Dazhi Piao,Meng Wang,Jie Zuo,Hao Zhou

School of Information and Communication Engineering,Communication University of China,Beijing 100024,China

Abstract:The dual-port compact multiple-input multiple-output(MIMO)dipole antennas with close spacing d of 0.5 λ and 0.3 λ are designed,and some electromagnetic band gap(EBG)structures are inserted between them to reduce mutual coupling.Those MIMO antennas with d=0.5 λ and 0.3 λ,and with different mutual couplings are fabricated and measured,the channel capacity and correlation coefficient(CC)are analyzed and compared in a rich multipath reverberation chamber(RC),an office and a conference room.Results show that if d is reduced from 0.5 λ to 0.3 λ,in the RCs,channel capacities of all the antennas are very close to that of the i.i.d.Rayleigh channel,although the average CCs are increased from 0.168 in the nonlossy RC to 0.269 in the lossy RC.In the office and conference rooms,compared with the RC,the average capacities of those antennas get a slight reduction,however,in most cases,the capacity of d=0.5 λ is larger than that of d=0.3 λ,and the antennas with EBG have a larger capacity compared with the antennas without EBG,with a corresponding reduction of CC.A non-line-of-sight(NLOS)scenario of through-the-wall is also investigated.

Keywords:compact MIMO antenna;channel capacity;spatial correlation;measurement

I.INTRODUCTION

It has been shown theoretically that the capacity of a multiple-input multiple-output(MIMO)system scales linearly with the min(nT,nR),fornTtransmit(Tx)antennas andnRreceive(Rx)antennas in the uncorrelated channels[1].Thus,to fully explore the potential of the MIMO system,multiple antennas are required in both the base station as well as the user terminal.To reduce the size of MIMO antenna array,compact MIMO antenna designs are strongly desired.However,insufficient spacing will increase mutual coupling of the antennas[2],increase the correlation of channel gains and reduce the channel capacity[3,4].Generally,it is considered that the channel decorrelation distance is 0.5λ(λis the free space wavelength)[5],thus in MIMO antenna design and performance evaluation,array element spacingdequaling or larger than 0.5λis usually considered,such as[3],[5–13],by measurement in indoor or outdoor environments,or by theoretical analyses and simulations.Studies dedicated to clarify the effect of smaller element spacing on MIMO systems are still so few,and whether the MIMO performance will be severely degenerated fordless than 0.5λin either or both the Tx and Rx ends,there are very different opinions.

In a rich multipath indoor environment,shown by ray-tracing simulation and measurement that[14],for Tx using cross-polarized dipoles separated by 2.45λand Rx using uni-polarized dipoles,whendin Rx is reduced below 0.5λ,there is no significant capacity decrease.Moreover,for an element spacing decreased from 0.5λto 0.2λ,the link capacity is not smaller than that for much largerd,which was explained that mutual coupling changes the radiation patterns of closely spaced antennas[15].

However,based on the measurement in an urban outdoor environment[16],ford=0.4λand 0.5λin Rx and Tx,respectively,the MIMO capacity got over 10% smaller than that of the independent and identically distributed(i.i.d.)Rayleigh channel;and it was also shown that ifdis reduced from 5λto 0.5λand less,the capacity of indoor MIMO channel would be greatly reduced and far less than that of the i.i.d.Rayleigh channel by simulations[17].Furthermore,in some indoor scenarios,it was verified that if the element spacing is decreased from 0.5λto 0.25λ,the channel capacity of a MIMO system would get a 6%-30%reduction related to array orientations and propagation conditions[18],and reduced by more than 10%and obviously smaller than that of the i.i.d.Rayleigh case[19].Also in an indoor scenario,for Tx employing cross-polarized elements with separation of 1λ,the capacity decreased obviously for element spacing less than 0.5λin Rx for uni-polarized elements[20].By the measurements in a reverberation chamber(RC)and in a suburban outdoor environment,it is shown that ifdis reduced from 1λto 0.5λand less in the Rx,the ergodic MIMO channel capacity will be obviously reduced by the increased correlation between the antennas[21].Based on network-theory framework and full-wave electromagnetic antenna simulations,it has been shown that whether the mutual coupling is included in the modeling,it would have great influence on the MIMO capacity whend<0.5λ[22].

