Cooperative Frequency Reuse for the Downlink of Cellular Systems

Cooperative Frequency Reuse for the Downlink of Cellular Systems Salam Akoum, Marie Zwingelstein-Colin, Robert W. Heath Jr., and Merouane Debbah Department of Electrical & Computer Engineering Wireless Networking and Communications Group The University of Texas at Austin University Station C83, Austin, TX 7872-24 University Lille Nord de France, F-59 Lille, UVHC, IEMN-DOAE, F-5933 Valenciennes, CNRS, UMR 852, F-5965 Villeneuve d Ascq, France SUPELEC Alcatel-Lucent Chair on Flexible Radio 3 rue Joliot-Curie 992 GIF SUR YVETTE CEDEX France Abstract We propose a space time coded cooperative diversity protocol that achieves improved quality of service for the mobile users in cellular systems. The protocol, called cooperative frequency reuse, exploits the cellular frequency reuse concept to create spatial diversity among neighboring base stations. After transmitting their individual signals in the channel reuse protected frequency subchannels in the first time frame, the base stations divide their transmit power between the relayed signals from the neighboring base stations and the signals intended for their own users. We discuss the performance of the proposed cooperation strategy by evaluating the fractional power allocations that lead to the best performance in terms of achievable sum rate and probability of outage. We use simulations to show that the proposed strategy, in the presence of full channel state information at the transmitter, yields considerable improvement over traditional direct transmission frequency reuse schemes. Index Terms Frequency reuse, cooperative space diversity, space time codes, cellular systems. I. INTRODUCTION Frequency reuse is fundamental to the cellular communication concept. It determines how much intercell interference is experienced by mobile users and therefore establishes the system performance and capacity []. Fractional frequency reuse is proposed for next generation wireless systems [2], [3], to improve cellular coverage and the data rate of celledge users. Frequency reuse, when combined with cooperation between base stations, can guarantee a higher quality of service for the mobile users. Cooperative space diversity [4], [5] is one such method of cooperation. It is implemented using antennas belonging to neighboring base stations, each with its own information to transmit, to create and exploit space diversity. Distributed space time codes can be constructed over the formed virtual antenna array to increase the reliability of the system [6] [8]. The work has been conducted within the project POSEIDON financed by the pole de compétitivité System@tic <http://www.systematic-parisregion.org>. R. Heath was supported by the National Science Foundation under grant CNS-626797 and CCF-8365. We design a distributed space time coded cooperative space diversity protocol, among neighboring base stations, over the the underlying frequency reuse concept. We call the proposed strategy cooperative frequency reuse (CFR. In contrast to the cooperative multi-cell transmission schemes available in the literature [9] [], where base stations jointly process the downlink signals of the mobile users, thereby creating a multiple input multiple output broadcast channel, we implement cooperation through a distributed space time code. Our model can be applied to cellular systems such as GSM and WiMAX. It is also suited for mobile flexible networks [2], where the base stations have limited or no backhaul communication. The proposed strategy is different from the cooperative transmit diversity in the multihop relay specification for WiMAX, the IEEE 82.6j standard [2]. In the latter, distributed space time codes are implemented across antennas of the deployed relays and the base station, in the same cell, over the same time and frequency resources. The CFR protocol, proposed in this paper, is implemented as follows. Over the first time block, each base station acquires the signals sent by the interfering base stations over the subcarriers not allocated for its transmission. In the following block, it re-encodes the signals intended for users of the adjacent cells and transmits it along with its own user s signal. Subsequently, this can be seen as relaying between base stations, where if base station A is transmitting, it acts as a source, base station A 2 acts as a relay and the user in cell A as the destination. In this paper, we establish the benefits reaped from the CFR protocol in terms of probability of outage and sum capacity gains in the cellular system. The CFR protocol is different from those proposed in the literature for cooperation among mobile nodes [4], [6], [7], [3]. These methods target the uplink of cellular systems and can be applied for communication between terminals in ad-hoc networks. CFR combines the inherent cellular frequency reuse concept with cooperative space diversity, and implements a distributed space time code across adjacent base stations.

