Optimal Radio Resource Management in Multihop Relay Networks Tolga Girici Anthony Ephremides Dept. of Electrical and Electronics Eng. Institute for Systems Research
Chenxi Zhu, Jonathan Agre Fujitsu Labs of America
TOBB Economics and Technology University University of Maryland 8400 Baltimore Ave., Suite 302 Ankara,06560, Turkey College Park, Maryland 20740 College Park, MD 20740
[email protected] [email protected] {chenxi.zhu,j.agre}@fla.fujistsu.com Abstract Mobile multihop relay networks (MMR) use relay stations (RS) to extend or enhance the coverage of a base station (BS) in a broadband cellular network. The base station is attached to a wired backhaul. Relay stations use wireless transmission to connect to the base station and to the mobile stations (MS), while direct BS-MS connection is also possible. Low cost relay technologies are recently considered for OFDM based broadband wireless technologies. Especially for low-cost relay stations that have single radio interface how to allocate proper amount of subframe, subchannel and power to stations and users is an important issue. This work develops an optimization based approach for radio resource management in MMR networks supporting heterogeneous traffic. We propose a frame by frame scheduling method, where subframes are allocated to each microcell in a TDMA fashion and the allocations in each microcell are performed in an OFDMA manner. Numerical results show that the use of relays significantly improve the quality of service.
I. I NTRODUCTION Cellular broadband wireless networks are designed to be able to provide mobile high rate and heterogenous services that have various quality of service (QoS) requirements. Such networks are envisaged to provide service to a cellular area of on the order of miles[1]. In such networks, users in different parts of a cell usually experience different signal qualities and thus different degrees of QoS. Users at the cell edge often suffer from bad channel conditions and observe lower SINR. In an urban environment, shadowing by big buildings and signal penetration and attenuation inside buildings or tunnels also degrade the signal quality significantly. Often it is not possible to improve the signal qualities to these under-serviced areas by increasing the transmission power or changing the antenna configurations. Reducing the cell size and deploying more base stations will improve the situation, but this is often not possible due to the associated high operating cost. Using radio relay stations is an effective way to increase the signal quality of the users by replacing a long, low quality link between a Base Station(BS) and a Mobile Station(MS) with multiple shorter, high quality links through one or multiple Relay Stations (RS). In recent years several broadband air interface technologies have been developed to provide Internet access multimedia services to end users. A notable example of these technologies is mobile WiMax. Transmission in WiMax networks is based on OFDMA, where several modulation, coding and power allocation schemes are allowed to give more degrees of freedom to resource allocation [1]. In this work we address the problem of OFDM based resource allocation in a cellular network with fixed relay stations. As RSs do not require their own wired backhauls, and are often less sophisticated than a full functional BS, RSs are less expensive to deploy and operate than a traditional base station. The standard for relay in WiMax networks is being developed by the 802.16j Relay working group [2].
Use of relay in cellular systems were studied in [3], [4], [5] and [6]. Most of these works considered solely data traffic. The aim in [3], [4] was improving the aggregate throughput or spectral efficiency by using relays in broadband systems, while in [5] fair subchannel allocation algorithms were proposed and in [6] a heuristic was proposed to jointly improve outage probability and throughput. Unlike all these works we distinguish different traffic types and propose a frame-by-frame scheduler, where in each time slot, the time slots, subcarriers and power in a frame are jointly allocated to each transmission. Our algorithm provides proportional fairness for data users, while satisfying delay requirements for real time sessions. Proportional fairness is a good balance between throughput and fairness for data users. We also convert delay requirements of real time users into rate requirements and treat them as constraints in the optimization problem as in our previously proposed resource allocation scheme for a system without relay stations in [7]. In a typical multihop relay network the traffic between the BS and MSs can be forwarded via multiple hops through RSs. However in this work we assume that there is at most one RS between the BS and a MS. A RS communicates to the BS like a MS, and communicates with the MS in its coverage