The 17th Annual IEEE International Symposium on Personal, Indoor and Mobile Radio Communications (PIMRC’06)
PERFORMANCE OF DOWNLINK SPATIAL-MULTIPLEXING IN URBAN MACROCELLULAR MULTI-USER MIMO SCENARIOS Thomas F¨ugen, Malgorzata Porebska, and Werner Wiesbeck Institut f¨ur H¨ochstfrequenztechnik und Elektronik, Universit¨at Karlsruhe (TH)
[email protected] Germany A BSTRACT The aim of this paper is to compare the performance of different smart antenna algorithms to the performance of a conventional SISO reference system in an urban multi-user MIMO scenario. A single cell with three 120 deg sectors and several moving users is used for evaluation. The scenario as well as the channel information is generated by means of a realistic urban channel model that consists of a model of the city of Karlsruhe, a mobility model and an accurate ray-tracing based wave propagation model. The smart antenna algorithms under test are two single-user MIMO algorithms (user specific beamforming, waterfilling) and two multi-user MIMO algorithms (block diagonalization, successive optimization). Simulation results show clearly the potential of downlink spatial-multiplexing to improve the system capacity, to reduce the exposure, the transmit power and therefore also the operating costs in future cellular mobile radio systems. I.
optimization algorithms proposed in [5]. Applying SA is leading to dramatically improvements of the link quality, and the system capacity. Less attention of research is given to the fact that SA can also be used in order to reduce the transmit power and the average exposure in the cellular mobile radio system. The goal of this paper is to give a quantitative description of all these profits. For an adequate performance evaluation an accurate modeling of the multi-user propagation channel and the antenna arrays is indispensable. In Section II. a new simulator is described that fulfills these requirements. Section III. summarizes the different SA algorithms under investigation. Finally performance results are presented in Section IV. showing the high potentials of SAs to improve the system capacity, to reduce the exposure (power density), the transmit power and therefore also the operating costs in future cellular mobile radio systems.
I NTRODUCTION
Recent research has shown the potential of smart antennas (SA) to satisfy the demand for high data rates in wireless communications. There are several approaches for the implementation of SA at the base station (BS). In this paper the performance of two different SA single-user transmission schemes is compared with two different SA multi-user transmission schemes in an urban macrocellular environment. The two SA single-user schemes are user specific beamforming and MIMO (multiple input multiple output) waterfilling. In both schemes the MTs within a cell are multiplexed by a conventional multiplexing method, i.e. TDMA, FDMA, or CDMA. User specific beamforming means that the BS serves each MT with an individual beam. The beam is pointing into the direction where the signal experiences the lowest pathloss. The waterfilling algorithm in contrast allows for spatial multiplexing between several independent data streams dedicated to one MT [7]. Using multiple antennas at the BS to support multiple MTs with one or more antenna per MT leads to a multi-user MIMO (Mu-MIMO) system. In the Mu-MIMO context spatial multiplexing allows the BS to communicate simultaneously with multiple MTs in the same radio spectrum (i.e. without separation in code, time or frequency) by exploiting differences in spatial signatures at the BS antenna array induced by spatially dispersed MTs. This technique is also known as SDMA (space division multiple access). If the channels of the MTs are sufficiently orthogonal SDMA allows a capacity increase proportional to the number of antennas at the BS and the number of MTs. The two Mu-MIMO transmission schemes studied in this paper are the block diagonalization and the successive c 1-4244-0330-8/06/$20.002006 IEEE
II.
