(first submission) experiments with compact antenna arrays for
TRANSCRIPT
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Experiments with Compact Antenna Arrays forMIMO Radio Communications
David W. Browne , Majid Manteghi , Michael P. Fitz , Yahya Rahmat-Samii† †† † ††
† ††UnWiReD Laboratory, Antenna Research and Measurements LaboratoryDepartment of Electrical Engineering
University of California at Los AngelesLos Angeles, CA 90095-1594
emails: [email protected]; [email protected]; [email protected]; [email protected]
Abstract The problem tackled in this study is one of MIMO transceiver implementation in which weconsider how to design and test compact antenna arrays that have the ability to preserve the native informationbearing capacity of a MIMO channel. Mutual coupling in antenna arrays is known to degrade the performance ofa MIMO system. However, no tests involving compact arrays have been performed using a MIMO transceiverarchitecture that is capable of measuring the effect of mutual coupling on system performance. In this study, twonovel compact MIMO antenna arrays were designed and integrated into a wideband MIMO radio testbed. Thesearrays are extremely compact yet have acceptable mutual coupling and radiation efficiency and resonate in threewide frequency bands. A measurement campaign was executed in which MIMO channel sounding measurementswere taken using the compact arrays and dipole arrays in a variety of indoor environments. The MIMOtransceiver used for channel sounding is able to measure the effect of mutual coupling on system performance. Acomparison of the relative performance between the compact antenna arrays, dipole arrays and the i.i.d. Gaussianchannel is presented. Results show that the proposed compact arrays outperformed dipole arrays in all scenariosand that MIMO capacity does not scale linearly in the number of antennas if the antenna arrays exhibit mutualcoupling.
I. INTRODUCTION
A well known result from information theory proves that an upper limit exists for the average spectral
efficiency of radio communications over a Gaussian channel using a single transmitter antenna and single receiver
antenna [1]. This limit can be overcome by radios with multiple transmit antennas and multiple receive antennas
that treat the Gaussian channel as a Multiple Input Multiple Output (MIMO) channel, [2], [3]. Not only can
MIMO overcome the limit proved in [1], but the average capacity of a MIMO Gaussian channel growsP ‚ PT R
linearly with . Linear growth of MIMO capacity scaling holds even when the propagationmina bP ßPT R
environment induces spatial correlation in the MIMO channel [4]. Theoretical models and measurement results
show that correlation between the MIMO sub-channels causes a loss of capacity relative to the nominalP PT R
This work was supported in part by a United States National Science Foundation research grant (ANI-0305302), by a grantfrom Marvell Semiconductor through the UC Discovery Program, and by a hardware donation from LEGO Denmark.
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MIMO Gaussian channel, [5], [6]. The mechanisms for correlation are mutual coupling in the antenna arrays and
a narrow multipath spread in the propagation channel, [7], [8]. Both mechanisms cause increased correlation when
the antenna array's inter-element spacing shrinks. Such a scenario is a problem in portable MIMO enabled devices
where the array must be shrunk into a volume whose dimensions are typically measured in fractions of the carrier
frequency wavelength.
The problem tackled in this study is one of MIMO transceiver implementation in which we consider how to
design and fabricate compact antenna arrays that preserve the native information bearing capacity of a MIMO
channel. A summary of select prior works relevant to this problem puts the current state of a solution in
perspective. A comprehensive overview of MIMO antenna and propagation studies is to be found in [9]. MIMO
channel capacity measurements using compact arrays with inter-element spacings have been reported Î#-0-
[11], [12], [13], [14]. However, the channel sounders used to make these measurements used time-multiplexed
switching between the radios and the array elements or used a single movable antenna to create a virtual array in
space. Uncorrelated phase noise across antennas in time-multiplexed sounders has been shown to result in
optimistic channel capacity measurements [15]. Furthermore, to capture the effect of mutual coupling requires
simultaneous excitation of the entire spectral band on all transmit elements and simultaneous signal capture of the
entire spectral band from all receiver elements. Such an excitation and capture scheme is true to the actual
signaling architecture used in real MIMO transceivers and is termed "full MIMO". MIMO channel capacity has
been characterized as a function of antenna array topology using a full MIMO testbed [6, 10]. However, these
studies only considered narrowband channels and large arrays with inter-element spacings . Only one Î#-0-
study is known to have designed and implemented compact arrays with spacings and tested theirŸ Î#-0-
performance on a full MIMO system [16]. However, the cases tested were limited to MIMO configurations# ‚ #
and the array topologies used at the receiver were not sufficiently compact to observe an effect on channel
capacity.
The work presented here is an experimental investigation of compact antenna array performance in a MIMO
transceiver that more completely addresses the problem of designing and testing compact MIMO arrays. A two
element antenna array and a four element antenna array were designed using criteria tailored to wideband MIMO
signaling and fabricated for integration into mobile devices. These arrays are extremely compact, with inter-
element spacings / , yet have acceptable mutual coupling and radiation efficiency and resonate in three wide %-0-
frequency bands. A measurement campaign was executed in which full MIMO channel sounding measurements
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were taken with each array in a variety of indoor environments. A complementary set of reference measurements
were also taken with a Uniform Linear Array (ULA) of dipoles of varying topology. A comparison of the relative
performance between the compact antenna arrays, the dipole arrays and the i.i.d. Gaussian channel will be
presented. Results from the measurement campaigns will show that:
ì Typical indoor environments provide sufficient multipath for an ideal MIMO system to achieve
capacities near that of an i.i.d. Gaussian channel.
ì The proposed compact arrays outperformed the dipole arrays in all scenarios. Using only two elements
of the 4-element compact array yielded similar performance to that of the 2-element compact array.
ì Î# A spacing is necessary in a ULA of dipoles to achieve the same performance as the much smaller-0-
compact array.
