Interference Model for Cognitive Coexistence in Cellular Systems

Interference Model for Cognitive Coexistence in Cellular Systems Theodoros Kamakaris, Didem Kivanc-Tureli and Uf Tureli Wireless Network Security Center Stevens Institute of Technology Hoboken, NJ, USA Abstract Cognitive radio is a key enabling technology of dynamic spectrum access for exploiting unused spectrum resources. This article focuses on modeling the opportunity for cellular systems which have the greatest spectrum scarcity problem. A system model is introduced for analyzing the opportunistic bandwidth within a cellular network through a spatial evaluation of the resources used by the primary and available to the secondary systems. Towards this purpose, two metrics are introduced signifying the spatial coherence of resources: the region of interference and the region of communications. Our results suggest significant underutilized resources that can be scavenged through secondary users to greatly improve the spectral efficiency of cellular networks. I. INTRODUCTION The concepts of cognitive radios and dynamic spectrum access [1] have spearheaded the evolution of new paradigms of interference aware multiple access and spectral reuse. At the same time policy changes [2] allowing opportunistic use enable new disruptive technologies as secondary systems provide added value to legacy systems with accelerated time to market evolution cycles. A market in dire need of such accelerated evolution cycles is that of cellular telephony and its imminent convergence to wireless data networks. Next generation networks (NGN) envision multi-network technologies that provide always available, best-connected services. Along this paradigm this article investigates the availability of underutilized spectral resources within the static infrastructure of a cellular network for capacity expansion through opportunistic spectral reuse. NGN technologies ubiquitously converge to frequency reuse of one to improve bandwidth efficiency, while increasing the cell density is often the strategy for increasing system capacity. However, the hub-and-spoke architecture along with the frequency division duplex (FDD) scheme and the power control mechanisms employed allow for spectrum holes through the exposed node effect. In the uplink channel, the bandwidth used by a transmitting mobile remains unutilized in the antipodal area of the cell due to power control. An opportunistic access scheme for a secondary system with a dynamic operational area of coverage (footprint), such as those proposed in [3] and [4] can exploit such spectrum holes through low power adhoc networks which control their interference to the primary system. We note that our discussion for spectral reuse is significantly different from the case of cognitive radio in TV bands. Since the mobiles receive at different frequencies, their involvement is limited to the interference they introduce to the secondary system, therefore the footprints of the primary and secondary system overlap, whilst in the TV bands scenario the systems remain spatially orthogonal. Following we formalize and quantify the available opportunistic resources that such a secondary system can exploit. We base our discussion on the geometric analysis of an intuitive system model of the cellular network. II. SYSTEM MODEL We represent the cellular network with a hexagonal pattern with the basestation (BS) located at the center of the hexagon and the mobiles (MSs) uniformly distributed around them. We assume that within the boundaries of a hexagon the MSs are associated with the BS at its center. The system model is based on the introduction of two new metrics to quantify the cellular system resources that could be opportunistically scavenged by a secondary system operating within the bounds of a cellular network: The region of interference (RoI) signifies the spatial coherence of resources around the location of a secondary user () and is a measure of the resource utilization seen by the. The region of communications (RoC) is a measure of the possible footprint the can have to utilize available resources without interfering with the primary system (i.e. the cellular network). These metrics are not related to specific frequency, time or other parameters that might constitute the cellular systems multiple access scheme, rather they represent a ratio of the respective RoI, RoC areas over the total cell area. Hence, we formulate the problem as a measure of the spatial coherence of the cellular system s resources, whether those are spectral channels, time slots or CDMA codes. As mentioned at the introduction, we focus our discussion to the uplink of the cellular system since out of the three identified sources of opportunistic resources, the frequency division duplex scheme is the only one still adhered to in next generation cellular networks. A. Region of Interference Assuming a uniform distribution of the MSs across the cell area, the interference seen by the can be estimated as the ratio of the interfering area over the cell area. As aforementioned, this measure of interference indicates the ratio of available resources to the secondary user to those of the primary user and can represent orthogonal frequency channels,

