Multi-Scenario Millimeter Wave Wireless Channel Measurements and Sparsity Analysis

Hang Mi,Bo Ai,2,3,*,Ruisi He,Xin Zhou,Zhangfeng Ma,Mi Yang,Zhangdui Zhong,Ning Wang

1 State Key Laboratory of Rail Traffic Control and Safety,Beijing Jiaotong University,Beijing 100044,China

2 Henan Joint International Research Laboratory of Intelligent Networking and Data Analysis,Zhengzhou University,Zhengzhou 450001,China

3 PengCheng Laboratory,Shenzhen 518000,China

4 National Institute of Metrology of China,Beijing 100029,China

5 School of Information Engineering,Zhengzhou University,Zhengzhou 450001,China

Abstract: Wireless channel characteristics have significant impacts on channel modeling,estimation,and communication performance.While the channel sparsity is an important characteristic of wireless channels.Utilizing the sparse nature of wireless channels can reduce the complexity of channel modeling and estimation,and improve system design and performance analysis.Compared with the traditional sub-6 GHz channel,millimeter wave (mmWave) channel has been considered to be more sparse in existing researches.However,most research only assume that the mmWave channel is sparse,without providing quantitative analysis and evaluation.Therefore,this paper evaluates the sparsity of mmWave channels based on mmWave channel measurements.A vector network analyzer(VNA)-based mmWave channel sounder is developed to measure the channel at 28 GHz,and multi-scenario channel measurements are conducted.The Gini index,Rician K factor and rootmean-square (RMS) delay spread are used to measure channel sparsity.Then,the key factors affecting mmWave channel sparsity are explored.It is found that antenna steering direction and scattering environment will affect the sparsity of mmWave channel.In addition,the impact of channel sparsity on channel eigenvalue and capacity is evaluated and analyzed.

Keywords: channel sparsity; channel measurement;mmWave channel;measures of sparsity

I.INTRODUCTION

The design and deployment of any wireless communication system are inseparable from the support of the channel model.Meanwhile,the extraction of channel characteristics is a key step in channel modeling [1–3].The special propagation characteristics of the wireless channel are usually caused by the multipath propagation between the transmitter (Tx) and the receiver(Rx).The multipath propagation includes a variety of propagation mechanisms,such as direction,reflection,scattering and diffraction.The signal received by Rx is the multipath superposition of different propagation mechanisms [4–6].The complex multipath propagation will make the channel exhibit fading characteristics,which will significantly affect the performance of communication system[7–9].

Nowadays,as the scale of wireless sensor networks increased,the amount of data has shown an explosive growth trend.Therefore,seeking a sparse representation of data or signals can greatly alleviate the pressure of storage and processing.Sparsity is a commonly used concept in signal processing,and it is defined as if the number of zero elements is far more than the number of non-zero elements,and the distribution of non-zero elements is irregular,the vector or matrix is described as sparse [10].Channel sparsity has been regarded as a nature of wireless channel,and there has been research using the wireless channel sparsity for channel measurement,modeling and estimation.Moreover,compressive sensing provides a powerful tool for sparse signals [11].In [12],the analog compressed sensing technology has proven the ability to lower sampling rates below the Nyquist rate in channel measurements.This relaxes the limitation of the sampling rate,especially in the mmWave and terahertz frequency bands.The sparse channel modeling has been proposed for measured and simulated channels over a frequency range of 6 to 8.5 GHz in [13].In addition,the cluster-based channel model commonly used in standards organizations can also be modeled using channel sparsity.For example,a sparsity-based optimization is used to recover channel impulse responses(CIRs) in [14].The use of recovered CIRs leads to improved clustering accuracy in comparison to identifying clusters directly in the raw CIRs.The development of sparse channel estimators based on sparse channel characteristics is also an interesting field[15].The signal matrix and system model can be simplified after utilizing the sparse channel representation,which will improve the performance of the channel estimator[16].