ì SNR loss due to antenna impedance mismatch accounted for less loss of capacity than did mutual
coupling induced correlation.
ì P ß P MIMO capacity does not scale linearly with if the antenna arrays exhibit mutual coupling.mina bT R
ì A majority of the capacity that can be lost by decreasing the array aperture at both the transmitter and
receiver is typically lost when only one side's array aperture decreases.
The remainder of the paper is organized as follows. Section II gives a description of the compact antenna
array design. Section III details the methodology used in a measurement campaign. Results from the measurement
campaign are presented in Section IV. Observations drawn from the results are given in Section V along with
conclusions about the design of compact antenna arrays for MIMO radio communications.
II. COMPACT ARRAY DESIGN
A. Printed Inverted-F Antenna
Printed Inverted "F" Antenna (PIFA) designs have low profiles, good radiation characteristics, and wide
bandwidth [18], [19], [20]. This makes PIFA an attractive choice for antenna designs targeting many current
mobile wireless systems. Another requirement of these systems is support for multiple resonant frequencies.
However, standard PIFA designs result in a single band antenna since the antenna's higher order resonant
frequencies are not close to its fundamental resonant frequency. In addition, both the radiation performance and
the return loss of a standard PIFA antenna may render it inefficient for use at these higher resonant frequencies. It
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has been shown that a PIFA can resonate at a second frequency by using a proper slot on the antenna body [21].
Different shapes and locations of the slot have been proposed for different applications. A PIFA can also be made
to resonate at a second frequency by including a J-shape slot [22], [23].
A novel tri-band PIFA design was used to produce a two element array and a four element array for use in
portable MIMO enabled devices [16]. The proposed PIFA antenna employs a quarter wavelength slot to provide
the second resonant frequency and a J-shape slot to provide a third resonant frequency. The resulting PIFA has
resonant frequencies at 2.45 GHz, 5.25 GHz, and 5.775 GHz with supporting bandwidths of 100 MHz, 200 MHz,
and 150 MHz respectively. The single element antenna model with its ground plane is shown in Fig. 1. The PIFA
measures 9mm 17mm 3mm. Fig. 2 shows the measured reflection coefficient of this antenna.‚ ‚
B. PIFA Array
Mutual coupling disturbs the scattering parameter characteristic and radiation pattern of the array's radiating
elements from that of their isolated state [24], [25]. This makes it necessary for the elements in a MIMO antenna
array to be designed jointly. However, a PIFA design is relatively robust to influence from another nearby PIFA
because of the radiating element's low profile and proximity to the ground plane [26]. A two-element PIFA array
was designed for use in MIMO enabled portable devices. The PIFA array's elements are separated by mm$"
( ). The manufactured array is shown in Fig. 3(b) alongside a laptop PCMCIA wireless LAN card, Fig.¸ Î%-0-
3(d), whose footprint it was designed to match. An Ansoft High Frequency Structure Simulator software package
was employed to calculate the input impedance as well as the far-field patterns of this array. The MIMO
transceiver testbed into which these compact antenna arrays were integrated operates in the 2.4 – 2.5 GHz band.
We only present the antenna's design for the 2.45 GHz resonant frequency since no system level measurements
were made at the 5 GHz bands. Fig. 7 shows the far-field pattern of a single PIFA on a ground plane with no
other PIFA elements (as seen in Fig. 1). Figure 8 shows the far-field patterns of a single PIFA on a ground plane
when a second PIFA is located mm away on the ground plane, as seen in Fig. 3(a), and terminated by .$" &! H
The far-field patterns are given for two elevation planes ( ° and °) and the azimuth plane9 9BD CDœ ! œ *!
( °). A comparison of Fig. 7 and shows that the radiation pattern of a single PIFA remains relatively)BC œ *! 8
unchanged in the presence of a second PIFA.
Fig. 9 presents the scattering matrix of the dual element PIFA array as a function of frequency. However, it
has been shown that the diagonal elements of the scattering matrix, , are not the best characterization of=33
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radiation efficiency for a multi-port antenna [27]. Some portion of the power accepted by each element will go to
the other ports through coupling between elements. This coupling is characterized by the off diagonal elements,
=34, of the scattering matrix. The combination of an antenna port's primary reflected signal with the coupled
signals can be constructive or destructive and depends on the phases of the component signals. Each antenna in a
wideband MIMO transmitter is subjected to a randomly phased excitation signal. The signal phases are again
randomized by the propagation environment before arriving at the receiver. MIMO antenna efficiency is then a
function of how randomly phased signals combine and cannot be determined from the traditional scattering matrix
characterization. A more meaningful measure of MIMO antenna efficiency, the Total Active Reflection
Coefficient (TARC) [27], is the ratio of the square root of total reflected power divided by the square root of total
incident power. The TARC can be calculated for the -port antenna system, ,R tt as,, œ +ST
>+>
3œ" 3œ"
R R
3 3# #œ , +
Í ÍÍ ÍÍ ÍÌ Ì" "k k k k† (1)
where is the incident signal vector, is the reflected signal vector and is the scattering matrix of the -port+t , Rt ST
antenna system. The TARC is calculated for different combinations of excitation signals applied to each port.
Each excitation signal has unity magnitude but a random phase. This random phasing of the excitation signals
probes the array in ways that cause constructive combining of coupled signals with the primary reflected signal
(worst case) and destructive combining of coupled signals with the primary reflected signal (best case). These
excitation signals more accurately simulate wideband MIMO signaling than do the signals used in scattering
matrix characterization. Note that signals combine in the linear scale (voltages) whereas the resulting power
signal, used in computing TARC, is the squared magnitude of the voltage signals. Therefore, the TARC can
increase rapidly as the number of array elements increases. The TARC of the 2-element PIFA array was
calculated for a set of twenty excitation vectors and the results are presented in Fig. 10. The calculated TARC are
lower than dB for different excitation vector combinations. This implies that the array has good efficiency*
across the range of possible MIMO signals.
