On the Performance of GSM/EDGE Transmit Diversity Schemes when Employing Dual-Polarized Antennas Jyri Hämäläinen, Risto Wichman, Jari Hulkkonen, Timo Kähkönen, Tero Korpi, Mikko Säily Helsinki University of Technology, P.O. Box 3, 25 HUT, Finland Nokia Networks, P.O. Box 39, 965 Oulu, Finland Abstract Base station antennas with cross-polarized antenna branches are commonly used in mobile communication systems. It is known that the use of vertically and horizontally polarized base station antennas results in unbalance between received powers in mobile station, while the channels corresponding to ±45 slanted, linearly polarized antennas are correlated. In this paper, we calculate the power unbalance and correlation between the channels in terms of channel cross polarization and base station antenna properties. Furthermore, link level performance of transmit diversity techniques, suitable to GSM/EDGE radio access network, is simulated. I. INTRODUCTION Uplink performance of the existing GSM/EDGE systems can be enhanced by various well known multiantenna techniques. Improved uplink performance can be utilized efficiently in the present networks if the downlink performance is also improved at the same time. Transmit diversity schemes that employ multiple transmit antennas in the base station and need only a single receiver antenna in the mobile station provide attractive solutions since the complexity requirements in the present mobile stations are strict, and therefore, advanced detectors with multiple receive antennas are not seen as a desired solution.
Transmit diversity techniques are effective when the correlation between the channels is low. Spatial diversity is a well known solution to decrease the correlation between antennas but a separation of several wavelengths is usually needed in base station. In practical systems, however, the most common at the moment is a two-branch diversity, which can be implemented employing cross-polarized antenna branches placed into a single antenna box and resulting in a compact antenna system. It has been proposed that there is small, if any, performance loss from using ±45 slanted cross polarized antennas instead of spatially separated antennas when diversity receivers are employed [], [2]. The performance analysis of the cross polarized antennas is different from that employed in case of spatially separated, co polarized antennas. The average received powers from spatially separated co polarized antennas are assumed to be equal and correlation between the signals depends mostly on the antenna distance. In case of cross polarized antennas, also the gain properties of antennas should be taken into account [3]. In addition to base station antenna properties, the effect of channel cross polarization and mobile antenna polarization needs to be considered [4]. In this paper we propose a model by which mean powers of signals with respect to vertical and horizontal polarizations can be computed. We also show how the correlation between the antenna branches can be deduced when dual-polarized antennas with nominal ±45 inclination to vertical linear polarization are employed. These results are of theoretical nature and show the relationship between the base station antenna correlation and the properties of the physical channel, base station and mobile station antennas. Finally, we provide performance results for some simple two antenna transmit diversity methods suitable to GSM/EDGE as a function of channel correlation. The paper is structured as follows: Section 2 presents the system model, mean power analysis is carried out in Section 3,and examples of power correlations are given in Section 4. Section 5 summarizes the transmit diversity modes suitable to GSM/EDGE and provides link-level simulation results as a function of envelope correlation and power unbalance between the diversity branches. The paper is concluded in Section 6. II. SYSTEM MODEL Consider a system utilizing dual polarized transmit antennas in the base station and a single receiver antenna in the mobile station. We study two basic base station antenna systems consisting of ) Vertically and horizontally polarized antennas 2) Linearly polarized, ±45 slanted from vertical Let us denote by h and h 2 the channel impulse responses corresponding to the first and the second antenna system. Then, for the first antenna system we have h = h V and h 2 = h H while h = (h V + h H )/ 2, h 2 = (h V h H )/ 2 for the second antenna system, where h V and h H refer to vertically and horizontally polarized channel components, respectively. The same h V and h H can be used to compare the given antenna systems only if the antenna response with respect to vertical and horizontal polarizations are the same in both systems. We adopt the model of [5] and assume that h V and h H are uncorrelated complex zero-mean Gaussian variables. Then the first antenna system suffers from power unbalance between antenna branches while the second antenna system is corrupted by antenna correlation, and the connection between the two phenomena is studied in the following.
