Title Measurement-Based Performance Evaluation of MIMO Spatial Multiplexing in a Multipath-Rich Indoor Environment

Author(s) Nishimoto, Hiroshi; Ogawa, Yasutaka; Nishimura, Toshihiko; Ohgane, Takeo

IEEE Transactions on Antennas and Propagation, 55(12), 3677-3689

Citation https://doi.org/10.1109/TAP.2007.910303

Issue Date 2007-12

Doc URL http://hdl.handle.net/2115/32296

©2007 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for
advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists,
Rights or to reuse any copyrighted component of this work in other works must be obtained from the IEEE. IEEE, IEEE
Transactions on Antennas and Propagation, 55(12), 2007, p3677-3689

Type article

File Information 04388117.pdf

Instructions for use

Hokkaido University Collection of Scholarly and Academic Papers : HUSCAP

IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 55, NO. 12, DECEMBER 2007 3677

Measurement-Based Performance Evaluation of

MIMO Spatial Multiplexing in a Multipath-Rich
Indoor Environment
Hiroshi Nishimoto, Student Member, IEEE, Yasutaka Ogawa, Senior Member, IEEE,
Toshihiko Nishimura, Member, IEEE, and Takeo Ohgane, Member, IEEE

Abstract—Multiple-input multiple-output (MIMO) spatial Coding and signal processing are key elements to successful
multiplexing that needs to separate and detect transmitted signal implementation of a MIMO system. However, issues related to
streams by using processing at the receiver end can increase antennas and electromagnetic propagation also play a signifi-
the data rates of transmissions on independent and identically
distributed (i.i.d.) channels. Such channels have been considered cant role in determining MIMO system performance [9]. A low
to exist in nonline-of-sight (NLOS) environments. However, actual correlation between channels is desirable because spatial mul-
communications may also be conducted in line-of-sight (LOS) tiplexing needs to demultiplex the received signals in order to
environments. While an LOS component can increase the received detect the transmitted streams at the receiver end. Availability
power level, it may also cause correlated channels that make it dif- of spatial multiplexing has been assessed for independent and
ficult to detect the transmitted streams. In this paper, we describe
the performance of 4 4 MIMO spatial multiplexing based on identically distributed (i.i.d.) Rayleigh fading channels caused
LOS and NLOS channel measurements in an indoor environment. by many scattered signals from surrounding objects. Fades be-
For eight configurations of uniform linear arrays (four antenna tween pairs of transmit-receive antenna elements (channels) are,
spacings and two array orientations), we evaluated the cumulative however, correlated in real propagation environments due to in-
distribution function (CDF) of the channel capacity and bit error sufficient antenna spacing [10]. Moreover, since mutual cou-
rate performance versus transmit power, and we analyzed them
in terms of antenna pattern, fading correlation, CDFs of MIMO pling effects [11]–[16] exist in a multiple antenna system, char-
channel elements, and CDFs of eigenvalues. Results show that, acteristics of each antenna vary from those of a single isolated
despite higher fading correlations and non i.i.d. channel character- antenna case. Therefore, in actual MIMO communication sys-
istics, the performance of MIMO spatial multiplexing in the LOS tems, there is no guarantee that channels are i.i.d. and even that
environment is better than that in the NLOS one. However, the MIMO channel elements obey identically distributed fading.
performance in the measured LOS environment largely depends
on the MIMO configuration. Uncorrelated channels generally may exist in nonline-of-sight
(NLOS) environments where there is no direct wave from the
Index Terms—Array element pattern, bit error rate (BER), transmitter to the receiver. However, there are many situations in
channel capacity, channel element distribution, eigenvalue dis-
tribution, fading correlation, indoor channel measurement, which communications are done also in line-of-sight (LOS) envi-
multiple-input multiple-output (MIMO), mutual coupling, spatial ronments. In such cases, while the LOS component can increase
multiplexing. the received power level, the channels lose independence and are
correlated. Highly correlated channels may make it difficult to de-
tect the transmitted streams. On the other hand, many radio prop-
agation measurement campaigns have already been conducted on
I. INTRODUCTION MIMO systems [17]–[24]. So far, most of researchers have eval-
uated the performance of the MIMO systems as a function of
HE multiple-input multiple-output (MIMO) system in
T which multiple antennas are placed at both the transmitter
and receiver end can potentially meet the growing demand for
average SNR. Because of the evaluation, some reports have pre-
sented that NLOS environments give higher channel capacities
than LOS ones [17], [22]. However, we must raise the following
higher capacity in wireless communications [1]–[5]. One of issue regarding these conclusions. In NLOS environments, the
the applications of the MIMO system is spatial multiplexing transmit power must be higher than in LOS environments in order
in which each transmit antenna sends an independent signal to obtain the same SNR. In [17], while channel capacities under
stream with equal power allocation [6]–[8]. When information the same SNR condition are evaluated for both LOS and NLOS
on the channel state is not available at the transmitter end, this environments, it is also briefly discussed that the comparison is
technique seems to be a promising way to increase data transfer not necessarily fair. Moreover, it has been reported in [23] and
speeds without expanding the frequency bandwidth. [24] that the actual SNR enlarged by the LOS component provides
higher channel capacities. The authors agree with their viewpoint
Manuscript received September 16, 2005; revised May 15, 2007. This work
was supported in part by a Research Fellowship for Young Scientists from the
andconsiderthattheperformanceevaluationoftheMIMOsystem
Japan Society for the Promotion of Science. should be done under the same transmit power condition.
The authors are with the Graduate School of Information Science and In measurement-based studies, MIMO systems have or-
Technology, Hokkaido University, Sapporo 060-0814, Japan (e-mail: dinarily been evaluated using channel capacities [17]–[24].
hn@ist.hokudai.ac.jp; ogawa@ist.hokudai.ac.jp; nishim@ist.hokudai.ac.jp;
ohgane@ist.hokudai.ac.jp). Channel capacity is, however, the limit of digital communi-
Digital Object Identifier 10.1109/TAP.2007.910303 cations given by the information theory. It would be achieved
0018-926X/$25.00 © 2007 IEEE
3678 IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 55, NO. 12, DECEMBER 2007

independent signal streams are transmitted from the TX an-

tennas, an -dimensional received signal vector is ex-
pressed as

(1)

where is an -dimensional transmitted signal vector,

and is an -dimensional additive white Gaussian noise
vector. An MIMO channel matrix consists of
channel responses between TX and RX antennas. These are
Fig. 1. A model of MIMO spatial multiplexing.
represented as follows:

