Multiple-Input Multiple-Output Wireless Communication Systems by broverya76


									         Multiple-Input Multiple-Output Wireless Communication Systems Using
                               Antenna Pattern Diversity

                                       Liang Dong, Hao Ling, and Robert W. Heath, Jr.
                                      Department of Electrical and Computer Engineering
                                          The University of Texas, Austin, TX 78712

   Abstract— Multiple-input multiple-output (MIMO) wireless                  cialize our results to the case where the antennas are collocated
communication systems employ multiple transmit and multiple re-              and thus only pattern and polarization, but not antenna spacing,
ceive antennas to obtain significant improvement in channel ca-               are the parameters of the spatial signatures. This is important
pacity. However, the capacity is limited by the correlation of sub-
channels in non-ideal scattering environments. In this paper, we             for mobile applications where space is extremely limited [11].
investigate MIMO systems that use antennas with dissimilar radi-             First we analyze MIMO channel capacity under correlated fad-
ation patterns to introduce decorrelation, hence increasing chan-            ing. The MIMO channel is decoupled into sub-channels to
nel capacity. We develop a ray tracing model that takes into ac-             quantify the effect of channel correlation. Secondly, we intro-
count both the propagation channel and the transmit and receive              duce a general channel model that shows how pattern diver-
antenna patterns. Using a computational electromagnetic simula-
tor, we show that: (1) MIMO systems that exploit antenna pattern             sity is the natural generalization of polarization diversity. We
diversity allow for improvement over dual-polarized antenna sys-             describe how orthogonality between patterns decorrelates the
tems; (2) The capacity increase of such MIMO systems depends on              signals in highly scattering environments, hence reducing the
the characteristics of the scattering environment.                           capacity loss due to channel correlation. Finally, using an elec-
                                                                             tromagnetic ray-tracing simulator, we show that the increase of
                                                                             channel capacity is determined by the selection of antennas of
                         I. I NTRODUCTION                                    different patterns, and by various propagation environments.
   Multiple-input multiple-output (MIMO) wireless communi-                      This paper is organized as follows. In Section II, we intro-
cation is one of the most promising technologies for improving               duce the mutual information and the channel capacity of the
the spectrum efficiency of wireless communication systems. It                 MIMO wireless system, and discuss the correlation between
is well known that the use of MIMO antenna systems allows                    sub-channels. In Section III, the proposed MIMO system that
the channel capacity to scale in proportion to the minimum of                exploits antenna pattern diversity is described, and pattern di-
the number of transmit and receive antennas in uncorrelated                  versity is expressed in the channel transfer matrix. Section IV
Rayleigh fading channels [1], [2]. Of course, real channels do               demonstrates the capacity increase obtained through antenna
not satisfy these ideal assumptions, thus recent work has fo-                pattern diversity via a ray-tracing simulator. Finally, conclu-
cused on measuring and characterizing real MIMO propagation                  sions are drawn in Section V.
channels [3]. In parallel, work is continuing on efficient space-
time coding strategies that achieve the benefits of MIMO com-                    II. MIMO C HANNEL C APACITY U NDER C ORRELATED
munication [4], [5]. However, thus far there has been little work                                        FADING
on one of the most important aspects of MIMO communication
                                                                                Consider a narrowband MIMO wireless system with nT
systems – the antennas that are used at both the transmitter and
                                                                             transmit antennas and nR receive antennas. The induced volt-
                                                                             ages at the receive antennas are related to the impressed volt-
   The correlation between sub-channels of the matrix channel
                                                                             ages at the transmit antennas as
limits the MIMO channel capacity considerably [6], [7]. One
way to reduce correlation is to use antennas with different po-                                   v(R) = AHv(T ) + n                      (1)