The design for the 2-element PIFA array was adapted to construct a 4-element array by using both sides of the
ground plane. The resulting volume occupied by the four PIFAs measures mm 7mm mm. Fig. 3(c)&! ‚ ‚ "&
shows two perspectives of the manufactured 4-element PIFA array. Two RT-Duroid substrates are attached back-
to-back to realize four microstrip lines to feed the array's elements. Due to the small distance between top and
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bottom elements, a high level of mutual coupling can be expected between elements 1 and 3 and between
elements 2 and 4. However, lower mutual coupling can be expected between elements 2 and 3 and between
elements 1 and 4. Fig. 11 shows one row of the scattering matrix of the 4-element PIFA array. The TARC of the
4-element PIFA array was calculated using four excitation vectors with random phases. The result is presented in
Fig. 12. We see in comparing the TARC in Fig. (10) and Fig. (12) for the two PIFA arrays that the TARC
increases rapidly with the number of elements.
We note that matching networks or intermediate circuits can be used to reduce the magnitude of the off
diagonal elements of the array's scattering matrix to reduce the TARC and increase the antenna efficiency. Once
such method is proposed in [28].
III. EXPERIMENT DESIGN
The purpose of this study is to characterize the performance of a MIMO system that uses a highly compact
antenna array at one end of the link and an antenna array with low mutual coupling at the other end. Such scenario
is relevant to indoor MIMO system deployments where a base station can support large arrays ( ) and? -. 0 Î#-
the mobile devices must use compact arrays ( ). As part of the characterization, we are interested in the? -. 0 Î#-
fundamental relationships between array topology, channel structure and system performance. We begin our
discussion of how this characterization was achieved experimentally by defining a mathematical framework for
MIMO systems and presenting relevant results from the literature. A measurement model is then presented that
describes how system performance was estimated from field data. Finally, we describe a measurement procedure
that was designed to characterize MIMO system performance using a full MIMO radio testbed that can be
outfitted with a variety of array topologies.
A. MIMO System Model
A primary measure of communication system performance is spectral efficiency. The upper bound on spectral
efficiency is channel capacity – defined loosely as the information rate density that a channel supports. Capacity
can be defined as a mathematically tractable quantity given a system model and set of simplifying assumptions
[29]. The following model and assumptions are typically made when deriving MIMO channel capacity:
i) A quasi-static narrowband MIMO system is modeled as,
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] œ \ Rt t tH , (2)
where is the received signal vector, is a multiplicative distortion matrix] − −t ‚ ‚P ‚" P ‚PV V XH
induced by the MIMO channel, is the transmitted signal vector, is an additive\ − R −t t‚ ‚P ‚" P ‚"X V
noise vector introduced by the receiver.
ii) We assume that is a circularly symmetric Gaussian random matrix whose elements are independentH
and identically distributed (i.i.d.) with zero meanÞ
iii) We assume that is a vector of complex Gaussian random variables whose elements are i.i.d. and zeroRt
mean.
iv) We assume that the transmitter has a priori knowledge of channel statistics and the receiver has perfect
knowledge of the channel, .H
The average channel capacity of the MIMO system modeled in (2) and given the assumptions above has been
shown to be [2],
G œ Ta b œ Œ H HHX5
H log det# PR# I , (b/s/Hz) (3)X
H
where is the expectation over all possible realizations of the is the fraction of the totalXHe f† T œ T ÎPH, total X
transmit power allocated to each transmit antenna and is the noise power in each receiver chain. The signal to5R#
noise ratio (SNR) at each receiver is defined as , in which It wasX 5h
t R#
4š ›Š ‹T Ît t th h h H4 4 4
H th is the column of . 4
also shown in [2] that capacity grows linearly with . This fact will become clearer in the next sectionmina bP ßPX V
when the MIMO channel is represented in eigen-space as a set of parallel and independent eigen-channels.
We define the MIMO capacity gain as the ratio,
K œG
Ga b a ba bH
H2
, (4)
where is the average capacity of a single sub-channel, , of given by,Ga b2 2 H
G œ " Ta b k kœ Œ 2 2X5
2 log#R#
# . (5)
The nominal capacity gain of an P ‚ P P ßPX V X V MIMO system is .ba bmina b
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B. Measurement Model
We now define a model and notation similar to the stochastic model and notation given above but which
distinguishes itself as being suitable for deterministic variables appearing in the analysis of measurement data.
Let the channel matrix of a known MIMO channel at frequency, , and position, , be 0 = 0 ß = −6 7 6 7P ‚P[ ‚a b V X
and time-invariant during the period of observation. We occasionally use the shorthand notation, , to represent[
[ [a b0 ß =6 7 and note that is a realization of the random matrix . The eigen decomposition of the HermitianH
symmetric matrix, , yields,[[H
[[ AH Hœ Y Y , (6)
where is a unitary matrix whose columns are eigenvectors of and Y œ− ‚ [[ -P ‚"3
X H A diag is a diagonalc dmatrix of the eigenvalues of .[[H
The instantaneous capacity, , of the channel, , has been shown to be [2],Ga b[ [
G œ Ta b Œ [ [[5
log det# PR# I , (7)X
H
or in terms of the eigenvalues of as,[[H
G œ " Ta b " Œ [ -5
3œ"
P
# 3R#
-
log , (8)
were denotes the number of non-zero eigenvalues of . TP œ P ßP- mina bX V [[H he relationship between the
eigenvalues and channel capacity is most clearly seen in (8). Indeed, each eigenvalue is a measure of the strength
of a channel in eigen-space. The orthoganality of the eigen decomposition implies that each of these eigen-
channels can be used to support an independent information stream. It has been established, both in theory [5] and
by measurement [6], that correlation between the elements of causes a loss of capacity. Increasing correlation[
in causes all but the strongest eigenvalue of to weaken, thereby reducing the channel's ability to support[ [[H
multiple independent parallel information streams.