U RBAN CHANNEL MODEL
A comprehensive urban channel model is used to calculate the multi-user MIMO channel. The model consists of three major parts: a realistic model of the propagation environment a mobility model and a model to calculate the multi-path wave propagation between the BSs and the multiple MTs. A model of the Karlsruhe city center is used as environment, see Fig. 1. The scenario includes the most relevant objects for a realistic description of the wave propagation in urban environments, i.e. buildings, trees and the street floor. To account for a time variant channel behavior the model of the environment is combined with a mobility model. The mobility model generates a number of MTs that move along the streets with a certain velocity. If a MT reaches a cross street it can change its direction with a certain probability. The result of the two models is a proper traffic situation, which serves as input data for the propagation simulations. A ray-optical approach is used for the wave propagation modelling, which allows for narrow-band as well as wide-band analyses of the channel. As propagation phenomena multiple reflections, multiple diffractions and scattering from vegetation and buildings are taken into account. More details to the urban channel model can be found in [4]. The paper includes also a comparison of the model to no-directional and directional wide-band measurements, showing a very good agreement. The output of the urban channel model are characteristic time series (snapshots) of double-directional channel impulse responses (IRs) between all BSs and all MTs. The IRs can directly be used for multi-user MIMO simulations.
The 17th Annual IEEE International Symposium on Personal, Indoor and Mobile Radio Communications (PIMRC’06)
The capacity of the link between the p-th BS array and the k-th MT using perfect channel knowledge at both link ends is given for both schemes by C(p,k) = log2 det
T RANSMISSION SCHEMES AND SIMULATION APPROACH
We consider a single cell in an urban macrocellular environment with O antenna arrays. Each array is illuminating a part (sector) of the communication cell. The number of antennas of the p-th BS array is denoted with Mp . Several MTs are placed in the cell. The number of the MTs in sector p is denoted with Jp . Each MT is equipped with an antenna array. The number of antennas of the k-th MT is denoted with Nk . For the transmission channel flat fading is assumed. For flat-fading channels the multipath components arrive at the receiver within a symbol period. Thus the channel between the p-th BS antenna array and the k-th MT can be described by a complex Mp × Nk channel matrix H(p,k) containing the complex channel coefficients. The complex received signal yk of MT k that is served by the p-th BS array is described by yk = D†k H(p,k) Mk xk + D†k nk + ξk
(1)
where xk denotes the complex transmit signal and nk is additive Gaussian white noise. The purpose of the modulation matrix Mk and the demodulation matrix Dk is to diagonalize the channel, so that the transmission of several independent data streams from the p-th BS array to the k-th MT is possible. The term ξk denotes inter- and intracell interference. The modulation and demodulation matrices can be calculated using the SVD of the channel matrix [6] H(p,k) = Dk Σk M†k
Rzk zk
(3)
In single-user systems the MTs within a sector are separated by a conventional multiplexing method (TDMA, FDMA, CDMA). Therefore no intracell interference occurs. In real systems the same resources are reused in other sectors after a certain reuse distance. This causes intercell interference. In this study it is assumed that the intercell interference between the sectors is perfectly nullified. This means that ξk = 0 and the noise covariance matrix in (3) for MT k is given by Rzk zk = Iσ 2 , where σ 2 is the power of Gaussian white noise.
Figure 1: Used macrocell scenario. III.
Rzk zk + H(p,k) Mk M†k H†(p,k)
(2)
where Σk is a diagonal matrix, containing the non-negative roots of subchannel gains for MT k. A. SA single-user downlink transmission schemes There are different possibilities to distribute the power among the subchannels in single-user transmission schemes. The optimal power distribution results from applying of the margin adaptive waterfilling algorithm (WF) to the elements of Σ2k [7]. This algorithm minimizes the transmit power under the constraint of a given capacity that has to be achieved. The second power distribution uses only the strongest subchannel and is referred to as user specific beamforming (BF). In cases of low SNR, user specific beamforming achieves the same performance as waterfilling but with less complexity.
