An Intra-Cluster Model with Diffuse Scattering for mmWave Communications: RT-ICM
11 An Intra-Cluster Model with Diffuse Scattering formmWave Communications: RT-ICM
Yavuz Yaman,
Student Member, IEEE , and Predrag Spasojevic,
Senior Member, IEEE
Abstract —In millimeter-wave (mmWave) channels, to over-come the high path loss, beamforming is required. Hence, thespatial representation of the channel is essential. Further, foraccurate beam alignment and minimizing the outages, inter-beaminterferences, etc., cluster-level spatial modeling is also necessary.Since, statistical channel models fail to reproduce the intra-cluster parameters due to the site-specific nature of the mmWavechannel, in this paper, we propose a ray tracing intra-clustermodel (RT-ICM) for mmWave channels. The model considersonly the first-order reflection; thereby reducing the computationload while capturing most of the energy in a large number ofimportant cases. The model accounts for diffuse scattering asit contributes significantly to the received power. Finally, sincethe clusters are spatially well-separated due to the sparsity offirst order reflectors, we generalize the intra-cluster model to themmWave channel model via replication. Since narrow beamwidthincreases the number of single-order clusters, we show thatthe proposed model suits well to MIMO and massive MIMOapplications. We illustrate that the model gives matching resultswith published measurements made in a classroom at 60 GHz.For this specific implementation, while the maximum clusterangle of arrival (AoA) error is degree, mean angle spreaderror is degrees. The RMS error for the cluster peak power isfound to be . dB. Index Terms — I. I
NTRODUCTION M ILLIMETER-wave (mm-Wave) communication is con-tinuing to emerge with several advantages over thecurrent wireless bands such as higher throughput, lower la-tency, reduced interference, and increasing network coordi-nation ability. Many indoor and outdoor measurements aimat modeling the mmWave channel characteristics [1], [14]–[16], [19], [26]–[29]. Beamforming is typically introducedto compensate for the higher path loss at higher mmWavefrequencies [2], [3]. However, spatial filtering of the channelrequires detailed knowledge of the angle spectrum of thechannel. Fortunately, clusters are spatially well-separated inmmWave channels, which allows creating a beam for eachcluster [9]. Furthermore, as the first order reflections and thedirect path cover as high as 99.5% of the received power[22], received clusters in mmWave can usually be consideredfor the first-order reflections only. On the other hand, well-known channel propagation mechanisms affect mmWave chan-nels differently. For example, while diffraction contributes tothe received power for microwave channels, its contribution
The authors are with Department of Electrical and ComputerEngineering, Rutgers University, Piscataway, NJ 08854 USA (e-mail:[email protected]; [email protected]). is negligible in mmWave channels [27]. Also, scattering islimited in lower frequencies, whereas, in mmWave channels,even a typical wall can scatter the incoming signal significantlydue to the tiny variations on its surface. Hence, a mmWavechannel model should take the diffuse scattering into accountin order to properly replicate the channel characteristics [7],[16], [35]. Measurement results show that in some NLOScases wider beamwidth antennas result in higher receivedSNR [28], [31] which leads to the fact that array design thatwould create optimum beamwidth is directly related to thespatial representation of the received cluster. Then, althoughthe clusters can be easily identified, an accurate intra-clusterangular model has vital importance. Hence, knowledge ofthe detailed cluster angular spectrum is essential for at leasttwo important applications including accurate beam alignmentalong with an optimum beamwidth and to minimization ofinter-beam interference.Measurements confirm that the mmWave channels are site-specific [17], [27] and that the channel characteristics dependhighly on the environment [20]. Hence, creating genericstatistical models for typical environments as in the case ofmicrowave bands is difficult [4]. For this reason, researcherstend to propose statistical channel models for specific envi-ronments [17]–[19], [22], [27]. To give generalized models, ahybrid geometry-based stochastic channel model (GSCM) [13]that combines stochastic and deterministic approaches wasrecently introduced [19], [29] and adopted by the mmWavewireless standards such as 3GPP [4], IEEE 802.11ad [8], IEEE802.11ay [9], MiWEBA [5] and COST2100 [6]. Although thehybrid method is more accurate than the statistical approach,while generating faster and more generalized results thanthe deterministic approach, nevertheless it does not providesufficient intra-cluster angular modeling accuracy necessaryfor beamforming and inter-cluster interference optimizations.Specifically, in 3GPP Channel Model [4], [29], the intra-clusterangular modeling is solely based on measurements and thenumber of paths within the cluster and their powers are fixedfor certain type of environments. On the other hand, 60 GHzindoor standards 802.11ad [8], 802.11ay [9] and 802.15.3c[10] adopt statistical intra-cluster model rooted from the S-Vmodel [11], [12] and angular behavior of the rays within thecluster are simply modeled as a random variable. While Quasi-Deterministic (Q-D) Channel Model [21], [30] takes mmWavescattering into account, its effect on the spatial domain in thecluster level is not addressed. As a result, to the authors’knowledge, a detailed intra-cluster mmWave channel modelthat studies the power distribution in angle domain has notbeen introduced yet. a r X i v : . [ c s . I T ] M a y In this paper, we propose a spatial ray-tracing mmWaveintra-cluster channel model (RT-ICM) that takes only first-order reflections into account. In our model, we also addthe scattering effect based on the material properties. Themodel outputs the power distribution both in angle and timedomain within the cluster and can be used for both indoorand outdoor mmWave systems in any type of environmentsgiven the conditions that the required physical parameters forray-tracing are provided. We further provide a MIMO channelmodel that consists of nonoverlapping clusters and discuss thatpencil-shape beamwidth provided by massive MIMO allowan increased number of single-order clusters in mmWave.Furthermore, we give the insights that, with the combination