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ADAPTIVE ANTENNAS AND MIMO SYSTEMS FOR WIRELESS SYSTEMS
Correlation and Capacity of MIMO Systems and Mutual Coupling, Radiation Efficiency, and Diversity Gain of Their Antennas: Simulations and Measurements in a Reverberation Chamber Per-Simon Kildal, Chalmers University of Technology Kent Rosengren, Flextronics Design
ABSTRACT MIMO systems are characterized by their maximum available capacity, which is reduced if there is correlation between the signals on different channels. The correlation is primarily caused by mutual coupling between the elements of the antenna arrays on both the receiving and transmitting sides. Similarly, diversity antennas can be characterized by a diversity gain that also is affected by mutual coupling between the antennas. We explain how such MIMO and diversity antennas with mutual coupling can be analyzed by classical embedded element patterns that can be computed by standard computer codes. In the MIMO example under investigation, the mutual coupling causes both reduced correlation, which increases the capacity, and reduced radiation efficiency, which decreases it, and the combined effect is a net capacity reduction. We also explain how radiation efficiency, diversity gain, correlation, and channel capacity can be measured in a reverberation chamber. The measurements show good agreement with simulations.
INTRODUCTION Mobile and wireless terminals are subject to strong fading due to multipath propagation, in particular when used in urban and indoor environments. The performance of the terminals in such environments can be significantly improved by making use of spatial, polarization, or pattern diversity. This means that the signals on, say, two antennas (with different position, polarization,
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or radiation pattern) are combined in such a way that there are shallower fading minima on the combined signal. This corresponds to an increase in the signal-to-noise ratio (SNR) in the fading dips, so the fading margins in the system link budget can be reduced. The increased SNR can alternately be used to increase the capacity of the communication channel if the system allows this. Then, particularly if we have several antennas on both the transmitter and receiver sides, we obtain multiple-input multiple-output (MIMO) systems. The present article describes how to characterize antennas for both diversity and MIMO systems. The so-called reverberation chamber [1] has for a couple of decades been used for some types of electromagnetic compatibility (EMC) measurements. It is a metal cavity that is sufficiently large to support many resonant modes, which are perturbed with movable stirrers inside the chamber, creating a fading environment. We have previously shown that the reverberation chamber represents an isotropic multipath environment of a similar type as that we find in urban and indoor environments, but with a uniform elevation distribution of the incoming waves [2]. The classical radiation efficiency characterizes the antenna performance in such a uniform and isotropic multipath environment, and we showed in [3] that this can be measured fast and accurately in a small reverberation chamber (Fig. 1). Furthermore, in [4] we showed that the diversity gain of a two-port antenna can be measured straightforwardly in a reverberation chamber. This has many advantages over alternative measurement methods, which involves driving
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The measurements in the reverberation chamber are in comparison fast, and repeatable even in other reverberation chambers of equal or larger size, provided the chambers have efficient stirring methods.
A B Three fixed wall antennas
C
Switch D 1
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n Figure 1. Photo (upper) and illustration (lower) of the reverberation chamber. The photo shows a setup
for measuring radiated power of a mobile phone in talk position relative to a mobile phone. The illustration shows a setup for measuring a six-element monopole circular MIMO array. The chamber is equipped with two mechanical plate-shaped stirrers. The six-element monopole array and reference dipole are located on a rotatable platform and rotated inside the chamber (platform stirring). The drawing also shows a head phantom inside the chamber, which is used to load the chamber for more excited mode. The chamber is available from Bluetest AB (http://www.bluetest.se, patent pending).
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The formula for MED is the same as for MEG, but the “realized gain” radiation field functions in the formula for MEG must be replaced by “directive gain” radiation field functions in the formula for MED, where the realized and directive gains are standard IEEE definitions.