B. Multi-user MIMO downlink transmission schemes In multi-user MIMO transmission schemes a group of users is allowed to share the same spectrum. This means that within this group the MTs are only separated due to their different spatial signatures (SDMA). In most cases the number of antennas of the BS array is not high enough to accommodate all MTs. Therefore, SDMA has to be used in conjunction with other multiplexing methods (TDMA, FDMA, CDMA) in order to separate the groups themselves. The two Mu-MIMO downlink transmission schemes considered in this work are the block diagonalization (BD) and the successive optimization (SO) algorithms [5]. These algorithms allow a fair resource allocation to the users. The optimization task of the algorithms is to search for weighting matrices which minimize the transmit power for the group of MTs under the constraint that each MT within the group achieves an individual demanded data rate. The BD algorithm suppresses the interference between all MTs by forcing the modulation matrix for MT k to lay in the null space of the matrix which combines the channel matrices of all other MTs in the same group. Thus H(p,k) Mµ = 0, ∀k = µ. The SO algorithm in contrast nullifies only the interference caused by already known signals. In their original version both algorithms can handle systems, in which the total number of MT antennas does not exceed the number of antennas of the BS array. However, in [5] an approach is proposed that extends the applicability of the BD and the SO algorithm to up to Jp ≤ Mp MTs, regardless of the array size of the MT, by coordinating the processing between the BS and the MTs. The algorithm is referred to as coordinated transmit receive processing (CTRP). In Tab.1 the procedures for finding the BD and SO modulation matrices using CTRP are described. The capacity for the k-th MT can be written for both algorithms as: C(p,k) = log2 det
Rzk zk + W†k H(p,k) Mk M†k H†(p,k) Wk Rzk zk
(4) Using the CTRP-BD algorithm, the receive signal yk of MT k is per definition free of intracell interference (ξk = 0). As we assume that no intercell interference occurs the sum capacity = Iσ 2 ). Usis limited by Gaussian white noise (i.e. RzBD k zk ing the CTRP-SO algorithm, the receive signal yk of MT k is
The 17th Annual IEEE International Symposium on Personal, Indoor and Mobile Radio Communications (PIMRC’06)
groups exceeds the number of antennas of the BS array. Additionally we have introduced a correlation threshold that ensures that MTs within a group are sufficiently orthogonal, i.e. if γk,l > 0.7 then MT k will not be grouped together with MT l. It might therefore happen that a group contains only one MT. As the MTs are moving during the simulation in the scenario, their IRs and therefore also the spatial correlation between their channels change. In real systems the correlation coefficients would be recalculated after each channel estimation. In this study we assume perfect channel state information in each snapshot. The correlation coefficients between the MTs can be recalculated for each snapshot. If in any group the correlation between the MTs exceeds the chosen threshold, the MTs with the high correlation are split (moved to a separate new group or to one of the existing groups, if there the threshold is fulfilled). The rearrangement of groups takes also place when one of the MTs during the movement changes the sector. The decision to assign a MT to a new sector is made on the basis of the average channel attenuation for each BS array from last 100 ms. The tree based scheduling is performed for each sector separately. The allocation of groups which are to be served in the same time (frequency) slot in different sectors is chosen to be random.
Table 1: Description of the BD and SO Algorithm Let Wk denote the first sk columns of the left singular vector of H(p,k) , where sk is the number of subchannels allocated to MT k. The total number of subchannels can be at most equal to the number of antennas of the BS-array p. For MT k = 1, . . . , Jp :
= W† H 1) define the effective channel matrix H k k (p,k) .
2) find the null space matrix: † † ... H † H † † . . . H CTRP-BD: Nk = Null H . 1 k−1 k+1 Jp † † ... H † . CTRP-SO: Nk = Null H 1 k−1 3) apply the SVD: N = U Σk V . CTRP-BD: H k k k k † R−1 H N = V Λk V† where CTRP-SO: Nk† H k zk zk k k k k k−1 †. Rzk zk = Iσ 2 + µ=1 Hk Mµ M†µ H k
4) calculate the power-loading matrix Pk using margin adaptive waterfilling on the diagonal elements of Σ2k (for CTRPBD) or Λk (for CTRP-SO) under the total power constraint Jp k=1 tr(Pk ) ≤ PT . 1
5) calculate the modulation matrix: Mk = Nk Vk Pk2 .