larizations and radiation patterns [8], [9]. Recent results on po-
                                                                                               (R) (R)      (R)
larization diversity show that up to six degrees of freedom are              where v(R) = [v1 v2 · · · vnR ]T are the voltages at the re-
available in the polarization channel of a rich scattering envi-                                         (T ) (T )   (T )
                                                                             ceive antennas, v(T ) = [v1 v2 · · · vnT ]T are the voltages at
ronment, thus the channel capacity can be increased dramati-                 the transmit antennas. H is the normalized channel transfer ma-
cally [10]. However, the sub-channels created by antenna po-                 trix modeling the small-scale fading process, A2 encompasses
larization diversity are not completely decorrelated in a real en-           the (spatially local-averaged) large-scale path loss and shadow-
vironment, such that the effective degrees of freedom are much               ing, and n is the additive white Gaussian noise (AWGN) vector.
less than six, therefore the capacity increase is limited.                   If we assume that the channel state information (CSI) is com-
   In this paper, we investigated the impact of antenna pattern              pletely known by the receiver but not by the transmitter, the
and polarization on MIMO communication channels. We spe-                     transmitted signal vector is composed of nT statistically inde-
  This work was supported by the Texas Higher Education Coordinating Board   pendent Gaussian components with equal power. For a narrow-
under the Texas Advanced Technology Program 003658-0744-1999.                band MIMO channel with uniform power allocation constraint,
the mutual information between the transmitter and the receiver     values of the eigenvalues. When a sub-channel is correlated
is given by [2]                                                     with another one, the corresponding eigenvalue becomes small,
                                                                    which results in a sub-channel with small gain. From (7) we
           M (H) = log2 det InR +             HH†            (2)    see that the correlated sub-channel contributes little to the total
                                           nT                       mutual information.
where ρ is the average signal-to-noise-ratio (SNR) at each re-        The decorrelation of sub-channels is conventionally provided
ceive antenna, † denotes conjugate transpose. The ergodic           by spatial diversity, that is, using spatially separated multiple
channel capacity C is the expectation of M (H) taken over the       antennas at the transceivers such that each transmitter-receiver
probability distribution of H. We will assume nT = nR = n           pair experiences a different fading channel. With insufficient
throughout the rest of the paper.                                   spacing of local antennas, however, strong correlation can be
   Suppose the communication is carried out using bursts (pack-     exhibited between sub-channels, and consequently the MIMO
ets). The burst duration is assumed to be short enough such         channel capacity is reduced considerably.
that the channel can be regarded as essentially fixed during a
burst, but long enough that the standard information-theoretic             III. A NTENNA PATTERN D IVERSITY IN MIMO
assumption of infinitely long code block lengths can be used.                            C OMMUNICATION
In this quasi-static scenario, it is meaningful to associate the
                                                                       To introduce sub-channel decorrelation to the MIMO sys-
“instantaneous channel capacity” with the mutual information
                                                                    tem which has insufficient antenna spacing, we propose a
given a realization of the channel matrix H. From (2), the mu-
                                                                    transceiver array which is composed of antennas with appro-
tual information can be further expressed as
                                                                    priate dissimilarity in radiation patterns, and allow the antenna
                            n                                       pattern diversity to be expressed in the channel transfer matrix.
                M (H) =          log2 1 +     λi             (3)    The antenna pattern diversity can be exploited in conjunction
                                                                    with spatial diversity to achieve better channel performance in
                                                                    implementation. However, only pattern diversity is addressed
where {λi } are the eigenvalues of HH† . At high SNR, the
                                                                    in this context for a clear demonstration.