Consider the complex antenna correlation ρ c in case of second antenna system. We have E{h ρ c = h 2 } E{ h 2 }E{ h 2 2 }. Since component channels h V and h H are uncorrelated, E{h h 2 } = (E{ h V 2 } E{ h H 2 })/2, E{ h 2 } = (E{ h V 2 } + E{ h H 2 })/2 = E{ h 2 2 }. The latter equality shows the well-known fact that the expected mean power in ±45 slanted antenna branches is equal. By combining the last three equations we obtain ρ c = η η +, η = E{ h V 2 } E{ h H 2 } = P V, () P H which provides the connection between the power unbalance η of the first system and the complex antenna correlation of the second system. Conventionally, the envelope correlation ρ env favoured to complex correlation when presenting performance results. Therefore, we recall the connection between complex and envelope correlations [5], [6] ρ env = π ( F ( 4 π 2, 2,, ρ c 2) ), (2) where ρ c 2 is the power correlation and F is the hypergeometric function, see [7], Section 5. Figure illustrates the connection between power unbalance and envelope correlation. Conventionally, it is understood that ρ env <.7 is necessary to achieve acceptable diversity gains. This limit is encountered when η is around db. Relations () and (2) together with Figure show that the most important task is to find a proper model in order to calculate the mean powers P V and P H. Then it is an easy task to find η and the corresponding correlation. Finally we note that according to Figure, ρ env ρ c 2 and there is not much difference whether results are presented in terms of envelope or power correlation. is Power and Envelope Correlations.9.8.7.6.5.4.3.2. Power Correlation Envelope Correlation 5 5 2 25 3 Power Unbalance [db] Fig.. unbalance. Power and envelope correlations as a function of power III. ANALYSIS OF MEAN POWERS The unbalance η between P V and P H is studied by adopting a two-dimensional version of the model proposed in [8]. We define P X (Φ) = P X π π p X (Φ, φ)g X (φ)dφ = PX P X BS (Φ), (3) X {V, H}, where G X ( ) is the horizontal antenna power gain pattern, p X (, ) is the power azimuth spectrum seen by base station, Φ is the direction of arrival (DoA) of the signal and PX is the mean signal power when using ideal base station antennas such that G X. The subscript X indicates that the corresponding variable is defined with respect to X- polarization. The first term on the right hand side of (3) contains the effects from the physical channel and the mobile antenna while the second term depends on the base station antenna gain pattern and the power azimuth spectrum seen by base station. Power gain patterns with nominal ±45 inclination to vertical linear polarization have been evaluated in [3] for a dualpolarized aperture coupled patch and a slanted dipole
Normalized power [db] 3 6 9 2 5 8 2 24 27 Total Power Vertical Polarization Horizontal Polarization 3 9 75 6 45 3 5 5 3 45 6 75 9 Azimuth [deg] Fig. 2. Power gain patterns for 45 slanted λ/2 dipole placed λ/8 wavelengths over an infinite groundplane [3]. configuration. Figure 2 recalls the power gain patterns for 45 slanted λ/2 dipole placed λ/8 wavelengths over an infinite groundplane [3]. The figure shows that G V /G H can be several decibels on sector edges. This base station antenna specific property introduces unbalance between P V and P H. When employing ±45 slanted antennas the unbalance can be directly mapped to the correlation, as noted in Figure, and we note that the design of antenna gain patterns is an important task from diversity system performance point of view. The unbalance of () can be now written in the form η = ν BS (Φ) P V PH, ν BS (Φ) = P V BS(Φ) PH BS(Φ). Since the unbalance ν BS ( ), introduced by the base station, can be calculated from (3) it remains to study the ratio between the mean powers P V and P H. If the mobile antenna polarization is vertical, the ratio defines the cross-polarization power ratio (XPR) of the environment. However, since the mobile antenna polarization is not fixed we need to further analyze the system. As in [5] we write h V = h V V + h V H, h H = h HH + h HV. (4) Hence, the signal with vertical departing polarization is further divided into vertically and horizontally polarized signal parts according to its arriving polarization. The signal with horizontal departing polarization is decomposed in a similar manner. According to [5], mutual correlations between all four subchannels are low and can be neglected. Therefore, we obtain P X = P XX + P XY, P XY = E{ h XY 2 }. (5) The next step is to separate the effect of the physical channel from the effect of the mobile antenna properties. For that purpose we write Here P MS P XY = P Ch Y XY P Y MS, X, Y {V, H}. defines the Y-polarized signal power captured by the mobile station. The mean power P Ch XY corresponding to the physical channel is defined by using the cross-polarization power ratios XPR V H = P V Ch V, XPR HV = P Ch, PV Ch H HH PHV Ch where the former ratio is the conventional cross polarization ratio. Furthermore, XPR HV is defined as a ratio between the expected powers of vertically and horizontally polarized ideal receive antennas when signal is transmitted employing an ideal horizontally polarized antenna. With the given notations we are able to write η = ν BS (Φ) + νms XPR V H ν MS + XPR HV, (6) + XPR HV + XPR V H where ν MS = P MS PH MS V MS /PH MS. The mean powers P and can be calculated in a similar manner as the mean powers P BS BS ( ) and P ( ) provided that required V H antenna gain patterns and three-dimensional channel model are known. IV. EXAMPLES We see from (6) that the ratio between P V V and P H depends on the properties of the physical channel (parameters XPR V H and XPR HV ) and on the