D. interfered by the data streams transmitted simultaneously by the p − th BS array to the MTs 1 . . . k − 1. As intercell interference is neglected, the interference term in (1) is given by k−1 ξk = µ=1 W†k H(p,k) Mµ xµ and the noise covariance matrix k−1 † † † 2 in (4) by RSO zk zk = Iσ + µ=1 Wk H(p,k) Mµ Mµ H(p,k) Wk . In the following the term BD refers to CTRP-BD and SO to CTRP-SO. C. Scheduling To apply the multi-user MIMO transmission schemes an algorithm is needed, which chooses the MTs that can be efficiently multiplexed in space within one group, while the different groups are multiplexed in time, frequency or code. In this paper a modified version of the tree based algorithm proposed in [3] is used for this purpose. The algorithm takes two constraints into account. First the number of MTs within the same group must be less or equal to the number of antennas of the BS array. Second MTs with high correlated channels should not be grouped together. The tree based algorithm uses a metric function that measures the efficiency of the transmission to the k-th MT when grouped together with the MTs already included in the group. In contrast to the metric function proposed in [3] we use the spatial correlation between the channels of the different MTs as metric. The spatial correlation between MT k and MT l served by the same BS array p is calculated by the product of their strongest right singular vectors [2] γk,l = |V(p,k) (:, 1)† V(p,l) (:, 1)|
(5)
γk,l represents the cosine of the angle between the MTs subspaces and takes the values between 0 for orthogonal channels and 1 for totally correlated channels. The tree based algorithm allocates the MTs to groups unless the number of MTs in those
Scenario, reference system and quality criteria
The ray tracing scenario that is used for performance evaluation is shown in Fig. 1. The BS site is placed well above average rooftop level on a 25 m high building, 2 m above its roof. In order to compare the performance of the different SA algorithms, a SISO (single input single output) reference scenario is used. In the reference system each sector is illuminated by a single commercially available BS antenna of type ”Kathrein Antenna 735 147”. The horizontal and vertical pattern of the antennas is taken from the literature [1]. The antenna gain is 18.9 dBi, the vertical half-power bandwidth 7◦ and the horizontal half-power bandwidth 65◦ . Each of the MTs is equipped with a vertical polarized λ/2 dipole (2.15 dBi antenna gain). To allow for MTs to share the same radio spectrum a conventional multiplexing method is used. In the SA scenarios the single sector antennas are replaced by uniform linear arrays. Each array is radiating into a 120◦ sector and consists of four antennas of type ”Kathrein Antenna 735 147” (λ/2 spaced). Each MT is equipped with 2 vertical polarized λ/2 dipoles (λ/2 spaced). In total 15 simulation scenarios with common BS site are generated by means of the channel model. Each scenario contains 30 MTs. The start positions of the MTs in each scenario are uniform distributed within the street grid. During simulation the MTs move on the street grid with a velocity of 50 km/h. To include spatially colored interference the simulation time for each scenario is set to 10 s, i.e. each MT moves in one scenario along ≈ 140 m. Each λ/4 a new IR is calculated, resulting in 3704 IRs (snapshots) per MT per route. The overall number of IRs in the 15 scenarios is therefore 3704 ∗ 30 ∗ 15 = 1666800. The different SA algorithms are evaluated by their QoS (Quality of Service), i.e. the optimization task of the BS is to achieve a desired arbitrary rate for each MT with a mini-
The 17th Annual IEEE International Symposium on Personal, Indoor and Mobile Radio Communications (PIMRC’06)