ofmassive MIMO and the proposed channel model, maximumspatial usage of the channel can be achieved using severalbeams with different beamwidths directed to detected clusters.The advantage of the proposed model is that it provides theaccuracy of the deterministic approach and the simplicity ofthe stochastic approach while comes with an intra-clustermodel addition to the hybrid approaches. We also show that theresults of the proposed model match well with the publishedindoor mmWave measurements.The paper is organized as follows. In Section II, the def-inition of the cluster used in the model is given along withthe assumptions. We introduce a basic geometrical model fora single-order reflection cluster in Section III and using thismodel, we propose the intra-cluster model with all aspects inSection IV. In Section V, the model is extended to MIMOscenarios and its implementation to the already providedmeasurements is given in Section VI. Finally, Section VIIconcludes the paper.II. C
LUSTER D EFINITION OF THE M ODEL
Let two stationary devices positioned and communicate witheach other at a distance as seen from the top view in Fig. 1. Arough surface acts as a reflector that creates the cluster whichincludes several rays that are generated by diffuse scattering.Note that only one ray obeys Snell’s Law [25] in the clustermodel and it is called specular ray , referring to the specularreflection. The others are going to be called diffuse rays ,referring to the diffuse reflections. Both ray types are shown inFig. 1. Only 2-D azimuthal plane is considered in the model.In our model, we strict the clusters to be generated onlyvia first-order reflections for NLOS scenarios. We also leteach reflector can create only one cluster. In other words,the number of first-order reflectors in the environment equalsthe number of clusters. Also, when we discuss multi-clusterscenarios, we assume the clusters do not overlap spatially.Although we pictured the devices as phased array antennas,the proposed model assumes them as point sources. Hence,each ray leaves from the transmitter, reflects from a uniquepoint at the reflector and then reaches to the receiver with aunique AoA.III. B
ASIC G EOMETRIC M ODEL (BGM)Unless otherwise is stated, all distances are in meters, andthe angles are in degrees. We illustrate angles in diagrams with Fig. 1: Cluster definition of the modelTABLE I: Geometrical Notations
Notation Definition d length between the transmitter and receiver h t length between the transmitter and the reflector h r length between the receiver and the reflector s length between the reflector normal at transmitter (RNT)and the reflector normal at receiver (RNR) d length between specular ray reflection point and the receiver d length between specular ray reflection point and the transmitter l length between diffuse ray reflection point and the receiver l length between diffuse ray reflection point and the transmitter s length between specular ray reflection point and the RNT s length between specular ray reflection point and the RNR s (cid:48) length between diffuse ray reflection point and the RNT s (cid:48) length between diffuse ray reflection point and the RNR φ specular ray angle of arrival (AoA) with respect to the RNR α offset AoA between specular and diffuse ray l neg reflector length that covers diffuse rays with negative αl pos reflector length that covers diffuse rays with positive αs pos length between the receiver-side reflector endpoint and the RNR α pos positive offset AoA limit due to reflector length α neg negative offset AoA limit due to reflector length Θ beamwidth of the transmitter beam l t length of the transmitter side illumination at reflection line l r length of the receiver side illumination at reflection line s t length between the transmitter side beam edge and the RNT clockwise rows if they are positive, counterclockwise rowsotherwise. A. Environment Setup
Considering the specular ray and one diffuse ray, all mainparameters can be defined as seen in Fig. 2. As seen, theshortest ray within the cluster is the specular ray.The distances given in the diagram are defined in TableI. Hence, the length of the specular ray is l sp = d + d .Similarly, the length of the diffuse ray is l dif = l + l (1)The formulation will be setup according to Fig. 2 and thenthe validation of the formulas for other scenarios will bechecked in Section III-E. Geometrical derivations are givenin Appendix A. B. Calculating Path Lengths and Angles
With the given distances d , h t and h r , specular ray lengthis l sp = (cid:112) s + ( h t + h r ) where s = (cid:112) d − | h t − h r | . The Fig. 2: Basic geometrical model of the clusterFig. 3: Relation between offset AoA and diffuse ray delayspecular ray AoA is φ = cos − (( h t + h r ) /l sp ) . Finally, thediffuse ray length for a given α is l dif = h r cos( φ − α )+ (cid:115) h t + (cid:18) s − h r cos( φ − α ) sin( φ − α ) (cid:19) (2) C. Timing Parameters and Time-Angle Relation
The time of arrival (ToA) of the line-of-sight (LOS) ray is, t los = d/c where c is the speed of light. Similarly, t sp = l sp /c and t dif = l dif /c are the ToA of the specular and diffuse ray,respectively. Finally, τ dif = t dif − t sp is the diffuse ray delay with respect to the specular ray.Fig. 3 displays the τ - α relation for different values of h t and h r while d is fixed to meters. The range for the α isselected as [ − ◦ , ◦ ] which is a typical angle spread of a Fig. 4: Diagram of offset AoA limitationscluster and the delays are given in nanoseconds. As seen, forany { h t , h r } pair, the function is not symmetric. That meansdelays are not necessarily equal for two equal opposite signedoffset AoAs. Another important result is that the delay-anglerelation highly depends on the environment. Even a very smallchange in distances yields much different delays for α < . D. Support Region
Several effects exist in practical scenarios that bound theangle spread of the receiver. We account those constraints on α and call the resultant available range as support region .We also define a region on the reflector surface that coversall the reflection points, called visible region . The visualmeaning of these terms is shown in Fig. 4. Support regionis limited primarily by the reflection geometry, secondarily bythe visible region. Visible region is limited by the reflectorlength and the transmitter beamwidth. We give the ranges inthe next subsections for each while the details are provided inAppendix A-B.
