the ”USA model, highlatitude, winter” and ”USA model, tropics” . The correspond-ing absorption coefficients are shown in Fig. 6 and Fig. 11afor the mmWave and terahertz band, respectively, which arecalculated using the ambient temperature of K and the sealevel pressure of atm. B. Impact of Absorption Coefficient on MIMO Capacity
In this subsection, MIMO performance is evaluated with there-radiation modeled as scattering. A 64x64 MIMO system at60 GHz is investigated with a realistic absorption coefficient http://hitran.iao.ru/gasmixture/simlaunch N u m be r o f s i ngu l a r v l aue s K = 130 dB, k(f) = 1e-7 m -1 , d= 20m N u m be r o f s i ngu l a r v l aue s K = 15 db, k(f) = 1e-3 m -1 , d= 20m N u m be r o f s i ngu l a r v l aue s K = 0 dB, k(f) = 0.03 m -1 , d= 20m N u m be r o f s i ngu l a r v l aue s K = -200 dB, k(f) = 1 m -1 , d= 20m Fig. 5: Empirical distribution of singular values of matrix H √ n for different K-factor. For K → −∞ dB, it converges to thequarter circle law.range between 10 -5 ∼ +3 . The uniform and the water-fillingpower allocations are plotted and labeled in Fig. 4 as OL-MP and
CL-MP , respectively.From Fig. 4, it can be observed that the capacity of MIMOlies between the theoretical bounds, which verifies the lemmasproposed in Section IV. An interesting observation is that theMIMO capacity increases with higher absorption coefficients.For example, under 5 dB SNR, we obtain a capacity ofonly 9.5 bps/Hz when the absorption is very low, i.e., theMIMO experiences a pure LoS channel. In contrast, we obtain100 bps/Hz with uniform power allocation and 130 bps/Hzwith water-filling when the absorption coefficient is high. Thisresult indicates that improved MIMO capacity can be expectedfor frequency windows where the absorption coefficient ofthe channel peaks. Finally, we notice that the capacity curveagainst the absorption coefficient starts to increase sooner forlarger distances, which can be explained by the fact that aphysically longer channel would contain more molecules tocreate more intense scattering. This phenomenon can also beseen in Fig. 2, where a longer distance results in a smaller Ri-cian K-factor. However, a longer transmission distance wouldalso lead to a larger path loss, which would eventually have anegative effect on MIMO capacity for the long-distance com-munications. The impact of distance on the MIMO capacitywill be evaluated in more detail in Section V-C.From the other perspective, the re-radiation changes thechannel transfer matrix from a deterministic one to a random
TABLE II: Atmosphere standard gas mixture ratio in percentage for different climates at sea level [37]
USA model: H2O CO2 O3 N2O CO CH4 O2 N2mean latitude, summer 1.860000 0.033000 0.000003 0.000032 0.000015 0.000170 20.900001 77.206000mean latitude, winter 0.432000 0.033000 0.000003 0.000032 0.000015 0.000170 20.900001 78.634779high latitude, summer 1.190000 0.033000 0.000002 0.000031 0.000015 0.000170 20.900001 77.876781high latitude, winter 0.141000 0.033000 0.000002 0.000032 0.000015 0.000170 20.900001 78.925780tropics 2.590000 0.033000 0.000003 0.000032 0.000015 0.000170 20.900001 76.476779 -6 -5 -4 -3 -2 -1 A b s o r p t i on c oe ff i c i en t ( m - ) USA model, high latitude, winterUSA model, tropics