properties of the transmit and receive antennas (parameters ν BS (Φ) and ν MS ). The conventional crosspolarization power ratio XPR V H has been studied in many measurement campaigns and a summary of the results can be found in [3]. Results indicate that in urban and sub-urban environments XPR V H varies between and 2 db. However, measurement results for the ratio XPR HV are not easy to find in the literature. Therefore, we concentrate on extreme cases ν MS = and ν MS. The first case occurs when the mobile antenna responses corresponding to vertical and horizontal polarizations are equal and the second case occurs when mobile antenna polarization is purely vertical. For the above-mentioned cases we have η = ν BS (Φ), η = ν BS (Φ)XPR, where the subscript of XPR has been neglected to emphasize that only the conventional XP R is needed. The first case is advantageous from the diversity point of view since only the unbalance introduced by the base station antenna is considered, while the second case also takes into account the effect of the physical channel. It is expected that the first case is more common in practise since mobile antenna orientation is more or less random and the electric field in the mobile antenna is coupled with the cover of the handset and also with the user s head. The second case provides a kind of worst case and it may appear if a conventional vertical whip antenna is mounted on top of a car. We still need to study the ratio ν BS ( ) before we can calculate the correlations. We note that the power azimuth spectrums p V (, ) and p H (, ) with respect to vertical and horizontal polarizations need not to be the same. However, it is not easy to find measurement results in the literature concerning the question. Therefore we have selected a simple approach, where equal power azimuth spectrums are applied to both vertically and horizontally polarized signals. Several alternatives to the power azimuth distribution has been proposed in the literature. For example, according to [9] Laplacian and Gaussian distributions can be used, depending on the environment and base station antenna height, p(φ, φ) = C L e 2 Φ φ σ, p(φ, φ) = C G e (Φ φ)2 2σ 2. Here σ is the deviation of the power azimuth spectrum, C L and C G are normalization constants, and the subscript referring to the signal polarization has been dropped out, because the same distribution function is used for both polarizations. Consider now correlations for two examples where base station antennas are ±45 slanted λ/2 dipoles placed λ/8 wavelengths over an infinite groundplane [3]. The first example employs Laplacian power azimuth spectrum with σ = 5, which corresponds to rural macrocell environment, where angular spreads tends to have moderate values. The second example uses Gaussian power azimuth spectrum with σ = 2 corresponding to urban macrocell environment where angular spreads tend to be higher. The mean powers PV BS BS ( ) and P ( ) are calculated by integrating (3) numerically. H Figure 3 depicts the power correlation ρ c 2 when σ = 5. We note that the curve indicating the lowest correlation corresponds to the system where the mobile antenna response with respect to vertical and horizontal polarizations is equal. Other curves provide the upper limit for correlation when a certain XP R is assumed. These worst cases occur when mobile antenna polarization is purely vertical. It is seen that the upper limit for power correlation is relatively high if the XPR in the physical channel is large. This is true especially at sector edges, where the antenna power gains with respect to vertical and horizontal polarizations have a large difference. In