1) Reflection Geometry: h t and h r change the geometrydrastically as seen from Fig. 3. Hence, two cases, h t > h r and h t < h r , should be checked separately.For case h t > h r , as seen from Fig. 2, a positive tilt angle σ is introduced that needs to be taken into account and calculatedas σ = sin − (( h t − h r ) /d ) .Then, accounting the leftmost and rightmost possible reflec-tions, φ − σ + 90 ◦ > α > φ − ◦ . Simliarly, for h t < h r , therange is given as φ + 90 ◦ > α > φ − σ − ◦ as σ < nowand bounds the negative α .
2) Visible Region:
Reflector length determines the visi-ble region geometrically, whereas system parameter transmitbeamwidth is another limitation. Reflector length limitation isillustrated in Fig. 2 for two cases. Ignoring the misalignmentproblems and sidelobes in the radiation patterns, we considerthe transmit beam is steered towards the specular ray anddivide it into two to determine the covered region on thereflection line. The diagram in Fig. 5 visualizes the approachfor two cases. Related parameters are listed in Table I. Hence,minimum of two limitations at both sides will determine the visible region . Analytically,
Fig. 5: Transmitter beamwidth limitationTABLE II: Resultant Support Range for α Case Support Range h t ≥ h r α − max { φ − ◦ , α neg (cid:48)} α + min { φ − σ + 90 ◦ , α pos (cid:48)} h t < h r α − max { φ − σ − ◦ , α neg (cid:48)} α + min { φ + 90 ◦ , α pos (cid:48)} w t = min( l t , l neg ) w r = min( l r , l pos ) (3)where w t and w r are the transmitter and receiver side visibleregion lengths, respectively. As an example, in Fig. 4, we letthe w t is limited by the reflector length. And the w r is limitedby the transmitter beamwidth. Note that the knowledge of thereflector length is not enough as l pos is not necessarily equalto l neg . Hence, along with d , h t , h r and Θ , both sides reflectorlengths, l pos and l neg , should be given as inputs to the modelas well. Derivations of l t and l r are given in Appendix A-B.In order to determine a range for the offset AoA due to thevisible region, we backtrack the received rays that reflect fromthe endpoints of the region. Then, the offset AoA upper andlower bounds due to the visible region are α (cid:48) neg < α < α pos (cid:48) (4)where α neg (cid:48) = φ − tan − (( d sin φ + w t ) /h r ) and α pos (cid:48) = φ − tan − (( d sin φ − w r ) /h r ) .Finally, combining with the reflection geometry limitationand having the tighter constraint on both sides, we give theexpressions for the resultant support region for h t ≥ h r and h t < h r in Table II with α ∈ [ α − , α + ] . E. Formulation Validation for Other Scenarios
In this subsection, we check the other scenarios of whichgiven equations so far were not considering in the analyt-ical setup. These scenarios can be basically defined as thereflections occur outside of the reflector normal frame whichis demonstrated in Fig. 4. In Fig. 2 and 5, other scenariosare shown as Case 2 for reflector length and transmitterbeamwidth calculation, respectively, while Fig. 6 is given forpath length calculations. We claim that the setup formulationsin the previous sections are still valid and refer the reader toAppendix A-C for the proofs. Fig. 6: Diagrams for the cases diffuse ray reflects from out ofthe normals frame for positive (with α p ) and negative (with α n ) reflectionsIV. I NTRA -C LUSTER C HANNEL M ODEL S ETUP USING B ASIC G EOMETRIC M ODEL
In this section, using the Basic Geometric Model, wegenerate a first-order reflection cluster structure that consistsof multiple rays as defined in Section II. Throughout the paper,we assume that both the channel and the transceiver-receiverpair are stationary which means the channel impulse responseis time-invariant.To estimate the channel parameters, we propose a determin-istic approach where we let infinitely many rays depart fromthe transmitter. In particular, in this section, we will intro-duce the deterministic model setup, give a theoretical clusterchannel impulse response (TC-CIR), calculate its parameters.Finally, we study how to bin the resultant profiles to get thepractical multipath channel impulse response. To do so, wecreate a novel mmwave spatial channel model.