Our goal in analyzing measured data will be to estimate by computing an ensemble average capacityGa bH
over sufficient measured channel realizations. First, we compute an estimate of the channel for a given frequency
and position in space, , and we compute an estimate of the average noise power, . These estimates are[ 5s 0 ß = sa b6 7 R#
then used to compute the instantaneous MIMO channel capacity, according to (7). This process isG 0 ß =sˆ ‰a b[ 6 7
repeated over a set of uniformly spaced discrete frequencies in the measurement band and over a uniform grid of
fixed positions in space. The ensemble average capacity is finally computed as,
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G œ 0 ß = 0 ß =s " T
OQ sˆ ‰ "" Œ a b a b[
57œ"
Q O
5œ"
# P 5 7 5 7R#log det I , (9)X [ [s sH
One of the goals of the measurement campaign will be to evaluate system performance in a variety
propagation scenarios. A difficulty that arises when comparing measured capacity from different measurement
sites is the bias caused by fluctuating SNR between sites. SNR fluctuates because average channel gain changes
from one site to the next and noise power changes as a function of time as radio hardware heats up. One solution
is to make a comparison of system performance between different sites using MIMO capacity gain. This is
computed from field measurements as,
K œsG s
G 2sˆ ‰ ˆ ‰
Š ‹[[
, (10)
where is the ensemble average capacity of the Single Input Single Output (SISO) channels represented byG 2sŠ ‹the elements, , of the channel matrix . If MIMO capacity gain is computed per site then it is a meaningful2s s[
metric for making a fair comparison of system performance across different sites.
Capacity of MIMO systems with dimensions less than is computed by choosing a subset of theP ‚ PX V
elements of and reallocating the total transmit power. For example, a measurement of is used to[ [s s% ‚ %
compute the capacity for the case by choosing the submatrix of comprised of the elements, , where$ ‚ $ 2s s[ a b3ß4
3ß 4 Ÿ T œ T Î3. The transmit power allocation is then recomputed, according to 3, so that a fair comparison of total
capacity can be made between the and cases.% ‚ % $ ‚ $
The relevance of the eigenvalues of to the channel capacity necessitates that we understand how their[[H
statistics are influenced by changes in the antenna array. The distributions of ordered eigenvalues of will be[[H
used to characterize changes in channel structure due to changing array topology. An approximation of these
distributions can be achieved by computing a histogram of the ordered eigenvalues of each . A Monte Carlo[[s sH
simulation is performed for the zero mean complex i.i.d. Gaussian MIMO channel to produce a set distribution
curves that serve as a reference for comparing the measured distributions. In making this comparison, care is
taken to normalize the average channel gain of the simulated channels to that of the measured channels so that,
" "
QOP R Ps Ð0 ß = Ñ œ 8
- -
" "" "" a b7œ" 3œ" 8œ" 3œ"
Q O
6œ"
3 5 7 3
RL L
sim
- -
- -sim
, (11)
where is the number of simulated channels. This normalization removes the SNR bias between measured andRsim
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simulated data so that a fair comparison can be made. Finally, we denote the difference between the mean of the
3th strongest measured eigenvalue and that of the simulated i.i.d. Gaussian channels as
? - -- -3œ 3 œ "ß ß P Þs
3 3(gauss) for … (12)
This difference will be useful in quantifying how much a measured channel's structure deviates from that of the
reference i.i.d. Gaussian MIMO channel.
C. Setup and Procedure
Over-the-air measurements were executed with a wideband MIMO radio testbed [30]. The testbed has modes
for both MIMO packet communications standards as well as channel sounding [31]. Radios in the testbed meet
the 5% Error Vector Magnitude and MHz spectral mask requirements on transceiver performance set forth by"'
the IEEE 802.11a standard. A Space-Frequency Orthogonal Multitone (SFOM) channel sounding and estimation
scheme was used to measure the channel frequency response, received signal power, and receiver noise power
[17]. These measured quantities were then used to compute capacity according to (7). The SFOM sounding
scheme employs the testbed's full MIMO architecture and not a time-multiplexed MIMO architecture used by
switched antenna array channel sounders or virtual antenna array channel sounders. A complete calibration of the
transceiver radios was performed prior to the campaign. Included in this calibration was the measurement of each
radio's gain, phase noise, complex spectrum and frequency offset. Benchmark tests on an Elektrobit C8 MIMO
channel emulator were performed to verify the testbed's calibration. These benchmarks included capacity
measurements for a 2 2 i.i.d. Gaussian channel and a 2 2 perfectly correlated channel. These tests produced‚ ‚
results consistent with the theoretical average capacity given by (3) and (5).
A ULA of dipole antennas was used as a baseline array for providing a performance reference. These dipoles,
shown in Figs. 3(a) and 4, are targeted for commercial 802.11a/b/g base station deployments and have features
that closely match those of the PIFA (except in size). Similarities between these dipoles and the PIFA are:
toroidal gain pattern with a –5 dB peak gain, vertically polarized, tri-band operation at GHz# #Þ%%ß &Þ#ß &Þ)a bcenter frequencies. Each dipole measures mm mm mm. The uniform spacings between dipoles in"(Þ' ‚ ' ‚ "$$Þ&
the linear array, , were chosen to match fractional wavelengths of the center frequency:?.
e f- - - -0 0 0 0- - - -ß Î#ß Î%ß Î) . The scattering parameters for the antenna arrays were measured for various antenna
spacings. A subset of the s-parameter matrix for dual element antenna arrays are presented in Table 1 and the s-
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parameter matrix for a 2-element PIFA array is show in Fig. 9. A subset of the s-parameter matrix for a 4-element
PIFA array is show in Fig. 11. Matching networks were not used during measurements. As a consequence, the
dipole array s-parameters are seen to generally degrade as decreases. Therefore, the radiation efficiency of the?.
dipole arrays is expected to degrade as the array aperture shrinks.