The wireless channel sparsity is affected by channel characteristic parameters,such as the number,power and delay of multipath components (MPCs).Meanwhile,channel characteristic parameters are closely related to frequency bands and propagation scenarios [17–20].This leads to different levels of channel sparsity in different frequency bands and scenarios.A smaller number of MPCs leads to a more sparse wireless channel from an intuitive point of view.Meanwhile,the propagation characteristics of electromagnetic waves in millimeter waves (mmWave) are quite different from the traditional sub-6 GHz frequency band [21],because mmWave has larger penetration loss and lack of diffraction ability [22,23].These reduce the number of MPCs that can be observed in mmWave channel measurements,and more energy is concentrated in the dominant MPCs[24–27].For example,the number of clusters and MPCs in the cluster in the mmWave channel is smaller than the traditional sub-6 GHz channel[28,29].Therefore,most research believes that the sparsity of the mmWave channel is more significant[30–32].However,it is biased to associate wireless channel sparsity only with the number of MPCs.The power of MPCs is also a key factor affecting channel sparsity[33–35]because the lowpower MPCs have little effect on channel sparsity.

Despite considerable efforts have been made in the mmWave channel sparsity,some important features are still inadequately considered in the existing literature.The reasons are threefold.i) The measurement scenario is usually single.There is no analysis and comparison of wireless channel sparsity in different scenarios.ii) There are some effective sparsity measures,such as Gini index[36],spatial degrees of freedom [37]and RicianKfactor [34].However,some literature still lacks the quantitative evaluation of channel sparsity [38,39].iii) Another main deficiency of existing research is the lack of exploration of the factors affecting channel sparsity,especially in different scenarios.For example,the distribution of scatterers in different scenario will also have a greater impact on channel sparsity.Therefore,it is necessary to explore the influence of different scenarios and scatterer distribution on mmWave channel sparsity.

To address the above mentioned gaps,we carry out mmWave channel measurements at 28 GHz in multiple scenarios.The main contributions and novelties of this paper are summarized as follows:

• A wideband mmWave channel sounder system is used to conduct channel measurements at 28 GHz in multiple scenarios.The measurement scenarios cover a variety of typical environments,including meeting room,empty corridor,data center/computer room,laboratory,and smart warehouse scenarios and their sub-scenarios.Each scenario has a special distribution of scatterers.

• Based on multi-scenario mmWave channel measurement,the effectiveness of the root-meansquare (RMS) delay spread in measuring channel sparsity is validated.Then,channel sparsity in different scenarios is evaluated and compared using the validated sparsity measures.The factors that affect the channel sparsity are explored,especially the propagation scenarios and the distribution of scatterers in the scenario.

• Based on the analysis of channel eigenvalue properties,channel sparsity is significantly affected by non-dominant eigen modes than dominant eigen modes.Different channel sparsity results in a different number of spatial streams to be multiplexed.Finally,combined with the analysis results of eigenvalue,the impact of channel sparsity on capacity is evaluated and analyzed.

The rest of the paper is organized as follows.Section II introduces the mmWave channel sounder system,including the system structure and configuration parameters,and Section III elaborates the measurement campaign in multiple scenarios.Section IV describes the channel sparsity measures and data processing,and the effectiveness of RMS delay spread in measuring channel sparsity is validated.In Section V,the evaluation and analysis results of wireless channel sparsity in multiple scenarios are presented.Finally,conclusive remarks are included in Section VI.