area (called RS-microcell) like a BS. Cost of RSs can be reduced by allowing a single transceiver at each RS. Therefore a RS cannot transmit and receive simultaneously, which is a major characteristic of our system model. We describe the system model in Section II in detail. In line with recent IEEE 802.16j standard the BS schedules microcell transmissions in a TDMA manner in a MMR frame. The BS first allocates a time interval (subframe) of the frame to each microcell, as explained in Section III. In the second stage of allocation the BS treats each microcell separately; it optimally divides the subframe for BS-RS and RS-MS composite links and also allocates the available bandwidth and power to each link in the microcell, which is explained in Section IV. We numerically evaluate the proposed algorithm in Section V and compare its performance with that of the algorithm previously proposed for a network of single BS in [7]. II. S YSTEM M ODEL
AND
N OTATION
Figure 1 shows a typical multihop relay (MMR) network. The base station is at the center, and there are a number (M) of RSs located in the cell area. We assume that the MSs are located randomly in the cell and they are fixed. Relay stations are also fixed and each MS is assigned to the BS or one of the RSs, based on the distance. 1
MSBS MS5
MS3
MS1
RS1 RS2
BS MS4
MS6 MSRS2
MS2
MSRS1
MMR-cell
Fig. 1. Topology of a MMR cell with a BS and two relay stations (RS1 and RS2 ). The BS is serving the MSs in the set MSBS directly (MS1 and MS2 ). Two relay stations (RS1 , RS2 ) are used to enhance the system throughput of BS and serve MSs in the set MSRS1 (MS3 , MS4 ) and MSRS2 (MS5 , MS6 ). The MMR cell includes the coverage area of the BS and all the RSs. 1 We
consider a fixed system but simulate mobility of MSs through fast Rayleigh fading and slow Log-normal shadowing.
In this work we consider frame by frame downlink resource allocation. Total frame duration is T f seconds and it is divided into time slots of duration Ts . Total bandwidth is W Hz, which is divided into Nsub subchannels of Wsub Hz bandwidth. We assume distributed grouping as the subchannelization method, where a subchannel is formed by randomly sampling subcarriers from the entire frequency range. Because of sampling, all subchannels are of equal channel quality with respect to a user. This way of subchannelization is especially advantageous in mobile systems with fast fading. While modeling the allocation problem we will consider time and bandwidth as a continuously divisible quantity. After finding the optimal values, they are quantized to integer multiples of subchannel bandwidth and time slot duration. We assume for simplicity that each user demands only one type of traffic, data, video streaming or voice. Let UD and UR be the set of data and real time (voice and video) sessions. Set of nodes assigned to RSi is denoted as MSRSi and set of nodes directly connected to BS is called MSBS . We assume that this assignment is fixed. The BS keeps separate queues for each user, while each RS also keeps separate queues for the set of nodes MSRS . We make the following definitions: •
•
•
Microcell: A microcell is formed by a group of MSs directly connected to a station (BS or RS). In the example in Figure 1 there are 3 microcells. Composite Link: There are three types of composite links. The set of transmissions through BS → RSi , RSi → MSRSi for all i = 1, . . . , M and BS → MSBS are all composite links. As an example in Figure 1, there are 5 composite links and hence the downlink frame is divided into 5 TDMA subframes. Tandem queue: A tandem queue l j is the two cascading queues BS → RSi → MS j , where j ∈ MSRSi . Let hBS j RS BS BS and h j be the channel gains for the links BS → RSi and RSi → MS j , respectively. Obviously h j = hk for RS all j, k ∈ MSRSi , because those queues follows the same BS → RSi link. Let qBS j and q j be the number of bits waiting in those queues to be transmitted.
We assume that a relay station has a single radio interface in order to reduce the cost, which also mandates the RS to communicate with the BS and with its MSs in disjoint time instants. Because of the single interface constraint of relay stations, transmissions BS → RSi and RSi → MSRSi should also be scheduled in a TDMA fashion. Considering this and for simplicity we follow a TDMA approach in scheduling transmissions of each composite link. Figure 2 illustrates a typical downlink frame.
W
BS MSBS TBS
BS RS1
RS2 MSRS2
RS1 BS MSRS1 RS2
T2
T1
... ...
BS RS
M
RSM MSRSM
TM
(a)
W
TBS i
TRS i Ti
(b)
Fig. 2. (a) Downlink subframe for the TDD frame structure of a MMR cell. BS and M RSs share the DL subframe on a TDMA basis. On the downlink, Ti includes all the time slots assigned to the traffic BS → RSi → MSRSi . (b) shows a microcell subframe. Transmissions in BS → RSi and RSi → MSRSi composite links are given TiBS TiRS seconds.
