13th European Conference on Antennas and Propagation (EuCAP 2019) Characterization of Frequency-Selective Massive MIMO Channels by Ray-Tracing Mehmet Mert Taygur, Thomas F Eibert Chair of High-Frequency Engineering, Department of Electrical and Computer Engineering, Technical University of Munich, Munich, Germany Email: {mehmet.taygur,eibert}@tum.de Abstract—Frequency-selective channel characteristics and network performance in a single-cell urban massive MIMO scenario are investigated by ray-tracing simulations The urban scenario consists of 64 single antenna users and 256 base station antennas The channels between the users and the base station antennas are computed by ray-tracing simulations for a 10 MHz bandwidth with 1001 samples in the frequency domain A frequency dependent Regularized Zero-Forcing (RZF) precoding scheme is utilized at the base station and the coherence bandwidth as well as the downlink data rate are calculated In addition to the ray-tracing simulations, a second channel study according to the WINNER II statistical model is carried out and the results from both methods are compared It is shown that achieving a coherence bandwidth on the order of MHz is possible for a typical small-cell deployment Furthermore, it is demonstrated that the coherence bandwidth can be improved by utilizing a large number of transmitter antennas, even if the receivers are not equipped with channel equalizers Index Terms—coherence bandwidth, downlink, massive MIMO, ray-tracing I I NTRODUCTION Massive Multiple-Input Multiple-Output (MIMO) networks are considered to be vital to accommodate the growing cellular data traffic in the future A pivotal difference of massive MIMO over the conventional multi-user MIMO is the possibility to achieve the channel capacity at the downlink with simple linear precoding/beamforming methods when the number of the transmitters is considerably larger than the number of the receivers [1] By means of spatial multiplexing provided by beamforming, the users can share the same time and frequency resources without significant interference [2] The performance of massive MIMO networks in urbanlike environments has been thoroughly studied during the last decade where theoretical limits of the approach as well as realworld performance data based on testbeds were introduced [3], [4] A great majority of these studies are based on either narrowband or flat-fading channels where the frequency selective channel behavior is not taken into account However, frequency selective channels may prevail quite often in cellular networks [5], especially for bandwidths extending up to several MHz, due to potential multipaths Few reserachers have addressed this issue by demonstrating the performance according to various statistical channel models or according to the measurement campaigns which cover small numbers of antennas and small geometries, such as found indoors [6]–[8] Predictably, neither approach can provide a sufficient insight about urban deployments, since the specific features of the propagation environment may not be correctly represented by statistical modeling whereas the considered measurement studies might be completely inaccurate for urban scenarios since they are based on different propagation environments Therefore, performance investigations relying on realistic channel models are needed for the characterization of the frequency selectivity in urban massive MIMO networks [9] In order to address this concern, ray-tracing simulations are used to analyze the frequency selective channel behavior for an urban massive MIMO network in this study As a very convenient electromagnetic simulation tool for electrically large problems (i.e., wavelength much smaller than the problem geometry), ray-tracing can provide more realistic insights about the underlying propagation channel than many other techniques The urban scenario is based on a small-cell deployment case where the area is small A 10 MHz channel around 2.5 GHz center frequency is analyzed in the frequency domain with 1001 samples (10 kHz resolution) and the average data rate as well as the coherence bandwidth for the downlink channel are evaluated A single-carrier transmission scheme is assumed in the downlink The receivers are not assumed to possess an equalizer, instead, the channel equalization is effectively carried out at the base station with a wideband precoding scheme Hence, the problems associated with the receiver equalization, such as noise enhancement, can also be avoided In addition to the ray-tracing simulation, another channel analysis has been carried out with the WINNER II Urban Microcell statistical model [10] and the results are compared in order to identify the differences and the similarities between both models II F REQUENCY-S ELECTIVE C HANNELS Frequency-selective channels occur often in environments with rich multipath propagation possibilities, where multiple echoes of the transmitted signal arrive at the receiver at different times The time-dispersive behavior