(2)
only if we employed an ideal transmission method that includes
coding and modulation. From the implementational viewpoint, (3)
we consider that not only channel capacity but also bit error rate
(BER) can be used to evaluate digital wireless communications.
On the basis of these ideas, we conducted a MIMO channel .. .. .. (4)
. . .
measurement campaign in an indoor propagation environment
where there are many scattered waves. While keeping a con-
stant distance between the transmitter and the receiver, we mea- Here, the superscript indicates a transpose. Also, , which
sured 4 4 MIMO channels with mutual coupling between an- is an element of the th row and the th column in the matrix
tennas in both LOS and NLOS conditions. The performance of , denotes a channel from the th TX antenna to the th RX
MIMO spatial multiplexing in both the environments was exam- antenna.
ined under the same transmit power condition. In this paper, we As will be stated next, the measured MIMO channels have
used channel capacity for the evaluation of ideal spatial multi- mutual coupling effects. When mutual coupling matrices in the
plexing, and used BER under a constant bit rate requirement for TX and RX arrays are defined as and , respectively,
the case of simple spatial filtering, which proved to be a more the measured channel matrix is expressed as
realistic and practical performance evaluation.
To investigate the effects of mutual coupling on the mea-
sured channel responses, we paid attention to array element (5)
patterns. Compared with the single antenna case, the antenna
gain with mutual coupling depends on the direction and the where is an real channel matrix which does not
array configuration. In particular in LOS environments, the vari- include mutual coupling effects. When all of antennas in an
ation of antenna gain changes the impact of the LOS compo- -element array are assumed to have the same load impedance
nent in the measured channel. We explored, therefore, the in- , an mutual coupling matrix is defined as
fluence of array element patterns on the statistical properties of
the measured channels and relationship between the influence
and the performance of MIMO spatial multiplexing. Moreover, .. .. .. ..
. . . .
as aforementioned, we examined the BER performance based
on the propagation measurement campaign. This means that,
(6)
MIMO spatial multiplexing is comprehensively evaluated in the
range from antennas and propagation to signal processing in this where is self/mutual impedance between the th and th an-
paper. tennas [11], [12]. Note that and can actually have
This paper is organized as follows. Section II defines the different definitions. In this paper, however, we do not discuss
model of MIMO spatial multiplexing. Section III outlines our them because it is beyond the scope of this paper. We obtained
measurement campaign and describes characteristics of the MIMO transfer matrices including mutual coupling effects from
measurement environment. Section IV reports the performance channel data measured in actual indoor propagation environ-
of 4 4 MIMO systems using the measured data. We draw ments (see later). Using the measured channels, the characteris-
conclusions from these results in Section V. tics and the performance of spatial multiplexing were evaluated.

III. MIMO CHANNEL MEASUREMENT SETUP

II. MIMO SPATIAL MULTIPLEXING The measurement campaign was carried out in a conference
room in a building of the Graduate School of Information Sci-
Fig. 1 shows the model of MIMO spatial multiplexing. We ence and Technology at Hokkaido University (Fig. 2). The room
assume that the transmission bandwidth is so narrow that the had many scatterers. The walls consisted of plasterboard around
fading is flat. Moreover, the MIMO system is assumed to have reinforced concrete pillars and metal doors. In this room, we
transmit (TX) antennas and receive (RX) antennas. If set up TX and RX tables and a vector network analyzer (VNA)
NISHIMOTO et al.: MIMO SPATIAL MULTIPLEXING 3679

.
Fig. 3. Antenna array orientations. (a) TX-x/RX-x. (b) TX-y /RX-y

to avoid deterministic waves, which were diffracted at edges of

the partition, arriving at the receiver.1 There was a metal screen
(whiteboard) on the wall behind the TX table. The height of its
bottom was 1 m, and antenna height was 0.9 m as illustrated in
Fig. 2(b). Channel data were obtained while no one was in the
room, to ensure statistical stationarity of propagation.
The and axes were defined as in Fig. 2(a). The MIMO
measurement campaign used uniform linear antenna arrays. TX
and RX antennas aligned along the axis are denoted as the
TX- /RX- orientation [Fig. 3(a)], and antennas aligned along
the axis are denoted as the TX- /RX- orientation [Fig. 3(b)].
To obtain spatially different fading channels, there were seven
positions on the TX and RX tables for the antenna array mount
along the and axes separated with an interval of (1.5
cm), as shown in the dashed circles in Fig. 2(a), where de-
notes the wavelength at 5 GHz (6 cm). The antenna array orien-
tation corresponds to the array position direction also as shown
in the dashed circles in Fig. 2(a). For example, the positions of
the TX and the RX arrays for the TX- /RX- orientation were
changed in the direction. The array’s antenna spacing (AS)
had four values: , and . By changing
the TX and RX array positions, we obtained spatially
different data. Because we had 1 601 frequency-domain data, a
total of different MIMO channel matrices
were obtained for each array orientation, antenna spacing, and
LOS/NLOS condition. All of the characteristics presented in the
next section were derived from statistical processing of all the
Fig. 2. Measurement site. (a) Top view. (b) LOS. (c) NLOS. 78 449 MIMO channel data.
We employed colinear antennas AT-CL010 (TSS JAPAN Co.,
to measure the channel responses. The measurement band was Ltd.) designed for omnidirectional characteristics on the hori-
from 5.15 to 5.4 GHz (250 MHz bandwidth), and it was swept zontal plane. All of the antennas had return loss less
with a 156.25 kHz interval (1 601 frequency sample points). than dB from 5.15 to 5.4 GHz. When a single-input single-
Each channel was averaged over 10 snapshots in order to reduce output (SISO) channel was measured in an anechoic chamber
thermal noise included in raw measurements. The TX and RX (AEC) by using the antennas as the TX and RX ones, the max-
tables were separated by 4 m, as shown in the dashed circles in imum amplitude variation of the observed direct wave was 0.7
Fig. 2(a). The LOS condition was taken as the absence of an ob- dB in this measurement band. Fig. 4 shows an example of a
structing object between the TX and RX tables [Fig. 2(b)]. The 1The large partition placed for the NLOS condition may have obstructed not
NLOS condition was created by placing a metal partition be- only the LOS component but also major scattered waves, as will be shown in
tween the TX and RX [Fig. 2(c)]. The partition was large enough Fig. 5.
3680 IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 55, NO. 12, DECEMBER 2007

