Creating Desirable Interference by Optimized Sectorization in Cellular Systems I. Riedel, P. Rost, P. Marsch and G. Fettweis Vodafone Chair Mobile Communications Systems, Technische Universit¨at Dresden, D-01062 Dresden, Germany Email:{ines.riedel, rost, marsch, fettweis}@ifn.et.tu-dresden.de

Abstract—Most mobile communication systems deployed use 3-fold sectorization with directed antennas to avoid inter-sector interference and to spatially reuse available radio resources. However, innovations in next generation networks such as multipleantenna systems and coordinated multi-point techniques allow mitigation or even exploitation of interference. In this paper, we discuss how sectorization and antenna directivity can be adjusted to intentionally avoid or create interference in order to maximize the throughput of non-cooperative and cooperative transmission concepts. A key result is: the introduction of cooperative transmission renders higher sectorization using a larger number of inexpensive antennas with low directivity per site attractive.

I. I NTRODUCTION A. Motivation Second generation mobile communication networks typically use three-fold sectorization, i.e. three base stations (BSs) are located at the same site and serve three different sectors. In order to avoid inter-cell interference, the sectors typically use orthogonal radio resources. This implies inefficient spectrum usage and is being addressed in third and fourth generation networks by aiming at significantly improved frequency reuse factors. Such systems, however, are strongly limited by intercell interference [1], and hence the main antenna design paradigm is to use directed antennas and downtilt in order to minimize interference. This design approach, however, needs to be revisited in the context of multiple-antenna systems and cooperative multipoint (CoMP) techniques [2]. Both concepts are likely to be used in next generation systems in order to exploit interference, rather than viewing it as being detrimental. In this context, the extent of sectorization, i.e. the choice of number of antennas per site and their directivity are degrees of freedom that can be used to avoid or create desirable interference that is best suited for a chosen transmission and cooperation concept. In general, high directivity antennas are not only able to reduce inter-sector interference, but also decrease the signal-tointerference-and-noise ratio (SINR) experienced at the sector borders. On the other hand, low directivity antennas increase both diversity and fairness in the system. In a system with low user density (and therefore lower user diversity), a situation might arise where a directed antenna does not serve any users at all, while other antennas at the same site are overloaded. This situation is less likely with low directivity antennas, where the area of guaranteed QoS is increased.

B. Interference Shaping In this paper, we consider a simplified setup with just one site, and are interested in the optimization of the number of single-antenna BSs N and the antenna directivity represented by the half-power beamwidth θ3 dB . Note that the usage of the term BS here reflects the fact that the entire spectrum is reused by each antenna, hence we have N -fold sectorization. For practical implementation, it might be more cost-effective to let one physical device serve multiple sectors, especially in the context of cooperative transmission, but this is an implementation issue and is beyond the scope of this work. We focus on the downlink and consider the case where each sector performs individual signal processing (such that the transmission to the assigned user terminal (UT) is subject to interference from all other sectors), as well as the case where all N sectors perform joint transmission to all N UTs served on the same resource. As the BSs are collocated, we assume the data exchange between individual BSs to be unconstrained. Our approach differs from existing work [3]– [6], as we not only consider the maximum achievable rate for a given channel, but also shape this channel and its parameters. C. Outline The underlying system and channel model used in our analysis is introduced in Section II. Non-cooperative transmission, Wiener filtering, and broadcast channel (BC) capacity are explained in Section III. We apply these transmission schemes to our system model and analyze their system throughput in Section IV. Finally, the paper is concluded in Section V. II. S YSTEM M ODEL A. Scenario We consider downlink transmission from a single site equipped with N single-antenna BSs to an arbitrary number of single-antenna UTs U ≥ N . We further assume a fully loaded system in which scheduling is performed such that each BS is connected to exactly one UT and the complete spectrum is reused by each BS. Henceforth, we focus on transmission taking place on one resource in time and frequency, where the aforementioned assumptions allow us to observe the transmission from N BSs to N UTs, regardless of the overall number of UTs. Clearly, for a large N the assumption of at least one UT per BS becomes unrealistic. However, this assumption strongly facilitates our analysis, and will be discussed in conjunction with our results.

