Evolution of Base Stations in Cellular Networks: Denser Deployment versus Coordination Yifan Liang, Andrea Goldsmith, Gerard Foschini, Reinaldo Valenzuela, and Dmitry Chizhik Department of Electrical Engineering, Stanford University, Stanford, CA 9 Bell Laboratories, Alcatel-Lucent, Holmdel, NJ Email: {yfl, andrea}@wsl.stanford.edu, {gjf, rav, chizhik}@alcatel-lucent.com Abstract It has been demonstrated that base station cooperation can reduce co-channel interference (CCI) and increase cellular system capacity. In this work we consider another approach by dividing the system into microcells through denser base station deployment. We adopt the criterion to maximize the minimum spectral efficiency of served users with a certain user outage constraint. In a two-dimensional hexagon array with homogeneous microcell structure, under the proposed propagation model denser base station deployment outperforms suboptimal cooperation schemes (zero-forcing) when the density increases beyond base stations per km, the exact value depending on the rules of outage user selection. However, closeto-optimal cooperation schemes (zero-forcing with dirty-papercoding) are always superior to denser deployment. Performance of a hierarchial cellular structure mixed with both macrocells and microcells is also evaluated. I. INTRODUCTION Channel reuse is an efficient way to exploit scarce radio spectrum resource in cellular networks. However, the resulting co-channel interference (CCI) usually becomes the bottleneck in system design. Network MIMO is an approach to combat CCI, where base stations cooperate as geographically dispersed multiple antennas. Wyner s early work [] addresses the uplink of linear and hexagonal cellular arrays with periodically positioned users whose communications are impaired with an identical interference level from the communication of neighboring cells. The user-base link follows an AWGN channel model. This model was later extended to include Rayleigh flat fading in []. Base station cooperation with a sum-rate objective was studied in [] for the downlink channel. The simplicity of the models considered in [] [] aimed at obtaining some analytical insight. Cellular systems with random user populations under idealized but much more realistic channel models were considered in [], [] and will also be used in this work. As in [], [], fair treatment of served users and an element of user outage is also included here. We also draw on cellular communication results in []. Dramatic declines in hardware cost facilitates another approach for CCI reduction: to upgrade the network infrastructure with a denser deployment of base stations that cover smaller cells. We assume the number of users in a given geographical area remains unchanged, so these smaller cells lead to a larger system capacity. With more base stations, This work was supported by grants from LG Electronics, Hitachi, and the Korea Electronics Technology Institute (KETI). every user intending to connect to the network will most likely find an idle access point in the vicinity base stations would ultimately be as dense as lampposts. As the coverage area of each cell shrinks, the transmit power from base stations can be scaled down. Consequently, multiple subscribers, even if simultaneously active, cause less severe CCI to each other. We consider two classes of networks, a homogeneous system where all base stations have the same antenna height and transmit power, and a hierarchial system where the microcell overlay is on top of an existing macrocell underlay. Network MIMO can be considered as a software approach to increase system capacity, which exploits advanced signal processing techniques and requires significantly more exchange of channel information among base stations. On the other hand, denser base station deployment is a hardware approach that fundamentally upgrades network infrastructure. In this paper we compare the two different evolving directions. We assume an idealized two-dimensional hexagon cellular array. Our optimization criterion is to maximize the minimum spectral efficiency of served users under a certain user outage constraint. Our results demonstrate the merits of denser base station deployment and determine the minimum base station density required to match the performance of network MIMO. The rest of the paper is organized as follows. We introduce the system model in Section II. Denser base station deployment is analyzed in Section III. In Section IV we consider base station cooperation and compare the performance of both techniques. The hierarchial cellular structure is studied in Section V and conclusions are given in Section VI. A. Topology II. SYSTEM MODEL We consider a two-dimensional hexagon cellular array, as shown in Figure. Assume the cell radius R = km. To avoid boundary effects, cells are arranged to tile a torus []. Initially the network has cells along each dimension, which is referred to as the baseline network. We focus on the downlink channel. In our analysis, regardless of base station density, we keep the number of users and the rectangular area fixed. When we increase the number of base stations in the network by a factor of N, the base station density α increases to α(n) = number of base stations coverage area N = R R = N 9R.