Fig. 6. CDFs of amplitudes (SISO case).

in the dashed circles in Fig. 2(a) when TX and RX ends each

Fig. 4. MIMO channel measurement system.
used a single antenna (SISO case). Thus, the antennas did not
have mutual coupling. Fig. 5(a) shows measured frequency-do-
main data. It is clear that the received power for the LOS condi-
tion was generally larger than the power for the NLOS one due
to the direct wave. Time-domain data shown in Fig. 5(b) are the
results of performing the IFFT on the frequency-domain data
shown in Fig. 5(a). The many peaks for the LOS and NLOS con-
ditions indicate that the measurement environments had many
scattered waves. The maximum peak was around 14 ns for the
LOS condition. This is considered to be from the direct wave
because the distance of 4 m between the TX and RX ends gives
a propagation time of ns and the peak dis-
appeared for the NLOS condition. Furthermore, unlike NLOS,
LOS gave larger amplitudes for the waves with short propaga-
tion delays within 60 ns.
We measured 82 spatially different SISO channels in the fre-
quency band from 5.15 to 5.40 GHz in the LOS and NLOS
conditions keeping the distance of 4 m between the TX and
RX tables. The measured SISO channels provided the cumu-
lative distribution function (CDF) of the wave amplitudes as
shown in Fig. 6. The received amplitudes for the LOS condi-
tion were about 7.6 dB higher at the 50% level compared with
those for the NLOS condition. The mean received power aver-
aged over space and frequency samples in the SISO-LOS mea-
surement was dB , and that
in the SISO-NLOS one was dB. Comparing
the mean received powers, was about 6.8 dB higher than
. Also, the mean received power was obtained
Fig. 5. Example of measurement data (SISO case). (a) Frequency domain. (b) under the SISO and LOS condition in the AEC in which the TX
Time domain. and RX tables were set 4 m apart. The data were averaged over
the space and frequency samples. which is the estimated
2 2 MIMO measurement system, for which the basic idea is direct wave power was dB . Since
the same for the 4 4 MIMO system. RF switches at the TX is composed of the direct and scattered wave power, the Ricean
and RX sides were used to select the TX antenna and the RX -factor in the LOS environment can be easily estimated by the
antenna. According to this selection, we chose each element in following calculation:
the 4 4 MIMO matrix. We normalized the measured channel
responses to calibration data that had been obtained when the ca- (7)
bles to the antenna ports from the RF switches were directly con-
nected. Therefore, the calibrated data did not have the frequency (8)
characteristics of the cables and switches. The unselected an-
(9)
tennas were automatically connected to 50 dummy loads.
Fig. 5 shows example measurements. These data were ob- The scattered wave power was, therefore, comparable to the di-
tained at the central positions on the TX and RX tables as shown rect wave power. Moreover, the scattered wave power in the
NISHIMOTO et al.: MIMO SPATIAL MULTIPLEXING 3681

LOS condition ( dB) was 2.87 dB directions, the gain tends to be small. On the other hand, espe-
higher than . It is natural that an LOS component causes cially in the cases of and , the gain in the 90
higher received power. However, this result indicates that, under direction is higher than in the single antenna case.
the LOS condition of this room, the direct wave also increased
scattered signal power. B. Fading Correlations
The channel response and MIMO channel matrix used To investigate the characteristics of the MIMO channels mea-
in the next section are given by the following normalizations of sured in the propagation environment, we examined fading cor-
the measured and relations [18]. The RX fading correlation between the
th and th RX antennas and the TX fading correlation
(10) between the th and th TX antennas are given by (12) and (13)
shown at the bottom of the next page. Here, and indicate
(11) the TX antenna number and RX antenna number, respectively.
represents the number of MIMO channel data and is the
We can say that the channel response is normalized to the direct number of total data (78 449). The absolute values of the fading
wave amplitude. correlations are in the range from 0 to 1. In addition, the corre-
lations and have and dif-
IV. PERFORMANCE OF 4 4 MIMO SYSTEMS ferent values, respectively, where an operator denotes the
total number of combinations of -subsets possible out of a set
A. Antenna Patterns of distinct items. That is, holds.
When multiple antennas are closely arrayed, they have mutual Using (12) and (13), we obtained the RX and TX fading corre-
coupling and their antenna patterns change. A MIMO system lations for the measured 4 4 MIMO channels. Since all of the
has antenna arrays at both ends, so we cannot ignore the effect MIMO cases have almost the same correlation values between
of the changing pattern on the MIMO performance. Thus, before the RX and TX ones, we will omit discussion on the TX cor-
presenting the measured characteristics of the MIMO channels, relations and discuss only the RX fading correlations .
we examine the antenna patterns for each four-element linear The correlations are drawn in the three-dimensional style as
array. shown in Fig. 8 because the combination of the RX antennas
Fig. 7 shows the patterns for each four-element uniform linear gives values. This plot is in the same style as in [18].
array treated in this measurement campaign (solid curves). Az- Fig. 8(a) and (b) show the correlations in the NLOS condition,
imuth patterns for , and are and Fig. 8(c) and (d) show them in the LOS condition. In ad-
shown in Fig. 7(a)–(d), respectively. For comparison, the pat- dition, Fig. 8(a) and (c) are for the TX- /RX- orientation, and
tern of a single antenna is shown with a dashed curve. We see Fig. 8(b) and (d) are for the TX- /RX- one. In the NLOS condi-
that the single antenna has an almost omnidirectional pattern tion, the fading correlations generally have low values, and they
when it does not have the mutual coupling effect. In the mul- become lower as AS increases. Higher correlations in the LOS
tiple antenna case, however, the patterns are significantly dif- condition are due to the LOS component that is a deterministic
ferent from an omnidirectional one. The antenna gain decreases signal.
as the AS becomes smaller. On the other hand, the patterns tend Focusing on the correlations in the LOS condition, we find
to become similar to the omnidirectional one as the AS becomes that the TX- /RX- orientation tends to provide higher correla-
larger. The numbers under each pattern correspond to the ones tions than the TX- /RX- one. We can consider two reasons for
in Fig. 3. Given the TX- /RX- orientation, the RX end is lo- this. The direct wave and reflected waves from the walls behind
cated in the 0 direction with respect to the TX end, and the the TX and behind the RX were conjectured to be dominant.
TX end is located in the 180 direction with respect to the RX These reflected rays along the axis lowered the correlation
end. Thus, the direct wave departs from the TX end in the 0 for the TX- /RX- orientation, but did not cause the decorrela-
direction, and arrives at the RX end in the 180 direction. On tion for the TX- /RX- case. We can analyze the other reason
the other hand, given the TX- /RX- orientation, the RX end is by considering the antenna patterns shown in Fig. 7. Narrow
located in the 90 direction with respect to the TX end, and the spacing seems to give high correlations for both of the orien-
TX end is also located in the 90 direction with respect to the tations in the case of . However, as mentioned in
RX end. Thus, the direct wave departs from the TX end and ar- Section IV-A, the cases of and give higher
rives at the RX end in the 90 direction. As for the 0 and 180 gain in the 90 direction, which corresponds to the direct path.