results in a nonflat channel frequency response, leading to potential distortions in the signal such as Inter-Symbol Interference (ISI) The time dispersion and the frequency selectivity can generally be quantified with two parameters, delay spread and coherence bandwidth, respectively The delay spread can be defined as Authorized licensed use limited to: RMIT University Library Downloaded on February 12,2021 at 10:14:18 UTC from IEEE Xplore Restrictions apply 13th European Conference on Antennas and Propagation (EuCAP 2019) the difference in the time of arrival between the first and the last echo whereas the coherence bandwidth stands for the frequency range over which the channel frequency response is considered to be relatively constant [5], [11] In general, the delay spread (Td ) and the coherence bandwidth (Bc ) are inversely proportional A large coherence bandwidth and a small delay spread indicates that high-speed communication is usually possible without suffering from ISI A Measures Against Frequency Selectivity H ∗ (f ) , |H(f )|2 + σn2 /σs2 (1) where σn2 and σs2 are the noise power and transmitted signal power, respectively Given an input signal X(f ), the received signal Y (f ) can be written as Y (f ) = X(f )H(f )L(f ) + σn L(f ) f (2) The second term at the right-hand side of Eq (2) (σn L(f )) denotes the additive noise after the equalizer Note that the f (a) Input signal (b) Noise |H(f )| In a typical urban cellular network, the coherence bandwidth can be on the order of only a couple of hundred kilohertz, which restricts the achievable data rate severely [5] Therefore, certain measures are usually implemented in order to make use of a larger bandwidth by mitigating the ISI There are two methods which are very commonly utilized to solve this problem: 1) Single-Carrier Equalization: An equalizing filter can be utilized to mitigate the ISI at the receiver side in a singlecarrier system, provided that the receiver has the channel state information [12] 2) Orthogonal Frequency Division Multiplexing: The data is divided into multiple sub-streams and is transmitted through multiple sub-channels (hence, multiple subcarriers) Since the coherence bandwidth is usually much larger than the bandwidth of a single sub-channel, ISI can mostly be avoided [13] Although frequency selective channels and the detrimental effects of ISI in wireless communications have been long studied, potential implications on massive MIMO networks have only recently attracted some attention Numerous studies have discussed the feasibility of the single-carrier frequency domain equalization (SC-FDE) over OFDM, as the sensitivity of OFDM to the RF chain imperfections may lead to severe performance issues at the downlink when the number of the base station antennas is large [14]–[16] SC-FDE is commonly carried out with a linear equalizer, such as Minimum Mean Square Error (MMSE) or Zero Forcing (ZF) equalizer, at the receiver sites An MMSE equalizer is generally considered to be more robust compared to ZF since it provides a better trade-off between ISI and noise enhancement In order to clarify the noise enhancement issue in receiver equalizers, consider a channel where the transfer function is given by H(f ) The MMSE equalizer for this channel (L(f )) can be expressed by L(f ) = σn |X(f )| |L(f )| f (c) Channel f (d) Equalizer |X(f )H(f )L(f )| |σn L(f )| f (e) Signal after channel and equalizer f (f) Noise after equalizer Fig Illustration of channel equalization The MMSE equalizer mostly recovers the original signal (e) but the characteristics of the noise mostly signal change after the equalizer (f) noise may not be considered as white anymore (rather colored), since some frequency components might be amplified or attenuated by the equalizer [13] B Massive MIMO Downlink A major benefit of utilizing a large number of transmitter antennas at the base stations is to achieve the channel capacity with simple linear precoding techniques, e.g., Regularized Zero-Forcing (RZF) [1] Such techniques can also be utilized to deal with the problems related to the frequency selectivity, hence, the equalization might be bypassed at the receiver side since ISI would effectively be suppressed at the transmitter side [7], [17] Such a pre-equalization process eliminates the potential noise enhancement issues which are usually observed on the systems with receiver equalizers [18] The effectiveness is strongly dependent on the characteristics of the underlying channel though, as indicated in [15] Let us now consider a single-cell network where the channel frequency response is given by the matrix H(f ) and the ˜ ) where channel estimation of the transmitter is given by H(f ˜ ), i.e., perfect CSI acquisition, is true The RZF H(f ) = H(f precoding matrix can be then written as ˜ ) g(f ) = H(f H ˜ )(H(f ˜ ))H + αI H(f −1 , (3) where I is the identity matrix, (.)H is the Hermitian transpose operator and α is a regularization constant A key attribute of Authorized licensed use limited to: RMIT University