TABLE I SYMBOLS TRANSMITTED FROM BASE STATION A AND A 2 OVER FOUR CONSECUTIVE TIME FRAMES OVER SUBCHANNELS N A AND N A 2 Base Station A m = 4k m = 4k m = 4k 2 m = 4k 3 A A 2 MS MS 2 n N A 2 β b, β a 2 β b 2, β a n N A a a 2 b b 2 Base Station A 2 m = 4k m = 4k m = 4k 2 m = 4k 3 n N A 2 b b 2 a a 2 Signals transmitted by A in block and block 2 respectively Signals transmitted by A 2 in block and block 2 respectively n N A β 2 b 2, β2 a β 2 b, β2 a 2 Fig.. Cellular system layout. Base stations A and A 2 serve users MS and MS 2 at the edge of their respective cells. II. SYSTEM MODEL We consider a downlink cellular network employing frequency reuse. For ease of presentation, we consider a two cell setup, where two sectors in two adjacent cells, cell A and cell A 2, interfere with each other, as illustrated in Figure. Denote by D the radius of each cell which is assumed to be identical for all cells. Let N be the set of subcarriers modulated by the system. We denote by N Ai the set of subcarriers modulated by base station A i to serve its users. By definition of frequency reuse, the subsets of subcarriers are such that N A N A2 = φ. Fractional frequency reuse, however, allows a fraction of these subcarriers to be shared between the base stations, and used to serve the users that are not interference limited. The signal received at the m-th OFDM symbol at the n-th subcarrier of user MS k in cell A i, where n N Ai, can be written as y k (m, n = h ik (m, ns k (m, n w k (m, n ( where s k (m, n represents the data symbol intended for user MS k from its serving base station A i. Process w k (m, n is the additive white Gaussian noise at the user k. h ik (m, n denotes the frequency response of the channel between base station A i and the mobile user MS k at the subcarrier n and the OFDM block m. Random variables h ik (m, n are taken from a continuous distribution with variance ρ k = E[ h ik 2 ]. Notice that the system does not have an interference factor because of the frequency reuse assumption. Channel coefficients are supposed to be perfectly known at the receiver and at the base station. We assume that ρ k diminishes as the distance r k between the mobile station and the base station increases, based on a given path loss model. III. COOPERATIVE FREQUENCY REUSE We develop and analyze a class of cooperative diversity protocols that we call cooperative frequency reuse. The proposed cooperative scheme builds on the frequency reuse restriction to relay the transmitted information through adjacent base stations thereby increasing the diversity of the cellular system. Instead of transmitting independently to their intended mobile stations as in classical frequency reuse, adjacent base stations acquire each other s information on their dedicated subchannels and then implement a distributed space time code to jointly communicate their transmissions. They benefit from the frequency reuse to decode each other s symbols in the first transmission block, then use the second block to reencode the neighboring base station s information thereby increasing the diversity of the system. This cooperative scheme is illustrated in Table I. It requires four time frames to send two symbols, the symbol rate is /2 symbol per channel use. As illustrated in Table I, cooperative frequency reuse divides the time frames into two blocks. Assuming one user per cell, the base stations serve mobile users MS and MS 2, located, respectively, in cells A and A 2. Over the first block, time frames 4k and 4k, base station A sends symbols a and a 2 to MS, in the subchannel N A. It simultaneously acquires base station A 2 transmissions to MS 2 on subchannel N A2. Similarly base station A 2 transmits b and b 2 to MS 2 on N A2 and listens for N A. Over the next block, time frames 4k 2 and 4k 3, both base stations act as relays and transmit on both subchannels N A and N A2. Base station A sends a decoded version of b and b 2, along with its own symbols a and a 2. Similarly, base station A 2 sends a decoded version of a and a 2 along with copies of b and b 2. The cooperative protocol implements a space time code inspired from the Alamouti space time code [4]. We assume, for this protocol, that the signals are perfectly decoded at the base stations during the first block of the transmission. To transmit information pertaining to both mobile users, the base stations divide their power allocations between two symbols. β denotes the fractional power allocated by base station A to send the information to MS. Consequently β = β is allocated to the information for MS 2. Similarly, β 2 and β 2 are the fractional power allocations at base station A 2. IV. PERFORMANCE ANALYSIS We characterize the performance of the cooperative frequency reuse algorithm of Section III in terms of maximizing achievable sum rate and minimizing probability of outage, assuming full channel state information at the transmitter. We compare the cooperative algorithm performance to the baseline algorithm for direct transmission under frequency