II.MMWAVE CHANNEL SOUNDER

A vector network analyzer (VNA) based channel sounder was used to conduct multi-scenario channel measurement in this paper.Figure 1 and Figure 2 respectively show the block diagram and prototype of the mmWave channel sounder system.Among them,the 1.3-2.3 GHz intermediate frequency (IF) signal is transmitted and received by VNA.In mmWave radio frequency(RF)signal transmitter,the IF signal is upconverted to the RF signal ranging from 27.5-28.5 GHz.Then the RF signal is radiated by the vertically polarized horn antenna,and the gain and half-power beamwidth (HPBW) of horn antenna are 20 dBi and 21◦,respectively.The Rx antenna is equipped with the uniform planar array(UPA)antenna,and it consists of 32 vertically polarized microstrip elements.The array antenna is calibrated in the anechoic chamber,and the antenna pattern of array element is shown by the arrow in Figure 2,where the maximum gain of array elements is 0 dBi.In mmWave RF signal receiver,the receive signals of different array elements are received through the switching of electronic switch.The received RF signal passes through the low noise amplifiers and down converter to generate the 1.3-2.3 GHz received IF signal.The VNA measures S21 parameters to obtain the channel frequency response.Meanwhile,in order to ensure the consistency of the reference clocks of all devices in the measurement system,the Rubidium clock is used in mmWave RF transceiver and VNA to provide a 10 MHz reference clock.The channel sounder system in this paper has a longer measurement distance compared to the scheme of directly measuring mmWave channels by VNA.Because the attenuation of the mmWave RF signal in the cable is much larger than that of the low-frequency IF signal.Lower cable loss means a higher signal-to-noise ratio(SNR).Therefore,we use long IF cables to extend our measurement system to greater distances.In addition,it should be noted that the difference between the channel measurement data has a significant impact on the analysis results when the channel sparsity is quantitatively studied.For example,larger measurement bandwidth and higher SNR will have more detectable MPCs.All of the above factors will affect the analysis results of channel sparsity.Therefore,the channel measurement data used in this paper all have the same measurement configuration.The parameters related to the measurement configuration are summarized in Table 1.It is noteworthy that the maximum detectable length of MPCs is 300 m,which ensures that the MPCs of high-order reflections can be well detected.Meanwhile,the IF bandwidth was set to 500 Hz to reduce the noise floor as much as possible.

Table 1.Configurations of measurement system.

III.MULTI-SCENARIO MMWAVE CHANNEL MEASUREMENT CAMPAIGNS

In this section,multi-scenario mmWave channel measurement campaigns are presented.The measurements were conducted in seven typical mmWave communication scenarios.For each Rx position in each scenario,the Tx horn antenna forms a virtual uniform circular array(UCA)by mechanical scanning.Meanwhile,in order to cover all angles in the scanning range,the scanning spatial resolution is set to 15◦,which is smaller than the HPBW of the horn antenna.The channel data is further used for sparsity measuring and analysis.

3.1 Typical Meeting Room Scenario

The dimensions of the meeting room are 10.78 m ×8.2 m and the ceiling height is 4 m.A 6.6 m × 4.1 m large table is placed in the center,and several small tables are around.Several chairs are around the tables,as shown in Figure 3.Tx is placed on one side of the conference table,as shown in Figure 3a.Rx is placed on the other side of the conference table,and five positions are measured along the direction shown in Figure 3b.The horn antenna of Tx is scanned in the azimuth domain from-45◦to 45◦,where the azimuth angle of 0◦means that Tx antenna steering toward the Rx antennas.

3.2 Empty Corridor Scenario

The empty corridor scenario is shown in Figure 4.The length of the corridor is 10.2 m and the width is 3.35 m.The characteristic of this scenario is empty and closed.No excess objects were placed in the corridor.The reflection path provided by the ceiling,walls,glass windows and two iron doors will be more obvious.Tx is placed at one end of the corridor,and Rx is placed at the other end near the window.Their positions are shown in Figure 4b,where the red dots indicate the measurement positions of Rx.

3.3 Data Center/Computer Room Scenario

Figure 5a shows a typical data center/computer room scenario.In this scenario,iron server cabinets are regularly distributed on the left side of the Tx.These can act as powerful reflectors during radio wave propagation.On the right side of the Tx,all kinds of objects are placed disorderly.These disordered objects can not only generate reflection and scattering paths but also can block the MPCs generated by other scatterers.

3.4 Typical Laboratory Room Scenario

Figure 5b shows a typical laboratory room scenario.This scenario includes tables,chairs,iron lockers,and various equipment on the lockers.Meanwhile,various office equipment is also placed on the desktop.The positions of Tx and Rx are labeled in Figure 5b.The characteristics of this scenario are similar to those of the real laboratory.Randomly placed objects in this scenario will affect the propagation of MPCs.