Fig. 6: Absorption curves in different climates(temperature= K , pressure= atm ). Absorption peaksare exhibited at resonance frequencies of oxygen and watermolecules.matrix. When the channel matrix is deterministic, it has a degree-of-freedom equal to one where the first singular valueis significant and the others are almost zero. The molecular re-radiation changes the singular value distribution of the channelmatrix. We show the empirical distribution of singular valuewith various absorption coefficient in Fig. 5. It can be seenthat the distribution converges to the well-known quarter-circlelaw, [51], with a large absorption coefficient. C. Impact of Absorption Coefficient on MIMO Channel Char-acteristics
In Fig. 6, the channel absorption coefficient against fre-quency is plotted for the mmWave band for high latitudewinter and tropic atmosphere. It is observed that the ab-sorption peaks at 60 GHz and 120 GHz, which are the res-onance frequencies of oxygen molecules. Absorption alsopeaks at 180 GHz, which is the resonance frequency of watermolecules. For the two climates, the significant difference inthe absorption coefficient at 180 GHz is due to the significantdifference in their water contents in the atmosphere. This resultclearly shows that the oxygen and water resonance frequenciesare the main frequencies in the high-frequency bands wherewe can expect high absorption and re-radiation.Next, we investigate the impact of the absorption peaks onMIMO channel characteristics. In particular, we are interestedto observe how the channel rank, K-factor and conditionnumber are affected by absorption peaks.For a 64x64 MIMO, Fig. 7 plots the channel rank, K-factorand condition number over the mmWave band for high latitudewinter (low water content) and tropic atmosphere (high watercontent). We know that the physical MIMO channel can bemodeled with m equivalent parallel channels with gains givenby the singular values λ i where m = min( n r , n t ) and i = , ,..., m . The channel rank is defined by the number of equivalent R an k ( H ) WinterTropic (a) Channel rank K - f a c t o r ( d B ) TropicWinter (b) K-factor
50 100 150 200 250 300Frequency (GHz)02468101214 C ond i t i on nu m be r tropicwinter (c) Condition number Fig. 7: Channel characteristics of a 64x64 MIMO channel overmmWave band. Channel rank, K-factor and condition numberare affected by absorption peaks at 60, 120 and 180 GHz.channels that provide decent SNRs greater than a threshold,which is assumed here as the receiver sensitivity of dB.Fig. 7a shows that the channel rank peaks at absorption peaks.However, the absorption is not high enough in the mmWaveband to yield a full rank channel (rank is still below 64).Fig. 7b shows that the K-factor of the mmWave band drops atabsorption peaks, which indicates that there are stronger multi-path signal components resulting from stronger molecular re-radiation at those peaks. For example, we see that the K-factoris about 10 dB at 180 GHz for the tropic atmosphere, whichindicates that the received signal power from the NLoS is asstrong as that received from the LoS. Finally, we find (seeFig. 7c) that the condition numbers at 60 GHz and 180 GHz C apa c i t y ( bp s / H z ) Tropic, Re-radiation as scatteringTropic - Re-radiation as noiseWinter, Re-radiation as scatteringWinter - Re-radiation as noise (a) Constant transmit power = 500 mW C apa c i t y ( bp s / H z ) Tropic, Re-radiation as scatteringTropic, SISOWinter, Re-radiation as scattering (b) Constant SNR = 15 dB
Fig. 8: 64x64 MIMO capacity for different atmospheres overmmWave band using CL-MP and SISO. Communication dis-tance is 10 m.decrease to almost 1, which indicates that the distribution ofthe eigenvalues is significantly improved at those peaks.
