This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the WCNC 2010 proceedings.
Design Criteria of Uniform Circular Array for Multi-User MIMO in Rural Areas Hajime Suzuki, Douglas B. Hayman, Joseph Pathikulangara, Iain B. Collings, Zhuo Chen, and Rodney Kendall CSIRO ICT Centre Sydney, NSW 2122 Australia Email:
[email protected]
Abstract—When multi-user multiple-input multiple-output (MU-MIMO) is applied to predominantly line-of-sight (LoS) environments, such as in the case of fixed wireless access in rural areas where a central access point (AP) equipped with an antenna array with NAP antenna elements serves NUT user terminals (UTs) each equipped with a single antenna, the problem of ill-conditioned channels arises. This paper investigates the performance of zero-forcing precoding based MU-MIMO downlink when the AP is equipped with a uniform circular array (UCA) in an LoS environment. The performance is analyzed as a function of the spacing and the number of AP UCA antenna elements for NAP ≥ NUT . The analysis reveals a complex yet orderly pattern of the performance nulls indicating different optimal antenna spacing for different number of antenna elements. The performance nulls can be largely eliminated by employing NAP ≥ 2NUT .
I. I NTRODUCTION Providing inexpensive high data rate internet access to the homes/residences in rural and remote areas presents many challenges. User terminals (UTs) are scattered over large geographic areas (e.g. tens of residences per 100 km2 ), and the cost of deploying a wired network is considered to be prohibitive. Alternatively, wireless technologies are expected to reduce the cost [1]. Terrestrial fixed wireless multiple access has been previously considered for rural areas, by using standardized wireless local loop (WLL) technologies [2], wireless local area network (WLAN) technologies [3], wireless metropolitan area network (WMAN) technologies [4], and more recently wireless regional area network (WRAN) technologies [5]. However, the spectrum efficiency achieved by those standard technologies is typically limited to less than 6 bits/s/Hz/cell. Hence either a broad frequency spectrum or a large number of base stations would be required in order to simultaneously provide high data rates to every user within a cell. The authors proposed the use of multi-user multiple-input multiple-output (MU-MIMO) [6] for increasing the spectrum efficiency of fixed wireless multiple access systems in rural areas [7]. With MU-MIMO, the access point (AP) is equipped with multiple antennas while UTs are each equipped with a single antenna. The authors have shown that the spectrum efficiency can be improved linearly as a function of the number of antenna elements at the AP, without increasing the total transmitting power, even in a predominantly line-of-sight (LoS) environment. This is achieved by the use of a uniform
circular array (UCA) at the AP, a low-complexity zero-forcing (ZF) precoding based downlink, and a simple user grouping method to avoid ill-conditioned channels [7]. The proposed MU-MIMO system suitable for fixed wireless multiple access systems in rural areas is termed Rural MIMO (R-MIMO). In the absence of site-specific geographical information, we assume that the UTs are randomly located in the horizontal plane and are to be given equal quality-of-service, and as such the use of UCA for R-MIMO is considered to be most suitable. In this paper, we focus on the design parameters for the R-MIMO AP UCA. In particular, R-MIMO downlink performance is analytically investigated as a function of the number of UCA antenna elements, element spacing, and the location of UTs. This paper is organized as follows. Section II reviews the structure and the signal processing of the proposed R-MIMO downlink. An analytical model is developed in Section III which is used to analyze the performance of the proposed R-MIMO downlink as a function of the AP UCA antenna configuration. Section IV concludes this paper. II. R-MIMO D OWNLINK Fig. 1 illustrates the proposed R-MIMO system. The AP is equipped with NAP omni-directional (in the horizontal plane) antennas installed at the height hAP from the ground. Each of the NUT UTs is equipped with a directional antenna at a height hUT pointed towards the AP. We refer to this configuration as an NUT UT × NAP AP system, and assume NAP ≥ NUT . In practise, the antennas are above local clutter, resulting in a channel which is dominated by the LoS path. Throughout the paper we assume inter cell interference is negligible. Fig. 2 (a) shows a block diagram of signal processing at the AP for the downlink. The downlink binary data (DD) for the mth UT is generated in the “UTm DD” block, m = 1, 2, . . . , NUT . The downlink binary data for each UT is then mapped onto a multi-level quadrature amplitude modulation (MQAM) or multi-level phase-shift keying (MPSK) symbols by the “MAP” block to produce downlink data symbols sD,m . The downlink channel can be estimated at UTs by sending known symbols from the AP and returning the estimated channel information from the UTs to the AP, or by utilizing reciprocity of the downlink and uplink channels in a time division duplexing system. The estimated channel information is used to perform conventional ZF precoding [8], [9] by the
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This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the WCNC 2010 proceedings.