(12)

(13)
3682 IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 55, NO. 12, DECEMBER 2007

Fig. 7. Antenna patterns for each four-element array with mutual coupling (solid curve), and single antenna pattern (dashed curve). (a) AS = 0:25. (b) AS =
0:50. (c) AS = 0:75. (d) AS = 1:00.

Consequently, the effect of the direct wave becomes stronger, systems can be strongly affected by propagation environments
so that we have higher correlations for the TX- /RX- orienta- and mutual coupling between antennas. Actual channel ele-
tion. The patterns for incidentally show a little dip ments, thereby, may have different statistical characteristics.
in the antenna pattern in the 90 direction. This decreases the As stated in the previous subsection, some LOS channels
effect of the direct wave and causes lower correlation values in have very high correlations, and are never independent. Here,
the TX- /RX- orientation. we attempt to determine whether the indoor MIMO chan-
nels are identical or not. Using the measured 78 449 MIMO
C. CDFs of Channel Elements in MIMO Matrices channels, we examined CDFs of amplitudes of each channel
Many MIMO channel models assume that each element in element as shown in Fig. 9. Data for the TX- /RX- orienta-
a channel matrix obeys i.i.d. fading. However, actual MIMO tion are shown in Fig. 9(a)–(d), and data for the TX- /RX-
NISHIMOTO et al.: MIMO SPATIAL MULTIPLEXING 3683

j
Fig. 8. RX fading correlations  j for the measured 4 2 4 MIMO channels. (a) NLOS, TX-x/RX-x. (b) NLOS, TX-y /RX-y . (c) LOS, TX-x/RX-x. (d) LOS,
TX-y /RX-y .

orientation are shown in Fig. 9(e)–(h). In addition, pairs of independent of the antenna spacing and array orientation, and
Fig. 9(a) and (e), (b) and (f), (c) and (g), and (d) and (h) show differ less than about 2 dB. Looking at the region where the
the CDFs for the cases of , and cumulative frequencies are less than the 10% level and the
, respectively. Each of the LOS/NLOS condition in the curves are almost straight lines, we can see that all the CDFs
graph has CDF curves . increase by almost an order of magnitude with an amplitude
The abscissa value is different from that in Fig. 6 owing to increment of 10 dB. Thus, the NLOS channels are Rayleigh
the normalization by (11). Also, for each case in the LOS fading channels. In the previous subsection, we verified that
condition, the average Ricean factor estimated from almost all of the cases under the NLOS condition give low
all the 16 CDFs of channel elements is put on each graph. fading correlations (Fig. 8). Hence, we can say that MIMO
First, as in Fig. 6, the MIMO channel elements in the LOS channels under the NLOS condition with AS equal to or greater
condition generally have higher amplitudes than those in the than obey almost i.i.d. Rayleigh fading. As for the cases
NLOS one. Second, except for the narrowest spacing cases of , the difference at the 10% level is a maximum
of , distributions under the NLOS condition are of approximately 3 dB. The authors consider that it was caused
3684 IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 55, NO. 12, DECEMBER 2007

2
Fig. 9. CDFs of amplitudes of the measured 4 4 MIMO channels. (a) TX-x/RX-x, AS = 0:25. (b) TX-x/RX-x, AS = 0:50. (c) TX-x/RX-x, AS = 0:75.
(d) TX-x/RX-x, AS = 1:00. (e) TX-y /RX-y , AS = 0:25. (f) TX-y /RX-y , AS = 0:50. (g) TX-y /RX-y , AS = 0:75. (h) TX-y /RX-y , AS = 1:00.

by different antenna gain among antenna elements, especially depending on the antenna spacing and array orientation. Since
significant gain loss in inner two elements #2 and #3, due to the LOS condition has the direct wave, the antenna gain has a
mutual coupling effects as shown in Fig. 7(a). great influence on the channel distributions. We can explain this
However, channels under the LOS condition do not behave behavior by using the antenna patterns shown in Fig. 7. When
in this way. The amplitudes and gradients of the CDFs differ the gain in the direct wave’s direction is high, CDFs become lo-
NISHIMOTO et al.: MIMO SPATIAL MULTIPLEXING 3685