reuse constraint. In the latter, each base station A i only transmits information to its user over the subchannel N Ai. The users are thus only noise limited. Assuming that the transmitted symbols s k (m, n are Gaussian distributed, we can express the achievable capacity Ck d of mobile station MS k, under direct transmission, as Ck d = log ( P h ik 2, (2 P = E[ s k (m, n 2 ] is the transmit signal power. is the variance of the additive white Gaussian noise. A. Achievable Sum Rate The first goal of this work is to find the optimal fractional power allocations β and β 2 that maximize the total sum rate of mobile users in adjacent cells. For the cooperative frequency reuse protocol, the signals are decoded in 6 OFDM symbols, as illustrated in Table I. For MS, the received signal in OFDM symbol m over subchannel n can be written as, y (m, n = c h (n c 2 h 2 (n w (m, n (3 where h (n denotes the channel between base station A i and MS on subchannels n = N A and n = 2 N A2. c i denotes the signal transmitted from base station A i, subject to total transmit power constraint of. The system of equations, corresponding to the 6 OFDM symbols being decoded, can be rewritten in the form Y = H a N with a = [a a 2 ] T denotes the symbols intended for MS. Subsequently, the achievable capacity C is, C = ( 4 log 2 det(i H H H E[N N H ] = 2 log 2 ( h( 2 2 (β h(2 2 h 2(2 2 β h (2 2 2 ( β 2 h 2( 2 h ( 2 β 2 h 2( 2 Similarly, for MS 2, the capacity is written as, C 2 = 2 log 2 ( h22(2 2 2 (β2 h22( 2 h 2( 2 β 2 h 22( 2 2 ( β h 2(2 2 h 22(2 2 β h 2(2 2 The rate optimization problem subsequently follows. Problem : Find β and β 2 such that the instantaneous sum rate f(β, β 2 = C C 2 is maximized, subject to β [ ], β 2 [ ]. The problem comes down to finding the values of β and β 2 that achieve the maximum of the function f(β, β 2 in the bounded region β, β 2 [ ]. Within this region, there are three types of points that can potentially be global maxima for the function, these are the relative maximum inside the region, the relative maximum on the borders and the corner points. The maximum of f(β, β 2 is thus the maximum of f β (β, β 2 = ; f β2 (β, β 2 =. (4 (5 2 f β (β, = ; f β (β, = ; f β2 (, β 2 = ; f β2 (, β 2 =. 3 f(,, f(,, f(,, f(,. where f βi is the derivative of f(β, β 2 = C C 2 with respect to β i. Evaluating the above equations in terms of β and β 2, one can show that β and β 2 that achieve the local maximum of the sum rate are always located on the boundaries of the region β, β 2 {, }. Numerical simulations in Section V confirm this result. Maximum sum rate is thus achieved by either sending all the power to the dedicated user, i.e., not using the cooperative behavior, or by allocating all the power to the user in the other cell, in which case, the base stations cooperate in switching roles in serving the mobile users, and the CFR algorithm is called switched-cfr. Note that β =, β 2 = correspond to the cooperation protocol in [8], where an Alamouti-like protocol is proposed for cooperative diversity. B. Probability of Outage We next evaluate the gain in performance of the cooperation algorithm when optimizing for probability of outage. We formulate the problem as jointly optimizing the fractional power allocation for both cells such that the outage probability of the users is minimized. The outage probability of MS k at the cell edge of cell A i is given by P k O(β, β 2 = P(C k < R (6 = P ( log 2 ( det(i Hk H H k E[N k N H k ] < R where R is the fixed threshold spectral efficiency of the system. For two users MS and MS 2, respectively at the edge of A and A 2, the reliability optimization problem is Problem 2: Find the optimal ˆβ, ˆβ2 such that P(C < R, C 2 < R is minimized. In other words, (7 ( ˆβ, ˆβ 2 = arg min (P(C < R, C 2 < R β,β 2 = arg min (P(C < RP(C 2 < R β,β 2 Finding the fractional power allocations that minimize the probability of outage requires finding the probability distribution of the instantaneous capacities C and C 2 as a function of β and β 2. This can be reformulated as finding the probability distribution of the summation of ratios of random variables h ik 2 with exponential distributions. P(C < R = P ( h( 2 2 (β h(2 2 h 2(2 2 β h (2 2 2 ( β 2 h 2( 2 h ( 2 β 2 h 2( 2 < 2 R The solution to this problem is not trivial. Histograms in Figure 3 of Section V show the distribution of the values of β and β 2 inside the boundary region [ ]. The fractional power allocations take values well inside the boundary region, suggesting a drastic improvement in the reliability of the system, as will be illustrated in Section V.