A. System Setup
Fig. 4 illustrates the infinitely many rays approach. In thisapproach, the number of rays within the visible region isassumed to be infinity. To approximate the infinity numberof rays, we digitize the support range with very small spacing( ∆ α ). So, the number of rays in digitized spatial domain is N dr = (cid:98) ( α − − α + ) / ∆ α (cid:99) where α + and α − are given inTable II. Then, the offset AoA of k -th ray in the cluster is α k = ( α − ) + k ∆ α where k = 0 , , . . . , N dr − , excluding thespecular ray offset AoA of 0, i.e. α sp = 0 .With these definitions, the BGM can be applied directly.The method scans all α values within the support range with ∆ α increments. For every α k , it calculates the τ k , the delayof k -th ray within the cluster. Hence, the length and delay forthe k -th ray in the cluster can be given as l k = h r cos( φ − α k )+ (cid:115) h t + (cid:18) s − h r cos( φ − α k ) sin( φ − α k ) (cid:19) (5) and τ k = t k − t sp where k = 0 , , . . . , N dr − , t sp is theToA of the specular reflection already defined in BGM and t k = l k /c is the ToA of the k -th ray.As a result, the baseband theoretical cluster channel impulseresponse (TC-CIR) becomes c T ( t sp , φ ) = a sp e jϕ sp δ ( t sp ) δ ( φ )+ N dr − (cid:88) k =0 a k e jϕ k δ ( t sp − τ k ) δ ( φ − α k ) (6)where a sp and ϕ sp are the amplitude and the phase ofthe specular ray; a k , ϕ k , τ k , α k are amplitude, phase, delay,offset AoA of the k -th ray, respectively. δ ( . ) is Dirac deltafunction and N dr is the number of rays. Note that c T ( t sp , φ ) is the function of time and angle of arrival of the specularray. In section IV-C and IV-D we will give the formulationfor estimating the amplitudes a k and phases ϕ k for the k -thray. B. Directive Diffuse Scattering Model
In mmWave channels, even very tiny variations in a typicalreflector create scattering since the wavelength is very small[5], [9], [16]. According to the measurement results at 60 GHzgiven in [22], received power due to the diffuse scatteringwas as high as of the total cluster power. Apparently,diffuse scattering is a non-negligible propagation mechanismin mmWave channels and hence has to be taken into accountwhen modeling the cluster channels. The angular shape of thescattering event should also be modeled in order to estimatethe directions (as well as the relative powers with respect tothe specular ray) of the diffuse rays.In [34], scattering event is modeled with 3 different patterns.According to the measurements, the directive pattern is themost accurate model and given in our context as ρ k ( ψ k , m ) = (cid:18) ψ k (cid:19) m (7)where ρ k ( ψ k , m ) is defined to be the relative diffuse scat-tering power coefficient of the k -th diffuse ray with respectto its specular reflected ray. It is a function of ψ k and m where ψ k is the angle between the specular reflected ray andthe diffuse reflected ray of the k -th diffuse ray and m is thedesign parameter that determines the width of the pattern. Notethat the function takes its maximum at ψ k = 0 , i.e. specularlyreflected ray of the k -th diffuse ray. And ρ k (0 , m ) = 1 for any m . Also, we assumed m to be equal for all k ; meaning thatthe roughness of the surface is same everywhere and doesn’tdepend on the grazing angle.As the Fig. 7 demonstrates, scattering is assumed to occurat each reflection point of the incident ray, and only one ray inthe scattered pattern can reach to the receiver. Also note thateach incident ray has its own grazing angle, θ k . In this context,BGM needs to be updated too. Consider the diffuse ray withthe grazing angle θ k in Fig. 7. Since only one reflected rayreaches the receiver, we only take one direction into accountwithin the scattering pattern. In order to calculate the offsetdirection ( ψ k ) of the k -th diffuse ray, first we need to find the Fig. 7: Updated cluster model diagram with the addition ofdiffuse scattering patterngrazing angle associated that ray, i.e. θ k . From Snell’s Law,grazing angle of the incident ray equals to the grazing angleof the reflected specular.Then, θ k = tan − h t | s (cid:48) | (8)where s (cid:48) is given in Appendix A. ψ k and α k are negativein the diagram. Hence, ψ k = 90 − ( φ − α k ) − θ k (9)We claim that the formulas are valid for all cases. The proofis in Appendix B. C. Power Calculation of the Rays
We define the transmission equation for the k -th ray suchthat the received ray power is given as P k = P T G T G R L k R k S k (10)where P T is the transmit power; G T and G R are thetransmitter and receiver antenna gain, respectively; L k , R k and S k are the losses applied to the k -th ray due to freespace, reflection and scattering, respectively. In the followingsections, we give an expression for L k , R k , S k .
1) Free Space Loss:
The path loss applied to the k -th rayin linear scale is L k = (cid:18) λ πl k (cid:19) , k = 0 , , . . . , N dr − (11)where λ is wavelength of the carrier frequency and l k is thelength of the ray that is given in Eq. (5).