Let PBS and PRS be the available power budget for the BS and each RS, respectively. We consider a channel
with Rayleigh fading and Log-normal shadowing. At each time frame the channel gain is assumed constant and we consider an equivalent AWGN channel. In order to determine the bandwidth efficiency as a function of SINR, we use the values in IEEE 802.16 standard [2]. A number of modulation/coding pairs that correspond to SINR thresholds and spectral efficiency values in [2]. Considering the SINR-spectral efficiency relation and by using β = 0.25, it is reasonable to use the following function for the number of bits that is transmitted through a link ! φ φ βp j h j φ φ φ r j = Ti w j log 1 + φ , φ = BS, RS, j ∈ MSRSi (1) w j N0 φ
φ
φ
Here Ti is the subframe duration that is allocated to the composite link φ (BS or RS) of microcell i. Let p j w j be the power and bandwidth user j in microcell i gets (φ = BS(RS) for the BS-RS (RS-MS) link). We perform resource allocation in two main steps: 1) Cellular Time Allocation: In this step TDMA-based time allocation among microcells is performed. Before performing TDMA allocation the BS also determines rate requirements for each real time session. 2) Microcell Resource allocation: In this step we optimally divide the subframe Ti , i = 1, 2, . . . , M of microcell i into two subframes Ti BS and TiRS ; and also perform joint power/bandwidth allocation for links in both composite links in the microcell. III. C ELLULAR T IME A LLOCATION RS For the data sessions let RBS j and R j be the average transmitted rate through the access and relay links of tandem queue of data user j ∈ MSRSi ∩UD . For the real time sessions, let rc,BS and rc,RS be the required rates for the tandem j j queues of session j at the current frame.
A. Real Time Rate Requirement Before allocating subframes to microcells, the BS determines rate requirements for real time users. First a number of real time session links are chosen to be served in the current frame. We use the following user satisfaction value for real time sessions: ! φ φ βP h (t) r0j log(δ ) j j φ φ (2) USV j (t) = − max D j log 1 + φ Dj N0W R j (t) φ
This metric resembles the Largest Weighted Delay First (LWDF) metric except the r0j /R j (t) term at the end. φ Here r0j is the bit arrival rate and R j (t) is the received rate for user j, where φ = BS for the BS-RS transmission φ φ φ and φ = RS for RS-MS transmission. Service rate is updated as R j (t + 1) = αR j (t) + (1 − α)rαj (t). Dmax and D j j are the maximum allowable delay and current head of line packet delay for the link. δ j is typically chosen as 0.05 and reflects the probability of exceeding the delay constraint. The BS chooses a number of links supporting real time sessions according to this metric, where UR′ denotes the set of chosen real time users. The rate constraint for a chosen real time session is defined as: ! φ q (t) j c,φ φ φ r j (q j (t), ω j (t)) = max r0j , , j ∈ UR′ (3) φ Dmax 0.5ω (t) j j φ
Here ω j is the transmission frequency of the corresponding link of user j, which is calculated as follows: φ
φ
ωi (t) = αω j (t − 1) + (1 − α)I(r j (t) > 0),
(4)
φ
where I(r j (t) > 0) is the function that takes value one if the node receives packets in time slot t, zero otherwise. Therefore this frequency decreases if the link transmits less and less frequently. Using this frequency expression in the rate function, we compensate for the lack of transmission in the previous time slots possibly due to bad channel conditions. B. Time Allocation for each Microcell In this section we will propose a method for allocating time intervals for each microcell. We assume uniform power allocation. By this assumption , the BS willbe able to allocate times for each microcell in a simple manner. φ
Let the spectral efficiency be defined as S j = log 1 + φ
Pφ φ n jW
φ
nats/s/Hz, ∀ j ∈ UD ∪UR , φ = BS, RS. Here, n j =
φ
φ φ
N0 φ. βh j
Then the number of nats transmitted is equal to r j = Ti w j S j nats. We can define time-bandwidth product as φ φ φ RS b j = Ti w j for j ∈ MSRSi and allocate resources subject to a time bandwidth constraint ∑ j∈UD ∪UR bBS j + b j ≤ W Tf . φ
