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Design and Evaluation of Scheduling Algorithms for LTE Femtocells Dipl.-Ing. Maciej Mühleisen, TU Hamburg-Harburg, Hamburg, Deutschland Dipl.-Ing. Kay Henzel, RWTH Aachen, Aachen, Deutschland Prof. Dr.-Ing. Andreas Timm-Giel, TU Hamburg-Harburg, Hamburg, Deutschland
Abstract With the continuous progress in technology, more complex and sophisticated mobile devices are available to end-users. Furthermore, services such as IP-TV and the introduction of cloud computing result in increased bandwidth demands. Two of the major challenges faced by mobile communication systems such as LTEAdvanced (LTE-A), trying to serve the demands, are the limited frequency spectrum and poor indoor coverage. Femtocells are capable to improve indoor coverage and provide high data rate services to customers. The unplanned deployment of femtocells by end-users can create high and difficultly to predict femto-to-femto- and femto-to-macrocell interference. This paper evaluates the potential gains in spectral efficiency achieved when femto-cells exchange information in order to enable centralised Radio Resource Management (RRM) by joint scheduling decisions. In order to show the degrees of freedom concerning radio resource assignment strategies, a detailed description of femtocell-to-femtocell interference scenarios is presented, outlining the constraints dictated by the LTE-A standard. After describing the problem in mathematical terms and showing its NP-hardness, the problem is reduced to the so-called Linear Assignment Problem. Based on this idea, centralised uplink assignment strategies were designed with the focus on maximising Cell Spectral Efficiency (CSE). In total four different strategies are presented including an optimal solution for upper bound results as well as heuristic algorithms with reduced runtime. These heuristics are based on methods used in Economics for the cognitive process of decision making under uncertainty. Presented results prove that optimised joint scheduling decisions can significantly increase the spectral efficiency.
1
Introduction
A key goal for 4G mobile radio systems is increased cell spectral efficiency (CSE). A promising approach to increase the CSE is a reduced frequency reuse distance. Using the whole available spectrum in every cell leads to the shortest possible reuse distance of reuse-1. While benefiting from the trunking gain with more resources available, cochannel interference mitigation becomes a challenging task in such scenarios. The same applies if femtocells are deployed using the same spectrum as the surrounding macrocells and adjacent femtocells. The Orthogonal Frequency Division Multiple Access (OFDMA) modulation technique used in LTEAdvanced (LTE-A) systems allows radio resource management with fine granularity and on short time scales. Together with new communication interfaces and protocols between eNodeBs (eNBs), it serves as an enabler for new radio resource management schemes, optimising overall system performance. This paper is organised as follows: Section 2 provides a formal description of the uplink resource assignment problem and a simplification to a linear optimisation problem. In Section 3 we present different algorithms to solve the problem for an opti-
mal or suboptimal solution. The performance of the algorithms is evaluated in Section 4. We present a conclusion in Section 5 and give an outlook on possible future work.
1.1
Related Work
The authors of [1] present a solution for an optimal uplink schedule including the impact of interference, but only assign one resource to each user per scheduling round. The problem is solved by Geometric Programming. In [2] the problem is formulated for the downlink and heuristically solved for optimal transmission power per user. In our previous work [3], we have presented optimal and heuristic solution algorithms for the uplink considering only two cells. In this paper we extend the previous work to more than two cells and introduce a new heuristic solution algorithm for the problem.
2
2.1
The Uplink Resource Assignment Problem Degrees of Freedom for LTE-A Uplink Scheduling
The LTE-A uplink resource scheduler is responsible to assign radio resources to users to transmit their data [4]. As a first degree of freedom it can decide which users should be scheduled in a scheduling interval, also called subframe or Transmission Time Interval (TTI) of 1 ms duration [5]. The scheduler must then decide how many Physical Resource Blocks (PRBs) each user gets. The set of assigned PRBs forms the Transport Block (TB) assigned to the user. The Single Channel Frequency Division Multiple Access (SC-FDMA) transmission scheme used in the uplink requires all TBs to be formed from PRBs adjacent in frequency domain. The scheduler can assign an individual transmission power to each TB. The LTE-A standard defines an uplink power control formula provided in (1) to calculate the transmission power PTX per PRB.
PTX = αPL + P0 + ∆
(1)
PL is the pathloss to the serving eNB. α and P0 are parameters applied for the whole cell allowing to fully or partially compensate the pathloss. If α is set to one and P0 is set to -106 dBm, all transmissions are received at -106 dBm, approximately 10 dB above a typical noise level of -116 dBm per PRB at the eNB. Interference can often be neglected at such low transmission powers. Such configuration, assuming sufficient power budged at the User Terminals (UTs), results in equal but not very high data rates for all UTs. Reducing α can increase the data rate of users with relatively low pathloss at the cost of additional interference. Setting α to zero results in constant transmit power P0 for all UTs. The offset Δ can be used to individually increase the transmission power of selected UTs to increase their data rate. An individual precoding factor can be applied to each used transmit antenna to support MIMO. The precoding factor is a complex value resulting in a shift of phase and amplitude of the transmitted signal. A single Modulation and Coding Scheme (MCS) is selected for all PRBs forming the TB. The MCS must be chosen according to the expected SINR of the TB at the receiver. Depending on the schedule of surrounding eNBs and frequency selective channel quality, the SINR can significantly differ depending on the selected PRBs.