C. Enhanced Cooperative Frequency Reuse To improve the performance of the CFR protocol, we implement a full Alamouti space time code over all subchannels. We allow the base stations, in the second transmission block, to allocate their transmission power to serve both users at the same time over both subchannels. We call the new scheme Enhanced Cooperative Frequency reuse (Enhanced-CFR. We introduce four fractional power allocation variables β in {β, β 2, β 2, β 22 }, where i corresponds to the base station A i and n corresponds to the subchannel N Ai. The OFDM symbols transmitted over four time frames are illustrated in Table II. We evaluate the probability of outage of the Enhanced-CFR algorithm, and we compare it to the performance of the CFR protocol. Notice that this protocol is a generalization of the CFR algorithm and that for β = β 2 =, and β 2 = β 22 =, this algorithm reduces to a distributed Alamouti code [8], this type of cooperation is called Alamouti-CFR. V. DISCUSSION AND NUMERICAL RESULTS We provide numerical results to evaluate the performance of the proposed cooperative frequency reuse protocol. We consider a two cell setup, where each cell has a radius of D = 2 m. Mobile users are randomly located inside their cell. The distance x from the mobile user to the base station is uniformly distributed in the interval [ D]. We assume a free pathloss model with a pathloss exponent equal to 2. The carrier frequency is 2.4 GHz. At this frequency, pathloss in db is given by ρ db (x = 2 log (x.4 where x is the distance in kilometers. The channels h ik are i.i.d. Gaussian distributed with variance ρ h =. We begin by evaluating the gain in achievable sum rate when the fractional power allocations β and β 2 are optimized for maximizing the instantaneous sum rate. Figure 2 shows the histogram of the distribution of the optimal β and β 2 over the interval [ ] when those are optimized for maximizing the sum rate. As shown by the analytical result in Section IV, the optimum fractional power allocations are either or. This suggests that the cooperative protocol, while increasing the achievable sum rate, through switched-cfr, does not add significant improvement in performance as a large percentage of the optimum β s are those that require no cooperation between the base stations. Figure 3 shows the histogram of the distribution of β and β 2 when optimizing for the average probability of outage. In this case, we average the probability of outage per large scale fading, that is we compute the sum rate for all β s for a multitude of Rayleigh fading channels realizations per user location. We then choose the fractional power allocations that minimize the probability of outage of two mobile users MS and MS 2. The histogram shows variations in the optimal β and β 2 inside the boundary region, suggesting significant improvement through cooperation. Next, we compare the performance of the CFR algorithm in terms of probability of outage when β and β 2 are optimized for sum rate and probability of outage respectively. We fix a % 5 % 25 % % 5 % 25 % β that maximizes the sum rate.2.4.6.8 β 2 that maximizes the sum rate.2.4.6.8 Fig. 2. histogram showing the frequency of occurence of the optimum fractional power allocations β and β 2 when optimizing the sum capacity, in the interval [ ] 6 % 4 % 2 % 6 % 4 % 2 % β that minimizes the Probability of Outage.2.4.6.8 β 2 that minimizes the Probability of Outage.2.4.6.8 Fig. 3. histogram showing the frequency of occurence of the optimum fractional power allocations β and β 2 when optimizing the probability of outage, in the interval [ ] target spectral efficiency R = 2 bits/sec/hz. Figure 4 shows the joint probability of outage for various signal to noise ratio levels. One can observe from the Figure that the CFR algorithm increases the rate of decay of the probability of outage in terms of SNR by a factor of four. Optimizing for the probability of outage adds a 2 db performance improvement over the CFR optimized for instantaneous sum rate. Finally, we compare the performance of the CFR algorithm with that of the enhanced-cfr algorithm of Section IV, where we optimize for four betas. Figure 5 plots the probability of outage behavior of the CFR, enhanced-cfr and Alamouti-CFR algorithms as the signal to noise ratio is varied. The fractional power allocations are chosen to minimize the probability of outage. We observe that the Alamouti-CFR achieves better performance than that of the baseline direct transmission algorithm, but falls short of the CFR algorithm. The enhanced-cfr algorithm achieves the best performance as it is a generalization of all the protocols discussed here-in. VI. CONCLUSION We presented a novel cooperative space time code named cooperative frequency reuse. The algorithm builds on the cellular frequency reuse to add cooperation between adjacent