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Figure 1: Example of 6-fold sectorization with two different directivities and possible UT locations Motivated by typical macro-cellular applications, we arrange the BSs in a circular array where BS n ∈ [1, N ] points in ◦ ◦ the direction θBS,n = n−1 N ·360 (boresight). Thus, the 360 are divided into N sectors (cf. Fig. 1). To ensure fair comparison of different site setups, we assume a sum power constraint such that the total transmit power P stays constant and BS n is assigned the fraction Pn with N Pn . (1) P = n=1

B. Antennas We assume independence of the orthogonal azimuthal (horizontal) and elevation (vertical) radiation patterns of the applied antennas. The azimuthal pattern of the BSs in the linear scale is given by   2 6 ln 10 θu,n aθ = exp − (2) + Abw , 5 θ32dB where θu,n = mods (θUT,u −θBS,n ) denotes the angle between the orientation θUT,u of UT u and the boresight θBS,n of BS n in degrees. Its value is bounded to [−180◦, 180◦ ) by the symmetric modulo operation mods(α) = α−360◦ (α+180◦ )/360◦ . The horizontal half-power beamwidth (HPBW) of the BS antenna is given by θ3 dB in degrees. Thus, the exponential term corresponds to the log-scale definition in [7]. However, backward attenuation is considered by an additive term Abw . Thus, the transition from backward attenuation to the main lobe is sufficiently smooth. In order to isolate the impact of the azimuthal radiation pattern, we assume that the UTs are located on a circle around the site. Hence, the path loss incurred by wave propagation will be identical for all users and the BS elevation pattern can be assumed as aφ = 1, which corresponds to an omnidirectional elevation pattern. Furthermore, each UT is equipped with an omnidirectional antenna with an antenna gain of 0 dBi. The total radiated power of an antenna can, in general, be obtained as [8]  360◦  180◦ aθ (θ)aφ (φ) sin φ dφ dθ. (3) PTx = 0◦

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Applying (2), this yields the BS antenna gain 720◦ PTx (aθ =1) = G= PTx (aθ) 720◦ ·Abw +2.1326·θ3dB ·erf

299.2065◦ θ3 dB

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Figure 2: Channel model where omnidirectional antennas have a gain of 0 dBi and the gain increases with decreasing HPBWs. Thus, it ensures that the radiated power per antenna stays constant for all θ3 dB . C. Channel model The path weight wu,n from BS n to UT u is given by  wu,n = G(θ3 dB ) · L · aθ (θu,n , θ3 dB ), (5) where the path loss L is independent of u and n due to the chosen scenario. Thus, the instantaneous channel realization can be obtained by hu,n = wu,n · zu,n ,

(6)

where the diversity of the channel is determined by the complex Gaussian random variable zu,n ∼ CN (0, 1) with unit-variance and zero-mean. Our approach differs from existing work [3]–[6] as we do not consider the maximum achievable rate for a given channel but shape the interference by adjusting the system size (reflecting the number of BSs) and the coupling (reflecting the antenna directivity) instead. In the no cooperation case, this means shaping the properties of an Interference Channel (IC) [9], [10] and in the full cooperation case, this means shaping the properties of a broadcast channel [11]–[13]. For reasons of complexity, no interference subtraction is performed at the user terminals. III. T RANSMISSION S CHEMES We assume that transmission takes place over a frequencyflat, block-static channel with Gaussian signaling and perfect coding with long codewords. The transmission equation reads as y = HFx + n, (7) where x and y denote the N ×1 transmit and receive vectors, respectively. The N × N channel matrix H is composed of the elements hu,n (cf. Fig. 2) and is predistorted by the N × N matrix F. The additive white Gaussian noise with n. coE nn† = σ 2 IN is denoted by the N × 1 vector  The  P IN . variance of the transmit signal is defined as E xx† = N This paper analyzes the performance of three different transmission schemes, which reflect different degrees of intra-site communication and cooperation. The first scheme represents the conventional approach, where all BSs operate independently. In this case, signals from all neighboring BSs interfere

and the resulting channel corresponds to the IC. Hence, the sum rate R is given by 2 N |hu,u | . (8) R= log2 1 +

2 N σ2 u=1 |h | + u,n n=u P

circle segment (cf. Fig. 1) ⎧ ⎪ Boresight ⎨θBS,u ◦ θMS,u= θBS,u+ 180 Sector border N ⎪ ⎩ 180◦ 180◦ θ ∼ U(θBS,u− N , θBS,u+ N ) Uniform.