2) Reflection Loss:
Reflection loss applied to the incidentelectric field can be characterized through the
Fresnel reflec-tion coefficient ( Γ ) [24]. There are two Fresnel equations fortwo polarization cases to calculate the Fresnel coefficient ( Γ ).The simplified versions of the equations for vertically andhorizontally polarized k -th ray in our model are given as,respectively, Γ (cid:107) k = − ε r sin θ k + (cid:112) ε r − cos ( θ k ) ε r sin θ k + (cid:112) ε r − cos ( θ k ) (12) Γ ⊥ k = sin θ k − (cid:112) ε r − cos ( θ k )sin θ k + (cid:112) ε r − cos ( θ k ) (13)where θ k is the grazing angle defined in Eq. (8) and ε r is the relative permittivity of the reflection material that is agiven parameter through the measurements. It is also worthyto note that ε r doesn’t depend on the carrier frequency [23],[33].As a result, reflection loss coefficients in linear scale for k -th ray are defined as R k = (cid:40) R (cid:107) k = 1 / | Γ (cid:107) k | if vertical pol. R ⊥ k = 1 / | Γ ⊥ k | if horizontal pol. (14)
3) Scattering Loss:
The scattering loss is studied in [32]and the loss coefficient for the specular component is given as ρ s ( θ ) = exp (cid:32) − . (cid:18) πσ h λ sin θ (cid:19) (cid:33) (15)where σ h is the standard deviation of the surface height ( h )about the local mean within the first Fresnel zone, λ is thecarrier wavelength and θ is the grazing angle. Here, variationson the surface, or surface height, h , is modeled as a Gaussiandistributed random variable [23].On the other hand, for the k -th incident ray, a relationbetween the power degradation at k -th specular ray and itsany diffuse ray is given in Eq. (7) via a scattering pattern.Hence, the scattering loss for the k -th ray can be given as S k = (cid:18) ρ s,k ρ k (cid:19) (16)where ρ s,k is the specular ray coefficient that expresses theloss applied to the k -th incident ray caused by the roughnessof the material and is given by ρ s,k = ρ s ( θ k ) and ρ k is thecoefficient that accounts the loss due to the power dispersionafter scattering given in Eq. (7).Finally, since we introduce amplitudes in the cluster channelmodel in Eq. (6), power can be converted to absolute value ofamplitudes via | a k | = √ P k . D. Phase Calculation of the Rays
Rays arrive receiver with different phases due to the differ-ence at their path length and at the grazing angle during thereflection. Hence, in order to be able to sum the ray powersproperly, phase information of each ray should be calculateddeterministically.
1) Phase Offset due to Path Distances:
The phase offsetof the k -th ray due to the path difference with respect to thespecular ray can be given as ∆ ϕ D,k = (2 π ( l k − l sp )) /λ .
2) Phase Offset due to Reflection:
Note that Fresnel equa-tions given in (12) and (13) are complex coefficients. Hence,we can define the phase offset introduced by the reflection tothe k -th ray as ∆ ϕ (cid:48) R,k = (cid:40) ∠ Γ (cid:107) if vertical pol. ∠ Γ ⊥ if horizontal pol. (17)In order to be able to calculate a total instant phase of a ray,we need to align with the same reference (specular ray phaseoffset) with the previous subsection. Hence, we correct thephase offset of the k -th ray due to the reflection with respectto the specular ray as ∆ ϕ R,k = ∆ ϕ (cid:48) R,k − ∆ ϕ (cid:48) R,spec
Overall, phase offset of the k -th ray with respect to thespecular ray can be given as ∆ ϕ k = ∆ ϕ D,k + ∆ ϕ R,k (18)Note that ∆ ϕ k = ϕ k − ϕ sp . Further, assuming ϕ sp = 0 , ∆ ϕ k = ϕ k . E. Binned Intra-Cluster Channel Model
Since all the rays are not resolvable by the receiver due tothe limitation on the resolution, an additional discrete binningis needed on top of the theoretical approach given in SectionIV-A.After binning (filtering and sampling) on both angle andtime domains, the resultant discrete baseband time-invariantchannel impulse response for the cluster (C-CIR) can be givenas following: c [ n sp , Ω sp ] = N r − (cid:88) i =0 a ( i ) e jϕ ( i ) δ [ n sp − i ∆ τ ] δ [Ω sp − i ∆ φ ] (19)where n sp and Ω sp are the ToA and AoA of the specularray in discrete time and angle domain. ∆ τ and ∆ φ are thetime and angle resolutions; a ( i ) and ϕ ( i ) are amplitude andphase of the i -th MPC, respectively and N r is the number ofmultipath components (MPCs). Finally, δ [ . ] is the Kroneckerdelta function.Eq. (19) defines the space-time characteristics of a clusterthat consists of N r MPCs. In other words, it maps thecomponents from the time domain to the angle domain (andvice versa) with respect to specular ray. N r is a system-dependent parameter that depends on the receiver, the signalbandwidth and/or the type of the measurement. Using eitherthe channel sounding with directional measurements techniqueor beamforming, spatial information of the overall channel canbe extracted. In this way, timing characteristics for each angleresolution can be assigned. So, the 2-D (spatial-temporal)channel model given in Eq. (19) is validated.In the binning procedure from Eq. (6) to (19), we as-sume that the angular resolution is determined by scanningincrements ( ∆ φ ) in measurement technique and by receiverbeamwidth ( Θ r ) in beamforming. We assume the channel isnarrowband for each angle resolution where the bandwidth of Fig. 8: Flowchart diagram of the C-CIR generation.the channel is larger than the signal bandwidth. Then thereis single MPC in time domain for each angle resolution.Mapping in both domains is performed such a way that theMPC is located in the middle of the bin while the MPCpower is obtained via phasor summation of the ray powerswithin the bin. Finally, MPCs that have power lower thanthe receiver sensitivity should be discarded. That is, whenever
10 log | a ( i ) | < P RS where P RS is the receiver sensitivity, theMPC is removed from the C-CIR.To summarize the overall proposed model in the paper, aflowchart given in Fig. 8 shows the operations to obtain thetime and angle domain representations of the cluster for aspecified communication system.V. E XTENSION TO
MIMO
A. Channel Impulse Response
In this paper, we created a channel model for the clusterin the channel. However, the extension model that covers theoverall channel can also be introduced. As a generic model,if receiver antenna has an omnidirectional antenna pattern, thediscrete channel impulse response that only considers single-order reflection clusters is given as h [ n, Ω] = N cl − (cid:88) j =0 c ( j ) [ n − T ( j ) , Ω − Φ ( j ) ] (20)where n, Ω is time and angle of arrivals at the receiver; T ( j ) and Φ ( j ) are delay and AoA of the j -th cluster; N cl isthe number of clusters and c ( j ) is discrete channel impulseresponse of the j -th cluster given in Eq. (19).Note that if we define the specular ray ToA and AoA ofa cluster to be the cluster
