VIEWS: 19 PAGES: 5 CATEGORY: Education POSTED ON: 1/12/2010 Public Domain
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- receiver. 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 ρ 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. ρ M (H) = log2 1 + λi (3) The antenna pattern diversity can be exploited in conjunction i=1 n 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, ρ M (H) ≈ log2 ( λi ) (4) each of which has a radiation pattern the same as one of the i=1 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. M 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) m=1 (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 k 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 (T 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 n 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- i=1 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 2 MIMO channel expressed in (3), with σi = λi being the eigen- m=1 lm † values of HH . The channel capacity is determined by the (10) And G can be expressed as M e−jk0 lm ˜ G= Gm (11) m=1 lm where ˜ (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 2 (LOS) multipath component. The relatively large gains σ1 and 2 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 n=6 Eigenvalues of HH* (dB) n=3 0 0 n=2 20 −20 −20 18 −40 −40 Local−averaged M(H) (bps/Hz) 16 −60 −60 −20 0 20 −20 0 20 (a) (b) 14 20 20 12 Eigenvalues of HH* (dB) 0 0 10 −20 −20 8 −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 1 Probability [Capacity > Abscissa] M(H6x6) / M(H2x2) 2.5 n=2 n=3 0.8 n=6 2 0.6 1.5 0.4 −30 −20 −10 0 10 20 30 0.2 M(H6x6) / M(H3x3) 1.8 0 1.6 0 5 10 15 20 25 (a) 1.4 1 Probability [Capacity > Abscissa] 1.2 −30 −20 −10 0 10 20 30 0.8 1.8 M(H3x3) / M(H2x2) 0.6 1.6 0.4 1.4 1.2 0.2 1 −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. [10] M. R. Andrews, P. P. Mitra, and R. deCarvalho, “Tripling the capacity −60 −60 of wireless communications using electromagnetic polarization,” Nature, −20 0 20 −20 0 20 vol. 409, pp. 316–318, Jan. 2001. (a) Receiver y−position (meter) (b) Receiver y−position (meter) [11] L. Dong, R. W. Heath, and H. Ling, “MIMO wireless handheld termi- nals using antenna pattern diversity,” submitted to IEEE Trans. Wireless Fig. 5. Eigenvalues of normalized HH† of the 6 × 6 MIMO channel in Case Commun., June 2002. 2. The transmitter is located at T2 , and the receiver moves along 2 tracks as: [12] P. F. Driessen and G. J. Foschini, “On the capacity formula for multi- (a) R2 LOS street. (b) R1 NLOS street. ple input multiple output wireless channels: A geometric interpretation,” IEEE Trans. Commun., vol. 47, no. 2, pp. 173–176, Feb. 1999. [13] W. C. Jakes, Microwave Mobile Communications, John Wiley and Sons, New York, 1974. is limited due to correlation between sub-channels. The MIMO [14] J. Perez, F. Saez de Adana, O. Gutierrez, I. Gonzalez, F. Catedra, I. Mon- channel capacity is affected not only by the antenna pattern se- tiel, and J. Guzman, “FASANT: fast computer tool for the analysis of on-board antennas,” IEEE Antenna Propagat. Mag., vol. 41, pp. 84–98, lection, but by the characteristics of the scattering environment Apr. 1999. as well. R EFERENCES [1] A. Paulraj and T. Kailath, “U.S. pattern No. 5345599: Increasing capacity in wireless broadcast systems using distributed transmission/directional reception (DTDR),” Sept. 1994. [2] G. J. Foschini and M. J. Gans, “On limits of wireless communications in a fading environment when using multiple antennas,” Wireless Personal Commun., vol. 6, no. 3, pp. 311–335, Mar. 1998. [3] A. F. Molisch, M. Steinbauer, M. Toeltsch, E. Bonek, and R. S. Thom¨ , a “Capacity of MIMO systems based on measured wireless channels,” IEEE J. Select. Areas Commun., vol. 20, no. 3, pp. 561–569, Apr. 2002. [4] V. Tarokh, N. Seshadri, and A. R. Calderbank, “Space-time codes for high data rate wireless communication: performance criterion and code construction,” IEEE Trans. Inform. Theory, vol. 44, no. 2, pp. 744–765, Mar. 1998. [5] V. Tarokh, H. Jafarkhani, and A. R. Calderbank, “Space-time block codes from orthogonal designs,” IEEE Trans. Inform. Theory, vol. 45, no. 5, pp. 1456–1467, July 1999. [6] D.-S. Shiu, G. J. Foschini, M. J. Gans, and J. M. Kahn, “Fading cor- relation and its effect on the capacity of multielement antenna systems,” IEEE Trans. Commun., vol. 48, no. 3, pp. 502–513, Mar. 2000. [7] I. E. Telatar and D. N. C. Tse, “Capacity and mutual information of wideband multipath fading channels,” IEEE Trans. Information Theory, vol. 46, no. 4, pp. 1384–1400, July 2000. [8] B. Lindmark, S. Lundgren, J. R. Sanford, and C. Bechman, “Dual- polarized array for signal-processing applications in wireless communi- cations,” IEEE Trans. Antennas Propagat., vol. 46, no. 6, pp. 758–763, June 1998.