A New Look at MIMO Capacity in the Millimeter Wave
aa r X i v : . [ c s . N I] O c t A New Look at MIMO Capacityin the Millimeter Wave
Sayed Amir Hoseini ∗† , Ming Ding † and Mahbub Hassan ∗†∗ School of Computer Science and Engineering, University of New South Wales, Sydney, Australia † Data61, CSIRO, Sydney, AustraliaEmail: [email protected], [email protected], [email protected]
Abstract —In this paper, we present a new theoretical discoverythat the multiple-input and multiple-output (MIMO) capacitycan be influenced by atmosphere molecules. In more detail,some common atmosphere molecules, such as Oxygen and water,can absorb and re-radiate energy in their natural resonancefrequencies, such as 60 GHz, 120 GHz and 180 GHz, which belongto the millimeter wave (mmWave) spectrum. Such phenomenoncan provide equivalent non-line-of-sight (NLoS) paths in anenvironment that lacks scatterers, and thus greatly improvethe spatial multiplexing and diversity of a MIMO system. Thiskind of performance improvement is particularly useful for mostmmWave communications that heavily rely on line-of-sight (LoS)transmissions. To sum up, our study concludes that since themolecular re-radiation happens at certain mmWave frequencybands, the MIMO capacity becomes highly frequency selective and enjoys a considerable boosting at those mmWave frequencybands. The impact of our new discovery is significant, whichfundamentally changes our understanding on the relationshipbetween the MIMO capacity and the frequency spectrum. Inparticular, our results predict that several mmWave bands canserve as valuable spectrum windows for high-efficiency MIMOcommunications, which in turn may shift the paradigm ofresearch, standardization, and implementation in the field ofmmWave communications.
I. I
NTRODUCTION
In the near future, the 5th-generation (5G) system is ex-pected to deliver a massive increase in channel capacity anddata rates. To achieve this, two key technologies have attractedlots of attention recently. The first one is the use of very highfrequency spectrum in the range of 30 GHz to 300 GHz, whichis also known as the millimeter wave (mmWave) spectrum.The second one is the massive multiple-input multiple-output(MIMO) technology, which advocates the use of a largenumber of antennas in wireless communications. The abovetwo technologies are compatible with each other. In moredetail, a short wavelength in mmWave helps to minimize theinter-element spacing of a MIMO system. As a result, a greatnumber of antennas can be equipped on mobile devices, whichis not practical for the current wireless systems that usuallywork in the sub-6GHz spectrum.For a given number of transmitter and receiver antennas,the common understanding is that the MIMO capacity is notfrequency selective, if the received signal strength is fixed toa certain level. Such conclusion has been validated in the sub-6GHz spectrum, but does this conclusion still hold when wemarch into the mmWave spectrum in 5G?
Note that the mmWave communication for cellular networksposes its own challenges, such as high free-space path loss,high Doppler shift and blockage [1]. Other than the abovefactors and according to more fundamental physics theories,another key difference between the existing wireless communi-cation in sub-6GHz frequencies and the future one in mmWaveis the reaction of atmosphere molecules, which can absorbsignal energy if excited in their natural resonance frequencies.Such natural resonance frequencies are usually in the mmWavespectrum. For example, if we consider normal atmosphere,Oxygen and/or water molecules will play a major role in themolecular absorption, and their natural resonance frequenciesare around 60 GHz, 120 GHz and 180 GHz. Interestingly, res-onating Oxygen and water molecules not only absorb signalenergy causing attenuation, they also re-radiate some of theabsorbed energy. This type of molecule-induced re-radiationis often referred to as molecular noise [2, 3], but it is actuallyhighly correlated to the signal waveform due to its re-radiationnature [4], and hence it can be considered as a distorted copyof the signal from a virtual non-line-of-sight (NLoS) path.The aim of this paper is to show how this molecular re-radiation can change the MIMO capacity performance as it isvery similar to scattering, which is known as a very importantfactor to provide spatial diversity for a MIMO channel. Sincethe molecule absorption intensity is related to the naturalresonance frequencies of the existing molecules in the realisticatmosphere on earth, (i.e., mainly the large amount of Oxygenand water molecules), the energy absorption and re-radiationare not flat