AP
z
y x UT
hAP
hUT Ground
Fig. 1: Example geometry of access point (AP) and user terminal (UT) (side view).
Channel Estimation
UTNUTDD
AP1 Tx AP2 Tx ZFP
where the superscript H denotes complex conjugate transpose. Let ||WD ||2 β= , (3) NAP PD
...
MAP MAP ...
...
UT1 DD UT2 DD
Gaussian noise at the UTs, respectively. T denotes transpose. GD is a NUT ×NAP matrix whose element gD,m,n is the complex channel coefficient between the nth AP transmitter and the mth UT receiver. Let −1 GH (2) WD = GH D GD D ,
APN APTx
MAP (a) Access point.
where PD is the average transmitting power from an AP transmitting antenna, and
β UTm Rx
Scaling
DET
DMAP
UTm DS
(b) User terminal.
Fig. 2: Block diagram showing proposed R-MIMO downlink signal processing.
2
||WD || =
NUT NAP
|wD,n,m |2 .
(4)
n=1 m=1
Then the precoding of the transmitted downlink symbols are performed by 1 xD = WD sD . (5) β
“ZFP” block. The nth symbol, n = 1, 2, . . . , NAP is transmitted from the nth AP transmitter, represented by the “APn Tx” blocks. Fig. 2 (b) shows a block diagram of signal processing at the UT for the downlink. The mth UT receiver receives the symbol rD,m . The received symbol at mth UT receiver is scaled by the scaling factor β, as explained below. The detection of transmitted symbols is performed by the “DET” block. “DMAP” block performs de-mapping of data symbol to binary data, which are passed onto mth UT downlink data sink “UTm DS” block. The signal model for the proposed R-MIMO downlink within one symbol time is described as
where sD = [sD,m ]T . The term 1/β constrains the total transmitting power from the AP to NAP PD . Substituting (5) into (1) gives
rD = GD xD + nD .
The equation (7) shows that the performance of the proposed R-MIMO downlink is a monotonic function of the scaling factor β. In the following section, we analyze β to identify optimal design parameters for the R-MIMO AP UCA.
(1)
rD = [rD,m ]T , xD = [xD,n ]T , and nD = [nD,m ]T are symbols received at the UTs, symbols sent from the AP, and complex
rD =
1 sD + nD . β
(6)
At each UT, the received signal, rD,m is multiplied by β, which is assumed known at the UT (for example based on training), to give (7) zD,m = sD,m + βnD,m . For the mth UT, the transmitted symbol estimate is sˆD,m = arg min |zD,m − si |. si ∈Q
(8)
This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the WCNC 2010 proceedings.