Library Downloaded on February 12,2021 at 10:14:18 UTC from IEEE Xplore Restrictions apply 13th European Conference on Antennas and Propagation (EuCAP 2019) Base Station Indoor-User Fig Illustration of the ray paths obtained from the simulation in the considered scenario Outdoor-User Fig Illustration of the cell plan the precoding matrix in (3) is that the individual elements of the matrix are not constants but rather functions with respect to the frequency The network performance can be characterized according to the downlink data rate for each user, as the data rate for kth user (Dk ) in the network can be written as σs2 H(k,:)(f ) g(:,k)(f ) SINRk (f ) = K i=1,i=k σs2 2 H(k,:)(f ) g(:,i)(f ) , + σn2 M Fu Dk = channel was assumed to be time-invariant Two different methods were utilized to generate two different channel matrices and a 10 MHz bandwidth between 2.495 GHz-2.505 GHz was sampled with a 10 kHz resolution (1001 sampling points) in each case 1) Ray-Tracing: Ray-tracing simulations are utilized to obtain the channel matrix for different frequencies where a single simulation provides results for a single frequency An individual element of the channel matrix Hij for a single frequency point fc can be expressed as log2 + SINRk (f ) df, (4) Hij (fc ) = Fl where σs is the total transmitted power, σn is the noise power, Fu and Fl are the upper and lower frequency limits the subscripts (k, :) and (:, i) denote the kth row and ith column of the corresponding matrices, respectively Note that the power allocation with respect to the frequency is assumed to be constant III M ETHODOLOGY A Urban Scenario The scenario consists of 48 indoor and 16 outdoor singleantenna users as well as a base station with 256 antennas The base station antennas are organized as a cylindrical array and are located on top of a building There are 16 buildings with usable indoor spaces (20 m×20 m) and in different heights (33 m-72 m) The user locations are assigned randomly The entire block covers a 160 m×160 m area The placement of the users and the base station antennas is illustrated in Fig B Channel Matrix The individual entries of the channel matrix indicate the path gain between a certain receiver and transmitter, and are complex valued functions with respect to the frequency The oc Vi,m (fc ) gen V (fc ) m=1 j (5) where Vjgen is the generator voltage at the jth transmitter, oc Vi,m is the open circuit voltage at the ith receiver due to mth ray coming from the transmitter and M is the total number of unique rays which are emitted from the transmitter and captured by the receiver Two separate simulations were performed for the indoor and outdoor users In the former case, maximum diffraction, refractions, reflections were allowed whereas the latter simulation was performed with diffraction and 10 reflections A relative permittivity of r = was assumed everywhere 2) Statistical Channel Model: A second channel was generated according to the WINNER II Urban Microcell model [10] The impulse response of the channel between the ith receiver and jth transmitter in the network can be represented with a delay line with 20 taps such that 20 An,ij δ(t − τn ) hij (t) = (6) n=1 where τn,ij and An,ij are the amplitude and the delay of nth tap and N is the total number of the channel taps The amplitudes of the channel taps are assumed to be decreasing Authorized licensed use limited to: RMIT University Library Downloaded on February 12,2021 at 10:14:18 UTC from IEEE Xplore Restrictions apply 13th European Conference on Antennas and Propagation (EuCAP 2019) exponentially as the delay increases, hence, τn,ij and An,ij are written as τ˜n,ij = −3.2 ln(υ)10−7.12 , υ ∼ U(0, 1), τn,ij = sort(˜ τn,ij ), (7) 20 −7.12 e−τn,ij /(10 pij = ) TABLE I AVERAGE AND RMS DELAY SPREADS FOR RAY- TRACING AND MODELS Ray-Tracing WINNER Avg Delay Spread (µs) 0.373 0.039 RMS Delay Spread (µs) 0.362 0.031 WINNER , n=1 −(31.1+41.1 log10 (0.707d)+γ)/20 Ω(d) = 10 −7.12 An,ij = κ Ω(dij ) e−τn,ij /(10 pij delay spread Trms,kl for the channel between kth user and lth transmitter can be expressed as , γ ∼ N (0, 4), ) , κ ∼ CN (0, 1), (8) Tavg,kl = where dij is the distance between the ith receiver and jth transmitter Using the impulse response given in (6), the individual elements of the channel matrix (Hij ) can be obtained with a Fourier transform C Quantifying Frequency Selectivity In order to quantify the frequency selectivity of the downlink channel, the coherence bandwidth of the channel is computed The coherence bandwidth is obtained by the frequency interval for which the frequency √ correlation function (FCF) drops by a factor of 0.707 (≈ 0.5) from its peak value [19] FCF is computed according to the downlink channels which are observed by the users The channel observed by the kth user (excluding noise) can be written as K ˘ k (f ) = σs2 H H(k,:)(f ) g(:,i)(f ) (9) i=1 The FCF for the same user (Rk ) can be written in terms of a limited number of channel samples As the channel information obtained from the simulations contain 