D. MIMO Capacity vs. Re-radiation as Noise/Scattering
The purpose of the evaluations in this subsection is tocompare MIMO capacity for two different situations: (1)when re-radiation is considered as noise versus (2) when it isconsidered as a scattered signal. Fig. 8a compares the capacityof 64x64 MIMO channel in the mmWave band when the re-radiation is assumed as noise versus scattering. The transmitpower is constant over the entire band. As one can observe,the capacity, when the re-radiation is considered as noise, isalmost flat over the entire mmWave band for both tropic andwinter atmospheres and just a very small decrease can be seenin high absorption frequencies which is due to both molecularattenuation and noise. In more details, the molecular noise isdominated by thermal noise and it can be seen the capacityis not frequency selective, which corroborates the commonunderstanding up to now.In Fig. 8b, the received SNR is assumed to be a constantvalue of 15 dB for the entire mmWave band to investigatethe effect of absorption intensity in an equal SNR condition.It can be seen that, when the re-radiation is considered as ascattered copy of the signal, results show a significant capacityincrease in particular frequencies. For example, the capacityis improved by around 150 % at 60 GHz for both tropic andwinter atmospheres. Moreover, more water molecules exist inthe tropic atmosphere which leads to a considerable capacityboost at 180 GHz in the tropic atmosphere in comparison withthose of the winter atmosphere. Note that the oxygen abortionat 120 GHz is not strong enough to affect the channel. C apa c i t y ( bp s / H z ) BF - rx/tx CSIOL-MPCL-MP - rx/tx CSISISO (a) distance = 5 m C apa c i t y ( bp s / H z ) BF - rx/tx CSIOL-MPCL-MP - rx/tx CSISISO (b) distance = 20 m C apa c i t y ( bp s / H z ) BF - rx/tx CSIOL-MPCL-MP - rx/tx CSISISO (c) distance = 35 m C apa c i t y ( bp s / H z ) BF - rx/tx CSIOL-MPCL-MP - rx/tx CSISISO (d) distance = 50 m
Fig. 9: 64x64 MIMO channel performance over mmWaveband for different precoding techniques. The transmit poweris 150 mW.Numerically speaking, we can calculate the capacity of aSISO channel, which turns out to be 5 bps/Hz. Accordingto the existing MIMO theory, for a full-rank 64x64 MIMOchannel with enough spatial multiplexing gain, the theoreticalcapacity will be expected to be × (cid:39) bps/Hz.As discussed before, the LoS MIMO channel suffers frompoor spatial multiplexing gain and can achieve the maximumcapacity only with some specific geometry configuration [52],which is not feasible for mobile communications. Thus, it canbe seen that MIMO capacity, when re-radiation is assumed C apa c i t y ( bp s / H z ) OL-MP - 60 GHzCL-MP rx/tx CSI - 60 GHzBF rx/tx CSI - 60 GHzOL-MP - 50 GHzCL-MP rx/tx CSI - 60 GHzBF rx/tx CSI - 50 GHz
Fig. 10: MIMO capacity using different techniques over com-munication distance. Total transmit power is 150 mW There-radiation is assumed as scattering.as noise, is close to that of a SISO channel. However, if themolecular re-radiation is taken into account as scattering, itcan equivalently create a rich scattering environment, and inturn, increase the spatial multiplexing gain.In summary, the mmWave MIMO system can take advan-tage of the molecular re-radiation to generate more capacityif the re-radiation can be exploited as NLoS signal, whichprevails the absorption attenuation.
E. Impact of MIMO Techniques in mmWave
In Fig. 9, we compare the beamforming and multiplexingperformance over the mmWave spectrum, when re-radiation isconsidered as scattering. Four different schemes are involved:optimal beamforming (BF), Closed-Loop multiplexing withwater-filling power allocation (CL-MP), and Open-Loop mul-tiplexing with uniform power allocation (OL-MP).It is observed that the Closed-Loop multiplexing techniqueresults in a notably higher capacity than beamforming at highabsorption frequency windows. This is because re-radiationacts as scattering and increases the multiplexing gain.Besides, we can see that the performance of Open-Loopmultiplexing is also affected by the absorption. Hence, wecan see that at 60 GHz and 180 GHz with a distance of 5 m,OL-MP outperforms the beamforming scheme. However, thisupper hand is not observed for the larger distance whenuniform power allocation is not efficient because of the lowSNR. Furthermore, a slight dip can be observed at 180 GHzin Fig. 9c, which shows that on the other hand, the molecularabsorption weakens the LoS signal.In Fig. 10, we present the performance impact of transmis-sion distance at 50 GHz and 60 GHz, i.e., the low absorptionspectrum vs. the high absorption spectrum. Eq. (25) showsthat the longer distance results in more scattering due to moremolecules in the channel, but a large path loss mitigates theadvantage of scattering. Therefore, at 60 GHz, it can be seenthat although OL-MP outperforms beamforming in a short-distance channel, it loses its superiority when the distanceis large. It can be explained as a consequence of allocatinguniform power to all equivalent channels which mostly cannotmeet the SNR threshold at a larger distance. Also, it can beobserved that there is not such a quick decrease at 50 GHzsince there is not much advantage of absorption in thisfrequency.
