ANTENNA SYSTEMS AND PROPAGATION FOR FUTURE WIRELESS COMMUNICATIONS
Channel capacity evaluation for a multiple-inputmultiple-output terminal in the presence of user’s hand T. Zervos, K. Peppas, F. Lazarakis, A.A. Alexandridis, K. Dangakis and C. Soras Abstract: The impact of the user’s hand holding a multiple-input-multiple-output (MIMO) terminal on system performance and specifically on channel capacity is investigated. A 4 4 MIMO system is considered with a personal digital assistant terminal equipped with a compact array of 4 patch elements. The proposed methodology is based on the use of radiation patterns of the antenna elements in the presence of the other elements and in the presence of a user’s hand. Radiation patterns are obtained by means of simulations as well as of measurements conducted in an anechoic chamber. Two MIMO channel models are considered, namely a correlation-based model and a geometry-based model, where the antenna patterns are incorporated. The evaluation of MIMO channel capacity demonstrates the impact of the specific terminal antenna array. Moreover, significant degradation of channel capacity is proved because of the presence of the user’s hand.
1
Introduction
Multiple-input-multiple-output (MIMO) systems have attracted significant research effort during the last decade because of their proven ability to offer significant increase in system performance with improved link quality, extremely high data rates and increased channel capacity. MIMO channel modelling has been investigated in depth to realistically represent a number of characteristics such as flat or frequency selective fading, mobility of users, macro or micro-cellular environment and so on. However, in most studies ideal antenna elements placed on a linear array are assumed both at the transmitter and the receiver neglecting thus the impact of the realistic antenna system used in a specific design. Besides the characteristics of the individual antenna elements, coupling phenomena appear when the elements form an array. Coupling effect is more important at the terminal side where limited space is available for the placement of antennas. Recent studies have been devoted in investigating the effect of mutual coupling in MIMO system performance applying various methodologies based on antenna radiation patterns, coupling matrix, impedance matrix and so on [1 – 6]. Besides, many research activities have been carried out to investigate the interaction between electromagnetic fields emitted by wireless terminals and user’s body [7, 8]. Beyond the safety standards point of view, the user’s body influences the radiation properties of the mobile terminal, which is significant from the antenna design point of # The Institution of Engineering and Technology 2007 doi:10.1049/iet-map:20060221 Paper first received 1st September 2006 and in revised form 26th July 2007 T. Zervos, K. Peppas, F. Lazarakis, A. A. Alexandridis and K. Dangakis are with Institute of Informatics and Telecommunications, National Centre for Scientific Research ‘Demokritos’, Athens, Greece T. Zervos and C. Soras are with the Department of Electrical and Computer Engineering, University of Patras, Patras, Greece E-mail:
[email protected] IET Microw. Antennas Propag., 2007, 1, (6), pp. 1137 –1144
view. Most of previous studies investigate the effect of human’s head [9], which is in close proximity to the user’s terminal as it is the case in voice-centric systems. Nowadays, wireless systems are being optimised for data communications and hence, new test case scenarios should be studied, for example the ‘multimedia viewing position’ of the terminal. In such a case, the effect of the user’s presence varies with the type and placement of antennas as well as the position of the hand holding the handset. For example, a high impedance mismatch occurs when the hand begins to mask the antenna [10]. Thus, the effect of user’s hand becomes very interesting for the case of MIMO terminals. In this paper we focus on the impact of the user’s hand on system performance and especially on MIMO channel capacity. First, we evaluate the influence of the user’s hand on antenna radiation patterns. Then, the radiation patterns are incorporated into certain MIMO channel models that are used for channel capacity evaluation. In the current work, two channel models have been selected, namely correlation-based and geometry-based models, where different methodologies have been applied for the incorporation of radiation patterns into each of these models. The former model captures correlation effects between the antenna elements, it is adequate for many propagation environments and it is simple