3.5 Smart Warehouse Scenario

In the smart warehouse scenario,a large number of automated robots are used.Meanwhile,different types of robots will perform different tasks in different warehouse scenarios.In the traditional sub-6 GHz frequency band,a large number of robots can cause link congestion when connected to the access points.As a result,more precise control of robot cannot be carried out,which will affect the operating efficiency of smart warehouse.Compared with sub-6 GHz communication systems,the mmWave system has greater advantages in smart warehouse scenarios,because it can provide larger bandwidth,lower latency and massive access,which can make the smart warehouse more safe and efficient.In this paper,the channel measurements are conducted in the smart warehouse laboratory,which includes three different sub-scenarios.The details are as follows:

3.5.1 Intelligent Forklift Truck Scenario

Figure 6 shows the sub-scenario of the intelligent forklift truck in the smart warehouse.The racking and intelligent forklift truck are shown in Figure 6a.The intelligent forklift truck will operate the goods on the racking after receiving the wireless command.In this scenario,steel racking and goods may provide the propagation paths.Figure 6b shows the position of the Tx and Rx during the measurement.Among them,the height of Rx is 1.5 m,which is consistent with the height of antenna on the intelligent forklift truck.

3.5.2 Stacking and Shuttle Car Scenario

Figure 7a shows the stacking and shuttle car in the smart warehouse scenario.Compared with racking,stacking mainly store smaller-volume goods.The shuttle car relies on the rails in stacking to move and carry goods.The Rx is installed on the shuttle car.It is found from Figure 7a that the stacking and rails are composed of steel frames.These steel frames may generate more and stronger reflection MPCs between the Tx and Rx.

3.5.3 Automated Guided Vehicle Scenario

Automated guided vehicles(AGVs)are used to move freight containers in smart warehouses,as shown in Figure 7b.The AGV will receive the transportation command through the wireless communication system and follow the planned route along the ground markings.However,multiple AGVs carrying freight containers will block each other during travel in this scenario,resulting in frequent changes in line-of-sight(LOS)and non-line-of-sight(NLOS)conditions.

IV.DATA ANALYSIS FOR WIRELESS CHANNEL SPARSITY

The intuitive explanation for the wireless channel sparsity is the number of MPCs.Therefore,the number of clusters or the number of MPCs within the clusters were once regarded as measures of channel sparsity.However,the low-power MPCs have a smaller impact on the channel sparsity,and this makes the number of MPCs more one-sided to measure the channel sparsity.Therefore,several channel sparsity measures including MPCs power are introduced and analyzed based on measurements in this section.

4.1 Measurement of Wireless Channel Sparsity

4.1.1 Gini Index

In[33],the Gini index,a concept from economics,is proposed to measure signal sparsity.Then,the effectiveness of the Gini index in measuring the wireless channel sparsity was validated in[34].The Gini index of wireless channel can be defined as follows[33]

where the power of MPCs in vectorpis arranged from the smallest to the largest,andpiis the power of the i-th MPCs.Nis the number of elements in the vectorp,and ∥· ∥1representsℓ1norm operation.The Gini index is normalized to between 0 and 1.When all the energy in the channel is concentrated on a single MPC,the most sparse channel is exhibited andG=1.When all the MPCs in the channel have the same power,the least sparse channel is exhibited andG=0.It is found from(1)that the Gini index considers the importance of the energy of MPCs in the overall sparsity of channel compared with the number of MPCs,thus it is used to measure the sparsity of the multi-scenario mmWave channel in this paper.

4.1.2 RicianKFactor

The RicianKfactor reflects the power ratio of the dominant components(LOS path or the path with the strongest power)and the remaining components in the channel,and it indicates the severity of fading in channel.As one of the most commonly used channel characteristic parameters,RicianKfactor is validated in measuring the wireless channel sparsity[34],and it is defined as

where|h|2maxand|h|2rrepresent the power of the dominant component and the remaining component in the channel,respectively.A large RicianKfactor usually corresponds to the reduced severity of fading in channel.In this paper,a larger RicianKfactor indicates that the power is more concentrated in dominant MPCs,which corresponds to a sparse channel.

4.1.3 RMS Delay Spread

The RMS delay spread is also one of the important channel characteristic parameters,which measures the delay dispersion characteristics of the wireless channel.Meanwhile,multipath propagation in wireless channel is the main cause of delay dispersion.Therefore,the RMS delay spread can reflect the distribution characteristics of MPCs.Refs.[12]and[34]both mention the use of RMS delay spread to measure channel sparsity.However,it has not been well validated.The RMS delay spread is the square root of the second central moment,and it is defined as

whereτirepresent the delay,andPidescribes the power of the corresponding delay.In this paper,the RMS delay spread is firstly used as a measure of wireless channel sparsity and the main reason is twofold:i) It is found from (3) that the power of MPCs is weighted and calculated into the RMS delay spread.This meets the requirement to cover power when measuring sparsity.ii)The delay dispersion characteristics described by RMS delay spread can reflect the MPCs distribution.For example,a large RMS delay spread corresponds to the severe delay dispersion in channel,and the non-sparse channel is exhibited under this condition.The effectiveness of RMS delay spread to measure wireless channel sparsity will be validated in Section 4.3.

