Spectral Efficiency in MIMO Systems Using Space and Pattern Diversities Under Compactness Constraints
Descripción
IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 57, NO. 3, MAY 2008
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Spectral Efficiency in MIMO Systems Using Space and Pattern Diversities Under Compactness Constraints Matilde Sánchez-Fernández, Member, IEEE, Eva Rajo-Iglesias, Member, IEEE, Óscar Quevedo-Teruel, Student Member, IEEE, and M. Luz Pablo-González
Abstract—The aim of this paper is to evaluate the performance of multiple-input–multiple-output (MIMO) systems using multimode patch antennas as basic elements. The focus is compactness in the antenna design and suitability for being deployed in relatively small terminals. To this purpose, the performance in terms of spectral efficiency of a MIMO system with small multimode patch antennas on the terminal side is presented. We assume no knowledge of the channel at the transmitter and perfect channel knowledge at the receiver. Several multielement multimodeantenna scenarios are compared to alternative scenarios with single-mode antennas. Index Terms—Multimode antenna, multiple-input–multipleoutput (MIMO), patch antenna, pattern diversity, spectral efficiency.
I. I NTRODUCTION
A
NY MULTIPLE-INPUT–multiple-output (MIMO) system provides a number of degrees of freedom for transmitting the information that depends on the number of antenna elements in transmission and reception. With this vision, achieving high spectral efficiency necessarily implies the use of many radiating elements. However, from the implementation point of view, multiple radiating elements are difficult to fit on a handheld terminal. Here, not only the number of physical elements but also the spacing between them is conditioned by the space available in the terminal, which makes the design at this point particularly challenging. In addition to spatial diversity, there are other ways of providing the diversity needed in a MIMO system, such as polarization diversity [1], [2] and pattern diversity, both of which are of particular interest in a compact antenna design. Pattern diversity has a straightforward application in MIMO systems, where the use of many antennas might be substituted or complemented by the use of different modes. The use of a multimode antenna, instead of several single-mode antennas, has been previously treated in the literature as a form of pattern diversity [3]–[6]. Nevertheless, to the best of our knowledge, Manuscript received March 28, 2007; revised August 2, 2007 and September 10, 2007. This work was supported by Project TEC 2005-07477c02-02 and Project CCG06-UC3M/TIC-0803. The review of this paper was coordinated by Prof. R. M. Buehrer. The authors are with the Departamento de Teoría de la Señal y Comunicaciones, Universidad Carlos III de Madrid, 28911 Madrid, Spain. Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TVT.2007.909279
the use of mixed spatial/pattern diversity strategies to achieve compactness by means of multiple multimode antennas has never been proposed. In terms of spectral efficiency, these schemes would suffer from three limitations: 1) spatial channel correlation, which has been treated throughout the literature in terms of different parameters [7]–[9]; 2) modal correlation [10]; and 3) mutual coupling [11]–[14]. Different authors have theoretically proposed multimode antennas; however, few designs for multimode antennas for MIMO application have been previously presented. For example, Svantesson [10] described two possible multimode antennas based on previous designs, such as biconical dipole and a microstrip disk [15]. In both cases, the described antennas are electrically large, with the purpose of substituting multiple antennas for one large multimode antenna. Recently, Waldschmidt and Wiesbeck [16] described a spiral antenna with multimode properties, also for MIMO application. Here, again, the antenna size is large. Therefore, although all these proposals constitute an alternative for MIMO systems by substituting multiple elements for multiple modes or radiation patterns, their application may be limited for two reasons: First, the spectral efficiency depends on the number of radiating modes, and this is constrained by design issues and mutual coupling. Second, they are not very suitable for use in size-constrained schemes, particularly if combining pattern and space diversities is an option to overcome the limitation of the number of active modes. The goal of this paper is to show that it is possible to improve the spectral efficiency of the MIMO system under compactness constraints in the terminal side, combining space and pattern diversities, i.e., by using several multimode antennas. This necessarily implies that multimode elements should be as compact as possible. To this aim, our purpose is to use compact multimode microstrip patch antennas in a linear array geometry, as shown in Fig. 1. The rest of this paper is organized as follows: In Section II, we introduce two multimode patch antennas that use lower order modes to achieve compactness [17], [18]. To this purpose, a combination of different short-circuited rings and circular patch (CP) antennas [19] is used. In Section III, we define a simple channel stochastic model that takes into account that several multimode antennas are being used. The model takes into account the antenna geometry, radiation patterns, and the angular spread (AS) statistics measured at the transmitter and the receiver. This model is a generalization of the model
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Fig. 1. Diagram example of the proposed scheme at the receiver side with two multimode antennas.