r
c,φ
For a real time user j ∈ UR required time bandwidth product can be directly computed as b j = jφ , φ = BS, RS. So the Sj resource allocation becomes only allocation of time-bandwidth for data sessions subject to residual time-bandwidth rc,BS
rc,RS
j RS ′ constraint ∑ j∈UD bBS + SjRS . We formulate the resource allocation problem as j + b j ≤ (W T f ) = W T f − ∑ j∈UR SBS j j follows: max ∑ log (α j R j + (1 − α j )r j ) (5)
b,r j∈U D
∑ bBSj + bRSj
≤ (W T f )′
(6)
≥ r j , φ = BS, RS, ∀ jUD
(7)
j∈UD
φ φ
bjSj
RS where R j = min{RBS j , R j } be the average received rate through the tandem queue. The problem above maximizes the proportional fairness of the tandem queues carrying data traffic and has a concave objective function increasing in each data session rate. The constraint set is convex, hence we can solve the problem by using Lagrange multipliers. Solution of this problem requires a simple binary search on λb that solves the following equations: + 1 e R j ∀ j ∈ UD −α (8) r j (λb ) = 1 λb ( SBS + S1RS ) j j ! ! rc,BS rc,RS 1 1 j j W T f = ∑ r j (λb ) + RS + ∑ + RS (9) SBS Sj SBS Sj j j j∈UD j∈UR
As we see, sum of time-bandwidth resources is a monotonic decreasing function of λb . Based on the result of this optimization, in order to share the frame in a TDMA manner, time allocated to composite links in microcell i can φ φ be computed as Ti (λb ) = W1 ∑ j∈MSRSi r j (λb )b j , φ = BS, RS, ∀i ∈ MC. C. Feasibility of the Problem The analysis above is made with a feasibility assumption. By feasibility we mean that the available resources RS are enough to support at least the required rates for real time sessions. Let us define T BS i and T i be the minimum required time to support the real time sessions in BS-RS and RS-MS links. We can find them by taking the φ φ RS limit T i = limλb →∞ Ti (λb ), where the data user rates become to zero. If ∑i∈MC T BS i + T i > T f , then we find the non-zero-rate link with worst channel condition and change its required rate to zero.
IV. C OMPOSITE L INK R ESOURCE A LLOCATION In this section we consider resource allocation in a single microcell. Let us consider transmission through composite links BS → RSi and RSi → MSRSi. Let Ti be the time allocated to microcell i. At this stage the BS makes RS BS RS the power (p = {pBS j , p j | j ∈ MSRSi }), bandwidth (p = {w j , w j | j ∈ MSRSi }) for links in this microcell and time (Ti = {TiBS , TiRS }) allocation for the BS − RSi and RSi − MSRSi composite links (illustrated in Figure 2(b)). The objective is to maximize the log sum of data rates for each tandem queue supporting data sessions. The constraints are the real time sessions rate requirements defined in the previous part, and total power, rate, time constraints. The constrained optimization problem is formulated as follow:
∑
max
w,p,Ti
log (αR j + (1 − α)r j)
(10)
j∈MSRSi ∩UD
s.t. TiBS + TiRS ≤ Ti
∑
pj
∑
wj
(11)
φ
≤ Pφ φ = BS, RS
(12)
φ
≤ W, φ = BS, RS
(13)
≥ r j , φ = BS, RS, ∀ j ∈ MSRSi ∩UD
(14)
≥ r j , φ = BS, RS, ∀ j ∈ MSRSi ∩UR
(15)
j∈MSRSi
φ
φ
φ
φ
Ti w j log Ti w j log
j∈MSRSi ! φ pj 1+ φ φ njwj ! φ pj 1+ φ φ njwj
c,φ
The problem above has a concave objective function increasing in each data session rate. The constraint set is convex, hence we can solve the problem by using Lagrange multipliers. The problem can be solved by taking derivative with respect to resources and Lagrange multipliers. Since the rate is an increasing function of resources the optimal can be achieved only when all the time, power and bandwidth is used. Therefore all Lagrange multipliers are positive. Performing some operations, we can write the number of bits transmitted to data user as a function of only λRS x and λT as follows: + RS r j (λx , λT ) =
W /λT
1 log 1+
PBS nBS W
+
RS x ) 1+ f x−1 ( λRS nj
λRS x nRS j
+
PRS nRS j W
eR j −α
RS RS Here λRS through function x determines the scaled SINR xi = β × SINRi
λRS x nRS j
(16)
= fx (xi ) = (1 + xi ) log(1 + xi ) − xi .