1001 samples in the frequency domain, the FCF can be expressed as [20] (1001 − r) Rk (fr ) = 1000 ˘ k (fx )H ˘ k (fx − fr ), H x=r r = 0, 1, , 1000 (10) Finally, the coherence bandwidth is found to be Bc,k = Fu − Fl 1001 1001 I |Rk (fr )| > 0.707 max |Rk | ,(11) r=1 with 1, if Q is true, I [Q] = 0, otherwise, (12) where Q is a logical statement Note that the maximum coherence bandwidth result is limited to 10 MHz during the simulations In addition to the coherence bandwidth, the RMS delay spread can also be investigated to estimate how selective the channel between a certain transmitter and user is The RMS Trms,kl = N n=1 N n=1 Pn,kl τn,kl , N n=1 Pn,kl Pn,kl τn,kl − Tavg N n=1 Pn,kl , (13) where Trms,kl is the average delay spread, N is the number of channel delay taps Pn,kl and τn,kl are the power gain and delay for the nth channel tap, respectively In the statistical model, Pn,kl and τn,kl can be directly calculated from (8) while in the ray-tracing model, the knowledge about the path lengths of individual rays may also be needed besides the amplitudes in order to compute the propagation delay IV N UMERICAL R ESULTS The frequency selective channel behavior and its effects on the network performance were characterized according to the channel delay spread, average downlink coherence bandwidth and average downlink data rate The delay spread information was based on the individual channels between individual transmitter receiver pairs without precoding while the coherence bandwidth was computed according to the effective channel observed by the receivers after precoding The coherence bandwidth and downlink data rate were calculated with respect to increasing numbers of transmitter antennas and for a frequency dependent precoding scheme where the individual elements of the precoding matrix are not constants, rather functions with respect to the frequency as given in (3) The results are shown in Table I and Figure The delay spread data shown Table I indicates that a coherence bandwidth of several MHz is quite possible to achieve since sub-microsecond RMS delay spreads occur for both models An intriguing difference can be observed between the ray-tracing and WINNER model results as the delay spread in the latter model is ten times smaller than in the former The coherence bandwidth data shown in Fig 4a is consistent with the delay spread findings as the coherence bandwidth according to the WINNER model is consistently larger than for the ray-tracing model and the bandwidth values are beyond MHz in both models The feasibility of utilizing a large number of transmitter antennas to improve the coherence bandwidth can be confirmed by ray-tracing results as the coherence bandwidth increases steadily The results from the WINNER model are not very conclusive in this regard since Authorized licensed use limited to: RMIT University Library Downloaded on February 12,2021 at 10:14:18 UTC from IEEE Xplore Restrictions apply 13th European Conference on Antennas and Propagation (EuCAP 2019) Avg Coh Band - Freq Dependent Precoding 10 Coh Band (MHz) R EFERENCES Ray-Tracing WINNER 80 100 120 140 160 180 200 220 240 Number of TX Antennas (a) Coherence bandwidth Avg DL Data Rate - Freq Dependent Precoding 100 80 Data Rate (Mbit/s) transmitting antennas at the base station Although the coherence bandwidth was found to be large enough to accomodate high speed transmission in the considered urban environment, utilizing a large number of antennas with a proper precoding technique provides noticeable improvements even if the user equipments lack channel equalizers 60 40 20 Ray-Tracing WINNER 80 100 120 140 160 180 200 220 240 Number of TX Antennas (b) Downlink data rate Fig Variation of the coherence bandwidth and downlink data rate for an increasing number of transmitter antennas the bandwidth is already at the maximum even for a small number of antennas The downlink data rate results shown in Fig 4b indicate also the WINNER model surpassing the raytracing model, however, the difference in the data rate was found to be growing as the number of the transmitter antennas is increased, unlike the case in the coherence bandwidth Note that such a discrepancy, where the difference in data rate grows as the difference in coherence bandwidth shrinks, may indicate that the channels generated with the WINNER model possess other favorable features over the channels generated with ray-tracing, such as better channel gain or smaller channel correlation, which can be further investigated V C ONCLUSION The coherence bandwidth and downlink data rate for an urban massive MIMO scenario was characterized with raytracing simulations and the WINNER II statistical channel model A 10 MHz channel bandwidth was considered and a frequency dependent RZF precoding 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Numerous studies have discussed the feasibility of the single-carrier frequency domain equalization (SC-FDE) over OFDM, as the sensitivity of OFDM to the RF chain imperfections may lead to severe