provided in [20] and is in the same line as the channel models proposed in [21] and [22], with the advantage of allowing a compact formulation for spatial and modal correlations. Finally, in Section IV, we present the results of our study, including both the calculated modal and spatial correlations at the receiver, and the computed spectral efficiency of our schemes, with several multimode elements (combining pattern and spatial diversities) in front of the classical elements with single-mode antennas (only spatial diversity). II. C OMPACT M ULTIMODE A NTENNA C HARACTERISTICS Microstrip patch antennas are compact and cheap, so they have a straightforward application in low-cost and small-sized terminals. They can be operated in different modes having different radiation patterns, but usually, a different mode means a different working frequency. Combining different patches with different geometries allows having different modes working at the same frequency. In this scenario, the key in achieving the smallest patch antenna size is to force the use of low-order modes. Two different compact multimode antennas are introduced in this section: The first one is a multimode patch antenna with two different modes, whereas the second one is a three-mode antenna. In both cases, the modes can be simultaneously excited at the same frequency, and the antenna bandwidth is a flexible parameter that could be targeted through different substrates if required. The detailed design of the antennas is given in [17] and [18]. The radiation patterns presented in the succeeding sections have been computed by using the commercial code CST Microwave Studio. A. Two-Mode Patch Antenna The first proposal is a two-mode microstrip patch antenna made with a short-circuited ring patch (SCP) operated at the TM01 mode and a CP working at the TM11 mode. The use of the two different geometries (SCP and CP) comes from the fact that the TM01 mode is a higher order mode for all geometries, except for the SCP, where this mode is the lowest one or fundamental [23]. This particularity allows the design of this antenna, because, with TM01 being the fundamental mode of a SCP antenna, its size is comparable to the CP operated at
Fig. 2. Radiation patterns of the two-mode antenna in the XZ plane. Modes TM01 and TM11 .
the TM11 mode. In addition, SCP is the only geometry that has a hole that facilitates the feeding of the upper antenna. The total size of the antenna in this design is 0.4 λ, including the ground plane. Assuming a reference system, the antenna is placed in the XY plane. The TM01 mode, which is independent of the antenna geometry, has its radiation maximum in the plane defined by the antenna (XY in our reference system) with a rotational symmetry radiation pattern (a “monopolar” type) and a null in the broadside direction (the zˆ axis in our reference system), whereas the TM11 mode always has a maximum in the broadside direction. The radiation patterns of the antenna are given in Fig. 2, together with an antenna sketch.1 Here, the pattern diversity can be clearly noticed to be covering the entire azimuthal plane (XZ plane). Consequently, not only do the TM01 mode and the TM11 mode allow an antenna that is compact enough for our purposes, but the radiation patterns also present opposite beam-pointing directions that will be convenient for modal correlation. B. Three-Mode Patch Antenna Trying to add a third mode to the previous antenna scheme leads to a not-very-flexible design, particularly with the restriction of compactness. Thus, for the three-mode antenna, the use of stacked SCPs for the three elements has been chosen. In addition, this will be useful for feeding purposes. The SCPs are operated at the TM01 , TM11 , and TM21 modes, respectively. The new mode also has a null in the broadside (ˆ z ) direction, but the beam-pointing direction is not θ = 90◦ , as in the TM01 mode, but is an intermediate direction. The antenna is bigger than that in the previous case, with a total size of 0.62 λ. 1 A complete characterization of the radiation patterns of the designed antenna would also need the radiation patterns in the Y Z plane. However, most of MIMO channel models just take into account the angular spread in the azimuthal plane (XZ in our reference system) [24]. Thus, only the azimuth performance is presented.
SÁNCHEZ-FERNÁNDEZ et al.: SPECTRAL EFFICIENCY IN MIMO SYSTEM USING PATTERN DIVERSITY
Fig. 3. Radiation patterns of the three-mode antenna in the XZ plane. Modes TM01 , TM11 , and TM21 .