4.2 Data Processing

The channel frequency responseH(f) in different scenarios is obtained through the VNA-based channel sounder.The channel impulse response (CIR)h(τ)can be obtained by performing the Inverse Fast Fourier Transformation (IFFT) operation on the channel frequency response.The Hann window is used to suppress side lobes.In addition,the Space-Alternating Generalized Expectation-Maximization(SAGE)algorithm is used to estimate parameters for each MPC including power and delay [40].Figure 8 illustrates an example of instantaneous power delay profile (PDP)|h(τ)|2and corresponding SAGE estimation results.It is found that the delay and power of MPCs estimated by SAGE are consistent with the measurement results.However,there are still some unreasonable samples with too small power in the estimation results of SAGE.Therefore,the noise threshold of 6 dB higher than the mean noise floor of measurement data is used to remove these unreasonable estimation results [41].The MPCs estimated with the power below noise threshold will be discarded.The SAGE estimation result after noise threshold denoising will be used in the calculations of(1)and(2).The RMS delay spread is directly calculated using the PDPs denoised by the method in Ref.[42].

4.3 Validation of Wireless Channel Sparsity Measures

In this paper,the Gini index,RicianKfactor and RMS delay spread are used to measure wireless channel sparsity.The effectiveness of Gini index and RicianKfactor in measuring channel sparsity has been validated in [34].The RMS delay spread is used for the first time to measure channel sparsity,and its effectiveness has not been validated in existing researches.Therefore,we analyze the effectiveness of RMS delay spread in measuring channel sparsity based on two validated sparsity measures–Gini index and RicianKfactor.

The correlation coefficients are used to describe the correlation between sparsity measures.When the RMS delay spread has a good correlation with the Gini index and RicianKfactor,its effectiveness in measuring channel sparsity will be validated.In this paper,the Pearson correlation coefficient[43]is used,and it is defined as

whereanddenote the mean values ofXandY,andnis the number of elements inXorY.The Pearson correlation coefficient is used to reflect the linear correlation between two variables,and its range is from–1 to+1.The value of–1 and+1 means complete negative and positive correlation respectively,and 0 means that there is no correlation between two variables.

The measurement data in different scenarios is used to calculate the Gini index,RicianKfactor and RMS delay spread according to the(1),(2)and(3),respectively.Figure 9 shows the relationship between three sparsity measures,and Table 2 lists the Pearson correlation coefficients between three sparsity measures.A larger Gini index indicates that the channel has a more sparse characteristic,and corresponds to a larger RicianKfactor.It is found from Figure 9a that the Gini index and RicianKfactor show a good positive correlation.This is consistent with theoretical analysis.The large RMS delay spread corresponds to a more non-sparse channel characteristic,and has a negative correlation characteristic with Gini index and RicianKfactor,which is consistent with the trend shown by the fitting curves in Figure 9b and Figure 9c.Meanwhile,the absolute values of Pearson correlation coefficients between three measures are all close to one in Table 2.This shows that there is a good positive or negative correlation between different sparsity measures.Since the Gini index and RicianKfactor have been validated to be effective channel sparsity measures,the RMS delay spread can also be regarded as an effective sparsity measure.

Table 2.Correlation coefficients between the three measures.

V.SPARSITY EVALUATION

In this section,we explore the factors that affect wireless channel sparsity from the two perspectives of antenna configuration and scenario.Three wireless channel sparsity measures are used in this section.Moreover,the impact of wireless channel sparsity on channel eigenvalue and capacity is evaluated and analyzed.

5.1 Sparsity Evaluation under Different Antenna Steering Directions

The effect of antenna steering directions on wireless channel sparsity is evaluated based on the channel measurements in Section III.The Tx antenna is assumed to be the origin of the coordinate system,and 0◦of the coordinate system is the direction in which steering the Tx antenna toward the Rx antennas,as shown in Figure 10.