especially in the mmWave spectrum. Thus, wepropose a conjecture that the MIMO capacity should vary withfrequency due to the impact of such molecular absorption andre-radiation. Then, we verify our conjecture via theoreticalstudies and computer simulations, and find that the MIMOcapacity increases dramatically in some high absorption bandsaround 60 GHz, 120 GHz and 180 GHz, thanks to the ubiqui-tous existence of Oxygen and water molecules.The intuition of our theoretical discovery is that the molec-ular re-radiation adds a random phase onto the distorted copyof the signal, which equivalently creates a richer scatteringenvironment that can improve the line-of-sight (LoS) MIMOcapacity commonly evaluated in the mmWave spectrum. Theimpact of our new discovery is significant, which fundamen-tally changes our understanding on the relationship betweenhe MIMO capacity and the frequency spectrum. In particular,our results predict that several mmWave bands can serveas valuable spectrum windows for high-efficiency MIMOcommunications, which in turn may shift the paradigm ofresearch, standardization, and implementation in the field ofmmWave communications.The rest of the paper is structured as follows. In Section II,we present the molecular absorption model for the calculationof attenuation and re-radiation, as well as the fundamentaltheory on the MIMO capacity. Section III analyzes the MIMOcapacity versus the molecular re-radiation, followed by simu-lation results and insightful discussion in Section IV. Finally,we conclude the paper in Section V.II. C
HANNEL MODEL AND
MIMO
CAPACITY
The molecular absorption model defines how differentspecies of molecules in a communication channel absorb en-ergy from the electromagnetic signals and how they re-radiatethem back to the environment. This section first explainsthe concept of absorption coefficient used to characterize theabsorption capacity of a given molecule species, followed bythe attenuation and re-radiation models that are built upon thiscoefficient.
A. Molecular absorption coefficient
The effect of a given molecule, denoted by S i , on the radiosignal is characterized by its molecular absorption coefficient K i ( f ) at frequency f . Such coefficient varies with pressureand temperature of the environment. The molecular absorptioncoefficients of many chemical species for different pressureand temperature are available from the publicly availabledatabases such as HITRAN [5] and
NIST Atomic Spectra [6].Nevertheless, the atmospheric air is a mixture of differentmolecule species that may change on an hourly basis [7].Therefore, different climate conditions also lead to differentabsorption in mmWave and they should be taken into accountwhen considering mmWave channels. In order to model molec-ular absorption, let us assume the mmWave radio channel isa medium consisting of N chemical species S , S , ..., S N ,and m i is the mole fraction per volume, i.e., the mixingratio of molecule S i in the channel medium. We furtherassume that the temperature and pressure of the medium are T and P , respectively. The medium absorption coefficient ,i.e., k ( f ) , at frequency f is therefore a weighted sum of themolecular absorption coefficients in the medium [8], whichcan be formulated as k ( f ) = N X i =1 m i k i ( f ) , (1)where k i ( f ) is the molecular absorption coefficient of species S i on condition of temperature T and and pressure P . Asdiscussed before, k i ( f ) can be obtained from HITRAN [5]and NIST [6]. In this work, to get the values of k ( f ) , wewill use some predefined standard atmosphere conditions andtheir corresponding ratio of molecules in the air, which aretabulated in [5]. B. Attenuation of radio signal
The attenuation of the radio signal at the mmWave frequen-cies is due to spreading and molecular absorption [9]. The totalattenuation at frequency f and a distance d from the radiotransmitter can be written as A ( f, d ) = A spread ( f, d ) × A abs ( f, d ) , (2)where A spread ( f, d ) and A abs ( f, d ) are respectively the atten-uation due to spreading and attenuation caused by molecularabsorption at frequency f .In more detail, the spreading attenuation is given by A spread ( f, d ) = (cid:18) πf dc (cid:19) , (3)where c is the speed of light. The attenuation due to molecularabsorption is characterized as [9] A abs ( f, d ) = e k ( f ) × d . (4)Many linear approximations for (2) have been proposed inthe literature for different frequencies (in dB or dB/Km) [10].The ITU Radio communication Sector (ITU-R) also providesvarious procedures to estimate specific attenuation due to thedominant molecules in the air (i.e., Oxygen and water) [11],both of