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around with the measurement equipment in an urban environment, or moving it around in an indoor environment. The measurements in the reverberation chamber are, in comparison, fast and repeatable even in other reverberation chambers of equal or larger size, provided the chambers have efficient stirring methods. Also, the measurements in many such reverberation chambers can be done by using only one single channel receiver, because we can repeat exactly the same environment in the chamber as many times as we like, and therefore we do not need to simultaneously measure the two channels and the single isolated antenna reference. In a real environment we need, in comparison, three measurement receivers to do diversity measurements, one for each branch and one for the reference, or a fast switch to select the three signals one after the other. These advantages are even greater when measuring MIMO systems, because the MIMO antenna has many ports at which the signals have to be measured simultaneously or otherwise under the same conditions. In the present article we describe how such reverberation chamber measurements can be performed, and compare with simulated results. First, however, in the next two sections we explain which performance parameters characterize single antennas and array antennas, respectively, in a multipath environment. The reverberation chamber used in the present measurements is the same as in [4] (Fig. 1). It has dimensions 0.8 m × 1.05 m × 1.6 m. The chamber makes use of frequency stirring, platform stirring [3], and polarization stirring [5] to improve accuracy. In all measurements we used 25 platform positions and two mechanical stirrer positions for each platform position. With 50 different stirrer positions in total, we also used 25 MHz frequency stirring and polarization stirring using three perpendicular monopoles on the inside of the chamber walls. The measurements were done at 900 MHz.
CHARACTERIZATION OF SINGLE ANTENNAS IN A MULTIPATH ENVIRONMENT DIFFERENT FADING ENVIRONMENTS The fading environment at the receive side can be characterized by several independent incoming plane waves. This independence means that their amplitudes, phases, and polarizations are arbitrary relative to each other. If the number of waves is large enough (typically a few hundred) or we move the antenna large distances in a less rich environment, the in-phase and quadrature components of the received signal become normally (Gaussian) distributed, and from this their associated magnitudes get a Rayleigh distribution, and the phases gets a uniform distribution over 2π. In addition, the arriving waves may have a certain distribution in the elevation and azimuth planes. It is natural to assume that the mobile terminal can be oriented arbitrarily relative to directions in the horizontal plane, which means that the azimuth angle is uniformly distributed. The terminals may have a certain given
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orientation relative to the vertical axis, and common environments (especially outdoor) have larger probability of waves coming in from close to horizontal directions than from close to vertical ones. Therefore, we may need an elevation distribution factor to describe real multipath environments. However, it is always desirable to have an isotropic reference environment with a uniform elevation distribution, in which all directions of incidence over the whole unit sphere are equally probable. This is convenient because it simplifies characterization of the antenna in the sense that performance becomes independent of orientation of the antenna in the environment. The reverberation chamber simulates such an isotropic environment.
MEG, MED, AND RADIATION EFFICIENCY Antennas in fading environments are sometimes characterized by the so-called mean effective gain (MEG). This can be calculated from the radiation field function of the antenna, and it is a function of the orientation of the antenna, its polarization, and the azimuth, elevation, and polarization distributions of the incoming waves in the environment. For the isotropic environment the MEG becomes equal to half the classical radiation efficiency. Actually, the MEG can, for an arbitrary environment, be separated into two factors, classical radiation efficiency and mean effective directivity (MED). In this way the MED would solely contain the effect of the environment and the shape of the radiation pattern, whereas the radiation efficiency contains all losses due to absorption and the impedance mismatch. The formula for MED is the same as for MEG, but the “realized gain” radiation field functions in the formula for MEG must be replaced by “directive gain” radiation field functions in the formula for MED, where the realized and directive gains are standard IEEE definitions [6]. Thus, the relation between MEG and MED becomes the same as between the classical realized and directive gains for line-ofsight systems. The radiation efficiency can be measured in a reverberation chamber.