Typical laboratory and meeting scenarios are used to evaluate channel sparsity at different antenna steering angles.Figure 11 shows the sparsity measures of different antenna steering angles in the laboratory and meeting scenarios.It is found that wireless channel is the most sparse when antenna steering angle is 0◦in the two scenarios.In this case,the Tx antenna steers their boresight toward the Rx antennas and the LOS path has the strongest power.Meanwhile,the power of the other NLOS paths is lower.Therefore,the Gini index and RicianKfactor are the largest and the RMS delay spread is the smallest,and the corresponding channel is the most sparse.In addition,it is found that channel sparsity is slightly improved when Tx antenna has a larger steering angle in the evaluation of Gini index and RicianKfactor.This is because the high-power specular reflection paths generated by the wall or window reach the Rx antennas when Tx antenna steers beam toward the wall or window at a suitable angle.The power of some MPCs is increased,and thus improves the level of channel sparsity.Compared with the Gini index and RicianKfactor,insignificant improvements in sparsity can be found in the evaluation of RMS delay spread.This is because the high-power specular paths from walls or windows have a large delay,and the RMS delay spread covers this effect.Therefore,this results in a higher RMS delay spread corresponding to the insignificant improvements in sparsity.Since high-gain and narrow-beam directional antennas are widely used in the mmWave frequency band,the width and steering directions of the antenna beam also affect mmWave channel sparsity.

5.2 Sparsity Evaluation in Different Scenarios

We evaluate and analyze channel sparsity in each scenario in Section III.Since different antenna steering directions will lead to different channel sparsity levels,the SAGE estimation results that Tx antenna steering angle is 0◦in Figure 10 and Rx antenna array measured at different positions are used to evaluate channel sparsity in different scenarios.Figure 12 shows the Gini index,RicianKfactor and RMS delay spread in different scenarios.It is found from Figure 4 that the corridor scenario is empty and closed.Almost no other cluttered objects in scenario act as scatterers for radio wave propagation.Therefore,its channel may be the most sparse in several scenarios from an intuitive point of view.However,the empty corridor has the smallest Gini index,RicianKfactor,and the largest RMS delay spread in Figure 12,which shows that its channel is not sparse.The non-sparse channel characteristics in empty corridor are more significant compared to other scenarios.Therefore,we analyzed the PDP of empty corridor for this kind of interesting phenomenon.Figure 13 shows the relationship between MPCs power and propagation distance and the estimation result of MPCs in empty corridor.In addition to the MPCs clusters with the propagation distance of less than 40 m,there are also high-power MPCs clusters at 61 m,65 m,86 m and 92.5 m.Such MPCs clusters are caused by multiple bounces of walls,ceilings,etc.Meanwhile,the width of the corridor is narrow and the scenario is empty.As a result,the phenomenon of multiple bounces of MPCs is more significant.The MPCs with multiple bounces,especially high-order reflections,have the characteristics of large delay and high power,which will significantly increase the RMS delay spread and decrease the Gini index and RicianKfactor.Therefore,the scenario of empty corridor exhibits more non-sparse characteristics.

For data center scenario,there are a lot of objects in the space that can act as scatterers.Meanwhile,there are several iron cabinets between the Tx and Rx propagation path,and their metal surfaces can be used as good reflectors to provide strong reflection paths.Therefore,the channel may be more non-sparse from an intuitive point of view.However,the sparsity level of data center scenario is higher than that of the empty corridor scenario according to the results shown in Figure 12.Even in the measure of RMS delay spread,the sparsity of data center scenario only at the midlevel in several scenarios.Figure 14 shows the PDP of data center scenario.It is found that the MPCs clusters are distributed near the LOS path,and the propagation distance of all MPCs is less than 35 m.Compared with the empty corridor scenario,data center scenario does not have MPCs clusters with longer propagation distance as shown in Figure 13.This makes it not exhibit the expected non-sparse channel characteristics.