ToA and AoA, assigning n = 0 , T ( j ) = n ( j ) sp where n ( j ) sp is the ToA of the j -th cluster. In orderto create a similar relation in angle domain, Ω should be fixedfor all clusters. However, we setup the BGM model assumingthe reference direction is the reflector normal at the receiver(RNR) and φ is called specular ray AoA with respect to RNR.Apparently, reference direction changes for each cluster. Here,we define LOS ray AoA as the new reference which would befixed for any first-order reflection scenarios within the channel.The transformation from φ to Φ is given as Φ = 90 − φ + σ where Φ is the AoA of the specular ray within the cluster withrespect to LOS ray; σ is introduced in subsection III-D1 and Fig. 9: Possible single-order clusters in a MIMO communica-tion within a typical living room environmentits visualization can be seen in Fig. 2. Hence for Ω = 90+ σ ( j ) where σ ( j ) is the tilt angle of j -th cluster, Φ ( j ) = φ ( j ) , i.e. φ ( j ) is the AoA of the j -th cluster. B. SISO Channel Impulse Response
So far, we did not state an explicit constraint whether thelink between the transmitter and the receiver is beamformed.However, when support region for α was being calculated inBGM setup, transmit beamforming is implicitly accounted bytaking the transmitter beamwidth into account. Also, the aimof the overall paper was stated as to give an angle domainpresentation of the cluster in order to minimize misalignmentsof the receiver beams. Then, for a single-input-single-output(SISO) NLOS scenario, if the receiver antenna is beamformedto the provided cluster direction, then the obtained clusterchannel impulse response (C-CIR) given in Eq.(19) becomesthe channel impulse response (CIR) and given as h [ n, Ω] = c [ n − T, Ω − Φ] (21) C. LOS Ray Parameters
Note that if the scenario is LOS, we will consider that one ofthe clusters will be through LOS, i.e. no reflection. As in otherray tracing algorithms, we model that cluster with the singleLOS ray. In this case, for n = 0 in Eq. (20), T = n los , i.e.LOS ToA in discrete time domain. For Ω = 0 , LOS ray AoA
Φ = 0 . Finally, its power in linear scale is given by P los =( P T G T G R /L los ) where L los is the LOS ray attenuation dueto the free space path-loss and given as L los = ( λ/ πd ) . D. MIMO Channel Impulse Response
In BGM setup, we discuss the cluster angle spread limitationdue to transmit beamwidth. In mmWave MIMO, due to thelarge array usage opportunity, antenna beamwidth can reachto very small values (smaller than ◦ with antenna elements[24]) which makes the transmit beamwidth dominant limita-tion factor in our intra-cluster model, especially for indoorenvironments. Same phenomenon occurs in outdoor mmWaveapplications if massive MIMO is used in the communicationsystem where even smaller beamwidth can be achieved. Thisis because h t is also a factor that determines the beamwidthlimitation and it should be relatively small to keep the transmit beamwidth as a dominant limiting factor. As a result, severalspatially separated single-order reflection clusters are providedwithin the channel via beamformed links. Fig. 9 gives anexample for a typical living room.Proceeding with the consideration of a dedicated transmit-receive beamformed link for each cluster, we can think of, infact, that each cluster constitutes a SISO channel. Then, for N cl beamformed links (clusters), MIMO channel matrix H can be, analytically, represented as H = h h . . . h N cl h h . . . h N cl ... ... . . . ... h N cl h N cl . . . h N cl N cl (22)where h pq is the channel impulse response for the link between p -th transmit beam and q -th receive beam. Apparently, in-tended beamformed links are denoted for p = q cases whereasthe interference between the links are shown as p (cid:54) = q .In this paper, we consider the clusters are perfectly separatedin the spatial domain. That is, the beams aligned to thedifferent first-order reflection directions do not overlap eachother. With this assumption, the extension to MIMO becomesstraightforward and the channel matrix reduces to H = h . . . h . . . ... ... . . . ... . . . h N cl N cl (23)where h jj is given in Eq. (21) for j = 1 , , . . . , N cl . E. Massive MIMO and Intra-Cluster Model
Now that the proposed model provides the detailed spatialrepresentation of the MIMO channel in the cluster level,several novel beamforming techniques can be introduced usingmassive MIMO approaches to increase the spatial usage ofthe channel. In this section, we give the insights of three,but several others can be introduced that exploit the proposedmodel. a) Adjusting the Optimum Beamwidth:
From array pro-cessing techniques, we already know that increased beam gaincan be achieved by narrowing the beam. Since the number ofantennas used to create the beam also determines the beamgain and beamwidth [24], now one can calculate the optimumbeamwidth and select the number of antennas within the portand create the desired beamwidth. b) Different Beamwidth for Each Cluster:
As we willshow in the implementation section, clusters have differentangle spreads which implies that each beam dedicated to acluster has its own beamwidth. Considering the large numberof antenna elements availability in massive MIMO systems, byadaptively selecting the number of antennas within the antennaports, beams with different beamwidths can be organizedeasily. Fig. 10: Measurement environment and the distance parame-ters when receiver is in the room center. c) Two Beams for Each Cluster:
Furthermore, the pro-posed model showed that the angle spectrum of the clusters arenot necessarily symmetric. Even for the vertical polarization ofthe antennas, in some cases, two clusters may be visible fromthe same first-order reflection. This gives an idea of creatingmore than one beam with different beamwidths for the samesingle-order cluster. In that case, another idea could be aligningthe beamwidth, not to the specular ray direction but such a waythat the beam covers the maximum energy.Overall, with the combination of the extensive array pro-cessing opportunities of the massive MIMO, the proposedmodel helps to acquire maximum energy from the channelwhile increasing the spatial efficiency.VI. I
MPLEMENTATION
In this section, we implement the proposed ray tracingchannel model, RT-ICM, using the experimental platformperformed in [14] and compare the proposed model resultswith the measurement results. For simulation purposes, we setthe N dr = 1000 as the larger values don’t make any significantdifference. A. Indoor 60 GHz - Classroom Environment [14]
In [14], several measurements are held to characterize thespatial and temporal behaviors of the indoor channels at60 GHz. Totally, 8 experiments are performed in 4 typesof environments. Those environments were room, hallway,room to room and corridor to room. Both measurement andstatistical results are provided for each measurement. Since thedata is collected using spin measurements, power angle profileof the channel is also created. In this paper, we will replicatethe measurement environment and the system parameters forthe two classroom measurements in [14] and implement theproposed channel model.