The radiation patterns of the three modes, together with an antenna sketch, are presented in Fig. 3. Again, the pattern diversity covers in azimuth (XZ plane) all the angles of interest. The main difference among them is the beam-pointing directions. Introducing a new mode in a restricted angular space may increase modal correlation. However, the third mode might still provide an advantage, from the compactness and cost point of view, compared to three single-mode antennas. All these correlations between radiation patterns (modal correlation) will be quantified in Section IV. III. C HANNEL M ODEL Most channel models in the literature for MIMO systems characterize the channel among radiating elements, under the assumption of only one radiation pattern per antenna, and many times, this radiation pattern is not even taken into account, considering omnidirectional antennas. Multimode antennas define several modes or radiation patterns that, from the point of view of captured energy, are separable (each mode has a separate port). In this scenario, the basic element in the antenna array is no longer the antenna but is each of the radiation patterns. Therefore, the multimode MIMO channel needs to characterize the fading path from each of the modes (ports) at the transmitter to the modes (ports) at the receiver. In this section, we develop a channel model that allows multiple multimode antennas on both sides: the transmitter and the receiver. Furthermore, in this model, we allow the possibility of 3-D spatial evaluation by including the radiation patterns as a function of azimuth θ and elevation φ. For simplicity, it will be assumed that each antenna at the transmitter and each antenna at the receiver have identical numbers of modes D, with radiation patterns in azimuth and elevation: G1 (θ, φ), G2 (θ, φ), . . . , GD (θ, φ). Within one antenna, all the D modes are simultaneously active, covering different spatial ranges and working within the same frequency. Possible differences in pattern efficiency for the different modes may lead to power imbalances between the different modes. This is taken into
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account in the radiation patterns Gi (θ, φ), with a normalization parameter that, for the sake of simplicity, is not included in the formulation. The MIMO channel is described by channel matrix H, with elements hn(j)m(i) describing the fading path from the ith port of the mth transmitting antenna to the jth port of the nth receiving antenna. The number of transmitting and receiving antennas is M (m = 1, . . . , M ) and N (n = 1, . . . , N ), respectively, but each of them has D (j, i = 1, . . . , D) active ports; therefore, the channel matrix dimensions are M D × N D. The entries of H could be correlated in space, time, and frequency [25]. Only spatial correlation is considered in our study. Under these premises, the channel model is characterized by the antenna geometry, the radiation patterns in transmission and reception, and the surrounding scattering environment. Element hn(j)m(i) can be modeled like the Green’s function [20] sampled at the position of the nth receiving antenna rn , given that the point source is located (rm ) at the mth transmitting antenna, i.e., Gi (θ, φ)Gj (θ , φ )S (k (θ , φ ), k(θ, φ)) hn(j)m(i) =
×e−jk(θ,φ)rm ejk (θ ,φ )rn dk (θ , φ )dk(θ, φ).
(1)
k(θ, φ) and k (θ , φ ) represent the wave vector space at the transmitter and receiver, respectively, depending on the azimuth and elevation angles. S(k (θ , φ ), k(θ, φ)) is a scattering function of the channel, which relates the plane wave emitted from the k direction impinging on the receiver on the k direction. The vector space can be sampled into L plane waves at the transmitter and L plane waves at the receiver to cover all the space. The plane waves2 depart from the {k1 , k2 , . . . , kL } directions at the transmitter and from the {k1 , k2 , . . . , kL } directions at the receiver. Then, from (1), matrix H can be written in (2), shown at the bottom of the next page. Thus, the channel matrix can be decomposed into the product of three matrices H = B†N SBM . BN and BM are beamforming rectangular deterministic matrices that are basically dependent on the antenna geometry and radiation patterns. S is a rectangular random matrix whose statistics will be modeled, depending on the angular scattering characteristics. Assuming that the channel entries are Gaussian and that the scatterers are independent, S is characterized by the joint power angular spectrum (PAS) [25]. This leads to a scattering matrix with Gaussian independent nonidentically distributed components. A separable PAS model [8], [26], [27] is used at the transmitter and receiver. This separability is supported by measurements in many channel scenarios [28]–[30]. Separable PAS leads to a power distribution within rows in matrix S that is given by the PAS at the receiver and among columns that matches the PAS at the transmitter. Thus, S can be further simplified, leading to the channel model shown in the following: 1
1
2 2 GΣASD BM H = B†N ΣASA
(3)