300 500 700 1000 1500 2000 3000
Frequency (GHz) -5 -4 -3 -2 -1 A b s o r p t i on C oe ff i c i en t ( m - ) US Model tropic - High H OUS Model High latitude winter - low H O (a) absorption coefficient, temperature= K , pressure= atm .(b) Signal Attenuation in tropic atmosphere. Fig. 11: Molecular absorption in terahertz band.
F. MIMO Performance in the terahertz band
In this section, we extend our investigation to the terahertzband. The channel is simulated with different transmit powerand distances. In the terahertz band, due to very high prop-agation loss, the applications are limited to short-range com-munications. Our assumption on the transmit power is basedon current technology [9] and a previous work on terahertzmassive MIMO [53]. Moreover, several channel distances areselected to cover various nominated terahertz applications. Forexample, terahertz nano-sensors are supposed to communicatein a very short distance in the order of 0.1-10 cm or less,while terahertz communications are also nominated to provideterabit per second ultra-high-speed video communication linkat around 1 m distance for home entrainment devices likeTV or virtual reality (VR) [54]. Terahertz application is alsoextended to wireless personal or local networks where thechannel distance is up to a few meters. Since the applicationof MIMO in nano-sensors communication is rare, we limit thesimulation to distances 1 and 10 m.In the terahertz band, the dominant absorption source in
500 700 1000 1500 2000 3000
Frequency (GHz) C a p ac i t y ( bp s / H z ) BF - Re-radiation as scattering - rx/tx CSIBF - Re-radiation as noise - rx/tx CSIOL-MP - Re-radiation as scatteringOL-MP - Re-radiation as noiseCL-MP - Re-radiation as scattering - rx/tx CSICL-MP - Re-radiation as noise - rx/tx CSISISO - Re-radiation as noise (a) distance = 1 m, transmit power = 1 mW
300 500 700 1000 1500 2000 3000
Frequency (GHz) C a p ac i t y ( bp s / H z ) BF - Re-radiation as scattering - rx/tx CSIBF - Re-radiation as noise - rx/tx CSIOL-MP - Re-radiation as scatteringOL-MP - Re-radiation as noiseCL-MP - Re-radiation as scattering - rx/tx CSICL-MP - Re-radiation as noise - rx/tx CSISISO - Re-radiation as noise (b) distance = 1 m, transmit power = 10 mW
300 500 700 1000 1500 2000 3000
Frequency (GHz) C a p ac i t y ( bp s / H z ) BF - Re-radiation as scattering - rx/tx CSIBF - Re-radiation as noise - rx/tx CSIOL-MP - Re-radiation as scatteringOL-MP - Re-radiation as noiseCL-MP - Re-radiation as scattering - rx/tx CSICL-MP - Re-radiation as noise - rx/tx CSISISO - Re-radiation as noise (c) distance = 10 m, transmit power = 1 mW
300 500 700 1000 1500 2000
Frequency (GHz) C a p ac i t y ( bp s / H z ) BF - Re-radiation as scattering - rx/tx CSIBF - Re-radiation as noise - rx/tx CSIOL-MP - Re-radiation as scatteringOL-MP - Re-radiation as noiseCL-MP - Re-radiation as scattering - rx/tx CSICL-MP - Re-radiation as noise - rx/tx CSISISO - Re-radiation as noise (d) distance = 10 m, transmit power = 10 mW
Fig. 12: 225x225 MIMO channel performance over terahertz band for various precoding techniques.the air is water molecules. We can see in Fig. 11a that allabsorption peaks in the tropic atmosphere are higher than thewinter atmosphere. The main difference is the mole ratio ofvapor molecules in the air. The channel attenuation includingmolecular attenuation in (4) and FSPL attenuation in (3)is illustrated in Fig. 11b. While the FSPL attenuation isincreasing linearly (in dB) over distance and frequency, themolecular attenuation is also increasing with distance but it isfrequency selective.Fig. 12a and 12b illustrate the capacity of the MIMO tech-niques with a 1 m distance. The transmit power is increasedfrom 1 mW in Fig. 12a to 10 mW in Fig. 12b. Similar tommWave when molecular re-radiation is considered as noise,molecular attenuation and noise lead to a lower capacity in thehigh absorption frequency windows for all precoding tech-niques. It follows the current understanding of the terahertzchannel and we can see regardless of the MIMO technique,the capacity drops sharply in high absorption windows. Onthe other hand, results change drastically when