mutual information can be approximated by
                                                                       Suppose the transmit antennas are collocated but have differ-
                            rank(H)                                 ent radiation patterns. The receive antennas are also collocated,
                  M (H) ≈             log2 ( λi )            (4)    each of which has a radiation pattern the same as one of the
                                            n                       transmit antennas. For a narrowband channel at fixed carrier
                                                                    frequency fc = c/λ, the channel transfer matrix G = AH,
Since λi ≤ n for a normalized H, an upper bound of the mutual
                                                                    where A is defined as before, H is the normalized channel
information (at high SNR) can be derived as [10]
                                                                    transfer matrix modeling both the multipath fading process and
                   M (H) ≤ rank(H) log2 ρ                    (5)    the antenna pattern diversity. By ray-tracing [12] from the
                                                                    transmit antenna to the receive antenna, the voltage on the ith
The equality is achieved when a total of rank(H) sub-channels       receive antenna excited by the transmission of the k th transmit
are uncorrelated. However, complete decorrelation is hard to        antenna is [13]
achieve in a practical scattering environment.
   In order to quantify the effect of channel correlation, the                      (R)
MIMO channel is decoupled into n single-input single-output                        vi,k   =β                   (R)
                                                                                                     Em · Fi (θm , φ(R) )
                                                                                                      k             m               (8)
(SISO) sub-channels. Performing the singular value decompo-
sition of the channel matrix H as H = UΣV, we can rewrite           where β is a proportionality constant (assume β = 1), M is
the input-output relationship as                                    the number of multipaths in the link, Fi (θ(R) , φ(R) ) is the ith
                                                                    receive antenna pattern, (θ(R) , φ(R) ) is the receiving angle of
                         y = Σx + u                          (6)
                                                                    each ray, and Em is the incident field of the mth multipath at
where, y = U† v(R) , x = AVv(T ) , and u = U† n. Because            the receiver. We have
Σ is a diagonal matrix, the MIMO channel is transformed into
                                                                                      e−jk0 lm                          (T )
                                   2 2            2
n SISO sub-channels with gains σ1 , σ2 , . . . , σn , where {σi }             Em =
                                                                               k               fm,k Fk (θm ) , φ(T ) ) vk
                                                                                                                m                   (9)
are the diagonal entries of Σ. The mutual information of the                            lm
MIMO channel is the sum of the mutual information of the n          where k0 = 2π/λ, lm is the path length of the mth multipath,
sub-channels [6],                                                   fm,k (·) is the functional of reflection and diffraction of the mth
                                            ρ 2                     multipath, and Fk (θ(T ) , φ(T ) ) is the k th transmit antenna pat-
                M (H) =          log2 1 +    σ               (7)    tern, (θ(T ) , φ(T ) ) the transmitting angle. Therefore G has com-
                                            n i
                                                                    plex scalar entries as
where we assume uniform transmitted power allocation on the                    M
transmit antennas. This is exactly the mutual information of                      e−jk0 lm
                                                                     Gi,k =                          (T                   (R)
                                                                                           fm,k Fk (θm ) , φ(T ) ) · Fi (θm , φ(R) )
                                                                                                            m                  m
MIMO channel expressed in (3), with σi = λi being the eigen-                  m=1
values of HH . The channel capacity is determined by the                                                                        (10)
And G can be expressed as
                              e−jk0 lm ˜
                    G=                 Gm                    (11)