TABLE II SYMBOLS TRANSMITTED FROM BASE STATIONS A AND A 2 OVER FOUR CONSECUTIVE TIME SLOTS OVER SUBCHANNELS N A AND N A 2 Base Station A m = 4k m = 4k m = 4k 2 m = 4k 3 n N A 2 β 2 a β 2 b β 2 a 2 β 2 b 2 n N A a a 2 β b β a β a 2 β b 2 Base Station A 2 m = 4k m = 4k m = 4k 2 m = 4k 3 n N A 2 b b 2 β 22 b 2 β 22 a 2 β 22 b β 22 a n N A β 2 b 2 β 2 a 2 β 2 b β 2 a Probability of Outage (Pout - -2-3 -4-5 FR CFR, R CFR, Pout -6 5 5 2 SNR (db Fig. 4. Probability of outage versus SNR for the classical frequency reuse, and the cooperative frequency reuse with 2 β optimizations of sum rate capacity, averaged over multiple user locations inside the cell. Probability of Outage (Pout - -2-3 -4-5 FR Alamouti-CFR CFR -6 enhanced-cfr 5 5 2 SNR (db Fig. 5. Comparison of the Probability of outage versus SNR for the classical frequency reuse, and the cooperative frequency reuse with 2 β and 4 β optimizations averaged over multiple user locations inside the cell. base stations. The base stations divide their transmission power between their own signals and the signals from neighboring cells. We studied the optimization of the fractional power allocations for both maximizing the sum rate of the mobile users and minimizing their joint probability of outage. We concluded that the algorithm has a drastic impact on increasing the reliability of the cellular system, without incurring additional complexity overhead. Future work includes considering the performance of the CFR with large scale fading channels and with no perfect CSI at the transmitter. REFERENCES [] A. Goldsmith, Wireless Communications. Cambridge University Press, 25. [2] S. W. Peters and R. W. Heath Jr, The future of WiMAX: multihop relaying with IEEE 82.6 j, IEEE Communications Magazine, vol. 47, no., pp. 4, Jan. 29. [3] 3GPP TR 36.84, Further advancements for E-UTRA physical layer aspects, 3rd Generation Partnership Project; Technical specification Group Radio Access Network, February 29. [4] A. Sendonaris, E. Erkip, and B. Aazhang, User cooperation diversity. part i. system description, IEEE Transactions on Communications, vol. 5, no., pp. 927 938, Nov. 23. [5] J. Laneman, D. Tse, and G. Wornell, Cooperative diversity in wireless networks: Efficient protocols and outage behavior, Information Theory, IEEE Transactions on, vol. 5, no. 2, pp. 362 38, Dec. 24. [6] J. Laneman and G. Wornell, Distributed space-time-coded protocols for exploiting cooperative diversity in wireless networks, IEEE Transactions on Information Theory, vol. 49, no., pp. 245 2425, Oct. 23. [7] M. Badr and J.-C. Belfiore, Distributed space time codes for the amplify-and-forward multiple-access relay channel, in IEEE International Symposium on Information Theory, 28. ISIT 28., July 28, pp. 2543 2547. [8] C. Hucher, G. R.-B. Othman, and J.-C. Belfiore, AF and DF protocols based on alamouti ST code, in IEEE International Symposium on Information Theory, 27. ISIT 27., June 27, pp. 526 53. [9] S. Shamai and B. Zaidel, Enhancing the cellular downlink capacity via co-processing at the transmitting end, in EEE VTS 53rd Vehicular Technology Conference, 2. VTC 2 Spring. I, vol. 3, 2, pp. 745 749 vol.3. [] S. Jing, D. N. C. Tse, J. B. Soriaga, J. Hou, J. E. Smee, and R. Padovani, Downlink macro-diversity in cellular networks, in IEEE International Symposium on Information Theory, 27. ISIT 27., Jun. 27, pp. 5. [] S. Shamai (Shitz, O. Somekh, and B. Zaidel, Multi-cell communications: An information theoretic perspective, Joint Workshop on Communications and Coding (JWCC, Florence, Italy, Oct. 24. [2] M. Debbah, Mobile flexible networks: The challenges ahead, in International Conference on Advanced Technologies for Communications, 28. ATC 28., Oct. 28, pp. 3 7. [3] M. Janani, A. Hedayat, T. Hunter, and A. Nosratinia, Coded cooperation in wireless communications: space-time transmission and iterative decoding, IEEE Transactions on Signal Processing, vol. 52, no. 2, pp. 362 37, 24. [4] S. Alamouti, A simple transmit diversity technique for wireless communications, IEEE Journal on Selected Areas in Communications, vol. 6, no. 8, pp. 45 458, Oct 998.