Based on the above analysis,how small the MIMO element spacing can be made without a significant capacity reduction is still a question,especially considering the mutual coupling and richness of propagation environment.Thus,in this paper,we try to conduct some investigations to get deeper insight into the working principle of compact MIMO antenna array.In particular,four kinds of dual-port MIMO antennas with element spacing of 0.5λand 0.3λwith different mutual couplings are designed and tested,individually.The system performance of those MIMO antennas in terms of channel capacity and signal correlations are analyzed and compared,in a rich multipath RC,and some real-world indoor secnarios including an office room and a conference room with line-ofsight(LOS)and non-line-of-sight(NLOS)propagations.

II.MIMO ANTENNA DESIGN

2.1 MIMO Antenna with Element Spacing of 0.5 λ

Firstly,a dual-port MIMO antenna composed of two electric dipoles working at 2.4 GHz separated by 0.5λis designed,as shown in Figure 1a and 1c.To reduce the mutual coupling between the antenna elements,an array of electromagnetic band gap(EBG)structures[23](1×10 unit cells)is inserted between the two dipoles,as shown in Figure 1b and 1d.The antennas are printed on a FR4 dielectric substrate with permittivityεr=4.4 and thicknessh=1.6 mm.

Figure 1.MIMO antenna with d=0.5 λ.(a)antenna without EBG.(b)antenna with EBG.(c)photograph of antenna without EBG.(d)photograph of antenna with EBG.(w1=3,w2=6,g1=2,l1=20,l2=19,unit:mm)

The simulated and measured S-parameters of the antennas are shown in Figure 2.It is observed that the antenna without EBG achieves a mutual coupling of about-14 dB in Figure 2a,and it can be reduced to-25 dB for the antenna with EBG at the central frequency of 2.4 GHz in Figure 2b.The far-field radiation patterns of antennas are also measured,which are given in Figure 3.The measured results are basically consistent with the simulation results.

Figure 2.S-parameters of MIMO antenna with d=0.5λ.(a)without EBG.(b)with EBG.

Figure 3.Radiation patterns of dipole 1 at 2.4 GHz for d=0.5 λ.(a)E-plane,without EBG.(b)E-plane,with EBG.(c)H-plane,without EBG.(d)H-plane,with EBG.

2.2 MIMO Antenna with Element Spacing of 0.3 λ

In order to investigate the MIMO performance of element spacing less than a half wavelength,a MIMO antenna withd=0.3λis also designed for comparison,which is shown in Figure 4a and 4c.For such closely spaced two antennas with the same working frequency,the mutual coupling is comparatively higher,thus an array of the EBG structures is also inserted between the MIMO antennas to reduce the mutual coupling.For such a case,the dipole antennas can be hardly impedance matched by just adjusting its sizes or shapes,thus,a matching stub is used to make the antenna matched to 50 ? load,as shown in Figure 4b and Figure 4d.

The S-parameters of the MIMO antenna withd=0.3λare illustrated in Figure 5.We can see that,for the MIMO antenna without EBG,the mutual coupling at the resonant frequency of 2.4 GHz is -10 dB,with the addition of EBG,it can be greatly reduced to lower than-17.5 dB.

Figure 4.MIMO antenna with d=0.3 λ.(a)antenna without EBG.(b)antenna with EBG.(c)photograph of antenna without EBG.(d)photograph of antenna with EBG.(w1=3,w2=6,l3=19.5,l4=20,l5=20.8,g1=2,p1=0.8,p2=8.3,p3=12.5,p4=7.2,unit:mm)

Figure 5.S-parameters of MIMO antenna with d=0.3λ.(a)without EBG.(b)with EBG.

According to Figure 2 and Figure 5,with the decrease of the element spacing from 0.5λto 0.3λ,the mutual coupling of antennas at the resonant frequency will be increased from-14 dB to-10 dB,with the insert of just one column of the EBG structure,a mutual coupling decrease of over 7 dB can be achieved.

The far-field radiation patterns of the antennas are given in Figure 6.The measured results are basically in agreement with the simulation results.Combining the results in Figure 3 and Figure 6,it is illustrated that,for both MIMO antennas,by inserting the EBG structure,the radiation patterns will get small distortions from that without EBG.

Figure 6.Radiation patterns of dipole 1 at 2.4 GHz for d=0.3 λ.(a)E-plane,without EBG.(b)E-plane,with EBG.(c)H-plane,without EBG.(d)H-plane,with EBG.

Figure 7.Measurement in office room.

III.MIMO ANTENNA MEASUREMENT SETUP

The behaviour of a MIMO system is closely related to the richness of multipath of the environment.Thus,in order to get a comprehensive knowledge of the MIMO performance for the designed four kinds of MIMO antennas with element spacing reduced from 0.5λto 0.3λand with various mutual couplings,the MIMO propagation experiments are carried out in both a rich multipath RC and some realistic indoor senarios including an office room and a conference room.