CHARACTERIZATION OF ARRAYS IN A MULTIPATH ENVIRONMENT ISOLATED ELEMENT PATTERN AND CORRELATION Classical array antennas for line-of-sight systems are characterized by their realized gain and radiation patterns. The radiation patterns can also be referred to as realized gain function. The realized gain function is the directive gain multiplied by the radiation efficiency. The latter has contributions due to absorption in lossy material in the antenna and its environment and mismatch at the antenna port. The radiation pattern of a classical array antenna is the product of two factors, the isolated element pattern (which is equal for equal elements at different locations and the array factor. The isolated element pattern as defined in [7] is the radiation from one element of the array when all the others are removed, but with the ground plane on which they are
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located present (if any). In theoretical work on diversity and MIMO systems the elemental antennas are often treated as isolated, but in the next paragraph we explain that this is not a valid description [8, 9]. The array factor cannot be used for MIMO antennas because the ports have uncorrelated signals.
EMBEDDED ELEMENT PATTERN AND RADIATION EFFICIENCY In classical array analysis the so-called active element pattern is introduced [7]. This is the radiation pattern of a single element when all the other elements are present, but are not excited and instead terminated with loads representing the source impedance on their ports. This is now more commonly and descriptively referred to as an embedded element pattern, a term already used in [10]. The excited antenna will induce radiating currents on the terminated non-excited antennas. Therefore, the embedded element pattern may be very different from the isolated element pattern. The embedded element pattern is used to describe blindness in classical arrays, whereas in MIMO antennas it plays an even more significant role. In a multipath environment the received signal on each port is transmitted or detected independent of the other ports; therefore, each port transmits or receives signals through their embedded element patterns. In such a way, the radiation efficiency at each port, as well as the correlation between the signals at all ports, are determined by the embedded element pattern. Both these quantities (radiation efficiency and correlation) are needed in order to theoretically predict diversity gain and maximum capacity. The embedded element patterns were used in the analysis of the diversity antenna in [8]. The embedded element pattern of an excited antenna port can be computed by most commercial computer programs, by terminating all non-excited ports with 50 Ω. The embedded element pattern can also be measured in a normal anechoic chamber. However, it is possible to characterize diversity and MIMO antennas without knowing the embedded element patterns explicitly. For instance, the reverberation chamber provides a way of measuring radiation efficiency and correlation, and also estimates of a complete communication channel without explicitly using the embedded element patterns, and from these channel estimates the diversity gain and capacity can be obtained.
EQUIVALENT CIRCUITS OF RECEIVE ANTENNAS The embedded element patterns are, like all radiation patterns, easiest to describe on transmit, when there is a current or voltage source connected to the antenna port, and the radiation efficiency is well defined. However, it is well known that reciprocity applies, so the performance of the same antenna for the receive case is described in terms of the same embedded element pattern and radiation efficiency as on transmit. Actually, if we mathematically formulate the embedded radiation field function (caused by a given source current at the port of an element) as a complex vector field function, we can include this in the equivalent circuit of
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the same antenna on reception, as given for an arbitrary antenna in [6, p. 78]. The complete complex radiation field function (also containing phase information) is needed in theoretical characterization in order to add the received voltages from several incident waves from different directions with correct amplitudes and phases.