    ˜                  (T                   (R)
    Gm,i,k = fm,k Fk (θm ) , φ(T ) ) · Fi (θm , φ(R) )
                              m                  m           (12)

Because the transmit antennas and the receiver antennas are col-
located, the difference in path length and phase of the rays trav-
elling between any transmitter-receiver pairs can be neglected.
The difference of the entries of G is solely caused by the an-
tenna pattern diversity implied in Gm .
   One observation is that using the dual-polarized transmitter-
receiver pair where two linear dipoles with equal gain are or-
thogonally collocated at each end, the two sub-channels are al-      Fig. 1. Street lattice with transmitter positions T1 and T2 , and receiver moving
                                                                     tracks R1 and R2 .
most uncorrelated with the presence of a strong line-of-sight
(LOS) multipath component. The relatively large gains σ1 and
σ2 of the sub-channels are provided by the quasi-orthogonal             The infinitesimal electric-dipole of electric source J or
structure of H, and the mutual information reaches its maxi-         current-loop of magnetic source M is used as the transmit
mum among normalized 2 × 2 channel realizations. However,            and receive antenna element. At each end of the communi-
the upper bound of mutual information (5) introduced in [10]         cation link, two orthogonally placed electric-dipoles with their
is loose in a MIMO system using pattern diversity with a large       feed points collocated form a 2 × 2 MIMO system. Three
number of transmitter-receiver pairs. As we will see in the sim-     such orthogonally placed electric-dipoles form a 3 × 3 MIMO
ulation, the mutual information provided by some sub-channels        system, and another three orthogonally placed current-loops,
are nearly zero. Although the rank of H is guaranteed, the           which are referred to as magnetic-dipoles, collocated with the
corresponding eigenvalues of HH† are small compared to the           3 × 3 electric-dipoles form a 6 × 6 MIMO systems. The radia-
dominant ones, which is a direct result of severe correlation of     tion pattern of the electric-dipole with vertical J in the spherical
the sub-channels.                                                                                       a
                                                                     coordinate system is E = sin(θ)ˆ θ , and the radiation pattern of
   In order to achieve uncorrelated sub-channels, the goal of        the magnetic-dipole with vertical M is E = − sin(θ)ˆφ . The a
antenna design is to make the incident fields of the transmission     carrier frequency is 1.8 GHz, that is, a carrier wavelength of
from one antenna align with the radiation pattern of the desired     0.167 m.
receive antenna, while being orthogonal to the patterns of other        Given the geometry input with material properties, transmit-
receive antennas. However, in the real electromagnetic world,        ter and receiver positions, and transmit antenna patterns, the
the sub-channels, which are characterized by the summation of        ray tracer FASANT gives outputs such as direction of arrival
the dot products in (10), can not be completely decorrelated.        (DOA), path length and field strength of each multipath arriv-
                                                                     ing the receiver.
                      IV. S IMULATIONS
   The ergodic channel capacity can be calculated given the dis-     A. Case 1
tribution of the eigenvalues of HH† . However, for a general            In case 1, the transmit antenna array is located at T1 , and the
covariance of fading and pattern diversity and a finite dimen-        receive antenna array moves along 4 tracks (-1, -35, 3)→(-1, 35,
sionality, the distribution of eigenvalues can be very difficult to   3), (1, -35, 3)→(1, 35, 3), (-1, -35, 1)→(-1, 35, 1), and (1, -35,
compute. In this section, the “instantaneous channel capacity”,      1)→(1, 35, 1), which are on the same street surrounding track
that is, the mutual information between the transmitter and the      R1 : (0, −35, 1.5) → (0, 35, 1.5). Therefore, as the receiver
receiver, is studied via numerical computation using an elec-        changes its position, it experiences both line-of-sight (LOS) and
tromagnetic ray tracer, FASANT [14]. It is a deterministic ray       non-line-of-sight (NLOS) channels.
tracing technique based on geometric optics and the uniform             Fig. 2 shows the eigenvalues of normalized HH† when
theory of diffraction.                                               the receiver changes its position along each track. Each of
   A street lattice in Fig. 1 is simulated as the geometry input     the transmit and receive antenna arrays is composed of three
of FASANT. The size of each building block is (10 × 10 × 10)         electric-dipoles orthogonally placed along x, y, z axes of the
m3 , and the street width is 10 m. The material properties of        Cartesian coordinate system and three such orthogonally placed
the building walls and the ground are: relative permittivity =       magnetic-dipoles. Therefore, every H along the tracks is a re-
2.0, relative permeability µ = 1.0, and conductivity σ = 0.08.       alization of the 6 × 6 MIMO channel. As shown in the figure,
There are two transmission points T1 : (20, 20, 5)m and T2 :         there are two dominant eigenvalues of HH† of each realiza-
(24, 10, 5)m, where T1 is in the middle of a street crossing.        tion of the channel, the next two are about 20 dB down, and
The receiver can move along two streets shown as the tracks          the weakest two are about 40 dB down the dominant ones. The
R1 and R2 .                                                          drop of weaker eigenvalues, especially in the LOS region from
                             20                                      20                                                                      22
  Eigenvalues of HH* (dB)