cated in a higher amplitude region and their gradients become

steeper. That is, the fading is Ricean with a large -factor. On
the other hand, when the gain toward the direct wave is low, the
amplitudes are distributed in a lower region. Consider the cases
of and in the TX- /RX- orientation. From
Fig. 9(a) and (c), we see that the channel distributions are sig-
nificantly different. In these graphs, the CDF of is in the
highest amplitude region and has the steepest gradient (largest
-factor) among the MIMO channel elements. For example, in
the case of , while is 0.0 dB, the -factor
of is 5.9 dB. In the case of is 0.7 dB
whereas the -factor of is 3.8 dB. On the other hand, the
CDF of is in the lowest region under the LOS condition.
Note that each antenna index corresponds to the one shown in
Figs. 3 and 7. Here, let us consider the channels and antenna
patterns shown in Fig. 7. As for channel in the TX- /RX-
orientation, the direct wave departs from TX antenna #4 in the
0 direction and arrives at RX antenna #1 in the 180 direc-
tion. As seen from Fig. 7(a) and (c), antennas #1 and #4 have
higher gain in the directions of 180 and 0 , respectively. Thus,
the direct wave is strongly received through channel . This
is why the CDF of is in the highest region and has the
steepest gradient for and . As for channel
in the TX- /RX- orientation, the direct wave departs from
TX antenna #1 in the 0 direction and arrives at RX antenna #4
in the 180 direction. Antennas #1 and #4 have lower gain in
the directions of 0 and 180 , respectively. The direct wave is 2
Fig. 10. CDFs of the measured 4 4 MIMO channel capacities for normalized
weakly received through channel . Thus, the CDF of is total TX power of 20 dB. (a) TX-x/RX-x. (b) TX-y /RX-y .
in the lowest region for and . The relation-
ship between the LOS component and antenna gain indicates
that these two particular cases caused very different distribu- hereinafter. Therefore, we can compare performances under the
tions among channel elements. Consequently, while it is well same total TX power condition. Using the above equation, we
known that in LOS environments fading channels do not have examined CDFs of the 4 4 MIMO channel capacities for a
independence due to the LOS component, the MIMO channel normalized total TX power of 20 dB.
elements under the LOS condition do not have the same statis- The results shown in Fig. 10(a) and (b) are capacities for the
tical characteristics. TX- /RX- and TX- /RX- orientations, respectively. All of
the capacities in the LOS condition are higher than those in the
D. CDFs of Channel Capacities NLOS condition for both array orientations. The LOS compo-
The channel capacity has been extensively used for evaluating nent in the LOS condition enlarges the received power. Under
the MIMO channel [7]–[10], [14]–[25]. This is the limit of dig- a constant total TX power condition, the higher received power
ital communications that could only be achieved if we employed due to the LOS component improves the capacity. It is clear
an ideal communication method (coding and modulation). As from (15) that the channel capacity is given by the eigenvalues
for the measured MIMO channel, the following equation gives of the MIMO channel. We can also say that the LOS compo-
the channel capacity of spatial multiplexing when channel state nent enlarges the maximum eigenvalue which significantly in-
information is available only at the RX side creases the channel capacity. Moreover, we can say that the LOS
component enlarges the maximum eigenvalue and this larger
(14) eigenvalue causes such a high capacity. The eigenvalues will be
discussed in detail in Section IV-F. On the other hand, the per-
formance of deteriorates in both LOS and NLOS
(15) conditions. This phenomenon can be analyzed by using the an-
tenna patterns shown in Fig. 7. As described in Section IV-A,
Here, denotes a determinant and indicates total the patterns in the case of show serious gain de-
TX power. are eigenvalues obtained by crease. We consider that this low antenna gain causes the de-
eigenvalue decomposition of . is TX power when cline in channel capacity. Except for the case of ,
the aforementioned SISO measurement in the AEC gives an av- we see that in the LOS condition the TX- /RX- array orien-
erage received of 0 dB. Note that in the tation tends to give larger capacities than the TX- /RX- one.
above equation represents the normalized total TX power, which We illustrate this reason by using the antenna patterns shown in
is used to evaluate the channel capacities and bit error rates Fig. 7. As mentioned in Sections IV-A and IV-C, the antennas
3686 IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 55, NO. 12, DECEMBER 2007

have higher gain than the single antenna in the 90 direction es- TABLE I
pecially in the cases of and . The direct signal SIMULATION PARAMETERS OF MIMO SPATIAL MULTIPLEXING
is considered to be strongly received in the TX- /RX- orien-
tation. This increases capacity. The reason that
gives a large capacity is conjectured to be lower fading correla-
tions [Fig. 8(d)]. Moreover, in the LOS condition, the CDFs of
the channel capacities strongly depend on the array configura-
tion (antenna spacing and orientation).
There is an idea that an LOS channel can be modeled approx-
imately as