MEASUREMENT PROCEDURE IN REVERBERATION CHAMBER The uniform multipath environment can be generated artificially in a reverberation chamber, which thereby provides a statistically repeatable laboratory-produced environment for characterizing mobile terminals and their antennas. The reverberation chamber can be used to measure radiation efficiency, which characterizes the performance of single antennas in an isotropic multipath environment according to the above. It can also be used to measure the diversity gain as described in [4], and channel capacities of MIMO antennas, described later. The procedure for measuring a diversity or MIMO antenna in a reverberation chamber is briefly described as follows. The diversity or MIMO array is located inside the reverberation chamber in such a way that it is more than 0.5 wavelengths from the walls and mechanical stirrers. We also locate a single antenna with known radiation efficiency far enough away from the array to avoid significant direct coupling, to produce a reference level (for nondirective antennas a spacing of a half to one wavelength is sufficient). We connect one of the array ports to a source (i.e., a network analyzer), and terminate all the other ports and the reference antenna in 50 Ω. We gather S-parameters between the port and the three wall-mounted antennas (used for polarization stirring) for all positions of the platform and mechanical stirrers and for all frequency points. The measurement procedure is then repeated for every antenna port, also with the uncorrected ports terminated in 50 Ω, for exactly the same stirrer positions and position of the array inside the chamber. Thus, the field environment is exactly the same when measuring every port. The complex transmission coefficients S21 between the connected port and each of the three fixed wall antennas, as well as the reflection coefficients S11 of each wall antenna and S 22 of the array port, are stored for every stirrer position and frequency point. Finally, we connect the reference antenna to the network analyzer and perform the same measurements as for the array. During the reference measurements, the array with all its ports terminated in 50 Ω must be present in the chamber. This is necessary because the loading of the chamber (and thereby the Q-factor) needs to be the same during measurements of both the reference antenna and the array, and because the array itself loads the reverberation chamber noticeably even when there is a lossy object such as a head phantom inside the chamber. In a small chamber it is advantageous to use frequency stirring (averaging) to improve accuracy. In such cases we correct the complex samples of S21 with mismatch factors due to both S11 and S22 before the
the reverberation chamber provides a way of measuring radiation efficiency and correlation, and also estimates of a complete communication channel without explicitly using the embedded element patterns, and from these channel estimates the diversity gain and capacity can be obtained.
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Two dipoles separated 15 mm 100 Ideal reference
Cumulative probability
Branch 1 and 2 separate 10–1 Theoretical rayleigh
Radiation efficiency branch 1 and 2
Selection combining 10–2 Effective diversity gain at 1% Diversity gain at 0.5%
10–3 –30
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n Figure 2. The cumulative probability distribution function of measured val-
ues of S12 in a reverberation chamber for an ideal reference antenna (corrected for its finite radiation efficiency) and a diversity antenna consisting of two parallel dipoles. frequency stirring, as explained in [5, Eq. 1]. We also normalize the corrected S21 samples to the reference level corresponding to 100 percent radiation efficiency. This is obtained from the corrected S 21 samples measured for the reference antenna and its known radiation efficiency. We refer briefly to these corrected and normalized samples of S21 as the normalized S21 values. The normalized S21 values represent estimates of the channel matrix H of multipath communication channels set up between the wall antennas and the MIMO array inside the chamber. Therefore, from the measured S-parameters the diversity gain and capacity can be obtained. This is explained below.
APPARENT, ACTUAL, AND EFFECTIVE DIVERSITY GAINS Diversity means that we use two antennas located sufficiently far from each other (space diversity) or otherwise with low coupling between them (polarization or pattern diversity). The received signal will then be uncorrelated on the two antennas, and it is very unlikely that there will be a fading dip simultaneously on both antennas. Therefore, by an appropriate combination of the two signals, the probability of a fading dip will be strongly reduced. There are several different possible combination schemes, such as switch diversity, selection combining, and maximum ratio combining, and the improvement in the fading margin can be as large as 10–12 dB. Diversity in the mobile terminal exists in Korean and Japanese mobile communication systems, and Universal Mobile Telecommunications System (UMTS) is prepared for it.