and easy to use. The latter model is suitable for more realistic propagation environments, introducing severe fading conditions, it has been standardised by 3GPP-3GPP2 [11], however it is more difficult to simulate. Our studies refer to a 4 4 MIMO system where a mobile terminal with limited size is included. At one end, a standard linear array is assumed playing the role of the base station. At the other end, a PDA terminal is considered with a compact array of 4 patch elements. The user’s hand has been modelled by means of a 3D electromagnetic (EM) simulator whereas a real model of the hand was made as a glass shell filled with an appropriate liquid mixture. Antenna radiation patterns were obtained through 1137
simulations and also through far field measurements in an anechoic chamber. The paper is organised as follows. In Section 2, the antenna configuration of the PDA is given and antenna patterns are simulated to demonstrate the effect of user’s hand. The procedure for measuring antenna patterns in an anechoic chamber is described and measured patterns are presented. Section 3 gives some basic information for the used MIMO channel models and explains how the obtained antenna patterns are incorporated in these models. Section 4 investigates channel capacity in the presence of user’s hand for the specific antenna array design. Finally, section 5 summarises the conclusions of the paper. 2
Terminal-hand prototype and model
The antenna configuration in this paper is based on the design of the planar inverted-F antenna (PIFA) model for dual band mobile terminal application. The antenna elements of the personal digital assistant (PDA) are folded PIFA patches designed for operation at 1800 and 2450 MHz frequency bands. In this work, we focus our studies on the lower band (1766 MHz). The geometry of an antenna element is shown in Fig. 1. A rectangular patch was folded on both sides of a dielectric layer with low permittivity (1r ¼ 2.33) and dimensions 77.5 75 mm. The dielectric layer is supported by a layer of foam with dimensions (length, width, thickness) 125 75 10 mm made from Rohacell (1r ¼ 1.03), which is propped on a finite ground plane with the same surface, 3 mm thick. The upper side patch is fed using a cylindrical feed pin of 0.2 mm radius and is connected to the ground plane via a cylindrical shorting pin of same radius. The input impedance of each PIFA element can be easily matched to 50 V by choosing the appropriate distance between the feed point and the shorting pin. The position of the elements on the PDA can be seen in Fig. 2a. The placement of the PIFA elements has been chosen to minimise the coupling between them. The polarisation of the elements tend to be elliptical and with the appropriate selection of the position of the feeding points (at alternate corners) the highest possible polarisation diversity can be achieved and thus the lower covariance [12] In Fig. 2b, it can also be seen a real model (mock-up) of the PDA that has been constructed using the same dimensions with the simulated model.
Fig. 1 Geometry of PIFA antenna a Top view b Side view 1138
Fig. 2 Models a, b PDA c, d PDA-hand
In order to study the effect of the human body, the ‘multimedia viewing position’ has been selected where it is assumed that the user is holding the terminal whereas the rest of his/her body does not influence the terminal’s operation. The user’s hand was modelled by means of an EM simulator following the concept of a homogeneous model and based on the dimensions given in [13] with some variations in order to hold the PDA properly. The exact dimensions of the hand while holding the PDA can be seen in Fig. 2c. Some more realistic hand models (e.g. with fingers) have also been tried, but EM simulation results were almost identical to the one provided by the ‘orthogonal block’ shaped hand. Therefore we adopted the latter model in order to easily fabricate the real experimental phantom hand. Owing to practical reasons, the measurements were performed using tissue simulating liquid used in homogeneous phantoms (1r ¼ 41, s ¼ 1.65 S/m at 1800 MHz) [13]. In order to have comparable results, we have used the same material parameters also in the EM simulations. It is noted that for radiation patterns and efficiency studies, slight differences of the actual 1r and s values are not expected to affect the results. The real model of the hand was made as a glass shell 5 mm thick and it was filled in with a liquid mixture prepared according to the recommendations of related standards [14]. The location of the hand was set at the right side of the PDA in such a way that it did not cover the antenna elements. In Fig. 2d, it