Now, let the BSs be able to exchange channel state information (CSI) and user data, this is supposed to be realizable as all BSs are collocated and use the same hardware infrastructure. This allows for intentional introduction of interference and exploitation of the same using methods introduced in the context of the broadcast channel [11], [13]. A good trade-off between performance and complexity is a linear predistortion using Wiener filtering (WF):  −1 N σ2 † † F = β · F = β · H HH + IN (9a) P

N β= (9b) † FF

While UTs in the boresight correspond to the best case scenario (they take advantage of the full antenna gain), UTs at the sector border represent the worst case scenario. Our parameters for comparison are the average and outage sum rates of the considered transmission schemes. The following results assume no constraints on N and θ3 dB although both are certainly limited by practical constraints such as space restrictions and deployment costs. Due to user density and scheduling, our assumption that each BS serves at least one user might not hold for an increasing N . Furthermore, not every antenna pattern that can be modeled theoretically is technologically realizable. However, the following analysis provides a qualitative comparison of the previously introduced techniques and points out the potential of new sectorization approaches in 4G networks.

The sum rate for WF can be given as 2 N |vu,u | log2 1 +

R= 2 u=1 n=u |vu,n | +

, N σ2

(10)

P

where vu,n denotes the elements of the matrix V = HF. In addition, we also consider the sum rate capacity which uses the dirty paper coding (DPC) concept [14] and corresponds to the sum rate capacity of a dual multiple access channel with the sum power constraint P [11], [15]: sum rate sum rate sum rate (P, H) = CDPC (P, H) = Cunion (P, H) CBC

U P † I = max log + h P h 2 2 N u u u , (11)

U u=1 N σn P ≥0; P ≤P u

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where hu =[hu,1 , hu,2 , · · · , hu,N ] denotes the channel coefficients from all BSs to UT u. As the complexity is infeasible for practical systems, this capacity serves only as an upper bound. IV. R ESULTS A. Simulation Setup The total transmit power P of a site and the noise power σ 2 at the UTs per subcarrier are chosen to be 47.78 dBm (60 W) and −125.24 dBm (thermal noise, 23◦ Celsius, 15 kHz subcarrier spacing, 7 dB UT noise figure), respectively. Considering a transmit power of 20 dBm per subcarrier (600 subcarriers), the path loss L is chosen as -135 dB so that the SINR for conventional site setups yields the required 5 to 10 dB to enable successful decoding. The backward attenuation of the antennas is chosen to be Abw =-20 dB. To analyze the impact of different site setups, three different user locations are investigated. Users are either located in the boresight of the corresponding BS antenna, at the sector border, or are uniformly distributed over the corresponding

(12)

B. Conventional approach - No intra-site cooperation Fig. 3a depicts the average sum rates as a function of N for the conventional approach of ignoring intra-site interference. If only one BS is deployed, intuitively this antenna should be omnidirectional to ensure coverage. An increase in the number of omnidirectional BSs leads to greater interference and a decreasing signal-to-noise ratio (SNR) due to the sum power constraint. In general, an increase in the extent of sectorization enhances the sum rate to a maximum value depending on the HPBW. The higher the directivity, the higher is the antenna gain and therefore a higher maximum sum rate can be achieved. However, for high directivity antennas the maximum value is reached at higher N as more sectors are needed to provide sufficient coverage. A further increase in N would only increase interference and thereby, deteriorate performance. While users in the boresight direction and uniformly distributed users benefit from narrow-beam antennas, users at the sector border suffer from decreased coverage. The picture changes when we look at the 10% outage sum rate, which is of particular interest in mobile communication systems as it is a relevant indicator of system fairness and thereby user satisfaction (cf. Fig. 3b). In the practically relevant range N ≤ 6, the outage sum rate benefits from wider beamwidths. Thus, users with bad conditions, especially those near the sector border, take advantage of the positive effect of cross-coupling in the IC, i.e. improved coverage. Even in the case of non-cooperative BSs, these results recommend application of antennas with a certain overlap. Thus, it is possible to enhance system throughput by choosing the deployment appropriately. Just by using 6 BSs with θ3 dB = 30◦ instead of the commonly used 3 BSs with θ3 dB = 60◦ , the average sum rate can be doubled and the outage sum rate is more than doubled.