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As an example we treat two parallel dipoles, with a given separation, at 900 MHz. Figure 2 shows the cumulative distribution function (CDF) of the measured normalized S21 samples in the reverberation chamber. We see that the curve of the ideal reference antenna (a dipole with known radiation efficiency) follows the theoretical Rayleigh distribution very closely (because the curve is corrected for the dipoles’ known radiation efficiency), which is the guarantee for a rich scattering environment. The CDFs of each branch of the diversity antenna also have the same shape as a theoretical Rayleigh distribution, but they are shifted to the left because their radiation efficiency is lower. Actually, the horizontal spacing between the CDFs of the two elements of the branches (i.e., dipoles) of the diversity antenna and the CDF of the ideal reference is equal to the radiation efficiency. If we apply selection combining of the normalized S21 samples of the branches, we get the improved CDF marked “selection combining.” The diversity gain is the difference between the selectioncombined CDF and one of the other CDFs at a certain CDF level, commonly chosen to be 1 percent. We can distinguish between apparent, effective, and actual diversity gains [4], depending on whether we use as a reference one of the branches of the diversity antenna, an ideal single antenna (corresponding to radiation efficiency of 100 percent), or an existing practical antenna to be replaced, respectively. In the latter case the practical reference antenna shall be located in the position relative to an object (e.g., a head phantom) that corresponds to the desired position of operation of the existing antenna as well as the replacing diversity antenna. Then the actual diversity gain is the apparent diversity gain multiplied by the radiation efficiency of the single existing antenna the diversity antenna shall replace. The effective diversity gain represents the gain over a single ideal reference antenna with no additional antenna close to it. By ideal we mean, as before, that it is impedance-matched to the transmission line feeding it and has no dissipative losses. We see that in our example in Fig. 2 the apparent diversity gain at 1 percent CDF level is 8 dB, whereas the effective diversity gain compared to the ideal single antenna reference is only about 3 dB. This means that if in a system we allow for a fading margin of 20 dB in order to receive with sufficient quality 99 percent of the time (i.e., 1 percent CDF level), we can reduce the fading margin by 3 dB if we use this specific diversity antenna (two parallel dipoles with 15 mm spacing) instead of a very good single antenna. The diversity gain could easily be made larger by using larger dipole spacing, or choosing two orthogonal antennas. The theoretical maximum is 10 dB by selection combining. The discrepancy between 3 and 10 dB is mainly due to low radiation efficiency. In the example this is caused by mutual coupling, giving large absorption in the 50 Ω load of the opposite dipole, as studied in [8]. The reduced diversity gain due to correlation has a comparatively small effect, as explained in the next paragraph. Figure 3 shows measured and computed apparent and effective diversity gains as a func-
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tion of the spacing between the dipoles. The difference between the two sets of curves is the radiation efficiency. The computed values are obtained using a classical embedded element model with sinusoidal current distribution on both dipoles [8]. The radiation efficiency is automatically accounted for by this model, as explained earlier. The diversity gain is calculated by calculating the correlation between the two branches’ embedded radiation patterns and transforming this to an apparent diversity gain using standard formulas from [11]. The correlation causes the reduction of the apparent diversity gain for small dipole spacing. It is also of interest to know the diversity gain for antennas used near the human body. Therefore, we measured in the reverberation chamber two parallel dipoles located 2 cm from a PVC cylinder filled with tissue-equivalent liquid of the same type used in head phantoms. The results are shown in Fig. 4. We have now also plotted the actual diversity gain, obtained by using as a reference a single dipole located at the same 2 cm distance from the PVC cylinder. We see that now we have actual diversity gains of more than 6 dB, even when the dipole separation is only 2 cm at 900 MHz. This is very promising for the use of diversity in mobile phones. Diversity antennas may give a large improvement in SNR when used in mobile phones, even if the two antenna branches are not orthogonally polarized, and even at 900 MHz.
12 Computed apparent diversity gain 11
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n Figure 3. Computed and measured apparent and effective diversity gain of two parallel dipoles as a function of their separation.
THE CHANNEL CAPACITY OF MIMO ANTENNAS
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10 Diversity gain 9
8 Diversity gain (dB)
In future mobile communication systems (after UMTS) it is proposed to use an array of antennas on both the base station and terminal sides to form several communication channels (i.e., a MIMO system). For instance, three and six antennas on transmit and receive sides, respectively, form 3 × 6 = 18 possible communication channels. The data is then on transmit distributed among the channels and combined again after reception in such a way that the overall channel capacity is maximized. This means that those of the 18 receive-transmit antenna combinations that provide fading maxima transfer many more bits per second than those transmit-receive antenna combinations that give minima. The maximum possible average channel capacity in a MIMO system can be calculated by using the formula below. As an example we use a 3 × 6 MIMO system setup in the reverberation chamber, consisting of three theoretical uncoupled antennas on one side (the three wall mounted antennas) and on the other side six close monopoles with a fixed radius and equal distance between each other located on a circular ground plane (the MIMO array under test). The three fixed wall antennas are mounted on three different perpendicular walls in the reverberation chamber far from each other, so the direct coupling is small. The MIMO array, on the other hand, is six closely located monopoles that interact strongly, and the mutual coupling depends on the spacing between them.