mum transmit power. The data rate is measured by the capacity. The capacity of the SISO reference system can be calculated by the Shannon formula. The capacity using SAs is given by (3) and (4). The task is to achieve for each MT a capacity of Copt = 2 bit/s/Hz. In order to obtain Copt a certain value of the signal to noise ratio (SNR) at the receiver is required. The SNR is determined by the transmit power of the BS, the channel attenuation, and the noise power σ 2 . Resulting from the movement of the MTs, the channel attenuation varies over the time. The transmit power of the BS must therefore permanently be adjusted in order to obtain a constant capacity. For narrow-band systems the noise power can not directly be obtained from the system bandwidth. It is set to −101 dBm. Using the SISO reference system and a constant transmit power of 1 W (30 dBm) the resulting median SNR of all IRs is 10 dB and the median capacity is 3.46 bit/s/Hz. In real systems the transmit power of the BS is limited. The maximum transmit power of the BS is set to 20 W (43 dBm) per sector. Using the reference system, the BF or the WF algorithm the whole power can be allocated to one MT in order to achieve Copt . Copt is not reached if the attenuation of the channel is too high. Using SO or BD the transmit power is distributed between the MTs within the group. The MT that needs the minimal transmit power to achieve the demanded data rate is processed first. This maximizes the number of satisfied MTs. Copt for one MT within a group is not reached, if the remaining transmit power is not high enough to compensate the channel attenuation. In contrast to many studies on Mu-MIMO a third quality criterion is used, i.e. the exposure in the surface area of the scenario. The exposure at a certain point (x, y, z) in the scenario produced by the p-th BS array when transmitting to MT k located at a given position is calculated by Sp,k,(x,y,z) =
PR,p,k,(x,y,z) 4π = PR,p,k,(x,y,z) 2 Ae λ GR
(6)
where Ae is the effective surface of the receive antenna, GR is its antenna gain, and PR,p,k,(x,y,z) is the receive power at a certain point (x, y, z). PR,p,k,(x,y,z) is influenced by the transmit power that is required to achieve Copt for MT k and by the instantaneous antenna pattern that is used at the BS p in order to serve the MT. As receive antenna an omni-directional antenna with an antenna gain of 0 dBi is used. Fig. 2(a) shows an example of the laminar exposure (2 m above ground) when the BS is transmitting to the indicated MT. The system corresponds to the SISO reference. The required transmit power to achieve Copt is 22.33 dBm. Fig. 2(b) indicates the laminar exposure using the BF algorithm. The required transmit power to achieve Copt is reduced to 14.91 dBm and therefore also the exposure is reduced. An overall evaluation of the exposure is possible using the ratio of each point (x, y, z) in the two figures: ∆S(x,y,z) = SSA,(x,y,z) /SRef,(x,y,z) , where SRef,(x,y,z) is the exposure of the SISO reference system and SSA,(x,y,z) of the SA system. The ratio of Fig. 2(a) and Fig. 2(b) is given in Fig. 2(c). In case of a moving MT each position of the MT produces a figure of the laminar exposure and therefore also a figure of the exposure ratio. As the simulation scenario contains multiple
(a) SISO reference system.
(b) User specific beamforming.
(c) Exposure ratio for BF vs. SISO reference system.
Figure 2: Laminar exposure for the SISO reference system, the BF algorithm, and the ratio of both. MTs each of the MT produces therefore own exposure figures. Taking all exposure figures a statistical description of the performance of the SA algorithms is possible by the cumulative distribution function (cdf) (see Section IV.). IV.
S IMULATION R ESULTS AND C ONCLUSION
Figure 3 shows the cdf of the achieved capacities for all IRs. It can be seen that in most cases Copt is reached. The mean SNR and SNIR for the different algorithms are given in Tab. 2. Due to the low SNR the WF algorithm uses in most cases only the strongest subchannel, therefore it achieves the same results as the BF algorithm. For both SA single-user transmission schemes the probability that a MT is served with Copt is 99.0%. In the reference system the probability is only 96.4%. The Mu-MIMO algorithms perform nearly equally (98.8%) and achieve almost the same performance as the SA single-user transmission schemes. From economic aspect it is beneficial to reduce the transmit power in wireless communications. For a given IR i the performance of a SA algorithm can be evaluated by the ratio between the transmit power that is required in order to reach
The 17th Annual IEEE International Symposium on Personal, Indoor and Mobile Radio Communications (PIMRC’06)
0.04
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Figure 3: Reached capacity per user.