We assume the factor N, N, is a perfect square, so the number of base stations along each dimension increases to N in the densely-deployed network. (j) 9 y x 9 (i) Fig.. Two-dimensional hexagon cellular array: baseline network. Shadowed area are out of the rectangle but reappear on the other side. B. Propagation Models We assume the maximum transmit power from any base station is P t = W in the baseline network. The thermal noise power is N =. W []. As cell coverage area reduces, mobile users are more likely to be close to the base station. It is well-known that propagation characteristics of wireless channels are usually different for short range and long range, so we consider the following two different models: Short-Range Model (SR). This model is applicable when a user is located in a close neighborhood of its corresponding base station. In this case we assume P r = P t (λ/πd) Gg, where P t and P r are transmit and receive power, respectively, λ is the carrier wavelength (. m at GHz), d is the distance between a mobile and a base station, G, the constant antenna gain, is taken to be. db, and g is exponentially distributed with mean, which models Rayleigh fading. Long-Range Model (Hata) []. This model applies to users faraway from the corresponding base station. In this case we also include the shadowing effect on receive power, given by log (P r /P t ) = L + G db + ψ + log(g), () where ψ [db] is zero-mean Gauss-distributed with standard deviation db, which characterizes the shadowing effect. L [db] is the path loss component given from Hata s model []. The propagation characteristics change at two distances. The cutoff distance d c is assumed to be twice the distance between adjacent base stations in the baseline network. It does not change with density. Considering the effect of the curvature of the earth adjusted for scattering on reasonably flat terrain, the channel strength beyond d c is set to be []. Each base station is also associated with a transition distance d t, randomly chosen between and meters, where the propagation changes from short- to long-range models. This models the location of an obstacle that blocks a user s LOS. For the fading component in the propagation models, we randomly sample a fading realization for the network and keep it fixed throughout the transmission. Here, our idealized channel model does not include time variation of fades. In the densely-deployed network each base station only covers a small area so the transmit power can be scaled down. The criterion is to maintain a specified received power at cell vertices, assuming no random shadowing and fading. We first consider a homogeneous microcell system where all transmit antennas have the same height h t = m. It can be shown that the transmit power scaling rule is P t (N) = P t N γ/, where γ =.9. log (h t ) []. In cellular networks with intra-cell orthogonal channel access, each cell is assigned multiple subchannels and can serve multiple users. Our focus are these users from different cells that occupy the same subchannel and interfere with each other. We assume the network always serves the same number of users regardless of base station density. One by one, each user is randomly placed into the network and assigned to the base station with the strongest propagation path. If the base station is already serving another user, the current user is referred to another orthogonal subchannel and not included in our analysis. These steps are repeated until users are placed into the network. III. DENSER BASE STATION DEPLOYMENT A. Open-Loop: Full Power Transmission In the downlink of a cellular system, mobile users generally have to estimate the channel strength to facilitate decoding. However, for simplified design base stations may not adapt the transmission strategy to the channel state information (CSI) and instead transmit at full power and at a constant rate, namely an open-loop scenario. For each user, we compute the received SINR h ii β(i) = j i h ij + N, () P t (N) where h ij is the channel gain from base station j to user i under the proposed propagation model. The corresponding spectral efficiency η(i) = log [+β(i)]. In Fig. we plot the empirical cumulative distribution function (cdf) F(η). The cdf curve shifts to the right as the base station density increases, since more users have relatively high spectral efficiencies. The benefit of denser base station deployment is a result of the shift from an interference-limited regime to a noiselimited regime. To serve the same number of users with an increasing number of base stations, some base stations will be idle and create a random guard region that tends to spatially separate the active base stations. In Fig., we plot the minimum achievable spectral efficiency with % users allowed in outage for different base density α. If either the interference or noise term in the denominator of () is set to, we obtain the signal-to-noise ratio (SNR) or the signalto-interference ratio (SIR), respectively. We observe that for