7 Actual diversity gain 6
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n Figure 4. Measured apparent, effective, and actual diversity gains of two par-
allel dipoles located 2 cm from a PVC cylinder filled with tissue-equivalent liquid at 900 MHz.
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Vi = −
25
2 jλ ∑ G i ( θ k , ϕ k ) ⋅ Ek , ηI k = Sufficient
(2)
many plane waves se
20
d te
ca
where η is the free space wave impedance, λ is the wavelength, and G i (θ,ϕ) is the embedded radiation field function of monopole i calculated on transmit when the impressed current at the input port is I. Thus, the unknown I is removed when G i (θ,ϕ) is divided by I. The embedded radiation field function is, as explained earlier, the radiation field function of the monopole in the presence of the other monopoles when they are terminated by 50 Ω. In this way we include that the monopoles are coupled, which comes into the radiation pattern. We also need to account for the mismatch at the antenna ports. This is characterized by a reflection coefficient,
0.24 λ
la
rre
co
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Un
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5
ρi = (Z0 – Zi)/(Z0 + Zi),
0 0
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10 15 Signal-to-noise ratio
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n Figure 5. Mean capacity for a 3 × 6 MIMO system calculated from measured
channel estimates at 900 MHz in the reverberation chamber. The MIMO array consists of six monopoles on a circular ground plane, and the spacing between neighboring monopoles are 0.24 λ, 0.14 λ and 0.06 λ.
(3)
where Z0 = 50 Ω in the termination impedance, and Z i is the impedance of the embedded element. To account for the mismatch we correct the received voltage Vi with the factor 2
1 − ρi ; that is, we transform Vi to a wave amplitude
When we measure the MIMO array in the reverberation chamber with three fixed wall antennas (as in our case), we can define 3 × 6 number of channels, and we can find the combined capacity of the 3 × 6 = 18 channels from the channel matrix H3×6-MIMO formed by the normalized S21 values. The instantaneous maximum capacity of the MIMO system takes the known form SNR C3 × 6 − MIMO = log2 det I M + HH * , 3
(1)
where H≡ H3×6-MIMO. We have measured channel estimates on the ports of the real antenna, so the coupling is included in the channel estimate. Therefore, we can use Eq. 1 directly and do not need to account for the coupling as a separate effect. We use all the measured samples of the 3 × 6 channel matrix H 3×6-MIMO to calculate the mean capacity C 3×6-MIMO as a function of the SNR by averaging all values of the instantaneous capacity. We repeat this for three different distances between neighboring monopoles (20 mm, 46 mm, and 80 mm). The resulting mean capacities for these three cases are plotted in Fig. 5 as a function of the SNR. We see that the capacity for small monopole spacings is reduced by a significant amount from that of the uncorrelated case (very large spacing). In order to calculate the theoretical capacity, we distribute a set {Ek} of k plane wave sources randomly and uniformly distributed over a sphere surrounding the MIMO array. The direction of incidence of source k is denoted θ k, ϕ k. The sources Ek in the set have independent and normal-distributed complex amplitudes of their θ- and ϕ-polarized components. We calculate the received voltage Vi on each monopole i due to the set of such incident plane waves by using the equivalent circuit on reception [6, p. 78],
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Ci = Vi 1 − ρi
2
that corresponds to S 21 in an earlier section. (Computer codes may give as output a radiation pattern normalized to 0 dB in the center of the main beam, a separate phase pattern Φ(θ,ϕ), and a realized gain in dB in their center direction. In such cases the Gi(θ,ϕ) can be obtained from the values, but the mismatch factor will already be included in G i(θ,ϕ), so we shall not correct for it afterward.) For the present monopole example, we first calculate G i (θ,ϕ) and Z i of each element by a commercial moment method code IE3D (www.zeland.se). Thereafter we generate 3 × 1000 sets of sources, with k = 1, 2, …, 20 sources in each set, and calculate 3 × 1000 values of received amplitudes C i . The received wave amplitudes are then put row-wise into channel matrix H after being normalized to a reference level. This is the square root