Fig. 11: Theoretical Power Angle Profile of the channel whenreceiver is in the center of the room.
1) Receiver is at the Center:
The top view of the measure-ment environment is drawn in Fig. 10. In this first scenario,transmitter is located at the corner and the receiver is inthe center of an . × m empty room. One side of theroom is covered with a blackboard while the others areindoor building walls. Transmitter has a horn antenna witha beamwidth of ◦ which is directed towards the receiver.And the angle resolution during the spin measurements atthe receiver is given as ◦ . As a result, although 4 potentialreflectors are present within the room, the only possible first-order reflections are through the ”Wall-1” and ”Blackboard”that are shown in Fig. 10. Hence, three clusters are considered:cluster 1 and 2 are created through the first-order reflectionsfrom wall-1 and blackboard, separately, cluster 3 is the LOSray. The transmit beamwidth for each cluster is assumed to be Θ = 45 ◦ . We set the diffuse scattering pattern order m = 17 for the plasterboard wall-1 and m = 35 for the blackboard(made of slate-stone). Finally, from the measurement result,we choose the power threshold as P RS = − dBm. Theparameters for the clusters are given in Table III.The resultant theoretical angle domain response of themodel is given in Fig. ?? . The ray that arrives with zeroAoA is the LOS ray. Resultant specular ray AoA cluster-1( φ (1) ) and cluster-2 ( φ (2) ) are, respectively, − ◦ and ◦ .Angle spread of the clusters are ◦ for cluster-1 and ◦ for cluster-2. The angular spectrum and the numerical valuesare in agreement with the measurement result figure providedin [14] which shows the AoAs as − ◦ and ◦ and theapproximate angle spreads as ◦ and ◦ .On the other hand, to compare the power spectrum in angledomain, power angle profile result after the binning (with ∆ φ = 5 ◦ ) is provided in Fig. 12. The received powers ofcluster-1 and cluster-2 relative to that of LOS ray are dBand dB. These also match with measurement results wherethey were approximately dB for cluster-1 and dB forcluster-2. Fig. 12: Binned Power Angle Profile of the channel whenreceiver is in the center of the room.Fig. 13: Measurement environment and the distance parame-ters when receiver in the room corner.
2) Receiver is on the Corner:
The measurement environ-ment is drawn in Fig. 13 for the second scenario where thereceiver is placed on the corner. The parameters are given inTable III. All other parameters that are not listed are the sameas in the previous scenario.Theoretical angle response given in 14 shows that thecluster-1 has an AoA of − ◦ whereas the cluster-2 AoA is ◦ . Their angle spreads are ◦ and ◦ . The measurementresult figure in [14] gives the AoAs as − ◦ and ◦ and thespreads approximately are ◦ and ◦ for the cluster-1 andcluster-2, respectively. Similar to the previous measurement,binned version of the angle spectrum is given in Fig. 15. Asseen, the relative received powers of cluster-1 and cluster-2are dB and dB. They are approximately dB and dB inthe measurements. TABLE III: Input Parameters of the Model
Measurements Clusters d h t h r l neg l pos ε r σ h [mm] P T [dBm] G T [dB] G R [dB] polarization Room-center Cluster-1 3.8 7.1 4.2 4 3 2.9 0.3 25 6.7 29 horizontalRoom-center Cluster-2 3.8 6.1 3.5 3 5.4 7.5 0.1 25 6.7 29 horizontalRoom-corner Cluster-1 7.1 7.1 1.2 2.2 4.8 2.9 0.3 25 6.7 29 horizontalRoom-corner Cluster-2 7.1 6.1 1.8 6.2 2.2 7.5 0.1 25 6.7 29 horizontal
Fig. 14: Theoretical Power Angle Profile of the channel whenreceiver is in the corner of the room.Fig. 15: Binned Power Angle Profile of the channel whenreceiver is in the corner of the room.VII. C
ONCLUSION
In this paper, we create a ray tracing channel model, RT-ICM, for a mmWave channel cluster that includes only thefirst-order reflection rays. We also take diffuse scattering intoaccount as the scattering has a non-negligible contributionin mmWave channels. Specifically, we aim at a spatial rep-resentation of the cluster at the receiver end. Further, sincethe mmWave channels are sparse and clusters are spatiallyseparated most of the time, we claim that the proposed intra-cluster model can be generalized to the MIMO channel modelsimply by replicating it for each cluster. We discuss that, in fact, the transmit beamwidth can be the dominant limitationfactor on the clusters angle spread in MIMO and massiveMIMO applications; thereby increasing the number of first-order clusters further. After implementing the model to aliterature measurement scenario, we show that the intra-clustermodel estimates the angular spectrum with high accuracy.A
PPENDIX
ABGM P
ARAMETERS
In this Appendix, we give the complete procedure of howthe BGM parameters derived.