α km the spectral efficiency corresponding to combined SINR coincides well with that corresponding to SIR. However when α km, noise becomes the dominant factor. Empirical cdf.9...... α() =.. α() =. α(9) =.. α() =. α() = 9. Fig.. Fig.. Empirical cdf F(η) for open-loop scheme. Combined Interference Only Noise Only Base Station Density α (km ) Interference suppression with increasing base station density. B. Closed-loop: Power Control In real systems with feedback paths between mobiles and base stations, i.e., a closed-loop scenario, we can shut down those base stations serving the outage users to eliminate unnecessary interference. Furthermore, for those non-outage users with strong channels, we can reduce the transmit power, hence their interference to others, as long as the target rate can still be supported. Recall that we want to maximize the minimum served rate subject to a certain user outage constraint. Two schemes for outage user selection were proposed in [], []. The one-shot closed-loop scheme directly eliminates users in the lowest th percentile of SINR, assuming full power transmission from each base station. The iterative closed-loop scheme starts from a system with all users active, and the maximum achievable common rate is determined subject to the transmit power constraint. The user that causes the transmit power constraint to be active is eliminated. We repeat the process and eliminate one user at a time until the outage constraint is satisfied. To determine the transmit power allocation that can support a given target common rate, a brute-force iterative search procedure was applied in []. Here we propose another scheme based on the Perron-Frobenius Theorem and binary search, which is computationally more efficient. It is well-known that for an irreducible matrix F with nonnegative entries, the eigenvalue with the largest magnitude, defined as the Perron- Frobenius eigenvalue ρ F, is positive []. Moreover we have the following result from []: Lemma III. If ρ F <, then P = (I F) u is the Pareto optimal solution to the component-wise inequality (I F)P u with P, () i.e., if P is any other solution to (), then P P componentwise. Here I is the identity matrix and u is any given vector with nonnegative components. We start with a system of K users. Denote the channel power gain matrix as M K K, where the element m ij is the channel power gain from base station j to user i. Note that idle base stations are shut down and not included in M. We separate the channel gain matrix into M = D + A, where D contains the diagonal elements and A contains the offdiagonal elements. To support an SINR β for each user, we need m ii P i β (N + ) j i m ijp j or, in matrix form, (I βd A)P βn D with P P t (N), where P = [P,, P K ] T is the power vector and is the vector with all ones. Note that we also have the maximum transmit power constraint P t (N) for each base station. From Lemma III. we conclude that β < ρ F (D A). Through a simple binary search we can easily identify the maximum β such that the Pareto optimal solution βn (I βd A) D satisfies the transmit power constraint P t (N). In Fig. we plot various curves to compare the performance of open- and closed-loop schemes. It is interesting to see that the one-shot closed-loop scheme generally achieves a spectral efficiency about bps/hz higher than the open loop scheme. There is a further gain of about bps/hz if we exploit the iterative closed-loop scheme. For α km, the iterative scheme actually approaches the noise-only upper bound. Two other curves, namely network MIMO with zeroforcing (ZF) and zero-forcing dirty-paper-coding (ZF-DPC), are also plotted in Fig.. These curves will be explained in the next section. IV. NETWORK MIMO: BASE STATION COOPERATION With full base station cooperation, the downlink in a cellular system becomes a MIMO broadcast channel, of which the capacity region is obtained through dirty paper coding (DPC) [9]. Many suboptimal but more practical schemes have also been explored for this scenario [], [] In the following, we briefly outline two schemes, ZF and ZF-DPC.