BS Parameter λT is the time cost. Note that for the BS-RS links channel gains are equal ( nBS j = n , ∀ j ∈ MSRSi ) BS therefore their SINRs are equal to nPBSW . These issues will be explained in detail in the final version of the paper. 1) Calculation of times: Each node in a composite link transmits using the same time interval, but different frequency bands, where the sum of the bandwidths is equal to W . Dividing the total time-bandwidth product to W we can find the time intervals allocated to BS-RS and RS-MS composite links:
TiBS (λRS x , λT ) =
rc,BS r j (λRS j x , λT ) + ∑ ∑ PBS PBS j∈MSRSi ∩UD W log 1 + BS j∈MSRSi ∩UR W log 1 + BS n W n W
(17)
TiRS (λRS x , λT ) =
rc,RS r j (λRS j x , λT ) + ∑ ∑ λRS λRS x x −1 j∈MSRSi ∩UD W log 1 + fx ( RS ) j∈MSRSi ∩UR W log 1 + fx−1 ( RS ) n n j
Total time equation is,
(18)
j
BS RS RS RS ST (λRS x , λT ) = Ti (λx , λT ) + Ti (λx , λT )
(19)
2) Calculation of total power: Sum of the powers in BS-RS and RS-MS transmissions can be found as follows: BS
BS P BS P rc,BS r j (λRS j n nBSW x , λT )n nBSW = + ∑ ∑ PBS PBS BS RS j∈MS ∩U j∈MSRSi ∩UD TiBS (λRS , λ ) log 1 + T (λ , λ ) log 1 + RSi R BS BS T T x x i n W n W BS
RS SBS p (λx , λT )
RS −1 λx −1 λx r j (λRS ) rc,RS nRS ) x , λT )n j fx ( nRS j j fx ( nRS j j RS RS S p (λx , λT ) = + ∑ ∑ RS RS −1 λx −1 λx j∈MSRSi ∩UD TiRS (λRS j∈MSRSi ∩UR TiRS (λRS x , λT ) log 1 + fx ( nRS ) x , λT ) log 1 + fx ( nRS ) RS
(20)
RS
j
(21)
j
RS Let λ∗T (λRS x ) be the Lagrangian multiplier that satisfies Equation (19). Since ST (λx , λT ) is a monotonic function RS∗ of λT , λ∗T (λRS such x ) can be found by a simple binary search. Then our algorithm becomes finding the optimal λx RS RS∗ ∗ RS∗ RS that S p (λx , λT (λx )) = P . The algorithm will be described in the final version in more detail.
V. N UMERICAL E VALUATION Figure 3 shows a sample MMR system, where the BS is at the center. The RSs are located at 1400m distance to the BS. MSs are located at ∓400,800,1200,1600 and 2000 meters. Each MS is assigned to the closest station in distance. BS
1400m
Fig. 3.
2000m
A sample MMR model for numerical evaluation
We consider a system with 30 subchannels of 267KHz bandwidth, frame duration of 2msec and slot length of 0.1msec. As for the path loss, we use the IEEE 802.16j channel model described in [8]. For BS → MS and RS → MS we use the Non-line-of-sight (NLOS) model with path loss of 31.5 + 35 log10 d + ψRS−MS dB (d in meters), where dB RS−MS ψdB ∼ N(0, 8dB). For BS → RS connections we use the LOS model with path loss of 36.5 + 23.5 log10 d + BS−RS ∼ N(0, 3.1dB). We assume that Rayleigh fading stays constant for 2 frames and logψdB dB, where ψBS−MS dB normal fading stays constant during 5 frames. At each frame we assume an AWGN channel with noise p.s.d. equal to N0 = −174dBm/Hz. Our traffic model is based on [9], and it is as follows: For each data session we assume a saturated queue. We assume 32kbps VoIP sessions, where a 320-bit packet arrives at every 10 time slots. Finally we assume 128kbps video streaming sessions, with a fixed video frame duration of 100msec. During each frame there are 8 packets (slices), where the packet interarrival times and sizes are random. Performance criteria are 1) 95th percentile delay for voice and video streaming sessions. 2) Average throughput for data sessions. 3) Log-sum of throughput for data sessions (Proportional fairness).