A. Derivation of φ and l dif From Fig. 2, φ = cos − ( h r /d ) where d = ( h r l sp / ( h t + h r )) . Plugging d , we get φ .From Fig. 2, l = h r / cos( φ − α ) and l = (cid:112) h t + ( s (cid:48) ) where s (cid:48) = s − s (cid:48) and s (cid:48) = l sin( φ − α ) . Plugging everythingto Eq. (1), Eq. (2) is obtained. B. Derivation of Support Region Limitations1) Geometry Limitation:
From Fig. 2, for α < , the tiltangle doesn’t increase the support region as any ray capturedby the receiver with AoA of φ − α ≥ ◦ cannot be a reflectionfrom that reflector. Hence, the lower bound for α is φ − ◦ .On the other hand, upper bound is a little tricky. The linegoes through the transmitter and receiver (LOS line) sets thenew limit to the upper bound and the tilting reduces the upperbound by σ . Similarly, for the case h t < h r , σ limits α on thelower bound to be α > φ − σ − ◦ , while the upper boundremains unchanged.
2) Reflector Length Limitation:
For α pos , s = d sin φ and s pos = s − l pos Then, φ − α pos = tan − s pos /h r . Similarlyfor α neg , φ − α neg = tan − (( s + l neg ) /h r ) .
3) Transmitter Beamwidth Limitation:
In Fig. 5, from theright triangle similarity, the angle between the RNT andthe departing specular ray is equal to φ . Hence, s t = h t tan ( φ − (Θ / . On the other hand, s = h t tan φ . Then l t = s − s t . And for l r , s + l r = h t tan ( φ + (Θ / . C. Formulation Validation of BGM1) Path Length Calculation Check:
For positive side reflec-tion, φ − α p < , but cos( φ − α p ) > , hence l > . However,since sin( φ − α p ) < , s (cid:48) ,p < . Thus, s (cid:48) ,p is larger than s but l is accurately computed based on the geometry. As a result,resultant calculations of l and l are correct.For negative side reflection, φ − α n > , and l is calculatedas expected. However, since s (cid:48) ,n > s , s (cid:48) ,n is negative. Notethat, when calculating l , s (cid:48) ,n is squared. Hence, l is resultedas expected too.
2) Reflector Length Calculation Check:
For positive sidereflection, since l pos is larger than s , s pos turns out to benegative. That yields φ − α pos < which is, actually, correctas α pos is larger than φ . For negative side reflection, nothingis unusual in the formulation.
3) Transmit Beamwidth Calculation Check:
As seen fromFig. 5, φ − Θ / < which yields s t < . However, l t iscalculated correctly. For l r , calculation is as expected.A PPENDIX BV ALIDATION OF THE D IRECTIVE M ODEL FOR A LL C ASES
We consider the cases, diffuse rays reflected from (1) the receiver side of the specular ray, (2) the back of the RNR,(3) the back of the RNT. For the case (1), the diffuse rays inFig. 7 with θ can be an example. In that case, α k and ψ k arepositive. Eq. (8) holds as the variables don’t change. Since wepaid attention to the angle signs during the formulation setup,Eq. (9) holds too. For the case (2), the diffuse ray in Fig. 7with θ is an example. α k and ψ k are still positive. From Fig.6, s (cid:48) is positive and grazing angle calculation in Eq. (8) isvalid. Since α k > φ , ( φ − α k ) < . Hence, θ k + ψ k > which is the case as spread angle exceeds the reflector normalat reflection point. Hence, Eq. (9) is valid too. However, inthe case of (3), for which the diffuse ray in Fig. 7 with θ isan example, the specular reflection of the diffuse ray reflectstowards the opposite direction of the receiver. However, Eq.(9) computes ψ (cid:48) k as shown in Fig. 7 which is inaccurate. Tocorrect it, additional − θ k ) should be added. That is,recalling that ψ k < , ψ k = 90 − ( φ − α k ) − θ k − − θ k ) = θ k − − ( φ − α k ) .A CKNOWLEDGEMENT
The authors would like to thank Prof. S. Orfanidis formany helpful discussions and his contributions to the effectof reflection and scattering propagation mechanisms as wellas the concepts regarding the antenna theory.R
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IEEE Access 4 (2016): 688-701. Yavuz Yaman received the B.S degree from the School of Engineering, Istan-bul University, in 2011; M.S. degree in electrical and computer engineeringfrom Rutgers University, Piscataway, NJ, in 2014. He is currently workingtoward the Ph.D. degree with the Department of Electrical and ComputerEngineering, Rutgers University, Piscataway, NJ. His research interests includechannel modelling, beamforming, channel estimation, antenna propagationsand phased antenna arrays.