Fig.. Open loop Closed loop, one shot Closed loop, iterative Noise only upper bound Network MIMO ZF Network MIMO ZFDPC Base Station Density α (km ) Comparison of open- and closed-loop transmission. A. Base Station Cooperation: ZF We consider the baseline network with K = base stations and users. Denote H K K as the channel gain matrix. Note that the propagation model in Section II-B actually gives the channel power gain and the corresponding power gain matrix is denoted as M in Section III-B. Here we take the square root and convert it to channel magnitude gain. There is also a random phase factor from Rayleigh fading, so the overall channel gain from base station j to mobile i is h ij = m ij e θ ij, where m ij is the power gain and θ ij are i.i.d. uniformly distributed on [, π). The ith row h T i of H is the gain vector from all base stations to mobile i. To implement a ZF scheme with q =. user outage, we first eliminate qk users of the smallest channel gain norms h i and shut down their corresponding base stations. The remaining channel gain matrix H is of size ( q)k ( q)k. The transmitted signals from base stations are X = [ ] w w ( q)k [x x ( q)k ] T = Wx, where x i N(, P i ) and w i is the pre-coding weight vector. The ZF scheme requires HW = I or equivalently h T i w j = for any i j, which implies that users do not interfere with each other. The received signal is y = HX + n = HWx + n = x + n, where n is the noise vector with i.i.d. components of mean and variance N. The objective is to maximize the minimum received SINR P i /N subject to the per-base power constraint V p P t where v ji = w ji, p = [P P ( q)k ] T and P t is the maximum transmit power from each base station. The solution is seen to be P i = P ZF for all i where P ZF = max j i v. ji B. Base Station Cooperation: ZF-DPC In ZF-DPC, we first assign an order to the users, for example {,,, K}. Next the weight vector w j are required to be orthogonal to h i for i < j, which ensures user j causes no P t interference to i. Furthermore, we encode users information through DPC, which has the desirable property that user j does not see i as an interferer for j > i. Overall the interference among users is perfectly removed. For the sake of completeness, in the following we outline the heuristic approach for outage user selection proposed in []. In ZF-DPC, we first eliminate qk users of the smallest channel gain norms h i and shut down the corresponding base stations. The resulting channel gain matrix is denoted as H with rows h T i. We then assign an order to the remaining ( q)k users. Note that for user j, the weight vector w j is orthogonal to channel vectors {h,, h j }, so the effective channel ĥj of user j is h j projected away from the subspace spanned by {h,, h j }. The effective channel ĥj generally shrinks with expanding subspaces. In view of fairness, users with small effective channel norms are placed in front of the encoding list. We adopt the following rule to determine a heuristic encoding order: without loss of generality assuming users ( q)k + to K are declared in outage, ) Initialize k =, candidate pool S = {,, ( q)k}; ) Project h i, i S away from the subspace spanned by [h π(),, h π(k ) ] to get ĥi. Choose among ĥi s the one with the smallest norm to be user π(k); ) k k +, S S {π(k)}; ) End if S empty, otherwise go to Step. The ZF-DPC scheme encodes information of each user in the order π() to π[( q)k]. For simplicity in the following we drop the notation π of permutation. This is not to be confused with the original user indices,, ( q)k. After outage user selection and non-outage user reordering, we perform a QR decomposition H = LQ such that L is lower triangular and QQ = I. We take the pre-coding matrix to be W = Q, so the received signal is y = HX + n = LQQ x + n = Lx + n. Our objective is to maximize the minimum received SINR L ii P i /N subject to a per-base power constraint which is still in the form of V p P t with V and W properly defined. The solution is shown to be P i = P ZFDPC / L ii for P t all i where P ZFDPC = max j i w ji/l ii. C. Performance Comparison The performance of network MIMO applied to the baseline network is also plotted in Fig.. To match the performance of ZF, we have to increase base station density α beyond km, the exact value depending on whether we exploit an open- or closed-loop scheme, and also on the user elimination procedure. ZF-DPC, on the other hand, is a close-to-optimal cooperation scheme but more complicated to implement. If the complexity of ZF-DPC is affordable, it is preferred because it even outperforms the noise-only upper bound, which implies that the benefit of ZF-DPC is not only interference suppression but also coherent power addition from all base stations.