2 We drop the dependence with the azimuthal and elevational angles for the sake of simplicity.
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where G is a complex Gaussian random matrix with independent identically distributed components and a variance of 1. ΣASA and ΣASD are deterministic diagonal matrices whose main diagonal is shaped with the corresponding angular power spectra, which are denoted as PASD (k) at the transmitter and PASA (k ) at the receiver. The trace of these matrices is normalized to be one. Angular spread of departure (ASD) and angular spread of arrival (ASA) are the ASs at the transmitter and at the receiver, respectively. Any study regarding channel capacity implies a particular sampling of the wave space defined by space vectors k and k and a particular antenna geometry. As a first approach and given that the elevational angle spread is being measured to be much less than the azimuthal spread [24], for simplicity, only the azimuthal angle will be considered. A similar approach has also been used in [6]. For the antenna geometry, uniform linear arrays (ULAs) are used. ULAs are fully characterized once given the number of elements and the spacing between elements, which are, in our study, represented by dt and dr in transmission and reception, respectively. The array is set along the x ˆ axis, as shown in Fig. 1, and both arrays at the transmitter and the receiver are facing. It should be noted here that mutual coupling between modes or antenna elements is not considered in our proposed model. However, it could be easily included by means of coupling matrix C, as shown in [11]. For low coupling scenarios, C collapses to the identity matrix. Given the mutual coupling values obtained among modes in our antenna schemes [17], [18] and assuming that the different elements of the array are well isolated, our computed coupling matrices were almost the identity matrix.
knowledge at the transmitter and perfect channel knowledge at the receiver, correlation implies decreasing the spectral efficiency of the system for any SNR scenario [31]. Thus, the characterization of correlation is of great interest. In addition, the particularity of our multimode multielement scenario brings up the necessity of characterizing the modal correlation. Modal correlation has been previously studied in terms of electromagnetical fields [10]. Here, we proposed a closed formulation for modal and spatial correlations that exclusively depends on the antenna geometry, radiation patterns, and channel scattering characteristic. Given the separable PAS assumption from the previous section, the correlation between the (m(i), n(j))th and (t(k), r(l))th entries of H leads to a separable correlation at the transmitter and receiver, i.e., ∆ RH (m(i), n(j); t(k), r(l)) = E hn(j)m(i) h†r(l)t(k) = (ΘT )m(i)t(k) (ΘR )n(j)r(l) . (4) This, with the channel structure defined in this section, gives 1 (5) ΘR = E HH† = B†N ΣASA BN M 1 ΘT = E H† H = B†M ΣASD BM . (6) N Matrix element (ΘT /R )n(i)r(k) accounts for spatial correlation between the ith mode of antenna n and the kth mode of antenna r. For the receiver case and the ULA array geometry, these correlation coefficients can be formulated as follows: π
2 (ΘR )n(i)r(k) =
A. Channel Correlation Channel correlation affects the system capacity in different ways, depending on the knowledge that the transmitter has about the channel. In our scenario, where we assume no channel
Gi (θ)Gk (θ)PASA (θ)e−j2π
dr λ
(n−r) sin θ
dθ.
−π 2
(7) In the same way, matrix element (ΘT /R )n(i)n(k) accounts for the modal correlation between modes i and k in antenna n.
jkL r1 G1 (θ1 , φ1 ) ejk1 r1 G1 (θ2 , φ2 ) ejk2 r1 .. G1 (θL , φL ) e .. .. .. .. GD (θ1 , φ1 ) ejk1 r1 GD (θ2 , φ2 ) ejk2 r1 .. GD (θ , φ ) ejkL r1 L L jkL r2 G (θ , φ ) ejk1 r2 jk2 r2 G (θ , φ ) e .. G (θ , φL ) e 1 1 1 1 1 2 2 L H= .. .. .. .. G (θ , φ ) ejk1 r2 G (θ , φ ) ejk2 r2 .. G (θ , φ ) ejkL r2 D D D 1 1 2 2 L L .. .. .. .. jkL rN , φ ) e GD (θ1 , φ1 )ejk1 rN GD (θ2 , φ2 ) ejk2 rN .. GD (θL L S(k1 , k1 ) S (k1 , k2 ) .. S (k1 , kL ) S (k2 , k1 ) S (k2 , k2 ) .. S (k2 , kL ) × .. .. .. .. S (kL , k1 ) S (kL , k2 ) .. S (kL , kL ) G1 (θ1 , φ1 )e−jk1 r2 G1 (θ1 , φ1 )e−jk1 r1 .. GD (θ1 , φ1 )e−jk1 r1 −jk2 r1 −jk2 r1 .. GD (θ2 , φ2 )e G1 (θ2 , φ2 )e−jk2 r2 G (θ , φ )e × 1 2 2 .. .. .. .. G1 (θL , φL )e−jkL r1 .. GD (θL , φL )e−jkL r1 G1 (θL , φL )e−jkL r2
(2) .. GD (θ1 , φ1 )e−jk1 rM −jk2 rM .. GD (θ2 , φ2 )e .. .. −jkL rM .. GD (θL , φL )e
SÁNCHEZ-FERNÁNDEZ et al.: SPECTRAL EFFICIENCY IN MIMO SYSTEM USING PATTERN DIVERSITY
For example, at the receiver and for the ULA antenna geometry, it is formulated as follows: π
2
Gi (θ)Gk (θ)PASA (θ)dθ.