can be seen a photo of the hand model holding the PDA. Both PDA and hand have been modelled with the aid of a 3D EM simulator (CST Microwave Studio). Two separate simulation runs were performed with the PDA in free space (‘PDA test case’) and with the user’s hand holding the PDA (‘PDA-hand test case’) in order to calculate s-parameters and antenna radiation patterns. The simulated s-parameters showed a very good resonance of the antenna elements in 1766 MHz and low mutual coupling between them. In order to validate and support the simulated results, measurements of the PDA with and without the presence of the hand have been taken in a fully anechoic chamber. IET Microw. Antennas Propag., Vol. 1, No. 6, December 2007
The PDA and the hand model were placed on a box made of styrofoam and mounted on a tripod situated on a remotely controlled turntable inside the anechoic chamber. Each antenna element of the PDA was connected to one of the ports of a vector network analyser (VNA) while the other elements were terminated at 50 Ohms. A calibrated reference horn antenna (EMCO-3115) was connected to the other port of the VNA and sited at the opposite side of the chamber. Full two-port s-parameters measurements at 1766 MHz were performed using the VNA calibrated at the antennas’ ports. Assuming free space conditions inside the anechoic chamber, the power gain of each element was derived from the measured s-parameters of the system. Three-dimensional radiation diagrams were obtained with a step of 58 in the elevation plane using the automatic turntable scan and with a step of 108 in the azimuth plane by manual positioning. Both u and w components were measured in separate measurement cycles and the total power gain was obtained as the sum of the two gain components. Using the above measuring procedure, we measured the gain of each element for both PDA and PDA-hand test cases. The simulated and the measured power gain 3D patterns of the antenna elements for the PDA alone at 1766 MHz can be seen in Fig. 3, whereas in Fig. 4 the corresponding patterns for the PDA with the presence of the hand are illustrated. From both figures, very good agreement between measurements and simulated results is observed. By comparing Figs. 3 and 4 it can be seen that the presence of the hand mainly affects the patterns of elements 3 and 4 where there is a serious degradation of the gain at the right side. There are also some minor changes in the patterns of elements 1 and 2. This is an expected result as elements 3 and 4 are in the close vicinity of the hand. In order to gain better insight regarding the impact of the user’s hand, we present in Fig. 5 the measured relative total gain (normalised to the maximum value for each port) patterns in yz and xy planes, for the PDA with and without the presence of the hand. The solid line represents the patterns for the PDA case, whereas the dashed one shows the patterns for the PDA-hand test case for each of the four antenna elements. It can be noticed that differences in the diagram shape mainly occur in the patterns of elements 3 and 4 in both planes where in some directions the gain falls more than 10 dB when the hand is present. 3
MIMO channel modelling
Assuming an MIMO system with nT transmitting antennas and nR receiving antennas, the receiver signal model is
Fig. 4 3D power gain patterns of the PDA with the presence of the hand (dBi) a Stimulated b Measured
written as y ¼ Hx þ n
(1)
where y represents the nR 1 received vector signal (in base band), H the nR nT channel matrix, x the nT 1 vector of transmit signals and n the nR 1 vector of additive noise samples. MIMO channel matrix H, is provided by suitable channel models that can be classified into two main categories: deterministic and stochastic models. In this paper, the following channel models will be considered: † A narrowband stochastic model, the so called correlationbased channel. † A frequency selective, geometry –based stochastic channel model, compliant with the 3GPP standards [11]. 3.1
Correlation-based channel model
In this model, the channel matrix H is given as follows [15] 1 H C 1=2 H ¼ C 1=2 g R iid T
(2)
where CR and CT are the nR nR and nT nT covariance matrices of the receive and the transmit antenna, respectively, Hiid denotes a nR nT matrix of independent and identically distributed Gaussian entries and g is a normalisation constant chosen so that E kH k2F ¼ nR nT for uncorrelated antennas (where k†kF is the Frobenius norm). In the present work, flat Rayleigh fading is assumed and no Doppler effect is taken into account, which is valid for low user speeds. To estimate the covariance matrices we follow the approach of continuous incident field distribution and calculate the covariance between i and j antenna elements as [2, 16] ð CR (i, j) ¼ CT (i, j) ¼ Ei (V) Ej (V) S(V) dV (3) V