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Figure 3: Average (left) and outage (right) sum rates for no cooperation (top) and intra-site cooperation with Wiener filtering (middle) and sum rate capacity of broadcast channel (bottom) under Rayleigh fading as a function of the extent of the sectorization N , the HPBW θ3 dB and the user location.

C. Intra-site Cooperation The average sum rate for joint Wiener filtering depending on the extent of sectorization is depicted in Fig. 3c. As expected, cooperative WF outperforms the non-cooperative case (for an increasing N ) due to the multiplexing gain. In general, the sum rate for WF is not as sensitive to directivity as in the case of no cooperation. However, for N ≤ 6 the HPBW chosen should be sufficiently large to ensure coverage. If N is increased further, narrow-beam antennas should be preferred (increased SNR with smaller θ3 dB ). Like in the non-cooperative case, users in boresight direction benefit from narrow beams while sector border users benefit from wide beams. The important 10% outage sum rates (cf. Fig. 3d) reveal that up to N = 7 omnidirectional antennas would be the best choice. Thus, users with high propagation path loss can take advantage of increased diversity. For N > 7, narrow-beam antennas perform slightly better than wide-beam antennas due to higher antenna gains. However, the additional diversity of antennas with wider beamwidths can be exploited to compensate for the lower gains of these antennas. The theoretical performance capability (if all sectors of a site cooperate and nonlinear precoding is applied) can be seen in Fig. 3e and 3f. The possible gain over WF is increased with growing N due to the multiplexing gain offered. Similarly to WF for N ≤ 7, the HPBW should be chosen wide enough to ensure coverage. For higher extents of sectorization, the average performance can be marginally enhanced by small HPBWs due to their higher antenna gain. However, looking at the 10% outage sum rate, users at the sector border are especially disadvantaged by such a choice. To enable exploitation of useful interference in the BC, omnidirectional antennas should be applied. However, the sum rate capacity of the broadcast channel cannot be achieved in practice. Furthermore, the computational effort required for nonlinear precoding techniques is tremendous and the performance degrades depending on channel estimation errors. Thus, the WF performance allows a good estimation of the benefits possible. The additional effort of intra-site cooperation is worth it only if enough desired interference, i.e. enough overlapping sectors, exists. If 6 cooperating sectors with θ3 dB = 60◦ utilizing WF are used, the average sum rate can be doubled and the outage sum rate almost tripled in comparison to commonly applied non-cooperative 3 BSs with 60◦ antennas. Further increasing the desired interference by applying 10 sectors with θ3 dB = 30◦ , the average sum rate can be more than tripled and the outage sum rate can be increased by over four times. However, these gains are only accessible with more hardware, availability of CSI feedback and rather complex signal processing. V. C ONCLUSIONS This paper analyzes the throughput of sectorized cellular systems considering non-cooperative as well as cooperative transmission schemes. To observe the behavior of sectorized sites with directed antennas we focused on a single-site setup.