(ΘR )n(i)n(k) =
(8)
−π 2
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the overlapping of the radiation patterns within each antenna. The transmitter is set to be in the best correlation scenario (no correlation); thus, the antenna spacing is set to dt = λ/2, and the ASD is chosen so that the channel correlation matrix at the transmitter is very close to the identity matrix. Assuming a downlink scenario, the equivalent correlation scenario is realistic since, in most mobile environments, the antennas in the base station (transmitter) might be placed as separated as needed to achieve this.
IV. R ESULT AND D ISCUSSION With the radiated power constrained to M D, the highest spectral efficiency that can be reliably achieved over an ergodic channel when there is no knowledge of the channel at the transmitter is
SNR HH† (9) C = E log det IN D + MD where SNR = 1/σ 2 . In this section, the performance of the two proposed multimode antennas for MIMO application will be compared with MIMO systems using single-mode antennas. The radiation patterns used for the multimode antennas are those obtained and shown in Section II. The comparison will be made in terms of the spectral efficiency defined in (9). Here, the simplification made in Section III, where we assume the same number of modes in the antennas at the transmitter and the receiver, is no longer valid. A downlink scenario is considered, the transmitter is equipped with M = {3, 4, 6} identical single-mode (D = 1) antennas with omnidirectional radiation patterns. At the receiver, we place N = {1, 2} identical multimode antennas described in Section II (D = {2, 3}). At the receiver, the separation between radiating elements is set to be dr = 0.8 λ, which allows, in both the two-mode- and three-mode-antenna cases, an implementable scenario, given that the dimension of the antenna is 0.4 λ and 0.62 λ, respectively. This separation is chosen to be a tradeoff between compactness and low spatial correlation. Higher values of dr would lead to lower correlation and, thus, better performance of the system; however, we intend to keep the whole antenna dimension down to a reasonable size to facilitate the deployment in small terminals. The whole antenna size would be, in the case of two modes, (N − 1)dr + 0.4 λ and (N − 1)dr + 0.62 λ for the three-mode antenna. As in single-mode MIMO systems, AS is a key parameter for performance. In particular, in multimode MIMO systems, a low AS might lead to scenarios where some of the modes within an antenna are not being used, as no power might be impinging at them. In a downlink scenario, the transmitter is usually elevated; thus, low ASs are perceived, and PASD (k) is usually modeled with a Laplacian distribution in azimuth [28]. On the other hand, the receiver is not usually in elevation and, most of the time, is surrounded by multiple scatterers, which leads to a high AS and PASA (k ) with uniform distribution. Given that we are focusing on placing the multimode antennas at the receiver, the scenario here is set to be realistic, except when explicitly indicated so, i.e., maximum AS and uniform distribution in azimuth of the power received. Thus, the correlation at the receiver will be mostly due to the antenna separation and
A. Modal and Spatial Correlations at the Receiver The correlation of interest is matrix ΘR , which characterizes both spatial and modal correlations. The correlation matrix for N = 2 and D = 2 and two different antenna spacings dr = {λ/2, 0.8 λ}, both of which are achievable to keep the antenna dimension bounded, is shown in the following:
1.0 ( ) 0.55 ΘR = −0.84 −0.24 λ 2
(0.8 λ)
ΘR
1.0 0.55 = −0.15 −0.24
0.55 1.0 −0.24 0.24
−0.84 −0.24 1.0 0.55
−0.24 0.24 0.55 1.0
0.55 1.00 −0.24 −0.07
−0.15 −0.24 1.0 0.55
−0.24 −0.07 . (10) 0.55 1.0