UT2
90
20 dB 60
120 15 10
150
AP2
30
5
φAP
θ
UT1 180
0 deg
AP1 r
d
APNAP
330
210
φ UT 240
300 270
UTNUT
(a) θ = 0 deg
Fig. 3: 2D Rural MIMO model. 90
20 dB
120
60 15
III. ACCESS P OINT A NTENNA C ONFIGURATION In this section, we analyze the performance of the proposed R-MIMO downlink as a function of the AP UCA antenna configuration when UTs are regularly distributed. Such a regular UT distribution can asymptotically be achieved by the proposed user grouping as discussed in [7] from randomly distributed UTs. In this paper, we focus on the downlink, while the performance of corresponding uplink was also analyzed in [7]. For simplicity, we assume a two dimensional model in this section. A more realistic model involving reflected paths from the ground was used in [7]. Omni-directional antennas with 0 dBi gain are used for both the AP and UTs for simplicity. We note that the results of the analysis is independent of the actual value of the UT antenna gain provided that the values of the antenna gain from UTs to the direction of the AP are the same for all UTs. A. Number of AP Antennas = Number of UTs Fig. 3 (top view) shows a simplified two dimensional model of the proposed R-MIMO system where UTs are regularly distributed with an equal angular spacing φUT . The distance from the center of the AP UCA to each AP antenna element and to each UT is r and d, respectively. The angular separation between neighboring AP antennas is φAP . In the case of NAP = NUT = N , φAP = φUT = φ. The rotation of the UTs with reference to AP UCA is θ as shown in Fig. 3. With this simple arrangement, the downlink channel coefficient from AP1 to UT1 can be modeled as [10] C d1,1 , (9) gD,1,1 = exp −j2π d1,1 λ where C is a constant independent of different antenna pair, λ is the wavelength, and d1,1 is the distance between AP1 and UT1 antennas given by (10) d1,1 = d2 sin2 θ + (d cos θ − r)2 .
10
150
30
5 180
0 deg
330
210
240
300 270 (b) θ = 44 deg
Fig. 4: Radiation pattern of 4 UT × 4 AP zero-forcing precoder. AP UCA antenna spacing is 0.5 wavelengths. Arrows indicate the direction of UTs.
Similarly, the channel coefficient for each of AP and UT antenna pair can be derived as a functions of d, r, λ, θ, φAP , and φUT . In the following, we nominally set d = 50 km to represent a long range rural fixed wireless system. In order to assess the relationship between the proposed R-MIMO downlink performance and the AP UCA antenna configuration, we first analyze radiation pattern as a function of the UT locations when AP UCA antenna spacing is 0.5 wavelengths. Fig. 4 shows the radiation pattern of 4 elements AP UCA when ZF precoding is applied for four UTs according to (2). The direction to each UT is denoted by an arrow with a unique line style. The same line style is used to denote the radiation pattern associated to each UT with the same line style. When θ = 0 degree (Fig. 4 (a)), the radiation patterns of the UTs at 90, 180, and 270 degrees form null to the direction of UT at 0 degree, and thus the
This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the WCNC 2010 proceedings.
(a) 2 UT × 2 AP
(b) 3 UT × 3 AP
(c) 4 UT × 4 AP
(d) 5 UT × 5 AP
(e) 6 UT × 6 AP
(f) 7 UT × 7 AP
Fig. 5: Scaling factor β as a function of UT rotation, AP antenna spacing, and the number of antennas. Black areas indicate where channel matrices are close to singular and zero-forcing precoding fails.
This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the WCNC 2010 proceedings.
•
•
•
•
•
When N is an even number, the channel matrix becomes singular at θ/φ = 0.5. This corresponds to the situation where the direction of each UT becomes right in the middle of the directions of two neighboring AP antennas. When N is an odd number, a particular AP antenna spacing always provides small β. Similar significant performance differences depending on the even and odd number of N have been reported recently in the area of estimating direction of arrival angles by using UCA [11]. A larger AP antenna spacing does not necessarily provide smaller values for β. In fact, optimal configuration can be obtained when AP antenna spacing is less than approx 0.5 wavelengths. For an even N , this limits the singularity to occur only when θ/φ = 0.5. For an odd N , this provides optimal BER performance at all UT rotations. As expected, the channel matrix becomes always singular when the AP antenna spacing becomes zero. As N increases, a larger AP antenna spacing (larger than 0 but smaller than approx 0.5 wavelengths) is required to avoid ill conditioned channel matrix. As the AP antenna spacing increases, the beamwidth decreases allowing in general better discrimination between UTs. However, the benefit is limited by the introduction of grating lobes as the spacing increases beyond λ/2.