molecular re-radiation is assumed to be scattering. In this case, the LoSchannel converts to a Rician or Rayleigh channel depending onthe channel absorption coefficient. As expected, multiplexingresults in a much better performance than beamforming sinceit can employ spatial multiplexing. For example, it can be observed in Fig. 12a that CL-MP outperforms the beamform-ing thanks to the tremendous multiplexing gain provided bythe rich scattering environment due to molecule re-radiation.In more detail, a significant capacity improvement can beobserved at very high absorption frequencies such as 540-560 GHz. Communication over such frequency windows isconsidered infeasible for terahertz communications in existingstudies. While at 500 GHz the beamforming and multiplexingcapacity are 15 and 17 bps/Hz respectively, those are about7 and 84 bps/Hz at 550 GHz. Thus, the absorption and re-radiation transforms the LoS dominant channel to a Rayleighchannel and reduces beamforming performance. The reasoncan be found in Section IV, where we have discussed that re-radiation decreases the K-factor and creates a rich scatteringchannel.However, it is also observed in Fig. 12a that the OL-MPresults in poor performance in comparison to CL-MP andbeamforming. The power allocation scheme downgrades touniform power allocation where an identity matrix is used forprecoding due to the lack of CSI at the transmitter. Thus,the capacity is equal to that of the re-radiation-as-noise caseand drops to zero in high absorption windows. When thepower is distributed uniformly, the equivalent SNR, ( P λ i mσ ) , of most parallel channels is less than 0 dB. Practically, thereceiver cannot detect the transmitted symbol when the signalis weaker than noise. These results are matched with theexisting literature that the open-loop multiplexing performancedrops dramatically in the low SNR [55].Fig. 12b illustrates a high SNR scenario. It shows the CL-MP and OL-MP result in a close capacity, significantly higherthan beamforming at very high absorption frequencies such as550 GHz. This is because the uniform power allocation is closeto optimum in a very rich scattering channel [48]. In otherwords, the water-filling scheme results in a uniform powerallocation.In summary, considering the same implementation chal-lenges of beamforming and CL-MP, OL-MP might still be apreferable choice for frequency up to 1 THz. But when thereis not enough signal strength at the receiver, the transmittershould have CSI to steer the beam toward the receiver.Furthermore, the advantage of CL-MP in comparison withbeamforming is that the former can take advantage of bothbeam shaping and multiplexing over parallel paths. However,CSI overhead can be very large for massive MIMO. Forexample, the channel transfer matrix has 50625 elements witha 225x225 MIMO system where each element is a complexvalue and required at least 16 bits of data. Nevertheless, thechannel coherent time in presence of molecular re-radiationhas not been investigated. The updating interval of CSI feed-back should be significantly shorter than the channel coherenttime to avoid using outdated CSI [56]. Thus, having the non-expired full CSI at the transmitter can decrease the effectivespectral efficiency of the reverse link [45].VI. C ONCLUSION
In this paper, we have presented a new perspective onmolecular absorption and re-radiation over the mmWave andterahertz band. We reviewed two alternative assumptions onthe effects of molecular re-radiation, noise versus scattering.While re-radiation has been mostly considered as noise in theliterature, we have also considered the recent idea that there-radiation is correlated to the main signal and thus can bemodeled as scattering. Hence, we combined both theories andcharacterized a multi-path channel which assumes the molec-ular re-radiation as scattering. Our simulation results showedthat the re-radiation can greatly improve MIMO performancein the mmWave/terahertz spectrum when it is treated as scatter-ing. We have shown that the frequency windows, which werepreviously considered as very high attenuation sub-bands, areactually more efficient in MIMO as they can take advantage ofmolecular re-radiation. Our results have further confirmed thatmultiplexing can be a viable alternative to beamforming evenin an LoS channel, which might fundamentally changes theconclusion drawn from the traditional MIMO communicationstheory. VII. F