Modal correlation is given by (ΘR )1(1)1(2) = (ΘR )2(1)2(2) = 0.55, and it is independent of the antenna separation considered. Spatial correlation is dependent on the antenna separation: For dr = λ/2, (ΘR )1(1)2(1) = −0.84, (ΘR )1(2)2(2) = 0.24, and (ΘR )1(1)2(2) = −0.24, whereas for dr = 0.8 λ, (ΘR )1(1)2(1) = −0.15, (ΘR )1(2)2(2) = 0.07, and (ΘR )1(1)2(2) = −0.24. It can be observed, as previously mentioned, that increasing the separation between antennas decreases correlation, and consequently, spectral efficiency will increase. To show the effect of adding a new mode in the antenna at the receiver (three-mode antenna), its matrix correlation is shown. Here, the correlation matrix for N = 2 and D = 3 and antenna spacing dr = 0.8 λ is given by
1.0 0.55 0.95 −0.15 −0.24 −0.25 1.0 0.74 −0.24 −0.07 −0.32 0.55 0.95 0.74 1.0 −0.25 −0.32 −0.37 (0.8 λ) ΘR = . 0.55 0.95 −0.15 −0.24 −0.25 1.0 −0.24 −0.07 −0.32 0.55 1.0 0.74 −0.26 −0.32 −0.37 0.95 0.74 1.0 (11) All the relations between the first and second modes are kept the same, as in the two-mode antenna. However, as mentioned in the antenna design, the correlation of the new mode with each of the previous modes is much higher than the correlation between the originals. For example, (ΘR )1(1)1(3) = 0.95, and (ΘR )1(2)1(3) = 0.74.
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Fig. 4. Comparative spectral efficiency for the set of two dual-mode antennas at the receiver. M = 4, dt = λ/2, N = {2, 3, 4}, D = {2, 1}, and dr = 0.8 λ.
B. Advantages of Arrays of Multimode Antennas The advantage of using multimode antennas as array elements will be presented in terms of their spectral efficiency (in bits per second per hertz). The scenarios chosen are those where M = N D, given that all the antennas in transmission are of single mode. We generate 5000 samples of H for each of the different scenarios proposed, and from there, with (9), the spectral efficiency is computed. To show the advantage of using a set of two dual-mode antennas (see the sketch in Fig. 4), a scenario with M = 4, N = 2, and D = 2 is shown with the antenna described in Section II, i.e., two antennas (N = 2), with each one having two radiation patterns (D = 2) in reception and M = 4 singlemode antennas in transmission. The total array size of our proposed scheme is 1.2 λ. The spectral efficiency of this system is compared with two configurations. 1) M = 4, N = 4, and D = 1: configuration with four omnidirectional radiation patterns at both sides. In this case, the receiver size is 2.4 λ, without taking into account the size of the omnidirectional antennas. 2) M = 4, N = 3, and D = 1: configuration with omnidirectional radiation patterns at both sides (three antennas at the receiver and four antennas at the transmitter). In this case, the receiver size is 1.6 λ, without taking into account the size of the omnidirectional antennas. Fig. 4 shows the comparative performance of this scenario. Here, with only the purpose of showing the effect of modal correlation in our proposed scheme, we also include another scenario where modal correlation is forced to be zero (M = 4, N = 2, and D = 2 with uncorrelated modes). The scheme with the set of two dual-mode antennas performs better than an equivalent scenario with N = 3 and D = 1, and in this situation, it should be highlighted that the antenna size proposed is smaller, just as two radiating elements are being used compared to three. The two ideal configurations, i.e., when there is no modal correlation and when the number of omnidirectional antennas at the receiver is equal to N = 4,