Power Correlation.9.8.7.6.5.4.3.2. XPR = 9 db XPR = 6 db XPR = 3 db XPR = db 8 6 4 2 2 4 6 8 Azimuth [deg] Fig. 3. Power correlation as a function of the mobile DoA assuming rural macrocell example with XPR =,3, 6, 9 db. practise the difference in antenna gain patterns with respect to vertical and horizontal polarizations depends on the applied antenna design, and many commercial antennas have better balance between horizontal and vertical gain patterns than the slanted dipoles used here as an example. In case of urban macrocell the deviation of the power azimuth spectrum is larger than in rural case. Therefore, the variation of the correlation is smaller and extremely high correlations are rare as seen from Figure 4. Finally, we note that power correlations of Figures 3 and 4 corresponding to ±45 slanted base station antenna system can be converted into power unbalances of the first antenna system consisting of vertically and horizontally polarized antennas by using the curve in Figure. V. TRANSMIT DIVERSITY IN GSM/EDGE In general, transmit diversity techniques can be divided into open-loop and closed-loop modes, where the latter technique employs partial channel state information (CSI) in the transmitter to adjust the signals transmitted from multiple base station antennas such that they combine coherently in the receive antenna Power Correlation.9.8.7.6.5.4.3.2. XPR = 9 db XPR = 6 db XPR = 3 db XPR = db 8 6 4 2 2 4 6 8 Azimuth [deg] Fig. 4. Power correlation as a function of the mobile DoA assuming urban macrocell example with XPR =,3, 6, 9 db. of the mobile station. Closed-loop transmit diversity modes are difficult to use in GSM/EDGE, because the standard does not support a fast reverse control channel for transmitting CSI as in, e.g., WCDMA. Therefore, we will concentrate in open-loop modes in the sequel. Antenna hopping (AH) and phase hopping (PH) are two well known open-loop methods suitable to GSM/EDGE. In antenna hopping the transmit antenna is changed during the interleaving period resulting in an increased channel diversity which can be converted into a performance gain through the channel coding. Similarly, phase hopping provides diversity gain through interleaving and channel coding. In GSM/EDGE, both AH and PH are done burstwise. In addition to antenna and phase hopping the socalled delay diversity (DD) provides an attractive solution, where the same signal is transmitted from both antennas with a certain delay []. The diversity gain from delay diversity is due to the increased multipath diversity, and the optimal delay depends on the channel profile and the receiver implementation, but in practise.5 symbol period gives close to optimal performance in most cases. The usage of delay diversity is
Diversity gain [db] 4 3.5 3 2.5 2.5.5 Delay Diversity + Phase Hopping Correlation Unbalance /./3..3/5.6.5/8..7/.9.9/6.4 /inf Envelope correlation / Power unbalance (db) Fig. 5. Diversity gain of delay diversity + phase hopping against single antenna transmission (AMR2.2). totally transparent to the receiver, and therefore, DD can be employed without changes to present standards. Delay diversity can also be combined with phase hopping as shown in []. Diversity gains of DD/PH and AH were simulated for GSM speech service assuming adaptive multi rate speech codec at 2.2 kbit/s (AMR2.2), which employs GMSK modulation and a /2 rate convolutional coding with interleaving over eight TDMA frames. The results are depicted assuming % frame error rate (FER) that is the limiting value for acceptable quality of connection. The radio channel is typical urban at 3 km/h mobile speed (TU3) [3], and correlated Rayleigh fading envelopes for the two component channels were generated according to [2]. The receiver employs a 6-state Max-log-MAP equalizer. At this stage we recall from Figure the theoretical one to one mapping between power unbalance and envelope correlation of the received signals. The relation is applied in the horizontal axis of Figures 5 and 6, which show the diversity gain of DD/PH and AH against single antenna transmission as a function of envelope correlation and power unbalance. It is found Diversity gain [db] 4 3.5 3 2.5 2.5.5 Antenna Hopping.5 /./3..3/5.6.5/8..7/.9.9/6.4 /inf Fig. 6. Envelope correlation / Power unbalance (db) Correlation Unbalance Diversity gain of antenna hopping against single antenna transmission (AMR2.2). that the DD/PH is more sensitive to antenna correlation than to power unbalance, while the opposite is true in case of antenna hopping. The performance of both DD/PH and AH rapidly decreases when correlation is larger than.7. Fortunately, according to Figures 3 and 4 this case is rare since even the upper bound for the correlation is most of the time less than.7. Moreover, in practise mobile antenna polarization contains both vertical and horizontal components ( < ν MS < ) and thus, upper bounds of Figures 3 and 4 are not encountered. VI. CONCLUSION A channel model to calculate antenna correlation/power unbalance between cross-polarized diversity branches was proposed. First, it was recalled that there is one to one mapping between antenna correlation and power unbalance between the diversity branches. Then a model to calculate the required mean powers was presented. Two example cases were studied showing that for ±45 slanted dipole antennas the upper bound for correlation can be relatively high at sector edges. Finally, diversity gain for antenna hopping and a combination of delay diversity and
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