The measurement sites were located in a multi-story building whose floorplan included laboratories,
classrooms, offices and corridors. Two measurement sites were chosen: a laboratory with electronic equipment,
cubicle partitions and office furniture; a very large empty hall with a few support columns and no furnishings. At
each site, a Line-of-Sight (LOS) and a Non-Line-of-Sight (NLOS) visibility scenario was chosen for placing the
transmitter (TX) and receiver (RX) radios. Positioning robots were used to move the transmitter and receiver
antenna arrays in over cm× cm azimuthal grid. These robots are built exclusively from LEGO components(! (!
(all plastic except for motors and wiring) and have a positioning precision of 1.59mm. Antenna arrays were
mounted on the robots at a height of m above ground. The relative angle between the TX and RX array"Þ$
endfires ranged between ° and ° at each site.#! (!
The measurement setup is summarized in Table 1. The measurement procedure is outlined in Pseudocode 1. A
total of narrowband channel matrices were recorded for each array topology tested at a site (theOQ œ %(&#
inner two loops of the pseudocode). This measurement procedure hopes to collects many channel realizations
across space, time, and frequency so that all degrees of freedom in the channel matrix's randomness are sampled
sufficiently. Given this assumption, the resulting ensemble average capacity, , provides a good estimate ofG sˆ ‰[the channel's average capacity at a site.Ga bH
IV. MEASUREMENT RESULTS
We begin our survey of measurement results with a detailed presentation of results from the NLOS empty hall
scenario. The results from this site exemplify trends observed throughout the measurement campaign. We
consider channel capacity and channel eigenvalue distributions measured for each type of antenna array. We then
present comprehensive results from all measurement sites so that a performance comparison for different antenna
arrays can be made across a variety of propagation scenarios. Comparisons are made using MIMO capacity gain
and the theoretical capacity of i.i.d. Gaussian channels for reference. Results presented in this paper are limited to
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MIMO systems with order , as these constitute cases where the impact of antenna designe fc dP ‚ P lP − "ß #ß $ß %
is most obvious in terms of the trends for increasing numbers of antennas.
A. Channel Capacity
Figs. 13(a)(b)(c) present measured MIMO channel capacity when using dipoles in a ULA with three different
transmit and receive dipole spacings . Each marker represents the frequency-averaged capacity atŠ ‹? ?. .(TX) (RX)ß
one position in an grid of spatial samples. The frequency-averaged capacity is computed according to the"" ‚ *
inner sum in (9) using discrete frequencies uniformly spaced over a MHz band centered at GHz. The%) "' #Þ%*
average capacities of an i.i.d. Gaussian channel, given by (3), are plotted as solid curves for reference.
Measurements in Fig. 13(a) agree well with the average capacities expected from i.i.d. Gaussian channels. For
the case, the nominal capacity predicted by (3) at the measured SNR of dB is b/s/Hz whereas the% ‚ % #*Þ* $%Þ*
measured capacity from (9) is b/s/Hz. As the antenna separation decreases first at the transmitter, Fig. 13(b),$$Þ&
and then also at the receiver, Fig. 13(c), the measured capacity decreases drastically (from b/s/Hz to $$Þ& #(
b/s/Hz to b/s/Hz for the case). Shrinking of just the transmit array aperture is responsible for the##Þ$ % ‚ %
majority (58%) of capacity that is lost when both array apertures shrink. The observed slight decrease in average
SNR, from dB to dB to dB for the case, is a symptom of increasing impedance mismatch#*Þ* #)Þ' #(Þ" % ‚ %
between the array and the radios. Impedance mismatch is expected to cause a decrease in the array's radiation&!H
efficiency and thus a lower signal power at the receiver. However, (3) shows that MIMO capacity has a
logarithmic dependence on SNR and can only account for a minor part ( b/s/Hz) of the total loss in capacity %
( b/s/Hz). Therefore, the dominating cause of lost capacity is attributed to the increasing correlation in the""Þ#
channel matrix as the array apertures shrink. Another observation to be made from Fig. 13 regards the relative
capacity loss between different MIMO configurations. The case is more robust to changes in antenna# ‚ #
spacing than the and cases. Whereas the capacity drops first to 89% in Fig. 13(b) and then to$ ‚ $ % ‚ % # ‚ #
80% in Fig. 13(c), the and cases drop first to 81% and 80% and then to 68% and 66% of their level in$ ‚ $ % ‚ %
Fig. 13(a).
Measurements in Fig. 13(d)(e) are for the same scenario as Figs. 13(b)(c) but with the transmit dipole array
replaced by a 4-element PIFA array. For the case, the capacity predicted by (3) at the measured SNR of% ‚ %
#&Þ) #*Þ" #(Þ' dB is b/s/Hz whereas the measured capacity from (9) is b/s/Hz. This is remarkable because the
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PIFA array capacity is 93% of the capacity of an i.i.d. Gaussian channel compared with the 80% of the compact
dipole array for the same (see Fig. 13(b)).?.(RX)
B. Channel Eigenvalue Distribution
Figs. 14, 15, and 16 show the distributions of ordered eigenvalues of the matrix for the measurements[[s sH
presented in Fig. 13(a)(b)(c). Also shown are the distributions of ordered eigenvalues from a Monte Carlo
simulation of i.i.d. Gaussian channels whose channel gain is matched to the measured channel according to (11).