Keeping the number of data and voice users at 20 each, we vary the number of video user from 20 to 50. Figure 4 shows the 95th percentile delay for voice sessions. We can observe that in the 2-RS system users at all distances delay stays under the required 100msec level, while for the system with no RSs, users at 1.6km and 2.0km experience severe delays. Since the coherence time for the log-normal fading is much longer than the voice delay constraint, delays for edge users by far exceed the required levels. 7
95th percentile voice delay (increasing number of video users (S)): D=V=20
2.5
300
Total data throughput (D=V=20)
x 10
0−RS 2−RS 2 bps
250
1.5
no RS
200
msec
S=20-50
1 20
25
30
35
40
45
50
55
60
150
Log−sum of throughput
280
2 RS 100
0−RS 2−RS
S=20-50
275
270
50
RS
265
0 400
600
800
1000
1200 distances(m)
1400
1600
1800
2000
260 20
25
30
35 40 45 Number of video users(S)
50
55
60
Fig. 4. 95th percentile voice delay vs. distance to the BS for increasing Fig. 5. Total throughput and log-sum of throughput of data users vs. number of video sessions. number of video sessions.
We observe in Figure 5 the trade-off between SINR improvement by RSs and time loss by relaying. For low number of video users 0-RS system provides better throughput and proportional fairness. However a video session costs more resources in a 0-RS system; total throughput decreases more with increasing number of video users in the 0-RS case. Therefore in the case of large number of video users (S > 40), a system with relays is expected to provide more throughput to data users. Also for number of video users greater than 30, relay system provides better proportional fairness. VI. C ONCLUSIONS In this work we proposed a joint time, power and bandwidth allocation scheme for downlink transmission in the presence of single-interface relay stations. The proposed scheme consists of two steps, namely subframe allocation for each microcell and joint time , power,bandwidth allocation for links in each microcell. Numerical results show that it is possible to increase the cell size and decrease the number of base stations by adding low-cost relay stations. Multihop relay systems satisfy the QoS requirements of all real time sessions, for the cases, in which regular cellular systems are not sufficient. R EFERENCES [1] A. Ghosh, D. Wolter, J. G. Andres, and R Chen. Broadband Wireless Access with WiMax/802.16: Current Performance Benchmarks and Future Potential. IEEE Communications Magazine, Feb. 2005. [2] IEEE 802.16j PAR. Amendment to IEEE Standard for Local and Metropolitan Area Networks - Part 16: Air Interface for Fixed and Mobile Broadband Wireless Access Systesm - Multihop Relay Specification. IEEE, Mar. 2006. [3] T. Irnic, D. C. Schultz, R. Pabst, and P. Wienert. Capacity of a Relaying Infrastructure for Broadband Radio Coverage of Urban Areas. IEEE 58th VTC 2003-Fall,.
[4] K. Park, C. G. Kang, D. Chang, S. Song, J. Ahn, and J. Ihm. Relay-enhanced Cellular Performance of OFDMATDD System for Mobile Wireless Broadband Services. ICCCN 2007, In Proc. of 16th, 13-16 Aug. 2007. [5] O. Oyman. OFDM2A: A Centralized Resource Allocation Policy for Cellular Multi-hop Networks. 40th Asilomar Conference on Signals, Systems and Computers, pages 656 – 660. [6] M. Kaneko and P. Popovski. Adaptive Resource Allocation in Cellular OFDMA System with Multiple Relay Stations. Proc. of IEEE 65th VTC 2007-Spring, pages 3026 – 3030. [7] T. Girici, C. Zhu, J. Agre, and A. Ephremides. Proportional Fair Scheduling Algorithm in OFDMA-based Wireless Systems with QoS Constraints. 12th International OFDM Workshop (Inowo 07), Hamburg, Germany, 2007. [8] IEEE 802.16j Relay Task Group. Channel Models and Performance Metrics for IEEE 802.16j Relay Task Group. IEEE, 2006-05-01. [9] IEEE 802.16 Broadband Wireless Access Working Group. Multihop System Evaluation Methodology: Traffic Models. IEEE, 2006-05-01.