1
R EFERENCES
[2] G. Del Galdo and M. Haardt. Comparison of zero-forcing methods for downlink spatial multiplexing in realistic multi-user MIMO channels. In Proceedings of the 59th IEEE Vehicular Technology Conference, VTC2004-Spring, volume 1, pages 299–303, 2004.
Table 2: Mean ratio of the transmit power and exposure when using one of the SA algorithms, and resulting mean SNR and mean SNIR.. ∆PT in dB ∆S in dB SN R in dB SN IR in dB
BF -8.37 -13.69 4.74 4.74
SO -6.58 -12.56 5.59 4.74
0.6
0.4
0.2
0 −30
−25
−20
−15 −10 ∆ in dB
−5
0
5
S
(b) Ratio of the exposure.
PDF
Figure 4: Reduction of transmit power and exposure using different SA algorithms. 0.45 0.4 0.35 0.3 0.25 0.2 0.15 0.1 0.05 0
1 2 3 4 number of users per group
Figure 5: Number of users per group.
[1] M. Baldauf, A. Herschlein, W. S¨orgel, and W. Wiesbeck. Safety distances in mobile communications. In Proceedings of the 2nd International Workshop on Biological Effects of Elektromagnetic Fields, pages 148–156, Rhodes, Greece, October 2002.
WF -8.39 -13.45 4.72 4.72
0.8 P(∆S < abscissa)
Copt : ∆PT ,i = PSA,i /PRef,i . The cdf of the ratios for all IRs is given in Fig. 4(a). The mean values for the different algorithms are given in Tab. 2. Using the WF and the BF algorithm the transmit power can be reduced in mean by 8.39 dB. The SO algorithm reduces the transmit power in mean by 6.58 dB and the BD scheme by 5.78 dB. The lower values compared to the SA single-user algorithms is due to the spatial correlation of the MTs within a group and the resulting sub-optimal characteristic of the beamforming pattern. Using WF or BF it is necessary to separate the MTs in time, frequency, or code, e.g. to accommodate 8 MTs 8 time slots are required. Multi-user MIMO allows to economize resources by communicating simultaneously with a group of MTs in the same radio spectrum. The probability for the number of MTs per group is given in Fig. 5. In mean 1.83 MTs are served within a group (median 2.0). The last quality criterion is the exposure that is produced in the simulation scenario when transmitting to a MT. The statistical behavior of the different SA algorithms compared to the reference system for all simulation scenarios is depicted in Fig. 4(b). The mean values are given in Tab. 2. As one can see a significant reduction of the exposure is possible using single-user as well as multi-user SA algorithms.
WF BF SO BD
BD -5.78 -12.69 4.74 4.74
SISO 4.67 4.67
[3] M. Fuchs, G. Del Galdo, and M. Haardt. A novel tree-based scheduling algorithm for the downlink of multi-user MIMO systems with ZF beamforming. In in Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP ’05, volume 3, pages 1121–1124, 2005. [4] T. F¨ugen, J. Maurer, T. Kayser, and W. Wiesbeck. Capability of 3D Ray Tracing for Defining Parameter Sets for the Specification of Future Mobile Communications Systems. Special Issue of the IEEE Transactions on Antennas and Propagation on Wireless Communications, to be published, October 2006. [5] Q.H. Spencer, A.L. Swindlehurst, and M. Haardt. Zero-forcing methods for downlink spatial multiplexing in multiuser MIMO channels. IEEE Transactions on Signal Processing, 52(2):461–471, 2004. [6] I.E. Telatar. Capacity of Multi-antenna Gaussian Channels. European Transactions on Telecommunications, 10(6):585–595, November 1999. [7] W. Yu, G. Ginis, and J.M. Cioffi. Distributed Multiuser Power Control for Digital Subscriber Lines. IEEE Journal on Selected Areas in Communications, 20(5):1105–1115, June 2002.