The laboratory scenario has the largest Gini index,RicianKfactor and the smallest RMS delay spread in Figure 12.Therefore,it has the most sparse channel among several scenarios.In the laboratory scenario,equipment and other objects on desktop and shelves may act as scatterers,which is similar to data center.However,compared to data center scenario,the laboratory does not have the reflectors that can produce strong reflection paths such as iron cabinets.This is confirmed in the curve of the relationship between MPCs power and propagation distance in laboratory scenario shown in Figure 15.The power level of reflection and scattering MPCs in Figure 15 is overall lower than that of Figure 14,which results in a larger Gini index and RicianKfactor.Meanwhile,the propagation distance of MPCs in Figure 15 is all within 25 m,which leads to a smaller RMS delay spread.Therefore,the channel of laboratory scenario exhibits the most sparse characteristics in all scenarios.

In stacking and shuttle car scenario,the Rx is located on the shuttle car surrounded by steel frames.From an intuitive point of view,dense steel frames may produce more and stronger reflection and scattering paths,and exhibit a non-sparse characteristic.However,the channel non-sparseness level in this scenario is only slightly higher than the most sparse laboratory scenario from the measures of Gini index and RMS delay spread in Figure 12.The steel frames near the Rx will produce a part of strong reflection paths in this scenario.However,the MPCs with multiple bounces will be blocked by other dense frames during the propagation process,and they cannot propagation farther to reach the Rx.This makes the r eflection and scattering paths mostly distributed around the LOS path,which leads to a smaller RMS delay spread and sparse channel characteristics.

According to the sparsity quantifciation and analysis results of the above several scenarios,it is found that the objects in the scenarios may not be able to act as scatterers in the channel to provide richer MPCs,and can block the MPCs generated by other effective scatterers,such as data center,stacking and shuttle car,and laboratory scenarios.Various objects are placed in these scenarios.Even if some objects are made of strong reflective materials such as metals or steel,they are more likely to block MPCs than propagate,so that the channel exhibits a more sparse characteristic.When the scenarios are closed and there are few objects,it is more conducive to the propagation of MPCs,such as empty corridor scenario.The closed feature creates conditions for the MPCs to bounce multiple times in the environment.Meanwhile,the feature of few objects makes these MPCs difficult to be blocked during propagation.This can be explained as the reverberation effect of electromagnetic waves in indoor wireless channels[44].The non-sparse characteristics of wireless channel are more obvious when the reverberation effect is significant.In addition,it is found from Figure 12 that the sparsity levels measured by the three measures are not completely consistent in a few scenarios.This is because different sparsity measures consider different factors.For example,the Gini index focuses on evaluating the energy distribution of MPCs,RicianKfactor evaluates fading in channel,and the RMS delay spread measures the channel delay dispersion characteristics.Meanwhile,different factors are often related to each other,and their mutual influence is difficult to quantify.Therefore,the sparsity results of different measures may not be completely consistent when the sparsity levels are similar.But for the scenarios with obvious differences in sparsity,the sparsity results of the three measures are consistent.

5.3 Channel Eigenvalue Analysis

Channel eigenvalue measures the number of eigen channels for spatial multiplexing [23].In this section,the eigenvalues ofH(f)HH(f) (the superscriptHdenoting conjugate transpose)in different scenarios are calculated and compared.Among them,H(f) ∈is the channel frequency responses withNTxTx antennas andNRxRx antennas,and the numbers of Tx and Rx antenna elements are 6 (different antenna steering angles)and 32(4×8 array antenna),respectively.Then,the channel eigenvalues are normalized using the following method:

whereλ′idenotes thei-th raw channel eigenvalue ofH(f)HH(f).

Figure 16a and Figure 16b show the normalized channel eigenvalue distribution and the corresponding CDFs in different scenarios.It is found from Figure 16a that the first two eigenvalues in different scenarios are roughly equal.This is because normalization removes the impact of distance on path loss,and the strong dominant eigenmodes corresponding to LOS paths are similar in different scenarios.From the third eigenvalue,the difference begins to appear due to the different distribution of NLOS clusters in different scenarios.The data center scenario has the largest first seven eigenvalues.This is because the iron cabinet produces the stronger and denser low-order reflection and scattering paths,resulting in higher channel eigenmodes in the first seven eigenvalues.However,the stronger first seven eigenvalues do not make the data center scenario show stronger non-sparse characteristics.Among the remaining non-dominant eigenvalues,the corridor scenario has the largest eigenvalue magnitude due to some MPCs with longer propagation delay.Therefore,the non-dominant MPCs corresponding to non-dominant eigenvalues have a more significant impact on channel sparsity.This is also confirmed by the eigenvalues distribution of the laboratory scenario.The laboratory scenario does not have the smallest eigenvalue for the first five dominant eigenvalues.However,it has the smallest non-dominant eigenvalues and exhibits the most sparse channel in all scenarios.In addition,larger non-dominant eigenvalues indicate richer non-dominant MPCs,which will increase the number of available spatial multiplexing streams and affect channel capacity.The impact of channel sparsity on capacity will be discussed in Section 5.4.