which can be derived from (3) and (4).Thus, the line-of-sight (LoS) received power at the receiverbecomes 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 existing molecules in communication medium will beexcited by electromagnetic waves at specific frequencies. Theexcitement is temporary and the vibrational-rotational energylevel of molecules will come back to a steady state and theabsorbed energy will be re-radiated in the same frequency.These re-radiated waves are usually considered as noise inthe literature. For example, the molecular absorption noise hasbeen studied in the literature since 1986 when a model for skyatmospheric noise for frequencies higher than 18GHz wasproposed in [3]. There are a number of works that havestudied the atmospheric noise for mmWave frequencies suchas [12], which experimentally measured the atmospheric noisevariation in Mauna Kea in Hawaii over many night anddays using a 143 GHz and 268 GHz transmitter. Recently, themolecular noise has been re-considered for higher frequenciessuch as Terahertz band ranging from 0.1-10 THz [2]. Molec-ular absorption is not white and its power spectral density(PSD) is not flat because of the different resonant frequenciesof various species of molecules. The PSD of the molecularabsorption noise that affects the transmission of a signal, N abs , is contributed by the atmospheric noise S BN and theself-induced noise S XN as addressed in [3, 8]: S N abs ( f, d ) = S BN ( f, d ) + S XN ( f, d ) , (6) S BN ( f, d ) = lim d →∞ ( k B T (1 − e − k ( f ) d )) (cid:16) c √ πf (cid:17) , (7) S XN ( f, d ) = P t ( f )(1 − e − k ( f ) d ) (cid:16) c πf d (cid:17) , (8)where k ( f ) is the absorption coefficient of the medium atfrequency f , T is the reference temperature ( K ) , k B isthe Boltzmann constant, P t ( f ) is the power spectral densityof the transmitted signal and c is the speed of light. The firstterm in (6), which is called sky noise and defined in (7) isindependent of the signal wave. However, the self-inducednoise in (8) is highly correlated with the signal wave [4], andcan be considered as a distorted copy of the signal wave [13].Thus, the received power of the re-radiated signal by moleculesat the receiver can be expressed by 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 molecules tomolecules [14], the received power in this case is affected by alarge number of phase-independent re-radiated photons. Thus,we assume a uniformly distributed random phase β random , forthe received signal, with its power given by (9). D. Channel Transfer Function
The channel transfer function for a single LoS channel isgiven by H LoS ( f, d ) = s(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 resulted from themolecular absorption and excluding the LoS component canbe represented by H a ( f, d ) = s (1 − e − k ( f ) d ) (cid:16) c πf d (cid:17) × e j πβ random = (1 − e − k ( f ) d ) (cid:16) c πf d (cid:17) × e j πβ random . (11)Hence, the total channel transfer function is the superpositionof the partial channel transfer functions, which is written as 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 random . (12) E. MIMO channel model and capacity
In this paper, we consider a MIMO system that is con-sisted of n t transmitting antennas and n r receiving ones.The received signal vector y at n r receiving antennas can beformulated as [15] 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 independentnoises with variance σ . The channel matrix H is defined by H , 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 coefficientassociated with the j th transmitter antenna and the i th receiverantenna. Note that h ij can be obtained from (12) for frequency f and distance d ij . A × MIMO system with a channelmatrix is illustrated in Figure 1.Fig. 1: A 3x3 MIMO system, the channel gain of array pairsbetween transmitter and receiversIn this paper, we assume that the transmitter has no channelstate information (CSI), and the transmitting power is equallydistributed among transmitting antennas. Consequently, thecapacity of MIMO channel can be written as C = log det( I n r + Pn t σ HH † ) , (15)where P is total transmitting power, and I is the identitymatrix [15]. Since the determinant of (cid:16) I n r + Pn t σ HH † (cid:17) canbe computed by the product of the eigenvalues of the matrix HH † , the MIMO capacity can thus be written in the form ofa product of non-zero eigenvalues as [16] C = κ X i =1 log (1 + P λ i n t σ ) , (16)where λ i denotes singular values of the matrix H , and hencethe squared singular values λ i denotes the eigenvalues of thematrix HH † . Note that κ denotes the number of non-zero λ i ,which is also called the rank of H with κ ≤ min( n r , n t ) [16]. H † = (cid:18) c ηπf (cid:19) × e − k ( f ) d + j π d λ + (1 − e − k ( f ) d ) / e j πβ n11 d e − k ( f ) d + j π d λ + (1 − e − k ( f ) d ) / e j πβ n12 d e − k ( f ) d + j π d λ + (1 − e − k ( f ) d ) / e j πβ n21 d e − k ( f ) d + j π d λ + (1 − e − k ( f ) d ) / e j πβ n22 d × e − k ( f ) d − j π d λ + (1 − e − k ( f ) d ) / e − j πβ n11 d e − k ( f ) d − j π d λ + (1 − e − k ( f ) d ) / e − j πβ n21 d e − k ( f ) d − j π d λ + (1 − e − k ( f ) d ) / e − j πβ n12 d e − k ( f ) d − j π d λ + (1 − e − k ( f ) d ) / e − j πβ n22 d (17)III. A NALYSIS ON THE