Fig. 3 3D power gain patterns of the PDA (dBi) a Stimulated b Measured IET Microw. Antennas Propag., Vol. 1, No. 6, December 2007
where Ei(V) and Ej(V) are the radiation field patterns of the corresponding antenna elements, V is the solid angle parameter and S(V) is the joint Angular Power Density Function. The distribution of S(V) has been modelled by various functions [17], however in this paper we use a simple approach [2], assuming S(V) uniform in azimuth w and independent of elevation u within a given incidence 1139
Fig. 5 Measured relative gain patterns (normalized) for the PDA (solid line) and for the PDA-hand (dashed line) a yz-plane b xy-plane
region. The incidence region is defined as
p Du p Du u þ , 0 w 2p (4) 2 2 2 2 Thus, Du ! 0 corresponds to incidence in the horizontal plane only, whereas Du ¼ p corresponds to incidence in the whole sphere. In the following, for an element l we are using the antenna gain pattern to calculate the values of the corresponding radiation field patterns El(V) in (3), taking into account that jEl(V)j2 ¼ jEoj2.Gl(V), where Gl(V) is the power gain pattern and Eo the isotropic lossless antenna field. All field values are normalised to a maximum available power excitation of 4p/h (h the free space impendence) at the antenna input port, resulting to jEoj ¼ 1 and thus jEl(V)j2 ¼ Gl(V). In this work, four fully uncorrelated lossless antennas are assumed at the transmitter and thus, CT ¼ I, that is the identity matrix. At the receiver side, the PDA is assumed with and without the presence of the hand. The antenna characteristics and the effect of the user’s hand can be incorporated into channel representation by calculating the elements of the covariance matrix CR by means of the radiation patterns of the antenna elements presented in Figs. 3 and 4. In [2], it is proved that for practical antennas, the covariance coefficient between two antenna elements given by (3) is approximately equal to the mutual resistance between these elements. Thus the losses because of antenna coupling are also included in the above described channel model. 3.2
Geometry-based stochastic channel model
In this channel model, a fixed number of scatterers are assumed to be located around the mobile terminal. In order to generate the appropriate channel parameters, a raybased approach has been adopted, that is by assuming that each scatterer carries one path only [11]. The received signal at the mobile terminal consists of K time-delayed multipath replicas of the transmitted signal, where K is the number of scatterers. These K paths are defined by powers 1140
and delays that are chosen randomly according to the channel generation procedure and each path consists of M subpaths. Assuming that the base station array consists of nT elements whereas the mobile terminal array of nR elements, the channel coefficients for one of the K paths are given by a nR nT matrix of complex amplitudes, denoted by Hk(t). Consequently, the overall channel matrix impulse response is given as follows H(t) ¼
K X
H k (t)d(t tk )
(5)
k¼1
where tk is the delay for the kth path. The element hk,R,T of the channel coefficient Hk(t), namely the channel impulse response between the receive antenna R and the transmit antenna T for the kth path, is given as follows rffiffiffiffiffiffiffiffiffiffiffiffiffi M Pk sSF X A (u )A (u ) hk,R,T (t) ¼ M m¼1 T k,m,AOD R k,m,AOA 2p vt cos u exp (jFk,m ) exp j (6) l where, Pk is the average power of the kth path, sSF the lognormal shadowing, AT(.), AR(.) the antenna patterns of the transmit and receive antennas, respectively, uk,m,AOD , uk,m,AOA the angles of departure and arrival, respectively, for the mth subpath of the kth path, Fk,m the phase of the mth subpath of the kth path, v the terminal velocity, l the wavelength and u is the angle between the direction of the impinging ray at the mobile and the direction of motion. This model has the capability of simulating urban microcell and macrocell as well as suburban macrocell environments. However, in our paper, we have focused on urban macrocell environments. The number of paths K and the corresponding number M of sub-paths per path are 6 and 20, respectively. No line-of-sight component has been taken into account and low user speeds have been assumed, equal to 0.5 m/sec. The model is used for the IET Microw. Antennas Propag., Vol. 1, No. 6, December 2007