of the average received power level at a single dipole, which is exposed by the same sets of sources as the simulated radiation patterns of the MIMO element. In this way, the radiation efficiency and mutual coupling are included in channel matrix H. We get in total 1000 H3×6-MIMO matrices for the 3 × 6 MIMO system. In Fig. 6 we show the resulting channel capacities for SNR = 15 dB for the 3 × 6 MIMO system. We see that the capacity based on measurements and simulations agree very well. Finally, we show in Fig. 7 some theoretical maximum channel capacities for the example MIMO antenna obtained by classical calculation of the embedded element patterns, assuming a sinusoidal current distribution on each quarterwavelength monopole and an infinite ground
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plane. The electromagnetic analysis is similar to that in [8] for a diversity antenna, but the number of elements is now 6. If we use the isolated element pattern and correct them with the radiation efficiency of the embedded element, we see a curve that naturally is lower than the isolated element curve for all element spacings. If we account for both the correlation and the radiation efficiency by using the original embedded radiation field functions (including losses and mismatch), the curve changes somewhat from the latter, but not significantly. Therefore, it is the radiation efficiencies of the embedded elements that affect the channel capacity the most, not the correlation between the received signals on their ports (at least for this six-monopole case). In order to save space we did not include any specific results for the radiation efficiency and its two contributions, dissipation and mismatch, but the larger contribution is, as explained, the dissipation in the neighboring elements.
CONCLUSIONS We have discussed how MIMO and diversity antennas can be analyzed in terms of classical embedded element patterns (when all other elements are terminated with dummy loads). These determine the correlation between the signals on the different ports. The radiation efficiency can be obtained as the ratio between the radiated power of the embedded element and the maximum available power at the input port. We have explained how the diversity gain and channel capacity can be found from the embedded element patterns in theoretical predictions. The characterizing quantities are radiation efficiency, correlation, diversity gain, and channel capacity. These can also be determined directly by measurements in a reverberation chamber, without having to determine the embedded element pattern. The radiation efficiency has much greater influence on the channel capacity than the correlation for the example array. The theoretical measured results for diversity gain and channel capacity agree well.
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0
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n Figure 6. Simulated and measured maximum capacity of the six-element
monopole MIMO antenna used in a 3 × 6 MIMO system for SNR = 15 dB. The measurements were done in the reverberation chamber.
3 x 6 MIMO Uncorrelated symptote
18
Capacity at SNR 15dB (b/s/Hz)
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nts
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REFERENCES [1] M. Bäckström, O. Lundén, and P.-S. Kildal, “Reverberation Chambers for EMC Susceptibility and Emission Analyses,” Rev. Radio Sci.. 1999–2002, pp. 429–52. [2] K. Rosengren and P.-S. Kildal, “ Study of Distributions of Modes and Plane Waves in Reverberation Chambers for Characterization of Antennas in Multipath Environment,” Microwave and Opt. Tech. Lett., vol. 30, no. 20, Sept. 2001, pp. 386–91. [3] K. Rosengren et al., “Characterization of Antennas for Mobile and Wireless Terminals in Reverberation Chambers: Improved Accuracy by Platform Stirring,” Microwave and Opt. Tech. Lett., vol. 30, no. 20, Sept. 2001, pp. 391–97. [4] P.-S. Kildal et al., “Definition of Effective Diversity Gain and How to Measure it in a Reverberation Chamber,” Microwave and Opt. Tech. Lett.., vol. 34, no. 1, July 5, 2002, pp. 56–59. [5] P.-S. Kildal and C. Carlsson, “Detection of a Polarization Imbalance in Reverberation Chambers and How to Remove it by Polarization Stirring when Measuring Antenna Efficiencies,” Microwave and Opt. Tech. Lett., vol. 34, no. 2, July 20, 2002, pp. 145–49. [6] P.-S. Kildal, Foundations of Antennas — A Unified Approach, Studentlitteratur, 2000.