MIMO
CAPACITY WITHMOLECULAR ABSORPTION
It is well known that the maximum achievable capacity ofa MIMO channel is proportional to the minimum number ofantenna elements at the receiver and the transmitter. However,in an environment that is lack of spatial diversity, such capacitywould be degraded due to the deficiency of parallel informa-tion paths, i.e., the rank of the MIMO channel, between thereceiver and the transmitter [17]. More specifically, in a richscattering environment, scatterers provide sufficient NLoS sig-nal components, leading to a better diversity and capacity. Butin the case of a LoS scenario, the LoS signal component willdominate the received signal, and thus decrease the channelrank due to the linear dependence of the LoS antenna arrayphases [18]. Thus, in a LoS scenario that is assumed for mostmmWave communications, the maximum MIMO capacity isachievable only with some specific array configuration [18],where the LoS rays are perfectly orthogonal, resulting in anopportunistically full-rank MIMO channel. However, this isnot practical for mobile communications, since such kind ofoptimal antenna setting requires a user steadily holding adevice toward a specific direction.Generally, the MIMO capacity becomes higher if the chan-nel transfer matrix H is full rank and well-conditioned . In moredetail, the rank of H determines how many data streams canbe multiplexed over the channel, and H is well-conditioned ifthe condition number, which is defined as λmaxλmin , is small andclose to one. In other words, the maximum MIMO capacitycan be attained when all λ i s are equal.With the absorption re-radiation, we can show that it helpsto provide equivalent NLoS paths for the LoS scenario, andthus increase the rank and decrease the condition number ofthe MIMO channel. Due to the page limit, we will relegatethe full analysis to the journal version of our work. Here, wefocus on a 2x2 MIMO channel as a toy example and plug (12)into (15), which yields (17) shown on the top of next page. In(17), η is a normalization factor of H and β n ij is the randomphase of re-radiated signal.To show the impact of the absorption coefficient on (17)and the MIMO capacity, the channel transfer function andsingular value are calculated for a practical range of absorption -6 -5 -4 -3 -2 -1 s i ngu l a r e v a l ue ( λ i ) × -5 λ λ -6 -5 -4 -3 -2 -1 λ m i n / λ m a x -6 -5 -4 -3 -2 -1 Absorption coefficient (m -1 ) C apa c i t y ( b i t/ s / H z ) Fig. 2: Singular value and condition number is affected bymolecular absorption. Higher absorption leading to two timesmore capacity in compare with SISOcoefficient in a normal air condition at 60 GHz, while thechannel distance is 50 m and arrays are in parallel formation. Itshould be noted that the actual value of absorption coefficientat 60 GHz is around . × − . In Figure 2, we plot the resultsin terms of the singular value and the condition number. Asone can observe, for a very small absorption coefficient thelargest singular value is much larger than the minimum one,leading to an ill-conditioned MIMO channel matrix. However,as the absorption coefficient increases, the singular values aregetting closer and the inverse of condition number increasesfrom zero toward one, which implies a higher multiplexinggain. Also, it can be seen from Figure 2 that the 2x2 MIMOcapacity doubles that of a single-input-single-output (SISO)channel for a very large absorption coefficient. In the nextsection, more results for the mmWave spectrum with realisticabsorption coefficients will be presented.V. S IMULATION AND DISCUSSION
A. Simulation set-up