simulation of systems with bandwidth 5 MHz whereas the central frequency is 1766 MHz. The considered channel model assumes that multipath occurs on a single plane and thus, antenna patterns have to be considered on a suitable plane. We select for further investigation two different positions of the PDA that correspond to propagation of the multipath signals at the principal planes xy and yz. In each case, the angles involved in (6) are computed on the considered plane. In order to incorporate the antenna characteristics, mutual coupling and the effect of user’s hand into the above described channel model, evaluation of the antenna radiation patterns AT(u) and AR(u) is required. At the transmitter side, a linear array with four elements each of them having 708 beamwidth is assumed in compliance with the 3GPP standard for 3-sector cellular environments [11, Section 4.5.1]. The receive pattern AR(u), is taken from suitable cuts (on xy and yz planes) of the data found in Figs. 3 and 4. Because of the fact that both simulations and measurements refer to E-field of a specific element with the presence of other antennas, the information regarding mutual coupling is also included in the above described model. 4 Channel capacity in the presence of user’s hand Let us consider a flat fading MIMO system with nT transmit and nR receive antennas. The capacity of this channel assuming that there is no channel knowledge at the transmitter is given by the well known formula [18] SNR HH H (7) C ¼ log2 det InR þ nT where SNR is the signal-to-noise ratio and H the channel matrix. For the frequency selective channel, the capacity over a bandwidth B is given by [15] ð 1 SNR ~ H ~ H( f )H( f ) df C¼ log2 det InR þ (8) B B nT ~ f ) is the Fourier transform of the channel matrix where H( H(t). If H has been calculated in accordance with the channel models described in previous sections, channel capacity evaluation includes the effects of mutual coupling between antenna elements and the impact of the user’s hand. 4.1 Capacity results for the correlation-based model The investigation of channel capacity in this case, requires the calculation of the covariance coefficients CR(i, j), between i and j antenna elements, using the radiation patterns for both the PDA and PDA-hand test cases. The above calculation is performed via (3) and a sufficient number of channel realisations are then calculated using (2) as well as the corresponding channel capacity by means of (7). The variance coefficients CR(i, i) derived from measured antenna patterns for both the PDA and PDA-hand test cases, are depicted in Fig. 6 as a function of the previously mentioned angle, Du. It is noticed that for Du ¼ 1808 the values of the variance coefficients represent the radiation efficiency of each element. the coefficients CR(i, j), where i = j, are not illustrated in that figure since their values are very small, close to 0.1. From Fig. 6, it is obvious that the presence of the hand results in a significant decrease in the values of the covariance coefficients. This decrease is more obvious for CR(3, 3) and CR(4, 4) where, while in IET Microw. Antennas Propag., Vol. 1, No. 6, December 2007
Fig. 6 Variance coefficients against Du for PDA and PDA-hand test case
the PDA case their radiation efficiencies are around 0.8, in the PDA-hand case the corresponding values become 0.52 and 0.23, respectively. As expected, the presence of the hand affects mainly the elements that lie closer, that is, 3 and 4. In Fig. 7 the average (ergodic) channel capacity as a function of SNR is illustrated as evaluated from both measured and simulated antenna patterns of the PDA. The range of SNR varies from 0 to 25 dB, whereas Du is 1808. As a reference case, the capacity of a 4 4 i.i.d. channel Hiid , is also plotted as a function of SNR. From Fig. 7, one can see that the impact of the presence of the hand on MIMO channel capacity is significant. Specifically for the case of simulated patterns, the presence of the hand results in a decrease of channel capacity at low values of SNR (0 dB) from 3.4 to 2.5 bits/s/Hz, that is a 26.5% decrease whereas at high values of SNR (25 dB) from 28.6 to 25.5 bits/s/Hz that is a 10.8% decrease. For measured patterns, the corresponding percentages of capacity degradation are 25% and 9.3%. Finally, it is worth noticing that the channel capacity achieved with the PDA alone, when computed through simulated patterns, is almost identical to the corresponding capacity of the 4 4 i.i.d. channel. This is rather expected since the simulation parameters used for the PDA correspond to approximately lossless antenna elements with efficiency close to 1 and low correlation. On the other hand, as shown in Fig. 6, the efficiencies of the antenna elements of the PDA prototype are significantly lower than 1. That fact has a direct effect on the capacity derived from measured patterns which is, in general, lower than that derived from