are shown for reference purposes, bringing up the advantage of our proposed antenna scheme, given the proximity of its performance to an ideal but less-compact scenario. The behavior of these antenna schemes under different AS scenarios at the receiver (ASA) is also interesting. The reason for this is to corroborate if the results previously shown for the best correlation scenario at the receiver still hold for other correlation scenarios (lower AS). In Fig. 5, it is shown that there is a range of ASA values where our proposed scheme still performs better than the configuration with three omnidirectional antennas, and it always performs better than the two omnidirectional scheme. The arrays made with the three-mode antennas also seem to be an alternative in achieving a reasonable performance with low size in the terminal. Two scenarios are shown: The first scenario is a two-element scenario with N = 2 and D = 3, and the second scenario is a single-element configuration with N = 1 and D = 3 for more size-constrained terminals (see the insets in Figs. 6 and 7). The total array size of our proposed design is 1.42 λ. The spectral efficiency of the first scenario is compared with three configurations. 1) M = 6, N = 6, and D = 1: configuration with six omnidirectional radiation patterns at both sides. In this case, the receiver size is 4 λ, without taking into account the size of the omnidirectional antennas. 2) M = 6, N = 5, and D = 1: configuration with omnidirectional radiation patterns at both sides (five antennas at the receiver and six antennas at the transmitter). In this case, the receiver size is 3.2 λ, without taking into account the size of the omnidirectional antennas. 3) M = 6, N = 4, and D = 1: configuration with omnidirectional radiation patterns at both sides (four antennas at the receiver and six antennas at the transmitter). In this case, the receiver size is 2.4 λ, without taking into account the size of the omnidirectional antennas. Fig. 6 shows the comparative performance of this scenario. Here, again, we also include another scenario where modal
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Fig. 5. Comparative spectral efficiency for the set of two dual-mode antennas at the receiver with different ASAs. M = 4, dt = λ/2, N = {2, 3, 4}, D = {2, 1}, and dr = 0.8 λ.
Fig. 6. Comparative spectral efficiency for the set of two three-mode antennas at the receiver. M = 6, dt = λ/2, N = {2, 4, 5, 6}, D = {3, 1}, and dr = 0.8 λ.
correlation is forced to be zero (M = 6, N = 2, and D = 3 without modal correlation). The proposed scheme with two three-mode antennas performs better, given that it is in between an equivalent scenario with N = 5 or N = 4 and D = 1. The two ideal configurations, i.e., when there is no modal correlation and when the number of omnidirectional antennas at the receiver is equal to N = 6, are shown for reference purposes, showing again the advantage of our proposed antenna scheme. The constrained-size scenario (N = 1 and D = 3), with a total size of 0.62 λ, is compared with two configurations. 1) M = 3, N = 3, and D = 1: configuration with three omnidirectional radiation patterns at both sides. In this case, the receiver size is 1.6 λ, without taking into account the size of the omnidirectional antennas.
2) M = 3, N = 2, and D = 1: configuration with omnidirectional radiation patterns at both sides (two antennas at the receiver and three antennas at the transmitter). In this case, the receiver size is 0.8 λ, without taking into account the size of the omnidirectional antennas. Fig. 7 shows that our antenna design with three actives modes outperforms a system with N = 2 omnidirectional antennas at the receiver. V. C ONCLUSION This study presents the suitability and advantages of using linear arrays whose elements are multimode antennas in sizeconstrained terminals. Two compact multimode antennas have been studied to this aim, and their performance when employed
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Fig. 7. Comparative spectral efficiency for one three-mode antenna at the receiver. M = 3, dt = λ/2, N = {1, 2, 3}, D = {3, 1}, and dr = 0.8 λ.