Fig. 3: A 3x3 MIMO system with uniform linear arraysTo evaluate the MIMO capacity in mmWave and show theperformance impact of the molecular absorption, we considera simple n × n MIMO system with Uniform Linear Arrays(ULAs), where the inter-element spacing s is equal to halfof the wavelength at both transmitter and receiver, and thechannel distance is D . The considered MIMO system isillustrated in Figure 3. Moreover, we consider uniform powerallocation to transmitter arrays operating in an open-space LoSscenario. The default values of the parameters are listed inTable I, and different values will be explained when necessary.In order to investigate the MIMO performance, we evaluatethe theoretical MIMO capacity with several configurations.In the first step, the parameters in Table I are used. Morespecifically, the channel transfer matrix in (14) is obtainedfrom (12), while the distance between each pair of transmitter-receiver antenna element is calculated by channel geometry.Finally, we compute the MIMO capacity using (16). Since weapply random phases on NLoS components created by molec-ular re-radiation, we conduct the evaluation of the MIMOcapacity with molecular re-radiation for 5000 times and showthe average result.TABLE I: Simulation parameters Transmitter and receiver distance ( D ) mInter-element spacing ( s ) . λ (wave length)Transmitter arrays angle ( φ ) ◦ Receiver arrays angle ( θ ) ◦ Number of arrays on each side ( n ) SNR dB We use the online browsing and plotting tools , whichis based on HITRAN databases [5] to generate absorptioncoefficients for different single gas or some predefined stan-dard gas mixture of atmosphere at sea level, as shown inTable II. Since the Oxygen and water molecules play mainroles in a normal air environment at mmWave bands and theOxygen ratio is invariant, we use the highest and lowest waterratio in Table II, i.e., the ”USA model, high latitude, winter” and ”USA model, tropics” . The corresponding absorptioncoefficients in mmWave bands have been shown in Figure 4for an ambient temperature of K and a sea level pressureof atm. It can be seen that there are three major absorptionspikes in the mmWave spectrum as follows, http://hitran.iao.ru/gasmixture/simlaunch Frequency (GHz) -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. 4: The absorption coefficient in two different atmosphere.The temperature is
K and the pressure atm. • A pair of them appear at around 60 GHz and 120 GHz,which are attributed to Oxygen molecules. Note that theabsorption coefficients are the same for both atmospherecases, i.e., ”USA model, high latitude, winter” and ”USAmodel, tropics” . This is because the percentage of Oxy-gen is comparable for those two cases. • The third one at 180 GHz is created by water (H O)molecules in the air. For a tropic atmosphere, the waterratio is higher than that of the winter atmosphere, andthus we can see a significant increase in terms of theabsorption coefficient among these two atmosphere cases.For comparison, we also investigate a hypothetical vacuumcase without absorption, i.e., we set the the absorption coeffi-cient to zero.
B. The MIMO Capacity vs. the Absorption Coefficient
In this subsection, we first assume a constant reception SNRover the entire frequency spectrum, and display the MIMOcapacity in bit/sec/Hz for mmWave bands for a 3x3 MIMOwith parallel ULA ( φ = 90 ◦ and θ = 90 ◦ ) in Figure 5. In thisfigure, the MIMO capacity with absorption is compared withthat without absorption. As one can observe, the capacity ofthe latter case is flat over the entire band and is not frequencyselective, which corroborates the common understanding upto now. However, when the absorption kicks in, a significantincrease shows up in certain frequency bands with highabsorption. For example, the capacity is boosted by around70 % at 60 GHz for both atmosphere cases. Furthermore,since the tropic atmosphere contains more water molecules, itleads to a considerable capacity increase at 180 GHz in tropicatmosphere in comparison with those of the winter atmosphereand the hypothetical vacuum case without absorption. Theconfidence interval of 90% also has been shown on capacitygraphs in Figure 5 in order to show the results distribution.Numerically speaking, we can calculate the capacity fora SISO channel, which turns out to be 6.66 bit/sec/Hz.According to the existing MIMO theory, for a full-rank 3x3MIMO channel with enough spatial diversity, the theoreticalABLE II: Atmosphere standard gas mixture ratio in percentage for different climates [5] USA model, mean latitude, summer, H=0 H2O: 1.860000 CO2: 0.033000 O3: 0.000003 N2O: 0.000032 CO: 0.000015 CH4: 0.000170 O2: 20.900001 N2: 77.206000USA model, mean latitude, winter, H=0 H2O: 0.432000 CO2: 0.033000 O3: 0.000003 N2O: 0.000032 CO: 0.000015 CH4: 0.000170 O2: 20.900001 N2: 78.634779USA model, high latitude, summer, H=0 H2O: 1.190000 CO2: 0.033000 O3: 0.000002 N2O: 0.000031 CO: 0.000015 CH4: 0.000170 O2: 20.900001 N2: 77.876781USA model, high latitude, winter, H=0 H2O: 0.141000 CO2: 0.033000 O3: 0.000002 N2O: 0.000032 CO: 0.000015 CH4: 0.000170 O2: 20.900001 N2: 78.925780USA model, tropics, H=0 H2O: 2.590000 CO2: 0.033000 O3: 0.000003 N2O: 0.000032 CO: 0.000015 CH4: 0.000170 O2: 20.900001 N2: 76.476779