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Distance between neighboring monopole (d/λ)
n Figure 7. Theoretical capacities of the six-element monopole MIMO antenna modeled by using sinusoidal current distribution on all monopoles, infinite ground plane, and models based on different approximations. The embedded elements curve represents the most complete model.
[7] R. C. Hansen, Microwave Scanning Antennas: Vol II, Array Theory and Practice, Academic Press, 1964. [8] P-S. Kildal and K. Rosengren, “Electromagnetic Analysis of Effective and Apparent Diversity Gain of Two Parallel Dipoles,” IEEE Antennas and Wireless Prop. Lett., vol. 2, no. 1, 2003, pp. 9–13. [9] J.W. Wallace and M. A. Jensen, “Termination-Dependent Diversity Performance of Coupled Antennas: Network Theory Analysis,” IEEE Trans. Antennas Prop., vol.52, no.1, Jan. 2004, pp. 98–105. [10] A. C. Ludwig, “Mutual Coupling, Gain and Directivity of an Array of Two Identical Antennas,” IEEE Trans. Antennas Prop., Nov. 197, pp. 837–41.
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[11] M. Schwartz, W. R. Bennett, and S. Stein, Communication System and Techniques, McGraw-Hill, 1965.
BIOGRAPHIES PER-SIMON KILDAL [M’82, SM’84, F’95] (
[email protected]) He received M.S.E.E., Ph.D., and Doctor Technicae degrees from the Norwegian Institute of Technology (NTH), Trondheim,in 1976, 1982, and 1990, respectively. From 1979 to 1989 he was with the ELAB and SINTEF, research institutes in Trondheim, Norway. Since 1989 he has been a professor at Chalmers University of Technology, Gothenburg, Sweden, where he has educated 11 antenna doctors. He has held several positions in the IEEE Antennas and Propagation Society: elected member of the administration committee 1995–1997, distinguished lecturer 1991–1994, associate editor of Transactions 1995–1998, and associate editor of a special issue in Transactions in 2004. He has authored or co-authored more than 167 papers in IEEE or IEE journals and conferences, concerning antenna theory, analysis, design and measurement. He gives short courses and organizes special sessions at conferences, and has given invited lectures in plenary sessions at several conferences. His textbook Foundations of Antennas — A Unified Approach (Studentlitteratur, 2000) (www.studentlitteratur.se/antennas) got an excellent review in IEEE Antennas and Propagation. ELAB awarded
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his work in 1984. He has received two best paper awards in IEEE Transactions on Antennas and Propagation. He is the originator of the concept of soft and hard surfaces in electromagnetics. He has done the electrical design and analysis of two very large antennas. The first was the 120 m long by 40 m wide cylindrical parabolic reflector antenna of the European Incoherent Scatter Scientific Association (EISCAT), located in North Norway. The second was the Gregorian dual-reflector feed of the 300 m diameter radio telescope in Arecibo, on a contract for Cornell University. He is presently involved in the design of feeds for the U.S. proposal of the square kilometer array (SKA). He holds many granted patents and patents pending, and based on these he has founded three companies, including COMHAT AB, which since 2002 is COMHAT-Provexa AB (www.comhat-provexa.com), and Bluetest AB (www.bluetest.se). K ENT R OSENGREN (
[email protected]) received a Master of Science degree in physics from the university of Gothenburg, Sweden, in 1996. Since January 1999 he is with Flextronics Design (former Intenna Technology), RF and Antenna Center, Kalmar, Sweden, as a senior antenna designer. Included in his employment, he is part-time at Chalmers University of Technology, Gothenburg, Sweden, where he is pursuing a Ph.D. on measurements of terminal antennas in a reverberation chamber.
IEEE Communications Magazine • December 2004