time slots or CDMA codes, thus being applicable to any multiple access mechanism. A key assumption on which we base our system model is that typically mobiles employ power control that effectively bounds their range to a radius equal to their distance from the BS. We define the RoI for a specific location within a cell as the area within which any MS transmitting will make those resources (channels, timeslots, etc.) unavailable to the. Consider the geometry shown in Fig. 1, where the transmitter ( ) is communicating to the receiver ( Rx ) with the same resources that the MS is communicating to the BS within a cell. to the assumed power control strategy, then for the MS to interfere with the, the following inequality must hold: d (MS, Rx ) α d (MS, BS) α < R C. (5) The problem becomes similar to that of finding the umbrella diagram as defined in [5]. Let C() be the polygon with A sides, modeling the sensitivity range of the secondary user receiver equal to the cell radius range. We define the convex polygon I i = H(BS i C() and we construct the perpendicular bisector L i of BS i in I i. Next we find the intersections of the bisector line segments. Since the intersection is the circumcenter of the triangle (, BS i, BS i+1 ), the bisector line segments L i and L i+1 (or their extensions) intersect on the boundary of cells H(BS i ), H(BS i+1 ). If we denote the polygon formed by the line segments L i as P (L i ) then RoI Rx = P (L i ) C() as depicted in Fig. 2. BS Tx d(ms,bs) D MS d(ms,) Rx RoI R C() Fig. 1. Opportunistic spectrum users in a cellular network Let PRx X, P T X x denote the power received at and transmitted from X respectively, and let d(x, Y ) denote the distance of X to Y. Assuming a distance-power gradient α, the power received by the BS (PRx BS) is: PRx BS PT MS x = d (MS, BS) α PT MS x = PRx BS d (MS, BS) α. (1) For Rx to decode received signals with an interference free range R: P D α P MS d (MS, Rx ) α + N 0 > P N 0 R α. (2) From equations 1 and 2 we can obtain an expression relating d (MS, Rx ) and d (MS, BS) with R > D as follows: ( ) N 0 R α PRx BS D α 1 d (MS, BS)α > d (MS, Rx ) α, (3) that is equivalent to: d (MS, BS) α < d (MS, Rx) α ( ) R α SNR BS D α 1. (4) Given a random location within the area of adjacent cells with centers at BS0,...BS3, C() signifies the maximum RoI in the case all MSs transmit at their full range equal to that of the cell radius (RC). If we constrain their range according BS3 Fig. 2. BS0 L3 L0 L2 BS2 Region of Interference L1 BS1 The high level algorithm to compute the area of RoI for any location with respect to the area of H(BS i ) is described below: FOR H(BS 0 ) : FIND BS i where C() H(BS i ) 0 COMPUTE R(BS i ) such that: MS i H(BS i ), d(, MS i ) d(bs i, MS i ) COMPUTE RoI() = ( i R(BS i)) (C()) B. Region of Communications Due to the advantageous positioning of the BS in a cellular system along with the fact that there are constant transmissions on the downlink, it is possible to determine a maximum power allowed for which the would be operating below the interference range of the BS. A straightforward approach would be to measure the relative downlink path loss from each

BS, assume a conservative uplink path loss and transmit at power levels that do not increase the Signal to Interference Noise Ratio (SINR) seen at the BS for the MSs. This implies that the range of the s transmission is proportional to its distance from the BS. Since we cannot know the distribution of the MSs across the adjacent BSs, the must constrain its transmission to a range less than the distance of the closest BS. We introduce the metric of region of communication to indicate the area within which an can effectively communicate to another. This is similar to the bidirectional communications range, taking into account the transmission power limitations imposed by the BSs in proximity. As before, we define the polygon P (L i ) as the region from which the transmission range of other secondary users can reach without increasing the SINR of adjacent BSs. Then we define R() as the polygon with A sides that encloses the transmission range of. Then RoC = P (L i ) R() depicted in Fig. 3. 0 db for communicating. Therefore we need to adjust both RoI and RoC as a function of the operational SNR and SINR respectively. We assume the following path loss model [6]: Let the received signal power P r be proportional to the distance, raised to the distance-power gradient α such that: P r P 0 = ( ) α d, (6) where P 0 is the received power at a reference distance and α varies typically from: 2 (free space loss), 3 (suburban) or 4 (urban environment). Then, the path loss (L P ) is given by: L P = L 0 + 10α log d, (7) where L 0 is the path loss at reference distance. In Fig. 2,3 we depict the RoI and RoC with boundaries at 0 db SNR and 0 db SINR respectively. Fig. 4,5 illustrate the adjusted RoI and RoC for SNR and SINR greater than 0 which correspond d to range adjustments by a factor of across the dimensions of C(), R() and P (L i ). RoC C'() L0 BS0 L1 BS1 L'0 R() L2 RoI' L'1 L3 L'2 BS3 BS2 L'3 Fig. 3. Region of Communications The high level algorithm to compute the area of RoC for any location with respect to the area of H(BS i ) is described below: FOR H(BS 0 ) : FIND BS i where R() H(BS i ) 0 COMPUTE R(BS i ) such that: MS i H(BS i ), d(, MS i ) d(bs i, MS i ) COMPUTE RoC() = ( i R(BS i)) (R()) C. SNR adjustment to RoI, RoC In the above discussion we have assumed perfect power control for MS to BS and to BS with 0 db SNR at the boundaries. However, the mobiles operate at higher SN R > 0dB, and similarly the s would require SINR greater than Fig. 4. SNR adjusted Region of Interference For the Region of Interference, the lines L i now bisect BS i in I i such that: and points L i : d (L i, Rx ) = d d (L i, Rx ) (8) R C () = d R C(). (9) For the Region of Communications, the lines L i now bisect BS i in I i such that: points L i : d (L i, Rx ) = d d (L i, Rx ) (10)