In each scenario,firstly the fabricated MIMO antenna withd=0.5λis employed at both the Tx and Rx ends,and the scattering parameters are obtained by a 4-port vector network analyzer(VNA)Ceyear AV3672D.Then,the procedure is repeated for both the Tx and Rx ends using the MIMO antenna withd=0.3λ.The channel matrix H was determined by the transfer parameters between each pair of the Tx and Rx antenna elements,with the remaining elements terminated by matched loads.The VNA is set to 1601 frequencies sweep sampling points over the 2-3GHz.

3.1 Experiment in Reverberation Chamber

RC is an electrically large cavity to provide a rich uniform and isotropic multipath fading environment[24,25],which can isolate external electromagnetic environment and provide us a very suitable experimental environment to measure the performance of MIMO system.The RC used in the measurement has a volume of 1.1×0.7×0.6m3with two metal stirrers,the detailed description about this RC could be found in[26].Both of a non-lossy RC and a lossy RC with one absorber(50 cm×20 cm)added in the middle of the link are considered,to change the richness and distribution of multipath.The distance between Tx and Rx ends is 0.55 m,and the heights of antennas above the bottom of RC are equal to 0.18 m.During the measurement,for each Tx and Rx antenna pair,the two stirrers were rotated from 0°to 360°,with 36 location points at 10° increments,and the channel responses are recorded for each angle of the rotation.

3.2 Experiment in Office Room

The MIMO performance measurements are also conducted in an office room,which is 5.5 m long,2.59 m wide and 3.2 m high.The layout of furniture,experimental equipment and antenna is shown in Figure 7.Two identical tested antennas are placed vertically to the floor at the Tx and Rx ends with a spacing of 1.5 m.There is no barrier between Tx and Rx ends,which is a clear LOS channel.During the measurement,to capture the small-scale propagation characteristics,the Tx antenna is fixed,and the Rx antenna is placed randomly in 36 locations inside a circle with a radius ofλ/2.

Figure 8.Measurement in the conference room.

3.3 Experiment in Conference Room

In addition to the small room above,the measurements have also been carried out in larger conference room with the dimensions of 6×5.42×3.2m3,in which the layout of furniture and antenna is shown in Figure 8.In the conference room,the measurement procedure is similar to that in the office above;however,two Tx and Rx spacings of 1.5 m and 3 m are investigated in a LOS case,individually,as shown in Figure 8.Moreover,a NLOS scenario of through-the-wall is also considered,in which the Tx and Rx are placed on the two sides of a wall in this room with a separation of 2.76 m.The thickness of the wall is 0.32 m,and there is a corridor outside the door.

IV.PERFROMANCE OF THE MIMO SYSTEM

4.1 Channel Capacity

The channel capacity has been extensively used for evaluating the MIMO channel,which is defined as the highest achievable bit rate of information that can be sent with arbitrary low probability of error.The equal power transmission strategy is generally employed to compute the capacity,the corresponding channel capacity formula is as follows[1]

where I is a 2×2 unit matrix,nT=2,det is the determinant of matrix,SNRis the signal to noise ratio.HHmeans the transpose conjugate of H.To illustrate the impacts of the richness of multipath on the MIMO capacity and eliminate the effect of the absolute received power,the channel matrix is normalized by[12],

where‖·‖F(xiàn)means the Frobenius norm,Kmeans all the parameters over which the capacity is analyzed,which includes all the spatial and frequency field the capacity is statistically analyzed.In this paper,K=36(number of antenna positions)×321(number of frequency points over 2.3-2.5GHz)×4(size of channel matrix).A 20 dBSNRis assumed in the calculation of the channel capacity obtained by the 2×2 MIMO system.

4.2 Correlation Coefficient

The correlation coefficient is a very important factor affecting the diversity and capacity performance of a MIMO system,for two complex random variablesuandv,it is defined as

For the 2×2 MIMO system,to get a comprehensive understanding of the statistical performance of H,totally 4 variables of correlation coefficient(CC)should be investigated in both the Tx sideand Rx side.For an example,means the correlation of the signals received by first Rx antenna,arriving from the first and second Tx antenna elements,similarly,means the correlation between the first and second Rx antenna elements,with respect to the first Tx antenna.Here,to be concise,their average results of cumulative distribution functions(CDFs)are computed for each case.The detailed procedure to get the CDF of each CC could be found in[27].