Because the eigenvalues of are a measure of channel "power" in eigen-space, their distributions are plotted[[s sH
on a logarithmic scale. Both measured and i.i.d. Gaussian channel eigenvalue distributions are generated from
histograms over a dB domain with a dB bin spacing using eigenvalues from channel matrices.'! !Þ& %(&#
In all cases, the measured eigenvalue distributions for the SISO cases agree very well with those expected
from the i.i.d. Gaussian channel. The eigenvalue distributions for the MIMO cases in Figs. 14 and 15 show that,
as decreases, the mean of the strongest eigenvalue increases while the means of the other eigenvalues?.(TX)
decrease. This is to be expected since an increase in correlation in the channel causes a MIMO channel to behave
more like a SISO channel. The change observed for the case is drastic and is even more pronounced when% ‚ %
?.(RX) decreases (Fig. 16).
Fig. 17 shows measurements from the same scenario as those of Figs. 15 but with the transmit dipole array
replaced by a 4-element PIFA array. A direct comparison between these figures shows that the smallest measured
eigenvalues of the PIFA array case deviate less from those of the i.i.d. Gaussian channel. The case in Fig.# ‚ #
17 shows that the mean of the second eigenvalue deviates slightly more from the i.i.d. Gaussian case than does the
# ‚ # case using dipole arrays. Fig. 18 shows that this deviation is not observed when using the 2-element PIFA
array even under the more demanding scenario when cm.?.(RX) œ "Þ&
Here we return to the observation that the case showed more robustness than did the and # ‚ # $ ‚ $ % ‚ %
cases in Fig. 13(a)(b)(c). Observe, from Figs. 14, 15, and 16, that the distribution of the second eigenvalue does
not change appreciably from that of the i.i.d. Gaussian case until both the transmit and receive arrays have shrunk.
However, for the and cases, the weakest eigenvalues are seen to deviate appreciably from their$ ‚ $ % ‚ %
corresponding i.i.d. Gaussian channel eigenvalues.
Fig. 19 shows how , defined above in (12), changes as a function of for the MIMO case with? ?-3 .(RX) % ‚ %
?.(TX) œ "Þ&cm. Results for both the compact 4-element PIFA transmit array and a dipole transmit array are
14
shown. As expected, the mean of the strongest eigenvalue grows while the remaining eigenvalues decrease as the
receiver array becomes more compact. Note that data points for the dipole array at cm and?.(RX) œ "#
?.(RX) œ "Þ& % ‚ %cm in Fig. 19 correspond to the MIMO measurements shown in Figs. 15 and 16. The PIFA
array has that are consistently closer to the nominal value of than those of the dipole array. This indicates?-3!
that the PIFA array is better at preserving the eigen-channels of the near i.i.d. Gaussian propagation channel.
C. Performance Relative to the i.i.d. Gaussian Channel
In this section and the next, we present comprehensive results from all measurement sites. These validate the
generality of trends observed for the NLOS empty hall scenario presented above.
Table 3 summarizes the ratio of the measured average capacity to that of an i.i.d. Gaussian channel for a " ‚ "
SISO system and MIMO systems using ULAs of dipoles with spacings of . Alle f# ‚ #ß $ ‚ $ß % ‚ % "-0-
measurement sites provided channels with sufficient multipath to support capacities near that of the i.i.d. Gaussian
channel.
Table 4 compares the performance of a dipole array and a PIFA array in terms of the ratio of the# ‚ #
measured average capacity to that of the an i.i.d. Gaussian channel. Table 5 does the same for the case. In% ‚ %
both tables, the PIFA array not only outperforms the dipole array, but supports most of the capacity of an i.i.d.
Gaussian channel. Furthermore, the dipole spacing required to achieve the same performance as the PIFA array in
the case is seen to be .% ‚ % œ Î#? -. 0-
Table 6 shows the ratio of the capacity lost from shrinking one dipole array to the capacity lost from shrinking
both dipole arrays. Typically, a majority of the capacity is lost by decreasing only one of the array's apertures.
In Fig. 20, the ratio of the average measured capacity to the average capacity of an i.i.d. Gaussian channel at
the same SNR is plotted for , and MIMO cases. Measurements for each array topology are# ‚ # $ ‚ $ % ‚ %
averaged over all sites. In all cases, a compact array was used at one end of the link and a dipole array of varying
?. was used at the other end. Capacity ratios closer to unity indicate that the channel behaves more like an i.i.d
Gaussian channel. We see that the case is fairly robust to increasing correlation (decreasing ) for both the# ‚ # ?.
? - ? -. 0 . 0œ Î) œ Î)- - dipole array and the PIFA array. However the dipole array suffers greater loss in the
$ ‚ $ % ‚ % or cases than does the PIFA array. Indeed, for both arrays, MIMO capacity is not seen to scale
linearly with the . A linear scaling of capacity would require that all curves lie on top of each other.mina bP ßPX V
15
D. MIMO Capacity Gain
Fig. 21 shows how MIMO capacity gain varies as a function of the receiver dipole array spacing for% ‚ %
each propagation scenario. Two array topologies are shown: a dipole transmit array with cm and a?.(TX) œ "Þ&
compact 4-element PIFA transmit array. The MIMO capacity gain of the PIFA array is consistently closer to the
nominal capacity gain of than the dipole array. The general profile of the capacity gain curve shows a threshold%
near cm beyond which both arrays having increasingly poor performance. This behavior was also noted?.(RX) œ $
above in Fig. 19 for the mean eigenvalue behavior.