5.4 Capacity Analysis

In this section,we evaluated and analyzed the impact of channel sparsity on capacity in different scenarios.The narrowband channel capacity is defined as[45]:

wheref=1,2,...,Ω is the sub-frequency indexes,and Ω is the number of frequency points.INRxis the identity matrix of sizeNRx×NRx,andρdenotes the average SNR.TheH(f) consists of 6 different steering angles of Tx and 32 array elements of Rx,and the channel capacity of different Rx positions in each scenario is evaluated.

In this paper,the channel measurement data is wideband,and it is composed of multiple frequency index.Therefore,the wideband channel capacityCwbcan be expressed in terms of the narrowband capacities as[46]:

In addition,the distance between Tx and Rx is different in multi-scenarios.Since the different distances between transceivers can cause different path loss or received power,the normalized channel frequency responseH(f) is used to make the path loss between Tx and Rx antenna unity in different scenarios.We use the following scaling factors to normalize channel frequency responseH(f)[47]

Figure 17 shows the CDFs of channel capacity in different scenarios.It is found that the laboratory scenario with the most sparse channel has the smallest channel capacity,and the empty corridor scenario with the least sparse channel has the largest channel capacity.The results indicate that sparse channel will lead to lower MIMO channel capacity.In addition,the distribution of channel eigenvalues ofHHHplays a key role in channel capacity[46].Combining the analysis results of Figure 16 and channel eigenvalues,the sparse channel is more likely to produce small non-dominant eigenmodes corresponding to small non-dominant MPCs power.This key impact is that small non-dominant MPCs power cause a larger capacity penalty.On the contrary,in non-sparse channels such as corridor scenario,higher-order reflections are more obvious.These high-order reflection paths have high power and result in lagre nondominant eigenvalues.Meanwhile,the correlation of high-order reflection paths in the delay and angle domains is weak due to multiple bounces.This will lead to a higher channel capacity.

VI.CONCLUSION

In order to evaluate channel sparsity based on measurements,a mmWave channel sounder system was constructed,and the multi-scenario mmWave channel measurement campaign was conducted at 28 GHz in this paper.Three sparsity measures are used,which are Gini index,RicianKfactor and RMS delay spread.Then,the factors affecting sparsity in the mmWave channel are explored based on sparsity measuring results.The width and steering directions of the antenna beam are found to affect channel sparsity.When steering the beam of Tx antenna toward Rx antennas,channel exhibits the most sparse characteristics.In addition,the distribution of scatterers also affects channel sparsity.It is found that dense objects can block the propagation of MPCs.On the contrary,empty and closed scenarios are more conducive to the propagation of MPCs,which makes them exhibit more non-sparse channel characteristics.Then,based on the properties of channel eigenvalue,the non-dominant MPCs corresponding to non-dominant eigenvalues have a more significant impact on channel sparsity.Finally,the channel capacity in different scenarios is evaluated and compared.The results indicate that sparse channel can cause a larger capacity penalty.The research in this paper enriches the understanding of mmWave channel sparsity and can be used in channel modeling and performance evaluation of communication systems.

ACKNOWLEDGEMENT

This work is supported by National Key R&D Program of China under Grant 2022YFF0608103,the National Natural Science Foundation of China under Grant 61922012,the Science and Technology Program of State Administration for Market Regulation under Grant 2021MK155,and the Fundamental Funds of National Institute of Metrology under Grant AKYZD2116-2.The authors would like to thank Mr.Chengyi Zhou and Mr.Huichao Shang from Beijing Jiaotong University for the help in wireless channel measurements.