aforementioned, the variation of the antenna gain due to mutual

(16) coupling changes the LOS component level, and this affects the
performance in the LOS condition.
where is an i.i.d. Rayleigh channel compo-
nent matrix and is an LOS component matrix E. BER
[4]. Note that amplitudes of channel components are included Earlier, we evaluated the performance of MIMO spatial mul-
in elements in these matrices. is a scattered ray compo- tiplexing using the channel capacity. As aforementioned, the
nent matrix in a multipath-rich environment with large antenna channel capacity obtained by (14) is the limit of the spatial mul-
spacing. In this case, addition of to the scattered ray com- tiplexing transmission. From the implementational viewpoint,
ponents leads to the large maximum eigenvalue and enhances we consider that evaluating the BER performance will be more
the channel capacity. However, as stated in Section III, the scat- practical. Thus, we conducted computer simulations of spatial
tered wave power in the LOS condition was 2.87 dB higher multiplexing by using measured channel data and examined av-
than that in the NLOS condition due to the short-delay paths erage BER performance under a constant bit rate requirement.
caused by the direct wave. The direct LOS ray and enhanced Table I lists the simulation parameters. As stated before, we
scattered ray components further increase the channel capacity had obtained 78 449 channel data for each MIMO configu-
in the LOS environment. Also, when the received signal is lin- ration, and we averaged all BERs for these channel data. We
early demultiplexed by a spatial filter, e.g., zero-forcing, the assumed that an independent QPSK-modulated uncoded stream
BER performance becomes better as the minimum eigenvalue was transmitted from each TX antenna with equal power.
becomes larger (see Sections IV-E and IV-F). It is not sure that Therefore, bits/symbol were constantly transmitted. We
the above model makes the minimum eigenvalue large, and it employed a spatial filter based on a zero-forcing (ZF) scheme
is difficult to arrive at the conclusion that spatial multiplexing to detect the streams at the RX side [6]. This scheme suppresses
in an LOS environment gives better BER performance. There- interference completely by using the ZF weight matrix given
fore, we examined the behavior of spatial multiplexing in the by the following equation
LOS environment based on not channel models but measure-
ment campaigns.
If we employ the LOS channel model given by (16), it is nec- (17)
essary to introduce the spherical-wave model [25] into in
order to consider the variation of the LOS component phase be- An -dimensional ZF output vector is obtained when the
cause the distance between the TX and RX ends was relatively RX signal vector is multiplied by as follows:
short. Here, let us consider a free space, i.e., . In the
case of in the TX- /RX- array orientation, the (18)
fading correlation between antenna elements #1 and #4, (19)
which have the widest spacing of , is 0.95. Under the SNR (20)
of 20 dB, the channel capacity in this case becomes 30% higher
than that in the case of (TX- /RX- case in a Ordered successive detection such as BLAST [6], [7] was not
free space). However, if an environment based on the channel applied. Results obtained by this processing show the perfor-
model (16) has dB, which is the estimated Ricean mance of the simplest MIMO system without any error correc-
factor in the measurement site, the correlation in the case tion codes. This simulation also assumed that the RX side has
of for the TX- /RX- array orientation is 0.56. perfect channel state information.
Even for the TX- /RX- array orientation, the correlations for Fig. 11 shows the average BER performance of 4 4 MIMO
any antenna pairs are 0.59. We confirmed that any array config- spatial multiplexing. Fig. 11(a) and (b) are graphs for the TX-
urations give almost the same channel capacity and BER perfor- /RX- and TX- /RX- orientations, respectively. Because of
mance in the environment of dB. Consequently, we , the bit rate is 8 bits/symbol. The abscissa is nor-
can say that the variation of the LOS component phase makes malized total TX power. We confirmed that the LOS condition
little impact on fading correlations and the performance of spa- gave higher correlations than the NLOS one (Fig. 8). However,
tial multiplexing in propagation environments where the scat- Fig. 11 clearly shows that the BER performance for the LOS
tered wave power is comparable to the direct wave power. As condition is better than that for the NLOS one. As mentioned in
NISHIMOTO et al.: MIMO SPATIAL MULTIPLEXING 3687

Fig. 12. CDFs of eigenvalues ofH H for the measured 4 2 4 MIMO chan-
x x y y
nels. (a) TX- /RX- . (b) TX- /RX- .

Fig. 11. Average BER performance of ZF processing for the measured 4 24

x x y
MIMO channels. (a) TX- /RX- . (b) TX- /RX- .y
Although significant degradation occurs in the case of
for both array orientations, under the LOS condition the
Section IV-D, the higher received power level given by the LOS antenna spacing and array orientation affect performance more
component improves the BER performance. than in the NLOS case. This is almost the same as the CDFs of
Channel capacities shown in Fig. 10 indicate that all the CDFs capacities stated in Section IV-D.
under the LOS condition are better than those under the NLOS
F. CDFs of Eigenvalues
one regardless of the array orientation. In contrast, not all of the
BERs under the LOS condition show better performance than An hermitian matrix has nonneg-
those under the NLOS one because the cases of se- ative eigenvalues. We represent them in descending order
riously deteriorate in both conditions. As stated in Section IV-C, . The number of positive eigenvalues equals the
the gain decrease of the inner two antenna elements #2 and #3 number of orthogonal channels between the TX and RX ends,
is especially noticeable in the patterns of the case and the eigenvalue is in proportion to the SNR of the channel.
shown in Fig. 7(a). When we used this antenna array as the TX, In other words, we can increase the transmission speed if the
more bit errors occurred on the streams from TX antennas #2 number of large eigenvalues increases. From (15), it is evident
and #3. Average BER was strongly affected by such deterio- that a channel capacity is determined by the eigenvalues of
rated streams. the matrix . In particular, it is easy to imagine that the
The channel distributions shown in Fig. 9 indicate that the maximum eigenvalue has the largest influence on the MIMO
NLOS condition generally gives the linear parts of CDFs an capacity. On the other hand, the ZF algorithm gives a tendency
increase of one order of magnitude with an amplitude increment that the SNR at the RX end decreases as the minimum eigen-
of 10 dB, and also that the LOS case has steeper curves owing to value decreases. This degrades the BER performance.
the direct wave. However, all the BER curves including those for Accordingly, we examined CDFs of eigenvalues of in
the LOS condition show almost Rayleigh fading with first-order each MIMO configuration.
diversity in the high power region. That is, the BER is reduced The CDFs of the eigenvalues are shown in Fig. 12. As well as
by an order of magnitude when the TX power increases by 10 Figs. 10 and 11, Fig. 11(a) and (b) are for the TX- /RX- and
dB. This behavior will be explained in the next subsection by TX- /RX- array orientations, respectively. Although a 4 4
using the minimum eigenvalue distributions. MIMO channel has four nonnegative eigenvalues, we show the
3688 IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 55, NO. 12, DECEMBER 2007