Fig. 7 Channel capacity against SNR for PDA and PDA-hand test cases 1141
simulated patterns. However, from the above analysis it is evident that the presence of the hand decreases channel capacity in a similar manner when considering simulated or measured patterns. Channel capacity simulations were also performed for both considered test cases with fixed SNR, equal to 10 dB, whereas Du varies from 0 to 1808. The average decrease in channel capacity as the result of the user’s hand was found to be approximately 2 bits/s/Hz for all the values of Du. In that sense, the capacity remains almost constant for various regions of the incident energy, defined by Du, which is because of the assumptions made for S(V) in Section 3.1. 4.2 Capacity results for the geometry-based model The evaluation of the channel capacity in this case, introduces additional computational complexity in comparison to the correlation-based test case because of the following reasons: † The frequency selectivity of the channel; the channel capacity involves the computation of the integral as shown in (8). † This model incorporates rapid changes of the propagation environment, which is reflected on the computation of the matrices Hk(t) of (5). † The incorporation of the impact of the mobile speed in channel model. The channel capacity has been calculated using simulated and measured antenna patterns on the yz and xy planes (observation planes) as explained in previous section. The results are depicted in Figs. 8 and 9 where the angles u, w represent the orientation of the PDA which primarily affects the mean values of angle of arrival and secondary the Doppler effect. The SNR is taken equal to 10 dB. From both figures, it is clear that MIMO channel capacity with and without the hand varies significantly with the orientation of the PDA. As a result, the impact of the user’s hand on capacity also varies with terminal’s orientation. Specifically, by the inspection of Fig. 8, the negative impact of the hand is maximised at angles u equal to 2180 and 1808 whereas around 08 it almost vanishes. This observation is valid for both measured and simulated patterns. Specifically, for high absolute values of u, the absolute difference in channel capacity for the PDA and PDA-hand cases is approximately 1.4 bits/s/Hz for simulated patterns
Fig. 8 Channel capacity (for yz observation plane) against u for PDA and PDA-hand test cases 1142
Fig. 9 Channel capacity (for xy observation plane) against w for PDA and PDA-hand test cases
and 1.5bits/s/Hz for measured ones. For values of u around 08, the difference varies from approximately 0 to 0.2bits/s/ Hz for simulated and measured patterns, respectively. Similar conclusions may be drawn by the inspection of Fig. 9. In this case, the difference between channel capacities is small for low values of w but it gradually increases with increasing w, starting from an angle approximately equal to 2008. This difference reaches its peak at 2708. From both Figs. 8 and 9, certain deviations are observed between capacity results obtained from simulated and measured antenna patterns. This is because of l variations between the prototype and the simulated model. Nevertheless, an interesting result is that for both measured and simulated radiation patterns the capacity results are consistent, namely similar relative differences are observed between the PDA and PDA-hand cases. Specifically, when considering propagation at the xy plane, the capacity degradation has a mean value of 0.5 bits/s/Hz according to simulated patterns and 0.35 bits/s/Hz according to measured ones. The standard deviation of that degradation is 0.3bits/s/Hz for both simulations and measurements. This consistency is clearer in yz plane, where for both measured and simulated patterns the capacity degradation caused by the user’s hand has a mean value of 0.75bits/s/Hz with a standard deviation of 0.5 bits/s/Hz. It should be noted, however, that although the orientation of the mobile terminal may significantly affect channel capacity, the random changes in the propagation environment incorporated by the geometry-based model may cause fluctuations of the capacity values as well. That is because of the fact that the antenna patterns in a given channel instance are not computed for a deterministic value of angle of arrival; these angles are characterised by probability distributions with given mean value and variance. Besides, the ray-based approach of this model implies that one multipath component consists of several random sub-paths, and