2.2
SINR calculation
The SINR of a PRB received in the uplink at the eNB is the ratio of the received signal power from the UT scheduled at this PRB and the sum of noise power and interference from other UTs in other cells transmitting on the same PRB. MultiuserMIMO (MU-MIMO) can introduce further interference from users in the same cell transmitting on the same PRB in time and frequency domain but intended for a different receive antenna (special layer). The received intended signal power PRX,s,p from UT s on PRB p can be calculated as PRX,s,p = PLs,p PTX,s where the pathloss PLs,p includes all influences of the channel on the amplitude of the transmitted signal. The received interference power PRX,i,p from UT i on PRB p can be calculated in the same way as PRX,i,p = PLi,p PTX,i. Noise power mainly results from thermal noise and receiver impairments, referred to as the receiver noise figure. The IMT-Advanced (IMT-A) evaluation guidelines [6] assume -174 dBm/Hz thermal noise and 7 dB receiver noise figure of the eNB receiver. This results in approximately -116.5 dBm noise power for a PRB having 18 kHz bandwidth. The resulting SINR can be calculated using formula (2) and simplified to formula (3) assuming all UTs use the same transmit power and the noise power can be neglected compared to interference power.
SINRs , p =
PTX ,s PLs , p
10
−11.65
mW + ∑ PLi , p PTX ,i
(2)
∀i ≠ s
SINRs , p ≈
PLs , p
∑ PL
∀i ≠ s
(3)
i, p
Since a TB consists of multiple PRBs it can experience different SINR values for different parts of the transmitted data. A commonly used model to describe the effect is the effective SINR model to calculate the average SINR for the TB [7]. Formula (4) allows to calculate the effective SINR of a TB transmitted on the PRBs in set P.
1 SINReff ,s = I −1 I( SINRs , p ) ∑ | P | ∀p∈P
(4)
I is an invertible function used for averaging and I-1 is its inverse. Mutual Information per Bit and Exponential Effective SINR are two commonly used and realistic functions [7]. Finally, the effective SINR estimation is used by the scheduler to select a MCS and therefore a data rate for the TB. More precisely a rate function R(SINReff,s, |P|, BLERmax) can be defined providing the data rate depending on the effective SINR and
number of PRBs and maximal tolerable block error rate BLERmax. The 3GPP LTE reference uplink scheduler [8] states that all UTs should get resources in every TTI and each UT should get the same amount of resources. Half of the UTs get one PRB less if the number of PRBs cannot be divided by the number of UTs without remainder.
2.3
Problem Formulation 1 1 1 2 2
3 3 4 4 5
eNB1
eNB2
Figure 1: Example resource assignment for two cells. Figure 1 shows an example resource assignment for two cells. The first cell serves two, the second one three UTs. The number in each PRB corresponds to the index of the UT transmitting in that PRB. According to the strategy of assigning an equal amount of resources to each UT, the TB size is two or three for eNB1 and one or two for eNB2. The three dimensional hypermatrix T with entries tc,s,z describes the schedule. The entry tc,s,z = 1 states that UT s in cell c transmits on TB z. The sum of each submatrix of the three-dimensional hypermatrix must be one to assure each UTs only gets one TB in each cell and each TB is only scheduled to one UT. As shown in Figure 1, each UT can be interfered by multiple different UTs depending on the location of the assigned TB. In this example UT 4 is served by eNB2 and receives interference from UT 1 and UT 2 of eNB1. We therefore define Pc,z as the set of PRBs forming TB z in cell c. Up is the set of all UTs transmitting on PRB p and Ip,s = Up \ s is the set of interferers to UT s on PRB p and is used in Formula (3) to sum up the interference power. It is precisely described by the assignment matrix T. Formula (4) can then be used to calculate the SINR of TB z in cell c by averaging over the PRB set Pc,z. The maximization goal is then described by Formula (5)
max ∑ ∑ ∑ tc ,s , z R( SINReff ,s , | Pc , z |) ∀c ∀s∈Sc ∀z∈Zc
(5)
which will maximise the sum data rate on all TBs in all cells. Here Sc is the set of all UTs served in cell c and Zc is the set of available TBs in cell c. Even if
the Shannon Formula is used to calculate the data rate R, the problem cannot be formulated as a Binary Linear Assignment Problem, since tc,s,z also appears in the denominator of the SINR calculation according to Formula (3).