CDFs of the maximum eigenvalues and minimum eigen- partition for the NLOS conditions and symmetric placement of
values only. Compared with the CDFs of channel capacities TX and RX tables. Therefore, to confirm the tendencies shown
shown in Fig. 10, we see that the order of CDFs of does not in this paper, we should carry out more practical measurement
necessarily correspond to that of the capacity distributions. This campaigns assuming actual wireless systems such as wireless
disagreement seems to be due to the effect of and , which LANs for our future works.
are not shown in Fig. 10 (see [26, Figs. 8, 9]). However, com-
paring the CDFs of the minimum eigenvalues and average
REFERENCES
BERs shown in Fig. 11, we see that the orders are the same.
[1] G. J. Foschini and M. J. Gans, “On limits of wireless communications
Moreover, in the linear parts of the CDFs of , almost all of the in a fading environment when using multiple antennas,” Wireless Pers.
values increase by about an order of magnitude with the incre- Commun., pp. 311–335, Mar. 1998.
ment of 10 dB. The BER performance and its gradient, in short, [2] I. E. Telatar, “Capacity of multi-antenna Gaussian channels,” Euro.
Trans. Telecommun., vol. 1, no. 6, pp. 585–595, Nov./Dec. 1999.
seem to be dominated by the CDF of the minimum eigenvalue [3] D. Gesbert, M. Shafi, D. S. Shiu, P. Smith, and A. Naguib, “From
when only the ZF spatial filter is employed. We confirmed that theory to practice: An overview of MIMO space-time coded wireless
channel capacity and BER are seriously degraded in the case of systems,” IEEE J. Sel. Areas Commun., vol. 21, no. 2, pp. 281–302,
Apr. 2003.
. The CDFs of the eigenvalues for [4] A. Paulraj, R. Nabar, and D. Gore, Introduction of Space-Time Wireless
tend to be in lower regions compared with the other cases. In Communications. Cambridge, U.K.: Cambridge Univ. Press, 2003.
particular, the minimum eigenvalues stay in the lower regions [5] A. J. Paulraj, D. A. Gore, R. U. Nabar, and H. Bölcskei, “An overview
of MIMO communications—A key to gigabit wireless,” Proc. IEEE,
independently of the environmental conditions. This phenom- vol. 92, no. 2, pp. 198–218, Feb. 2004.
enon causes the degradation of the MIMO performance. [6] G. D. Golden, G. J. Foschini, R. A. Valenzuela, and P. W. Wolniansky,
As aforementioned, for the TX- /RX- orientation, the an- “Detection algorithm and initial laboratory results using V-BLAST
space-time communication architecture,” Electron. Lett., vol. 35, no.
tennas have high gain in the LOS direction (90 direction in 1, pp. 14–16, Jan. 1999.
Fig. 7) especially in the cases of and . The [7] G. J. Foschini, G. D. Golden, R. A. Valenzuela, and P. W. Wolniansky,
CDFs of the maximum eigenvalues in these cases prove to “Simplified processing for high spectral efficiency wireless communi-
cation employing multi-element arrays,” IEEE J. Sel. Areas Commun.,
have large values. Thus we can say that they are significantly vol. 17, no. 11, pp. 1841–1852, Nov. 1999.
affected by the direct wave. [8] G. J. Foschini, D. Chizhik, M. J. Gans, C. Papadias, and R. A. Valen-
zuela, “Analysis and performance of some basic space-time architec-
tures,” IEEE J. Sel. Areas Commun., vol. 21, no. 3, pp. 303–320, Apr.
V. CONCLUSION 2003.
[9] M. A. Jensen and J. W. Wallace, “A review of antennas and propagation
We have evaluated channel capacities and average bit error for MIMO wireless communications,” IEEE Trans. Antennas Propag.,
vol. 52, no. 11, pp. 2810–2824, Nov. 2004.
rates of 4 4 MIMO spatial multiplexing by using measured [10] D.-S. Shiu, G. J. Foschini, M. J. Gans, and J. M. Kahn, “Fading corre-
MIMO channel data in an indoor multipath environment for the lation and its effect on the capacity of multielement antenna systems,”
5.2–GHz frequency band. The LOS and NLOS conditions for IEEE Trans. Commun., vol. 48, no. 3, pp. 502–513, Mar. 2000.
[11] I. J. Gupta and A. A. Ksienski, “Effect of mutual coupling on the perfor-
various MIMO configurations were analyzed in terms of the an- mance of adaptive arrays,” IEEE Trans. Antennas Propag., vol. AP-31,
tenna patterns, fading correlations, CDFs of channel elements, no. 5, pp. 785–791, Sep. 1983.
and CDFs of eigenvalues. [12] H. Iura, H. Yamada, Y. Ogawa, and Y. Yamaguchi, “Optimal antenna
matching and mutual coupling effect of antenna array in MIMO re-
It is well known that an LOS environment does not produce ceiver,” IEICE Trans. Commun., vol. E90-B, no. 4, pp. 960–967, Apr.
independent fading because an LOS component causes high 2007.
fading correlation. From the measurement results, we confirmed [13] H. Steyskal and J. S. Herd, “Mutual coupling compensation in small
array antennas,” IEEE Trans. Antennas Propag., vol. 38, no. 12, pp.
this fact and also found that the LOS condition is not an iden- 1971–1975, Dec. 1990.
tically distributed fading environment when each channel ele- [14] P. N. Fletcher, M. Dean, and A. R. Nix, “Mutual coupling in multi-
ment is observed by antennas including mutual coupling effects. element array antennas and its influence on MIMO channel capacity,”
Electron. Lett., vol. 39, no. 4, pp. 342–344, Feb. 2003.
However, MIMO spatial multiplexing in the LOS environment [15] P. Uthansakul, M. Uthansakul, and M. E. Bialkowski, “Improving
provides higher capacities and lower bit error rates than in the MIMO system capacity by compensating mutual coupling in transmit-
NLOS environment under the same TX power condition. Hence, ting/receiving array antennas,” in Proc. IEEE Antennas Propag. Soc.
Int. Symp., Jun. 2004, vol. 2, pp. 1724–1727.
the utility of MIMO spatial multiplexing in an LOS environment [16] J. W. Wallace and M. A. Jensen, “Mutual coupling in MIMO wireless
has been proved. Meanwhile, the antenna gain in an array with systems: A rigorous network theory analysis,” IEEE Trans. Wireless
narrow antenna spacing deteriorates because of mutual coupling Commun., vol. 3, no. 4, pp. 1317–1325, Jul. 2004.
[17] A. F. Molisch, M. Steinbauer, M. Toeltsch, E. Bonek, and R. S. Thomä,
effects. The decrease in gain will cause performance degrada- “Capacity of MIMO systems based on measured wireless channels,”
tions in MIMO systems with numerous antennas. Under the IEEE J. Sel. Areas Commun., vol. 20, no. 3, pp. 561–569, Apr. 2002.
LOS condition, the performance of MIMO spatial multiplexing [18] H. Özcelik, M. Herdin, H. Hofstetter, and E. Bonek, “Capacity of dif-
ferent MIMO systems based on indoor measurements at 5.2 GHz,” in
strongly depends on the MIMO configuration. Inst. Elect. Eng. Europ. Pers. Mobile Commun. Conf. (EPMCC 2003),
This paper has presented the performance of 4 4 MIMO Apr. 2003, pp. 463–466.
spatial multiplexing in a measurement site. We also conducted [19] T. Mitsui, M. Otani, C. H. Y. Eugene, K. Sakaguchi, and K. Araki,
“Indoor MIMO channel measurements for evaluation of effectiveness
2 2 MIMO measurement campaigns in the same and different of array antenna configurations,” Proc. IEEE VTC 2003-Fall, vol. 1,
indoor environments [26]–[28]. These measurement campaigns pp. 84–88, Oct. 2003.
yielded almost the same conclusions as the ones presented in [20] P. Kyritsi, D. C. Cox, R. A. Valenzuela, and P. W. Wolniansky, “Cor-
relation analysis based on MIMO channel measurements in an indoor
this paper. However, our measurement setups in these two en- environment,” IEEE J. Sel. Areas Commun., vol. 21, no. 5, pp. 713–720,
vironments were not practical but artificial, e.g., a large metal Jun. 2003.
NISHIMOTO et al.: MIMO SPATIAL MULTIPLEXING 3689