A notable anomaly in Fig. 21 is that, for the two LOS lab measurements, capacity gain first increases as the
receiver array aperture shrinks and then finally drops. This result surprised the authors and the measurements
were repeated two weeks later at which time the anomalous results were again observed. It was found that, in the
LOS lab scenario alone, the SISO capacity estimate, , decreased faster with decreasing than typicallyG 2sŠ ‹ ?.(RX)
observed at other sites. However, the MIMO capacity decreased at a rate similar to that observed at other sites.
This caused the MIMO capacity gain ratio to increase for cm cm cm before finally decreasing.?.(RX) − "# ß ' ß $e f
The MIMO capacity gain for systems is shown in Fig. 22. Two array topologies are shown: a 2-# ‚ #
element dipole array and 2-element PIFA array replace the 4-element transmit arrays discussed in Fig. 21. Again,
we see the PIFA array outperforming the dipole array. Unlike the case, the PIFA array does not lose% ‚ %
capacity gain when cm. This is consistent with observations reported in [16] and with the results?.(RX) œ "Þ&
presented in Fig. 18 where the eigen distributions are is still nearly that of the i.i.d Gaussian channel. Note also
that the LOS lab measurements capacity gain initially increases as seen in the case.% ‚ %
Finally, we present results for a system in Fig. 23 in which only elements 1 and 2 of the 4-element# ‚ #
PIFA array were used. We see that the 4-element array performs as well as the 2-element PIFA array until
?.(RX) œ $cm and always outperforms the dipole array (see Fig. 22). The choice of elements 1 and 2 in the 4-
element PIFA array was based on the selection criteria discussed in Section III-B and not because it provided the
best results of any element pairing. Elements 1 and 2 had the second best scattering parameter set (element pairs
c d c d1 and 4 and 2 and 3 had the best) and were located under the ground plane.
V. CONCLUSION
A 2-element compact antenna array and a 4-element compact antenna array were designed for use in MIMO
enabled mobile devices. These arrays are extremely compact yet have acceptable mutual coupling and radiation
16
efficiency and resonate in three wide frequency bands. A measurement campaign was executed in which a MIMO
transceiver testbed was outfitted with the compact arrays and dipole arrays of varying topology. Channel
sounding measurements were taken using each array in a variety of indoor environments. A comparison of the
relative performance between the compact antenna arrays, the dipole arrays and the i.i.d. Gaussian channel was
presented. The following observations can be made from the measurement results:
i) : The radiation pattern and efficiency of the proposed Printed Inverted-F AntennaPIFA Performance
design was similar to that of a like-featured but much larger dipole antenna. Furthermore, the
characteristics of the individual PIFA in a compact array remained relatively unchanged from those of
the isolated PIFA because of low mutual coupling between elements. These properties of the PIFA
make it ideal for use in MIMO antenna arrays.
ii) : All measurement sites provided channels with sufficient multipath to allow Multipath Richness " ‚ "
SISO systems and MIMO systems to achieve capacities near that of an i.i.d.e f# ‚ #ß $ ‚ $ß % ‚ %
Gaussian channel using a uniform linear array of dipoles with spacings of . This indicates that, on"-0-
average, the channel's multipath is sufficiently rich to support nearly four independent channels in
eigen-space.
iii) : The loss of SNR, due to impedance mismatch betweenImpedance Mismatch vs. Channel Correlation
dipole antenna arrays and radio hardware, accounted for a minor portion of the capacity loss
experienced when shrinking the dipole arrays. Changes in eigenvalue distribution of the channel matrix,
caused by the increasing correlation in the channel, accounted for the major portion of lost capacity.
This result prioritizes the design requirements for MIMO antenna arrays.
iv) : When using uniform linear arrays of dipoles, a majority of theSingle vs. Dual Compact Arrays
capacity that can be lost by decreasing the array aperture at both the transmitter and receiver is typically
lost when only one side's array aperture decreases. This result is relevant to indoor MIMO system
deployments where a base station can support large arrays ( ) and the mobile devices must? -. 0 Î#-
use compact arrays ( ).? -. 0 Î#-
v) : In a ( ) MIMO system with a dipole spacing ofPIFA Array vs. Dipole Array Performance % ‚ % # ‚ #
"-0- at receiver ULA, the 4-element (2-element) PIFA transmit array achieved 93-97% (98-100%) of
the i.i.d. Gaussian average capacity while the dipole transmit array only achieved 80-87% (85-100%) of
the i.i.d. Gaussian average capacity.
17
vi) : In a MIMO system with a dipole spacing of in a receiver ULA,Equivalent Dipole Spacing % ‚ % "-0-
a dipole transmit array with a dipole spacing of was necessary to achieve average capacities-0-Î#
similar to that of the 4-element PIFA transmit array. This is a remarkable result given that the 4-element
PIFA array elements occupy a volume mm mm mm 2 3mm that is 100 times lessa ba b* ‚ #Ð"( Ñ $" ‚ Ð Ñ
than that of the dipole array mm mm .a b"(Þ' ‚ $Ð Î#Ñ ‚ "$$Þ&-0-
vii) : Consider the case of a MIMO system using Uniform Linear Array of dipoles with aCapacity Scaling
fixed dipole spacing of at one end of the link. It was observed that the configuration was far-0-Î) # ‚ #
more robust to capacity loss with decreasing dipole separation at the other end of the link than were the
$ ‚ $ % ‚ % $ ‚ $ % ‚ % or configurations. However, the same degree of and capacity loss was less
evident with the PIFA arrays. Here, the relevant difference between the dipole array and? -. 0œ Î)-
the PIFA array is that the first suffers strongly from mutual coupling while the second does not. This
suggests that MIMO capacity does not scale linearly with in the presence of mutualmina bP ßPX V
coupling. Previous studies show that, for antenna spacings , MIMO capacity scales linearly in Î%-0-
the presence of correlation induced by the propagation channel [4], [16]. However, mutual coupling
appears to be the dominating cause of correlation when antenna spacing is .Ÿ Î)-0-
viii) : Despite the robust performance of the configuration, it was seenCoupling/Efficiency Tradeoff # ‚ #
from a TARC analysis of the compact PIFA arrays and from the measured drop in SNR with shrinking
dipole array aperture that coupling should be minimized if the radiation efficiency is to be maximized.