V. HIERARCHIAL CELLULAR STRUCTURE The network in Sec. II has a homogeneous structure, i.e all base stations have the same antenna height and transmit power. This best models a system with transmit antennas mounted in similar geographical environments. However, a hierarchial cellular structure, which consists of both macrocells and microcells, is perhaps a more realistic scenario. We expect that with G networks, much like we are starting to see with G, the macrocells are deployed first and the microcells are deployed next for indoor coverage and hotspots handling. In the following we consider this hierarchial cellular structure. The macro overlay consists of base stations, which retain their antenna height ( m) and transmit power ( W). Microcells are added to the system similar to the homogeneous network, but their transmit antenna are mounted at a lower height h µ t = 9 m []. The maximum transmit power from microcell base stations will be scaled down to maintain the received power at cell vertices, assuming no random shadowing and fading. Each base station is associated with a random transition distance ( m) as the watershed of short- and long-range. For microcells this models the location of the wall of the building where the antenna resides. Moreover, when a mobile user is within the short-range of a microcell, we add a db additional path loss (one wall penetration) between the mobile and all other base stations. In Fig. we plot the achievable spectral efficiency with % user outage for both open- and closed-loop schemes. Performance of cooperation approaches (ZF and ZF-DPC) are also plotted as benchmarks. The comparison of Fig. and illustrates that the hierarchial cellular structure performs worse than the homogeneous microcell structure: the openloop scheme is always inferior to ZF; the base station density needs to increase beyond km and km, respectively, for one-shot and iterative closed-scheme to match the performance of ZF. Furthermore, we never enter the noise limited regime in the hierarchial cellular network. The limited benefit of the hierarchial cellular structure is a result of the user associate rule. Table I shows that many macrocell base stations are still active even if we deploy more microcells. The channel between a mobile user and a macrocell antenna may be weak, but the high transmit power from macrocell base stations compensates the link loss so the mobile user is again served by the macrocell base. As a result, the benefit of microcells is not well exploited and many active macrocell base stations cause strong interference to each other. VI. CONCLUSIONS We have studied how denser base station deployment can reduce CCI based on a two-dimensional hexagon cellular array. A propagation model is proposed to characterize the difference between short-range and long-range users. Our performance criterion is to maximize the minimum achievable spectral efficiency subject to a certain user outage constraint. The benefit of denser deployment is compared with that of base station cooperation. For a homogeneous network, it is observed that denser deployment outperforms suboptimal cooperation schemes (ZF) when the density increases beyond base stations per km, the exact value depending on the rules of outage user selection, while close-to-optimal cooperation schemes (ZF-DPC) are always superior to denser deployment. A hierarchial cellular structure with microcell overlay on top of an existing macrocell underlay is also considered. For this system performance gain is limited because a relatively large number of macrocell base stations are active and cause strong interference when transmitting at high power. Fig.. Open loop Closed loop, one shot Closed loop, iterative Noise only upper bound Network MIMO ZF Network MIMO ZFDPC Base Station Density α (km ) Comparison of hierarchial cellular structure and cooperative network TABLE I NUMBER OF ACTIVE MACRO BASES FOR VARIOUS NETWORKS N 9 9 Active Macro 9 REFERENCES [] A. Wyner. Shannon-theoretical approach to a Gaussian cellular multipleaccess channel. IEEE Trans. Inform. Theory, :, Nov. 99. [] O. Somekh and S. Shamai(Shitz). Shannon-theoretic approach to Gaussian cellular multi-access channel with fading. IEEE Trans. Inform. Theory, :, July. [] O. Somekh, B. Zaidel, and S. Shamai (Shitz). Sum rate characterization of joint multiple cell-site processing. In Proc. Canadian Workshop Inform. Theory, Montreal Quebec, June. [] G. Foschini, H. Huang, K. Karakayali, R. Valenzuela, and S. Venkatesan. The value of coherent base station coordination. In Proc. Conf. on Inform. Sciences and Systems, Baltimore MD, March. [] G. Foschini, K. Karakayali, and R. Valenzuela. Coordinating multiple antenna cellular networks to achieve enormous spectral efficiency. IEE Proc. Comm., ():, August. [] S. Shamai, O. Somekh, and B. Zaidel. Multi-cell communications: An information theoretic perspective. In Proc. Joint Workshop on Communications and Coding, Donnini(Florence), Italy, October. [] M. Hata. Empirical formula for propagation loss in land mobile radio service. IEEE Trans. Veh. Tech., 9():, August 9. [] R. Horn and C. Johnson. Matrix Analysis. Cambridge University Press, 99. [9] H. Weingarten, Y. Steinberg, and S. Shamai. The capacity region of the Gaussian MIMO broadcast channel. In Proc. ISIT, page, Chicago IL, June. [] G. Caire and S. Shamai (Shitz). On the achievable throughput of a multiple-antenna Gaussian broadcast channel. IEEE Trans. Inform. Theory, 9:9, July. [] C. L. I, L. Greenstein, and R. Gitlin. A microcell/macrocell cellular architecture for low- and high-mobility wireless users. IEEE J. Select. Areas Commun., (): 9, August 99.