BS0 R'() L'0 RoC' L'1 L'3 L'2 Fig. 6. Region of Interference normalized to the Cell Area at 0 db SNR MS BS and Fig. 5. SNR adjusted Region of Communications R C () = d R C(). (11) Since is set to be the the reference distance at which the RoI SNR and RoC SINR are zero, we can relate the range adjustment to the operational SNR from the Path Loss equation as follows: ( ) d {SNR, SINR} = L P L 0 = 10 α log (12) For a more analytic discussion on the relation of the distance and the power between the secondary user and the primary system we refer the reader to [7]. A. Region of Interference III. SIMULATION RELTS Fig. 6 illustrates the simulation results of the RoI algorithm across one cell when the power control strategy of the primary system is 0 db (SNR BS MS = 0 db). The grayscale color scheme represents the RoI normalized to the total cell area and exhibits an interesting pattern due to the effect of the hexagonal representation. The RoI varies less than 6% across the entire cell area and we expect it to be more homogeneous across the cell in a real world cellular system. The interpretation of the figure below would suggest that with a cellular system operating at minimal SNR, with perfect power control and at full capacity, at any given location within the cell, less than 50% of the total resources are utilized. Fig. 7 illustrates the effect of different power control strategies as a function of SNR for different power-distance gradients (α). The computation for negative SNR is justified given the ability of the BS to have increased gain through modulation (CDMA, SS) or advanced antenna configurations (Beamforming, MIMO) that further improve the Path Loss characteristics of the MS to BS transmission, reducing the interference to and from the secondary user. Assuming that Mobile Stations will always connect to the closest BS, which is equivalent to the assumption of uniform distribution, the above discussion becomes valid for any frequency reuse pattern, where the hexagonal bounds become boundaries enclosing the MSs for each BS. It is noticeable that the expected available resources quickly diminish with more realistic power control strategies of 5 db and higher. Mean RoI 0.9 α=2 α=3 α=4 10 5 0 5 SNR BS MS (db) 10 15 Fig. 7. B. Region of Communications Average RoI across Cell vs. SNR BS MS Fig. 8 illustrates the simulation results of the RoC algorithm across one cell at to SINR equal to 0

db. The figure depicts the ratio of RoC over the Cell Area which is proportional to the square of the distance from the basestation. Fig. 9 depicts how the RoC varies as a the distance between the BS and the transmitter increases, and how it would vary without the constraining region of P (L i ). The P (L i ) constrain ensures that only the area within which an can receive as well as transmit to another is calculated given the power control limits to avoid interference with the cellular system. RoC α = 2 α = 3 α = 4 d =.3Rc d =.6Rc d =.9Rc 0 10 5 0 5 10 SINR (db) Fig. 10. RoC vs. SINR at BS to distance of, an.9 of the Cell Radius Fig. 8. Region of Communications normalized to the Cell Area at 0 db SINR RoC Area Fig. 9. With Li constraint Without Li constraint 0 0 1 d(bs, Tx ) RoC with increasing distance of the transmitter from the BS Fig. 10 depicts how the RoC varies as a function of the operational SINR for to communications. Three different distances from the BS are considered at, and 0.9 of the total Cell Radius and for varying power-distance gradients. IV. CONCLUSIONS We have formalized and simulated two metrics for assessing the opportunistic resources available to secondary users within a cellular system. We have evaluated that the available resources on the uplink are significant regardless of the location within the cell, yet greatly depend on the cellular systems power control strategy and propagation environment. The communication range of a secondary user is significantly reduced as the user approaches the basestation. Strategies to overcome this limitation might include the availability of out of band channels used only for users very close to the BS or spread spectrum underlay modulation schemes that could operate at negative SINR. REFERENCES [1] J. Mitola, Cognitive radio: An integrated agent architecture for software defined radio, Ph.D. dissertation, Royal Institute of Technology (KTH), Stockholm, Sweden, 2000. [2] P. Kolodzy, Spectrum policy task force report, Federal Communications Commission, Tech. Rep. Rep. ET Docket no. 02-135, November 2002. [3] T.Fujii, Y. Kamiya, and Y. Suzuki, Multi-band ad-hoc cognitive radio for reducing inter system interference, in Personal, Indoor and Mobile Radio Communications, 2006 IEEE 17th International Symposium on,. IEEE, September 2006, pp. 1 5. [4] X. Liu and S. Shankar, Sensing-based opportunistic channel access, Mobile Networks and Applications, vol. 11, no. 4, pp. 577 591, 08 2006. [5] J. Zhang and G. Fan, A cellular network planning technique to minimize exposure to rf radiation, in ICPPW 04: Proceedings of the 2004 International Conference on Parallel Processing Workshops (ICPPW 04). Washington, DC, USA: IEEE Computer Society, 2004, pp. 338 344. [6] K. Pahlavan and P. Krishnamurthy, Principles of Wireless Networks: A Unified Approach. Upper Saddle River, NJ, USA: Prentice Hall PTR, 2001. [7] A. Sahai, R. Tandra, S. M. Mishra, and N. Hoven, Fundamental design tradeoffs in cognitive radio systems, in TAPAS 06: Proceedings of the First International Workshop on Technology and Policy for Accessing Spectrum. New York, NY, USA: ACM Press, 2006, p. 2.