Therefore, although mutual coupling may not cause an appreciable loss in MIMO system# ‚ #
capacity, compact antenna arrays should still be designed to minimize mutual coupling in order to
maximize radiation efficiency.
ix) : In all scenarios of a MIMO configuration with a dipole spacing 4 atMulti-Mode MIMO # ‚ # Î-0-
receiver ULA, using only 2 channels of the 4-element PIFA array at the transmitter yielded similar
performance to the 2-element PIFA array and better performance than the dipole arrays with a larger
aperture. Therefore, the 4-element PIFA array is an excellent candidate for milti-mode transceiver links
that adapt their signaling from up to MIMO using a 4-element arrays." ‚ " % ‚ %
The fact that these observations are consistent for both LOS and NLOS scenarios in two very different indoor
propagation environments suggests that they hold more generally for indoor MIMO system deployment. These
18
observations strongly motivate the need for careful design of compact antenna arrays used in MIMO enabled
mobile devices.
ACKNOWLEDGMENT
The Authors would like to thank Michael Parker at the UCLA Department of Computer Science for
developing software for the positioning robots.
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20
TABLES AND FIGURES
Pseudocode 1: Measurement Campaign Procedure1 For each measuremnt site:2 For each pairing of TX-RX array types: {dipole-dipole arrays, PIFA-dipole arrays}3 For each dipole spacing: š ›? ?. .
(TX) (RX)ß
4 For each grid position: …e f= œ "ß ßQ7
5 Transmit the sounding signal6 Receive the channel distorted signal7 Measure MIMO capacity at each frequency: …e f0 œ "ß ßO5
8 Move the arrays to their next grid position.9 end10 Change the dipole spacing.11 end12 Change the pair of antenna arrays13 end14 Move to the next site.15 end
TABLE 1 Dual Element Array s-Parameters at 2.49GHz
s (dB) s (dB)Dipole Array
cm cm
cm cm
PIFA Array ( cm) 0
"" "#
.
.
.
.
.
????
?
œ #%Þ' #&Þ' ##Þ$œ "#Þ$ #%Þ" #!Þ"œ 'Þ" #'Þ# "&Þ)œ $ "(Þ) ""Þ!
¸ $ # .5 .3"%
TABLE 2 Measurement Campaign Summary
Site Visibility Separation
Center FrequencySignal Bandwid
lab LoS madjacent labs NLoS mempty hall LoS 3 mempty hall NLoS 28 m
2.49 GHz
"!"!"
thSignal Power
TX Signal Type# Tones per TX
Grid PositionsGrid Spacing
16 MHz15 dBm per TXSpace-Frequency Multitone
6.1 cm
O œ %)Q œ "" ‚ *
Dipole Array Antenna Spacings (cm)? ?
- - - -. .
Ñ
0 0 0 0
(TX) (RXß œ "Þ&ß $ß 'Þ"ß "#Þ$
¸ Î)ß Î%ß Î#ß- - - -
TABLE 3Ratio of Measured Capacity to Capacity of i.i.d. Gaussian
Channel when Using Uniform Linear Arrays of Dipoles with? ? -(TX) (RX)
. . 0œ œ "-.
" ‚ " # ‚ # $ ‚ $ % ‚ %
"Þ!! "Þ!! !Þ*' !Þ*'
!Þ** !Þ** !Þ*' !Þ*'
"Þ!! "Þ!! !Þ*# !Þ*!
"Þ!! !Þ** !Þ*) !Þ**
Hall LOS
Hall NLOS
Lab LOS
Lab NLOS
TABLE 4Ratio of Measured Capacity to Capacity of i.i.d. Gaussian
Channel for MIMO Using Compact Transmit Arrays and# ‚ #
a Dipole Receive Array with .? -(RX). 0œ "
-
PIFA TX Array Dipole TX Array
Hall LOS
Hall NLOS 0.9
Lab LOS
Lab NLOS
? -(TX).
") 0œ
!Þ** "Þ!!
) !Þ**
!Þ** !Þ)&
"Þ!! "Þ!!
-
TABLE 5 Ratio of Measured Capacity to Capacity of i.i.d. Gaussian
Channel for MIMO Using Compact Transmit Arrays and% ‚ %
a Dipole Receive Array with .? -(RX). 0œ "
-
PIFA Dipole TX Array
TX Array
Hall LOS
Hall NLOS 0.9
Lab LOS
Lab NLOS
? - ? -(TX) (TX). .
" ") #0 0œ œ
!Þ*% !Þ)& !Þ*$
$ !Þ)! !Þ*'
!Þ*' !Þ)# !Þ*&
!Þ*( !Þ)(
- -
!Þ*(
TABLE 6 Ratio of Capacity Lost from Decreasing in One Array vs.?.
Capacity Lost from Decreasing in Both Arrays.?.
? - ? - ? - ? -(TX) (RX) (TX) (RX). . . .0 0 0 0
" ") )œ " ß œ œ ß œ "
- - - -
# ‚ # % ‚ % # ‚ # % ‚ %
!Þ !Þ
!Þ !Þ
Hall LOS 0.47 0.54 0.60 0.54
Hall NLOS 0.37 0.46 54 57
Lab LOS 47 0.52 43 !Þ
!Þ !Þ !Þ
52
Lab NLOS 69 0.62 59 58
mean 0.50 0.54 0.54 0.55