4.3 Measurement Results

The CDFs of channel capacity and correlation coefficient for the MIMO antennas with element spacing of 0.5λand 0.3λwith and without EBG are plotted in Figure 9 for RC and office room,and in Figure 10 for the conference room,furthermore,their statistical mean values are also given in Table 1.For concise,the four kinds of antennas are denoted by Case A(0.3λwithout EBG),Case B(0.3λwith EBG),Case C(0.5λwithout EBG),and Case D(0.5λwith EBG).

It can be seen from Figure 9a and 9c that,in the nonlossy RC,the channel capacities obtained by all the four types of MIMO antennas have almost no difference,and in the lossy RC with one absorber,only Case A got a slight reduction of 2.38%compared with Case D,although the CC in the lossy RC is obviously increased with respect to that in nonlossy RCs,and the mean values are increased from about 0.168 to 0.269,as can be seen from Figure 9b and 9d and Table 1.Noticeably,from Figure 9e we can see that,in the office room,the capacity differences of the four MIMO antennas get large,the antenna of 0.5λwith EBG is the largest,and the case of 0.3λwithout EBG is the lowest,which can be well explained by an increased CC,shown in Figure 9f.

Table 1.Average channel capacity and correlation coefficient(CC).

Figure 9.Channel capacity and correlation coefficient in RC and office room.(a)capacity in RC without absorber.(b)CC in RC without absorber.(c)capacity in RC with absorber.(d)CC in RC with absorber.(e)capacity in office room.(f)CC in office room.

Figure 10.Channel capacity and correlation coefficient in conference room.(a)capacity of LOS 1.5 m.(b)CC of LOS 1.5 m.(c)capacity of LOS 3 m.(d)CC of LOS 3 m.(e)capacity of through-the-wall with door open.(f)CC of through-the-wall with door open.(g)capacity of throughthe-wall with door close.(h)CC of through-the-wall with door close.

Figure 10 shows us that,for the same Tx and Rx separation of 1.5 m,the channel capacity in the conference room will be larger than that in the smaller office room for most of the antenna types,however,with an increased CC,which means that channel capacity is not fully associated with the CC.Comparing the results of 3 m with that of 1.5 m in the same conference room,the channel capacity will get a reduction of about 5.62% for the correspondent antennas,with a related increasing of CC,in most cases.Moreover,in almost all these cases,the capacity of MIMO antenna with EBG will be obviously larger than the corresponding antenna with no EBG,with a relevant reduced CC,which could be explained by the enhanced spatial diversity caused by the increased radiation directivity with EBG inserted.For the NLOS scenarios of through-the-wall,the MIMO antenna of 0.3λwithout EBG will be clearly smaller than the results in the LOS scenarios,with a related increased CC,and for the other types of antenna,the channel capacities are almost between the results of 1.5 m and 3 m LOS cases,with similar values of CC.The CCs in the case of open door are smaller that than the corresponding results in the case of closed door for all types of the antenna,however,which will not always result in a larger channel capacity.

V.CONCLUSION AND DISSCUSSION

To get a deeper understanding of the working principle of compact MIMO system,four kinds of dualport MIMO antennas with compact element spacingdequaling to 0.5λand 0.3λwith different mutual couplings are designed and fabricated.The MIMO channel characteristics are measured and compared in a rich multipath RC and some real-world indoor environments with LOS and NLOS propagations.Results show that,whendis reduced from 0.5λto 0.3λ,in the uniform rich multipath RC,the channel capacity does not get obvious reduction and are very close to that of the i.i.d.Rayleigh channel.In the realistic office and conference room,in most situations,the capacity of the array withd=0.3λwill be slightly smaller than that ofd=0.5λ,and the capacity of the array with EBG will be larger than that with no EBG caused by an enhanced radiation directivity.

Conclusions can be drawn that,in the sufficiently rich multipath environment,compact MIMO antenna array can have a good capacity performance.Smaller correlation coefficients will always lead to larger MIMO capacities;however,the MIMO capacity are not fully related to the correlation performance,which is a complex result of the array geometry,the radiation properties of the antenna elements,and their interactions with the propagation environment.Although only a 2-ports MIMO system is considered here,the performance of MIMO capacity and spatial correlation from measurements can provide valuable references for the MIMO system with larger size.The compact and low-coupled MIMO antenna array with more ports working at different frequency bands from Sub-6 GHz to millimeter wave will be devised and investigated in the future.

ACKNOWLEDGEMENT

This work was supported by the National Natural Science Foundations of China(Grant No.61771435).