On Fractional Frequency Reuse in Imperfect Cellular Grids Patrick Mitran and Catherine Rosenberg Department of Electrical and Computer Engineering University of Waterloo Abstract—Current point-to-multipoint systems suffer signifi- cant performance losses due to greater attenuation along the signal propagation path at higher frequencies, transmit power constraints of mobile users and base stations, and interference from neighboring cells. Fractional Frequency Reuse (FFR) is a technique to counteract these effects. Typically, the proposed FFR technique partitions a cell into a reuse 1 area, centered near the base-station and a reuse 3 area, located near the edges of the cell, with reuse 3 regions scheduled to minimize interference from neighboring cells. Unfortunately, virtually all analysis of FFR has been done under a perfect hexagonal lattice cellular grid, while no practical deployment has this degree of symmetry. In this paper we revisit the analysis of FFR for non-ideal cellular grids for cases with fading. We find that while for some non-ideal grids, a combination of reuse 1 and 3 is indeed optimal, for many others a combination of reuse 1 and 4 provide better performance. Thus, we conclude that for practical cellular layouts, the optimal re-use pattern for the edge of the cells is not necessarily 3 as commonly assumed, but is topology dependent. Index Terms—Cellular Networks, Frequency Reuse, Fractional Frequency Reuse I. I NTRODUCTION High data rate point-to-multipoint systems are now gaining widespread acceptance. Recent standards such as WiMAX (IEEE 802.16e) [1] and LTE [2] employ multiple access techniques based on OFDM. LTE for example, employs OFDMA on the downlink and Single-Carrier-FDMA, a form of precoded OFDMA with lower peak-to-average power ratio, on the uplink. Thus WiMAX and LTE allow users to be multiplexed by allocating time-frequency blocks to each user. Among the challenges in providing high data rates and quality of service to mobile data users are: high path loss and greater signal attenuation due to higher frequencies, transmit power constraints at mobile users, and interference from neighboring cells. Frequency reuse is a common technique to increase data throughput of point-to-multipoint systems. At one extreme, in a frequency reuse 1 system (FR(1)), each cell reuses the entire frequency band at the cost of creating possibly high interference. Among the advantages of such a scheme are that for users near the base-station, it can be shown that a very high rate per unit bandwidth is possible due to the large bandwidth available since those users do not typically suffer from significant interference. On the downside, for users near the edge of the cell, significant interference can result in low SINR, and thus only a low rate per unit bandwidth (and even potentially a lack of coverage) is achievable. Another alter- native is a scheme such as frequency reuse 3 (FR(3)). Here, each cell may use only one third of the system bandwidth, with neighboring cells using the remaining two thirds based on some coloring pattern. Cell-edge users now suffer significantly less interference and hence can achieve much higher rate per unit bandwidth, although users at the center of a cell do worse than in FR(1). Note that to use FR(3) a hexagonal lattice-like layout is necessary for cell placement (otherwise one cannot guarantee that a 3 color pattern can always be found). Under a set of simplistic assumptions (a perfect hexagonal grid for the placement of base stations, a log(1+SINR) rate function and no fading), it can be shown that for each point in a cell, the rate per unit bandwidth, normalized to account for the re- use pattern, is either maximized by FR(1) or FR(3). We will show later that, this is not true under a set of more realistic assumptions, i.e., some users would do better with higher reuse factor (e.g, 4, 7, 9, ...). It can also be shown that the total system throughput is maximized with FR(1) among all single frequency reuse schemes where the system throughput is defined as the sum of all user rates under a proportional fair scheduling policy. This is true even under a set of realistic assumptions, although this throughput maximization is done at the expense of edge users who receive low rates. Typically, cellular operators try to achieve a reasonable trade-off between throughput and coverage (i.e., the rate offered to edge users). In conventional cellular systems this trade-off is attained by selecting FR(3). Even in next generation cellular systems, one of the main challenges is to find the right trade-off between the total system capacity (though there is no clear consensus on how this capacity should be defined) and coverage defined as the rate received by edge users 1 while increasing the capacity using interference mitigation techniques. To obtain such a trade-off, one may consider a scheme using a mix of frequency reuse r 1 and r 2 >r 1 [9], [3], commonly called fractional frequency reuse, or FFR. Roughly speaking, in an FFR(r 1 ,r 2 ) system, the frequency band B of the system (of size B) is divided into r 1 parts for T 1 per cent of the time and into r 2 parts for the rest of the time. Assuming time-sharing and a cycle of unit length, each cell is assigned one of the r 1 (resp. r 2 ) parts for communicating with core-cell (resp. edge-cell) users during T 1 (resp. T 2 ). It should be noted that an equivalent way to describe FFR is the following. We split the band B into 2 parts B 1 and B 2 of bandwidth B 1 and B 2 respectively. B 1 (resp. B 2 ) is further split into r 1 (resp. r 2 ) subbands. Each cell receives 2 subbands based on two distinct coloring patterns (one corresponding to r 1 and one to r 2 ), one subband of size B 1 /r 1 and one of size B 2 /r 2 with B 1 + B 2 = B. Here, all bands are used simultaneously without time-sharing. Clearly one of the challenges is to choose r 1 and r 2 , another one is to compute B 1 and another one is to decide which mode r 1 or r 2 to use to schedule users associated with a given cell. Two broad approaches to FFR are: • static: users are scheduled by their base station in one of the 2 modes r 1 or r 2 based on their position, or path 1 The term “edge user” should not be taken literally since with fading any user can potentially be an “unlucky” user irrespective of its position.