Frequency (GHz) C apa c i t y ( bp s / H z ) with re-radiationno re-radiationSISO (a) Frequency (GHz) C apa c i t y ( bp s / H z ) with re-radiationno re-radiationSISO (b) Fig. 5: 3x3 MIMO capacity in the presence of molecular re-radiation (constant reception SNR)capacity will be increased to × . ≃ bit/sec/Hz. Asdiscussed before, the LoS MIMO channel suffers from poorspatial diversity and can achieve the maximum capacity onlywith some specific geometry configuration [18], which is notfeasible for mobile communications. Thus, it can be seenthe MIMO capacity without absorption is close to that ofa SISO channel. However, if the molecular re-radiation istaken into account, it can equivalently create a rich scatteringenvironment, and in turn increase the spatial diversity and theMIMO capacity, as shown in Figure 5.Note that in Figure 5, we assume a constant receptionSNR. However, the actual attenuation varies with the fre-quency because (i) the free-space path loss increases withfrequency, and (ii) the molecular absorption also attenuatesthe signal. Hence, it is interesting to investigate whether theabsorption attenuation will mitigate the MIMO performanceimprovement in high absorption frequency bands. For thispurpose, a constant transmit power of 1 W and a constantnoise power of -100 dBm are chosen in our next simulation.Note that such parameter setting provides an SNR valuesimilar to that was used in the previous step. The resultsare exhibited in Figure 6, where the other parameter valuesare the same as those in Figure 5. As one can observe, theabsorption attenuation has a marginal impact on the MIMOcapacity improvement discussed before. To show this, we alsosimulate a SISO channel and plot its capacity in Figure 6,where we can see that the capacity slightly degrades at highabsorption frequency bands at around 60 GHz and 180 GHz.In summary, the mmWave MIMO system can take advantage Frequency (GHz) C apa c i t y ( b i t/ s e c / H z ) SISO with re-radiation - tropic3x3 MIMO with re-radiation - tropic3x3 MIMO no re-radiation3x3 MIMO with re-radiation - winter
Fig. 6: 3x3 MIMO capacity (constant transmitter power).of the molecular absorption and re-radiation to generate morecapacity, which prevails the absorption attenuation.
C. The MIMO capacity vs. The Antenna Number
As discussed before, one of the key benefits of the mmWavecommunication is its potential incorporation with the massiveMIMO technology to generate a tremendous MIMO capacity.Hence, in this subsection, we investigate the molecular ab-sorption effect on the MIMO capacity for a large number ofantennas. Figure 7 displays the MIMO capacity as the numberof antennas in both receiver and transmitter increases. All the
Number of antenna elements C apa c i t y ( b i t/ s e c / H Z ) tropic atmosphere no absorptionwith absorption 50 GHzwith absorption 55 GHzwith absorption 60 GHzwith absorption 65 GHzwith absorption 70 GHz Fig. 7: The MIMO capacity increases linearly as the antennanumber increases.simulation parameter values are based on Table I except thearrays angles, i.e., θ and φ , which are chosen randomly. Oursimulation is repeated 5000 times and the average results havebeen shown for { , , , , } GHz.As can be seen from Figure 7, with molecular absorption,the MIMO capacity increases linearly as the number of anten-nas increases. Such performance gain is much more obviousfor ∼ GHz around the natural resonance frequencyof Oxygen, which creates an opportunistic spectrum windowfor high-efficiency MIMO communications in mmWave. Alsonote that without molecular absorption, the MIMO capacity isfrequency non-selective and does not increase with the numberof antennas due to the dominant LoS transmissions. Suchcontrast comparison can be easily seen from Figure 7.V. C
ONCLUSION
In this paper, we investigated the MIMO capacity formmWave, where the gas molecules in our atmosphere likeOxygen and water not only can increase the path loss, butalso can re-radiate a copy of signal wave and equivalentlycreate multi-path channels. Our results showed that in certainfrequency bands, where the absorption coefficient is signifi-cantly high, the MIMO channel can achieve a capacity that isclose to the theoretical limit, thanks to the great improvementin spatial diversity. Our new discovery fundamentally changesour understanding on the relationship between the MIMO capacity and the frequency spectrum, especially for mmWavecommunications with massive MIMO.R
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