[21] K. Yu, M. Bengtsson, B. Ottersten, D. McNamara, P. Karlsson, and M. Yasutaka Ogawa (M’78–SM’90) received the B.E.,
Beach, “Modeling of wide-band MIMO radio channels based on NLoS M.E., and Ph.D. degrees from Hokkaido University,
indoor measurements,” IEEE Trans. Veh. Technol., vol. 53, no. 3, pp. Sapporo, Japan, in 1973, 1975, and 1978, respec-
655–665, May 2004. tively.
[22] C. Waldschmidt and W. Wiesbeck, “Compact wide-band multimode Since 1979, he has been with Hokkaido Univer-
antennas for MIMO and diversity,” IEEE Trans. Antennas Propag., vol. sity, where he is currently a Professor of the Graduate
52, no. 8, pp. 1963–1969, Aug. 2004. School of Information Science and Technology.
[23] D. P. McNamara, M. A. Beach, P. N. Fletcher, and P. Karlsson, “Ca- During 1992–1993, he was with ElectroScience
pacity variation of indoor multiple-input multiple-output channels,” Laboratory, the Ohio State University, as a Visiting
Electron. Lett., vol. 36, no. 24, pp. 2037–2038, Nov. 2000. Scholar, on leave from Hokkaido University. His
[24] T. Svantesson and J. Wallace, “On signal strength and multipath rich- interests are in adaptive antennas, mobile communi-
ness in multi-input multi-output systems,” in Proc. IEEE Int. Conf. cations, superresolution techniques, and MIMO systems.
Commun. (ICC’03), May 2003, vol. 4, pp. 2683–2687. Dr. Ogawa received the Young Researchers’ Award of IEICE Japan in 1982
[25] J.-S. Jiang and M. A. Ingram, “Spherical-wave model for short-range and the Best Paper Award from IEICE Japan in 2007.
MIMO,” IEEE Trans. Commun., vol. 53, no. 9, pp. 1534–1541, Sep.
2005.
[26] Y. Ogawa, H. Nishimoto, T. Nishimura, and T. Ohgane, “Performance
of MIMO spatial multiplexing in indoor line-of-sight environments,” Toshihiko Nishimura (M’98) received the B.S. and
Proc. IEEE VTC2005-Fall, vol. 4, pp. 2398–2402, Sep. 2005. M.S. degrees in physics and the Ph.D. degree in elec-
[27] Y. Ogawa, H. Nishimoto, T. Nishimura, and T. Ohgane, “Performance
2
of 2 2 MIMO spatial multiplexing in indoor environments,” in 2005
tronics engineering from Hokkaido University, Sap-
poro, Japan, in 1992, 1994, and 1997, respectively.
IEEE/ACES Int. Conf. Wireless Commun. Appl. Computat. Electro- In 1998, he joined the Graduate School of
magn., Apr. 2005, pp. 486–489. Engineering (reorganized to Graduate School of
[28] H. Nishimoto, Y. Ogawa, T. Nishimura, and T. Ohgane, “Availability Information Science and Technology) of Hokkaido
of MIMO spatial multiplexing in line-of-sight channels,” Proc. IEEE University, where he is currently an Assistant Pro-
VTS APWCS2005, pp. 40–44, Aug. 2005. fessor of the Graduate School of Information Science
and Technology. His current research interests are in
MIMO systems using smart antenna techniques.
Dr. Nishimura received the Young Researchers’ Award of IEICE Japan in
2000 and the Best Paper Award from IEICE Japan in 2007.

Takeo Ohgane (M’82) received the B.E., M.E.,

and Ph.D. degrees in electronics engineering from
Hokkaido University, Sapporo, Japan, in 1984, 1986,
Hiroshi Nishimoto (S’05) received the B.E. and and 1994, respectively.
M.E. degrees from Hokkaido University, Sapporo, From 1986 to 1992, he was with the Communi-
Japan, in 2003 and 2005, respectively. cations Research Laboratory, Ministry of Posts and
He is currently working toward the Ph.D. degree Telecommunications. From 1992 to 1995, he was on
at the Graduate School of Information Science and assignment at ATR Optical and Radio Communica-
Technology, Hokkaido University. His research in- tions Research Laboratory. Since 1995, he has been
terests are in MIMO propagation measurement and with Hokkaido University, where he is an Associate
MIMO communication systems. He has been a Re- Professor. During 2005–2006, he was with the Centre
search Fellow of the Japan Society for the Promotion for Communications Research, University of Bristol, U.K., as a Visiting Fellow.
of Science since 2005. His interests are in MIMO signal processing for wireless communications.
Mr. Nishimoto received the IEEE VTS Japan Dr. Ohgane received the IEEE AP-S Tokyo Chapter Young Engineer Award
Chapter Student Paper Award and the Young Researchers’ Award of IEICE in 1993, the Young Researchers’ Award of IEICE Japan in 1990, and the Best
Japan, both in 2007. Paper Award from IEICE Japan in 2007.