Fig. 5 reveals a complex yet orderly pattern of the scaling factor β as a function of the spacing and the number of AP UCA antenna elements. The results indicate that, when the AP antenna spacing is fixed, the performance of the proposed system is not a monotonic function of the number of AP antenna elements. Fig. 6 shows the variation of β (90% of UT rotation has the value of β less than or equal to the specified value, here in called 90 percentile β) as a function of the
30 25
20 log β (dB)
ZF precoding can suppress the other user interference. When θ = 44 degree (Fig. 4 (b)), the AP UCA fails to form beams to the direction of UTs using the ZF precoding. At θ = 45 degree, the four radiation patterns become identical, which correspond to the situation when the channel matrix becomes singular. Thus it is anticipated that such ill-conditioned channel can result depending on the exact geometry of the AP UCA and the location of the UTs. Fig. 5 shows the variation of β as a function of UT rotation θ, the AP antenna spacing rφ, and the number of antennas N . The total transmitting power of the AP is set to (d/C)2 irrespective to the number of AP antennas. The values of β less than 0 dB represents the performance better than that of 1 UT × 1 AP. In order to easily identify the location of the degraded performance, black is assigned to the values of β equal or larger than 10 dB, while white is assigned to values of β equal or less than 0 dB. A smaller β, represented by the whiter areas in Fig. 5, indicates a better downlink performance while the black areas indicate where the proposed system fails. Very interesting patterns in the variation of β is observed. This is considered to be the result of complex geometric relationship between the parameters. Following observations can be made:
20 15 10 5 0
2
4 6 8 10 12 14 Number of AP antennas = Number of UTs
16
Fig. 6: 90 percentile β as a function of the number of AP UCA antenna elements with NAP = NUT .
number of AP antenna elements, when the AP antenna spacing is fixed to 0.5 wavelengths. Depending on the exact geometry, 0.5 wavelengths spacing may produce a favorable performance (e.g. 9 and 16) or unfavorable performance (e.g. 11 and 14). This complicates the choice of the number of AP UCA antenna elements and its spacing. In the following section, we propose a method to reduce the areas of degraded R-MIMO downlink performance. B. Number of AP Antennas > Number of UTs In order to reduce the area where the channel matrices are ill-conditioned, we propose the use of the number of AP UCA antenna elements larger than the number of UTs. Fig. 7 shows the variation of the scaling factor β when the number of AP antennas is fixed to 8 and when the number of UTs are changed from 5 to 3. We observe that when the number of UTs becomes less than or equal to half the number of AP antennas, many areas, including at the AP antenna spacing of 0.5 wavelength, result in smaller β. Fig. 8 shows the variation of 90 percentile β when NUT = floor(NAP /2). It can be seen that β is significantly reduced compared to the case NUT = NAP = N shown in Fig. 6. We note, however, the use of the half or smaller number of UTs compared to that of the AP antennas does not guarantee that β is small. Depending on the exact geometry, areas of large β still exist, albeit the probability of such a situation is significantly reduced. IV. C ONCLUSION This paper investigated the performance of ZF precoding based MU-MIMO downlink when the AP is equipped with a UCA in an LoS environment, and provided the design criteria. Proposed further research includes the analysis of different precoding methods with different antenna array configuration in LoS environments.
This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the WCNC 2010 proceedings.
6
20 log β (dB)
4 2 0 -2 -4 -6
(a) 5 UT × 8 AP
2
4
6 8 10 12 Number of AP antennas
14
16
Fig. 8: 90% β as a function of the number of AP UCA antenna elements with NAP = floor(NUT /2).
ACKNOWLEDGMENT The authors would like to thank anonymous reviewers for their valuable comments. R EFERENCES
(b) 4 UT × 8 AP
(c) 3 UT × 8 AP
Fig. 7: Scaling factor β as a function of UT rotation, AP antenna spacing, and the number of UTs. The number of AP antennas is 8.
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