in such arrays has been presented in terms of spectral efficiency. The antennas are based on patch antennas working in their fundamental modes with a particular stacking that allows up to three different simultaneous radiation patterns. The use of fundamental or low-order modes allows the required compactness. The use of compact multimode patch antennas is fundamental for the implementation of the proposed mixed spatial/pattern diversity schemes. A channel model that takes into account not only the spatial correlation but also the modal correlation has been developed. The spectral efficiency of different scenarios with multimode antennas is computed, showing the advantage of this proposal compared to scenarios with single-mode elements in terms of compactness. It is the combination of pattern and space diversities that gives such advantage. In summary, we have proposed mixed schemes that combine both space and pattern diversities for MIMO systems, and we have evaluated how they perform from the point of view of spectral efficiency. This performance has demonstrated to be better compared to schemes of similar physical size, where only space diversity is used. R EFERENCES [1] J. Perez, J. Ibanez, L. Vielva, and I. Santamaria, “Approximate closedform expression for the ergodic capacity of polarisation-diversity MIMO systems,” Electron. Lett., vol. 40, no. 19, pp. 1192–1194, Sep. 2004. [2] L. Dong, H. Choo, R. W. Heath, Jr., and H. Ling, “Simulation of MIMO channel capacity with antenna polarization diversity,” IEEE Trans. Wireless Commun., vol. 4, no. 4, pp. 1869–1873, Jul. 2005. [3] C. Dietrich, K. Dietze, J. Nealy, and W. Stutzman, “Spatial, polarization, and pattern diversity for wireless handheld terminals,” IEEE Trans. Antennas Propag., vol. 49, no. 9, pp. 1271–1281, Oct. 2001. [4] T. Svantesson, “On the potential of multimode antenna diversity,” in Proc. IEEE Veh. Technol. Conf., 2000, vol. 5, pp. 2368–2372. [5] T. Lee, C.-T. Chen, and T.-T. Lin, “Design of pattern diversity antenna for mobile communications,” in Proc. Int. Symp. Antennas Propag. Soc., 1996, vol. 1, pp. 518–521. [6] A. Forenza and R. Heath, “Benefit of pattern diversity via 2-element array of circular path antennas in indoor clustered MIMO channels,” IEEE Trans. Commun., vol. 54, no. 4, p. 760, Apr. 2006. [7] W. Lee, “Effects on correlation between two mobile radio base station antennas,” IEEE Trans. Commun., vol. COM-21, no. 11, pp. 1214–1224, Nov. 1973.
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SÁNCHEZ-FERNÁNDEZ et al.: SPECTRAL EFFICIENCY IN MIMO SYSTEM USING PATTERN DIVERSITY
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Matilde Sánchez-Fernández (S’99–AM’02–M’04) received the M.Sc. degree in telecommunications engineering and the Ph.D. degree from Polytechnic University of Madrid, Madrid, Spain, in 1996 and 2001, respectively. Since April 2000, he has been an Assistant Professor with the Departamento de Teoría de la Señal y Comunicaciones, Universidad Carlos III de Madrid. Previously, she was with Telefónica as a Telecommunication Engineer. She has performed research with the Information and Telecommunication Technology Center, University of Kansas, Lawrence; Bell Laboratories, Murray Hill, NJ; and the Centre Tecnològic de Telecomunicacions de Catalunya, Barcelona, Spain. Her current research interests are MIMO techniques, turbo codes, mobile communications, and simulation and modeling of communication systems.
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Eva Rajo-Iglesias (S’97–M’02) was born in Monforte de Lemos, Spain, in 1972. She received the M.Sc. degree in telecommunications engineering from the University of Vigo, Vigo, Spain, in 1996 and the Ph.D. degree in telecommunication from the Universidad Carlos III de Madrid, Madrid, Spain, in 2002. From 1997 to 2001, she was Assistant Professor with the Universidad Carlos III de Madrid. In 2001, she joined the Polytechnic University of Cartagena, Cartagena, Spain, as an Assistant Professor for a year. She came back to the Universidad Carlos III de Madrid as a Visiting Lecturer in 2002, and since 2004, she has been an Associate Professor with the Departamento de Teoría de la Señal y Comunicaciones. She has visited Chalmers University of Technology, Göteborg, Sweden, three times as a Guest Researcher, during the autumns of 2004, 2005, and 2006. She has coauthored more than 40 contributions in international journals and conference proceedings. Her main research interests include microstrip patch antennas and arrays, periodic structures, and optimization methods applied to electromagnetics.
Óscar Quevedo-Teruel (S’05) was born in Madrid, Spain, in 1981. He received the M.Sc. degree in telecommunications engineering from the Universidad Carlos III de Madrid in 2005. He is currently working toward the Ph.D. degree with the Departamento de Teoría de la Señal y Comunicaciones, Universidad Carlos III de Madrid. His research interests are patch antennas and optimization techniques applied to electromagnetic problems.
M. Luz Pablo-González received the M.Sc. degree in telecommunications engineering from the Universidad Carlos III de Madrid, Madrid, Spain, in 2003. She is currently working toward the Ph.D. degree with the Departamento de Teoría de la Señal y Comunicaciones, Universidad Carlos III de Madrid. Her main research interests include channel coding, MIMO systems, UWB techniques, and cooperative diversity in wireless sensor networks.
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