UTURE W ORK
The theoretical discovery in our research can potentiallychange our understanding of wireless communications overthe mmWave/terahertz band. Future work would focus on the experimental measurements, which requires a set of well-designed measurement scenarios to detect the re-radiationand show its correlation with LoS signal. To investigate there-radiation, a high and a low absorption scenarios can beexperimented. This can be realized through manipulating thedensity of channel molecules, e.g. oxygen at 60 GHz, or mea-suring in slightly different frequencies where the absorption issignificantly different, e.g. 57, 60 and 63 GHz. Furthermore,the re-radiated signal characteristics should also be measuredand characterized. Finally, the performance of a MIMO systemshould be measured with various precoding schemes.The experimental future work, however, must overcomeseveral challenges: 1) the high-frequency equipment used inthe experiments may not be sensitive enough to detect there-radiated energy, 2) the detection of phase is difficult forhigh-frequency signals, especially when other factors such aswall and roof reflection also affect the signal propagation, and3) it may be difficult to control the oxygen and vapor ofthe communication medium, especially considering the verylimited absorption changes over environment parameters.R
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Academic Press Library in Signal Processing: Volume 2 ,ser. Academic Press Library in Signal Processing, N. D. Sidiropoulos,F. Gini, R. Chellappa, and S. Theodoridis, Eds. Elsevier, 2014, vol. 2,pp. 187 – 293. Sayed Amir Hoseini is a postdoctoral researchassociate at the University of New South Walesat ADFA-Canberra. He received the BSc degree inElectronic Engineering from the Isfahan Universityof Technology and the MSc degree in Electronic andCommunication Engineering from the AmirkabirUniversity of Technology (Tehran Polytechnic), inIran in 2008 and 2011, respectively. He completedPhD in Computer Science and Engineering at theUniversity of New South Wales (UNSW Sydney) in2017. He worked at CSIRO | DATA61 and CentralQueensland University as a postdoctoral researcher. Since mid-2020, hehas joined School of Engineering and Information Technology at UNSW-Canberra. His research interests include Wireless Communications, PhysicalLayer Security, and UAV Communication.
Ming Ding (M’12-SM’17) received the B.S. andM.S. degrees (with first-class Hons.) in electronicsengineering from Shanghai Jiao Tong University(SJTU), Shanghai, China, and the Doctor of Phi-losophy (Ph.D.) degree in signal and informationprocessing from SJTU, in 2004, 2007, and 2011,respectively. From April 2007 to September 2014, heworked at Sharp Laboratories of China in Shanghai,China as a Researcher/Senior Researcher/PrincipalResearcher. He also served as the Algorithm DesignDirector and Programming Director for a system-level simulator of future telecommunication networks in Sharp Laboratoriesof China for more than 7 years. Currently, he is a senior research scientistat Data61, CSIRO, in Sydney, NSW, Australia. His research interests includeinformation technology, data privacy and security, machine learning and AI,etc. He has authored over 100 papers in IEEE journals and conferences, all inrecognized venues, and around 20 3GPP standardization contributions, as wellas a Springer book “Multi-point Cooperative Communication Systems: Theoryand Applications”. Also, he holds 21 US patents and co-invented another 100+patents on 4G/5G technologies in CN, JP, KR, EU, etc. Currently, he is aneditor of IEEE Transactions on Wireless Communications and IEEE WirelessCommunications Letters. Besides, he has served as Guest Editor/Co-Chair/Co-Tutor/TPC member for many IEEE top-tier journals/conferences and receivedseveral awards for his research work and professional services.