                              0                                       0                                                                                                                              n=2

                            −20                                     −20
                            −40                                     −40

                                                                                                              Local−averaged M(H) (bps/Hz)
                            −60                                     −60

                                   −20           0         20              −20           0         20
                                                (a)                                     (b)                                                  14

                             20                                      20
  Eigenvalues of HH* (dB)

                              0                                       0
                            −20                                     −20

                            −40                                     −40

                            −60                                     −60                                                                       6

                                    −20         0          20               −20         0          20                                             −30   −20   −10            0             10   20   30
                                  (c) Receiver y−position (meter)         (d) Receiver y−position (meter)                                                        Receiver y−position (meter)

Fig. 2. Eigenvalues of normalized HH† of the 6 × 6 MIMO channel in Case                                     Fig. 3. Mutual information of the 2 × 2, 3 × 3 and 6 × 6 MIMO channels
1 . The transmitter is located at T1 , and the receiver moves along 4 tracks as:                            in Case 1, averaged over neighboring 8 receiving positions. The LOS region is
(a) (-1, -35, 3)→(-1, 35, 3), (b) (1, -35, 3)→(1, 35, 3), (c) (-1, -35, 1)→(-1, 35,                         y ∈ [13.33, 26.67] m. Average receive SNR = 20 dB.
1), (d) (1, -35, 1)→(1, 35, 1).

                                                                                                            (20, −35, 1.5) → (20, 35, 1.5), and the (almost) NLOS street
y = 13.33 m to y = 26.67 m, reveals strong correlations be-
                                                                                                            R1 : (0, −35, 1.5) → (0, 35, 1.5).
tween the sub-channels.
                                                                                                               Fig. 5 shows the eigenvalues of normalized HH† of the
   Fig. 3 compares the local-averaged mutual information of the                                             6 × 6 MIMO system, where each of the transmitter and re-
6 × 6 MIMO system with that of the 2 × 2 and 3 × 3 MIMO                                                     ceiver antenna arrays has three electric-dipoles orthogonally
systems. In the 2 × 2 MIMO system, each of the transmit and                                                 placed along x, y, z axes, collocated with three such orthogo-
receive antenna arrays is composed of two electric-dipoles or-                                              nally placed magnetic-dipoles. Fig. 5(a) shows the eigenvalues
thogonally placed along y and z axes, such that in the LOS                                                  of channel realizations when the receiver changes its position
region, the system is similar to a conventional dual-polarized                                              along R2 , the LOS region. Fig. 5(b) shows the eigenvalues
communication system. In the 3 × 3 MIMO system, the array                                                   of channel realizations when the receiver changes its position
is composed of three electric-dipoles orthogonally placed along                                             along R1 , the NLOS region. The better decorrelation of sub-
x, y and z axes. The average receive SNR is 20 dB. The figure                                                channels in a rich scattering environment (NLOS region) is re-
shows the increase of mutual information of the 6 × 6 and 3 × 3                                             vealed as the increase in value of the smaller eigenvalues.
MIMO systems that use collocated antennas exploiting pattern
                                                                                                               Fig. 6 compares the complementary cumulative distribution
diversity, over the mutual information of the dual-polarized an-
                                                                                                            functions (CCDF) of instantaneous channel capacities of the
tenna system as the 2 × 2 MIMO case. The antenna pattern
                                                                                                            2 × 2, 3 × 3 and 6 × 6 MIMO systems, where the receiver
diversity is provided by the scattering environment, as a result,
                                                                                                            changes position along the LOS and NLOS streets. For the 2×2
the MIMO channel that exploits antenna pattern diversity in the
                                                                                                            MIMO system, the transceiver antenna array is composed of
LOS region has less capacity increase as shown in the figure.
                                                                                                            two collocated electric-dipoles along x and z axes, which forms
   Fig. 4 shows the ratios of mutual information of systems of                                              a dual-polarized system in the LOS region. The 3 × 3 MIMO
different numbers of dimension as above. Comparing mutual                                                   system has three collocated electric-dipoles at the transceiver
information of the 6 × 6 system with that of the 2 × 2 system,                                              along x, y and z axes. The average receive SNR is 20 dB. As
we find that the “instantaneous capacity” in any position of the                                             shown in the figure, the large increase in channel capacity of a
scattering environment is not ideally tripled, contrast to what                                             MIMO system that exploits antenna pattern diversity, referring
was claimed in [10]. This result is expected from the eigen-                                                to a dual-polarized MIMO system, is more likely to occur in a
value plot of Fig. 2, because of the non-negligible correlation                                             rich-scattering environment (NLOS region).
between sub-channels. Besides two dominant sub-channels as
in a dual-polarized system, additional sub-channels of a system
with multiple collocated antennas at transmitter and receiver are                                                                                             V. C ONCLUSION
correlated in a practical scattering environment. The electrical                                               A MIMO wireless system that exploits antenna pattern di-
components and the magnetic components of the field are also                                                 versity has been presented. Although the antennas are collo-
highly correlated.                                                                                          cated at the transmitter and receiver, with appropriate dissim-
                                                                                                            ilarity in antenna pattern, the system offers large channel ca-
                                                                                                            pacity promised by the MIMO architecture. The MIMO sys-
B. Case 2
                                                                                                            tem with multiple collocated transmit and receive antennas can
   In case 2, the transmit antenna array is located at T2 , and                                             achieve capacity increase over the dual-polarized system. How-
the receive antenna array moves along the LOS street R2 :                                                   ever, in a practical scattering environment, the capacity increase