2.4
Linear Assignment Problem
Rather than trying to find an optimal assignment of UTs to TBs in each cell, the problem could be reduced to the question which UTs should use the same resources to maximise the CSE. For this, the same amount of UTs must be served in each cell or at least the scheduler must assure that in a particular TTI the same number of UTs is served in all cells. This way the TBs of all cells are aligned and the same PRBs are used for transmission. It is then irrelevant which PRBs are assigned to the UTs grouped to use the same resources. For two cells with n UTs in each cell a n x n matrix R can be constructed, where each entry ri,j represents the sum data rate of nodes i and j from the two different cells, assuming they are scheduled to use the same resources. This is known as the Linear Assignment Problem [9]. The goal is to find an assignment matrix A with entries ai,j, where ai,j = 1 means that UTs i and j use the same resources. Since each UT cannot be scheduled more than once, all row and column sums of A must be one. The goal is to maximise the throughput ||T||1, T = RA, where ||x||1 describes the sum of the entries of vector x. The problem formulation can be extended to k > 2 cells by extending R and A to hypermatrices with k dimensions. The throughput vector T still has n entries, each representing the sum data rate of the k UTs from different cells grouped to use the same resources. Maximising ||T||1 is then known as the Multidimensional Assignment Problem [10].
3
Scheduling Algorithms
3.1
Optimal Solution
The optimal solution for the Linear Assignment Problem, resulting from two cells, can be found using the Munkes-Hungarian Algorithm [9] with polynomial runtime complexity O(n3). The Multidimensional Assignment Problem resulting from more than two cells (k > 2) is NP-Hard [10] and can only be solved by enumerating all combinations (brute force). The algorithm complexity is then O((n!)k).
3.2
Greedy Heuristic
than the result from the Greedy Algorithm and coincidently also matches the optimal solution.
A Greedy algorithm to obtain a non-optimal solution to the problem was described in [11]. For each step the assignment with highest sum data rate is selected and the corresponding UTs are grouped. The algorithm requires i steps to terminate and has to find the largest out of (n – i - 1)s entries in each step. Resulting overall complexity is therefore O(n(s+1)).
3.3
Maximum Regret Heuristic
The drawback of the Greedy Algorithm is that by selecting the combination yielding the highest sum data rate in each step other favorable groupings can potentially become unavailable in future steps. An example matrix R for k = 2 cells with n = 3 UTs each is given in (6).
1 10 2 R = 10 12 10 3 10 4
4
Scenario and Results
4.1
Simulator and Scenario
Simulations were carried out using the Open Source Wireless Network Simulator (openWNS) [13]. The simulator was previously used for independent IMT-A evaluation within the European WINNER+ project [14] and partially validated analytically [15], [16]. Based on the IMT-A Indoor Hotspot (InH) scenario consisting of two cells with square cell area, a multicell scenario was created. A three cell scenario is shown in Figure 2.
(6)
In this example the resulting sum data rate of the second terminal of both cells is always high, regardless of the interfering UT, and highest (r2,2 = 12) if the two UTs are using the same resources. All the combinations resulting in sum data rate 10 are then no longer possible. The highest possible value r3,3 = 4 is then selected and finally the last possible one r1,1 = 1. The resulting throughput vector T = [12, 4, 1], ||T||1 = 17 is actually one of the worst possible combinations. The Maximum Regret Algorithm [12] tries to improve the result by not just selecting the best combination in each step but rather trying to select one not likely disabling other favorable combinations in the next step. Therefore, for the two dimensional case, in each step the regret for each row i and column j is calculated. The regret Δr,i of row i is defined as the difference between the largest and second largest element in that row. Accordingly Δc,j is the regret for column j. The row regret for the example matrix (5) is Δr = [10-2, 12-10, 104] = [8, 2, 6] and the column regret Δc = [7, 2, 6]. The largest element Δmax = 8 is selected and the larger of the two values producing the regret is chosen for scheduling. In this case r1,2 = 10 is selected and the appropriate row and column is removed from the matrix. The algorithm is repeated for the remaining matrix resulting in the row regret Δr = [0, 1] and column regret Δc = [7, 6]. Δmax = 7 is the largest regret and r2,1 = 10 is added to the solution. The resulting throughput vector T = [10, 10, 4], ||T||1 = 24 is significantly greater
Figure 2 Scenario Circular cells rather than the square InH ones are used to assure symmetry. All cells have identical cell radius rcell and a fixed number of UTs is placed randomly in each cell. All cells have two closest neighbors with shortest cell edge distance dinter. The eNBs, forming the cell centers, are placed on a circle with fixed angle α = 360° / k between two neighboring cells, where k is the number of cells.
Value 3400 MHz 20 MHz 96 for user data InH NLoS -174 dBm/Hz 7 dB 4 dBm per PRB 13 MCS Chase Comb. 100 m 1s 20
Table 1 Simulation Parameters
The steps in the distribution are a result of the 13 enabled MCSs. With fixed schedule and fastfading disabled, each UT will transmit with constant data rate throughout the simulation run. 1 Random Greedy Maximum Regret Hungarian
0.9 0.8 0.7 0.6
P(x