If the sectors of a site do not cooperate, intuitively, the best choice would be an infinite number of sectors with infinitely narrow beams. Since such antennas cannot be produced, performance saturates and N should be chosen approximately as 200 θ3 dB . While high directivity antennas improve the average sum rate, antennas with slightly wider beams enhance the outage sum rate due to improved coverage (especially at the sector borders). If BSs cooperate, the sum rate increases linearly with the extent of sectorization. Although the outage sum rate for DPC is maximized by omnidirectional antennas, the outage performance of the implementable WF benefits from narrowbeam antennas for N > 7. For N ≤ 7, wide-beam antennas with better coverage improve the average as well as the outage performance. In our future work, we will consider randomized user locations and the effects of path loss, shadowing, vertical elevation pattern and downtilt. The cooperation schemes will be extended to range from partial intra-site cooperation to multisite cooperation. Additionally, we will address the uplink. R EFERENCES [1] P. Gupta and P. Kumar, “The Capacity of Wireless Networks,” IEEE Trans. Inf. Theory, vol. 46, no. 2, pp. 388–404, 2000. [2] S. Shamai and B. Zaidel, “Enhancing the Cellular Downlink Capacity via Co-Processing at the Transmitting End,” in Proc. of the IEEE Semiann. Vehicular Technology Conf. (VTC’01 Spring), vol. 3, Rhodes, Greece, May 2001, pp. 1745–1749. [3] M. A. Nasr, H. A. Shaban, and W. Tranter, “Outage Probability and Percentage of Cell Area for OFDMA Cellular Systems with Sectoring,” in Fifth Annu. Conf. on Communication Networks and Services Research (CNSR’07), 2007. [4] F. Athley, “On Base Station Antenna Beamwidth for Sectorized WCDMA Systems,” in Proc. of the IEEE Semiann. Vehicular Technology Conf. (VTC’06 Fall), 2006. [5] J. Niemela and J. Lempiainen, “Impact of the Base Station Antenna Beamwidth on Capacity in WCDMA Cellular Networks,” in Proc. of the IEEE Semiann. Vehicular Technology Conf. (VTC’03 Spring), 2003. [6] I. Riedel, R. Habendorf, E. Zimmermann, and G. Fettweis, “Multiuser Transmission in Cellular Systems With Different Sector Configurations,” in Proc. of the IEEE Semiann. Vehicular Technology Conf. (VTC’08 Fall), Calgary, Canada, 2008. [7] 3rd Generation Partnership Project; Technical Specification Group Radio Access Network, “Spatial Channel Model for Multiple Input Multiple Output (MIMO) Simulations (Release 9),” 3rd Generation Partnership Project (3GPP), Tech. Rep., December 2009. [8] C. A. Balanis, Antenna Theory Analysis and Design. John Wiley & Sons, Inc., 2005. [9] R. Ahlswede, “The Capacity Region of a Channel with two Senders and two Receivers,” The Ann. of Probability, vol. 2, no. 5, pp. 805–814, 1974. [10] T. Han and K. Kobayashi, “A new Achievable Rate Region for the Interference Channel,” IEEE Trans. Inf. Theory, vol. 27, no. 1, pp. 49– 60, Jan. 1981. [11] S. Vishwanath, N. Jindal, and A. Goldsmith, “Duality, Achievable Rates, and Sum-Rate Capacity of Gaussian MIMO Broadcast Channels,” IEEE Trans. Inf. Theory, vol. 49, no. 10, pp. 2658–2668, Oct. 2003. [12] G. Caire and S. Shamai, “On the Achievable Throughput of a Multiantenna Gaussian Broadcast Channel,” IEEE Trans. Inf. Theory, vol. 49, no. 7, pp. 802–811, Jun. 2003. [13] H. Weingarten, Y. Steinberg, and S. Shamai, “The Capacity Region of the Gaussian MIMO Broadcast Channel,” in IEEE Int. Symp. Inform. Theory, Chicago (IL), USA, June 2004, p. 174. [14] M. H. M. Costa, “Writing on Dirty Paper,” IEEE Trans. Inf. Theory, vol. 29, May 1983. [15] N. Jindal, S. Vishwanath, and A. Goldsmith, “On the Duality of Gaussian Multiple-Access and Broadcast Channels,” IEEE Trans. Inf. Theory, vol. 50, no. 5, pp. 768–783, 2004.