                                                                                                                            Probability [Capacity > Abscissa]
  M(H6x6) / M(H2x2)

                            2.5                                                                                                                                                                                        n=2
                                                                                                                                                                0.8                                                    n=6

                            1.5                                                                                                                                 0.4
                                  −30          −20          −10            0            10           20            30

  M(H6x6) / M(H3x3)

                            1.6                                                                                                                                       0   5   10                   15        20   25

                                                                                                                            Probability [Capacity > Abscissa]
                                  −30          −20          −10            0            10           20            30

  M(H3x3) / M(H2x2)


                            1.2                                                                                                                                 0.2

                                  −30          −20          −10            0             10          20            30                                            0
                                                               Receiver y−position (meter)                                                                            0   5   10                 15          20   25
                                                                                                                                                                                   (b)   Capacity (bps/Hz)

Fig. 4. Ratios of mutual information of 6 × 6 to 2 × 2, 6 × 6 to 3 × 3, and
3 × 3 to 2 × 2 MIMO systems in Case 1.                                                                                    Fig. 6. CCDFs of instantaneous capacities of the 2 × 2, 3 × 3 and 6 × 6
                                                                                                                          MIMO channels in Case 2. Average receive SNR = 20 dB. (a) The receiver
                                                                                                                          moves along the LOS street R2 . (b) The receiver moves along the NLOS street
                             20                                                 20                                        R1 .
  Eigenvalues of HH* (dB)

                              0                                                  0

                            −20                                                −20                                         [9] C. B. Dietrich, K. Dietze, J. R. Nealy, and W. L. Stutzman, “Spatial,
                                                                                                                               polarization, and pattern diversity for wireless handheld terminals,” IEEE
                            −40                                                −40                                             Trans. Antennas Propagat., vol. 49, no. 9, pp. 1271–1281, Sept. 2001.
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                            −60                                                −60                                             of wireless communications using electromagnetic polarization,” Nature,
                                    −20        0           20                             −20        0           20            vol. 409, pp. 316–318, Jan. 2001.
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channel capacity is affected not only by the antenna pattern se-                                                               tiel, and J. Guzman, “FASANT: fast computer tool for the analysis of
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