thus the contribution of each one in the total channel response needs to be considered. Antenna gains are computed for all these generated angles, which results in variations of the capacity values. On the contrary, in the correlation-based model where uniform multipath was assumed, the orientation of the terminal had minimal impact on channel capacity. Figs. 10 and 11 illustrate the average channel capacity as a function of SNR where the propagation planes are yz and xy, respectively, with u, w equal to 1808. The range of SNR varies from 0 to 25 dB. Both figures illustrate the negative impact of the presence of the hand on channel capacity. In IET Microw. Antennas Propag., Vol. 1, No. 6, December 2007
5
Fig. 10 Channel capacity ( for yz observation plane) against SNR for PDA and PDA-hand test cases
Fig. 11 Channel capacity ( for xy observation plane) against SNR for PDA and PDA-hand test cases
In this paper, the impact of user’s terminal hand on MIMO channel capacity was addressed. The mobile terminal was a PDA equipped with four patch antennas. The applied methodology relies on the evaluation of antenna radiation patterns and their incorporation into suitable channel models. A PDA and a hand model were simulated, although a PDA prototype and a real hand model were also available. Antenna radiation patterns were obtained through simulations as well as through measurements in an anechoic chamber for the PDA with and without the presence of hand. Two channel models have been considered, namely correlation-based and geometry-based. For the PDA alone, MIMO capacity results in higher values when the correlation model is used compared to the geometry-based model. This is rather expected since the latter model simulates a very complicated environment with severe fading conditions. Moreover, the orientation of a PDA with a realistic antenna array may influence the achieved capacity in the realistic propagation environment of a geometry-based model. No such effect was observed for flat fading with uniform multipath conditions as in correlation model. The effect of the user’s hand is quite significant as indicated by the results obtained from both channel models, with the largest degradation observed at low SNR values. This degradation is primarily the results of power losses introduced by the presence of the user’s hand. For the correlation-based model, capacity degradation is around 25% for low SNR values. In the geometry-based case, the effect of the hand varies significantly with the orientation of the PDA. In a case where the presence of the hand has a large impact, even 40% capacity degradation was found for low SNR values. Finally, quite similar capacity results were obtained through simulated and measured radiation patterns. 6
Fig. 10, referring to the simulated patterns, channel capacity decreases from 3.2 to 1.9 bits/s/Hz at low values of SNR (0 dB) that is 41% decrease. For high values of SNR (25 dB), channel capacity decreases from 13.5 to 11.1 bits/s/Hz that is 18% decrease. The above percentages become 51% and 12%, respectively, using the measured patterns. By the inspection of Fig. 11, the channel capacity degradation referring to the simulated patterns varies from 43 to 20% for low and high values of SNR, respectively. These results are also validated by the measured patterns with very small deviations from the above mentioned values. Our analysis for both channel models proved that the presence of user’s hand significantly degrades MIMO channel capacity that should not be neglected during terminal design and performance evaluation of the system. Thus, special care should be taken for the placement of multiple antenna elements on mobile terminals in order to ensure adequate antenna separation and at the same time to keep them as far as possible from the user’s hand. It is noted that various test cases could be considered regarding the position of the hand when holding the terminal. Finally, in order to realistically evaluate various MIMO systems and techniques, performance degradation from 10% up to 40% should be taken into account because of the presence of the user’s hand, depending on the specific antenna array, the position of the user’s hand and the SNR range. IET Microw. Antennas Propag., Vol. 1, No. 6, December 2007
Conclusions
Acknowledgments
The work was partly supported by IST NoE ACE. The authors would like to thank their partners in Universidad Politecnica de Madrid (UPM) and Kungliga Tekniska Ho¨gskolan (KTH) for providing the design and prototype of the PDA antenna array. 7
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IET Microw. Antennas Propag., Vol. 1, No. 6, December 2007
