Downlink throughput evaluation in relay-enhanced variable data rate ...

Downlink Throughput Evaluation in Relay-Enhanced Variable Data Rate Enabled Cells Pekka Pirinen Centre for Wireless Communications University of Oulu P.O. Box 4500, FI-90014 University of Oulu, FINLAND Email: [email protected]

Abstract—Cellular system deployment can utilize relays both for the capacity improvement and for the coverage extension. This paper studies the performance of the relay enhanced circular cells via the metrics of throughput mean and variance, number of the relay stations, and outage probability. Single-hop links are used as a reference case. Link throughput varies according to four modulation levels whose coverage areas are calculated according to two different path loss models. A new relay position algorithm is proposed to jointly maximize the non-overlapping coverage of relays and minimize the number of them. The provided numerical examples show that the proposed relay placement scheme outperforms random deployments especially at low relay densities. In general, high relay station densities are required for two-hop communications to approach the average throughput of a single-hop scenario. However, the opportunistic two-hop deployments are beneficial also from the interference management and total network load balancing point of view. Index Terms—path loss, link, geometry, two-hop.

I. I NTRODUCTION Relays offer a mechanism to share the load of the cell from single-hop links to two-hop links whenever the link geometry is suitable for that. Coverage extension is also possible by relay deployment near the cell edge. Relaying-based concepts are further discussed, e.g., in [1]. Standardization activities on relay enhancements are ongoing, e.g., in IEEE 802.16’s Relay Task Group [2]. European integrated project WINNER [3] has incorporated relay deployment as one concept for future wireless broadband system. Cost efficiency of the fixed relay enhanced networks has been evaluated, e.g., in [4] and [5]. Recent performance examples of the relay deployment via system level simulations have been shown in [6]. This paper focuses on the opportunistic usage of relays in a circular cell throughput evaluation. Single-hop links are also studied as a reference. Multiple modulation levels are assumed based on the path loss dependent signal-to-noise ratio thresholds and respective spatial coverage areas. Relay station positions are considered to be either at fixed, pre-determined distances or to be randomly placed along the given distance range. Respectively, the angles of the RS positions from the BS follow either the pre-determined algorithm or random uniform distribution over the full circular plane. The aim is to compare the performance of single- and two-hop scenarios. Furthermore, in two-hop case, the pre-determined algorithm is compared to the random RS placements at selected alternative parameter settings.

978-1-4244-4067-2/09/$25.00 © 2009 IEEE

The rest of the paper is composed as follows. Section II describes the system model with considered path loss models, modulation level break distances, and selected twohop scenarios. Section III discusses the created numerical throughput results. Finally, the concluding remarks are given in Section IV and then the references are listed. II. S YSTEM M ODEL A. Path Loss Models WINNER and IEEE 802.16j Relay Task Group non-line-ofsight (NLOS) path loss models [7] and [8] are used for path loss prediction in this study. WINNER II C2 NLOS path loss in dB scale is denoted as P LW (d)[dB] = [44.9 − 6.55 log10 (hBS [m])] log10 (d[m]) + 33.46 + 5.83 log10 (hBS [m]) + 20 log10 (f [GHz]/5.0)

(1)

where distances are in the range 50 m < d < 5 km and the base station antenna height is hBS = 25 m and the carrier frequency f is in GHz. In addition, the mobile station antenna height is assumed to be hMS = 1.5 m. Similarly, the IEEE 802.16j path loss model for NLOS links is written as P LI (d)[dB] = 38.4 + 35 log10 (d) + 20 log10 (f [GHz]/5.0) − 0.7hm

(2)

where the antenna height hm can be either the relay station (RS) antenna height for BS-RS and RS-RS links or the MS antenna height for BS-MS and RS-MS links. B. Link Budget Based Break Distances for Variable Throughput Classes Fig. 1 depicts the assumed circular cell model where the various shades of gray correspond to the four utilized throughput classes. Near the base station the average wireless link quality is high enough for 64-QAM modulation to be applied. Further away from the BS the signal quality decreases with distance so that the modulation method needs to be gradually downgraded to 16-QAM, QPSK and eventually to BPSK. The cell radius is set to distance r4 , which is the maximum BPSK range.

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TABLE I T WO - HOP THROUGHPUT CLASSES [Mbps] BPSK QPSK 16-QAM 64-QAM MS dBS-MS d BS-RS

BS r1 r2

r3

r4

55.30 Mbps 27.65 Mbps 13.82 Mbps 6.91 Mbps

d4 dRS-MS d RS 3 d1 d 2

BPSK 3.455 4.607 5.528 6.142

QPSK 4.607 6.91 9.214 11.057

16-QAM 5.528 9.214 13.825 18.433

number of allocated RSs increases.  0, for     θ + π, for  n−1   π  θ + , for  n−2 2   θn−4 + π4 , for θn = π θ + , for  n−8 8   π  θ + , for  n−16 16   π  θ + , for  n−32 32   π θn−64 + 64 , for

64-QAM 6.142 11.057 18.433 27.65

n = 1, n = 2, 3 ≤ n ≤ 4, 5 ≤ n ≤ 8, 9 ≤ n ≤ 16, 17 ≤ n ≤ 32, 33 ≤ n ≤ 64, 65 ≤ n ≤ 128.

(5)

In (5), the angle θn represents the direction of the nth RS with respect to BS that is located at the center of the circular cell. Two successive angle allocations are always on opposite sides Fig. 1. System scenario for one- and two-hop links with spatially varied of the disk. Sequences of four quadrants are followed before throughputs. splitting the angle again. In this study the algorithm is stopped at n = 128 but it can be continued further in the same fashion if needed. Case 2: Random locations of fixed relay stations obey Based on (1) and (2) and other link budget parameters the switching distances can be solved as spatially uniform distribution over the one-hop cell coverage area. f [GHz] Pt −SN R−N0 −N F −34.46−5.83 log10 (hBS [m])−20 log10 ( Case 3: Mobile stations are used as relay stations. All ) 5.0 44.9−6.55 log10 (hBS [m]) dW = 10 (3) associated nodes are uniformly distributed over the circular cell. The main differences between Cases 2 and 3 are in the path for the WINNER path loss model and loss models and somewhat in RS positions. RS placements of Case 2 may have restrictions whereas Case 3 has the Pt −SN R−N0 −N F −38.4−20 log10 (f [GHz]/5.0)+0.7hm 35 dI = 10 (4) highest degree of randomness. Operational link distances are the shortest for Case 3 due to low antenna heights and transmit for the IEEE path loss model. Pt is the transmit power in powers and high noise figures. Case 1 addresses pre-scheduled dBm, SN R denotes the required signal-to-noise ratio in dB, directions (angles) for each incremental RS. This assures good N0 is the power spectral density of thermal noise in dBm, non-overlapping RS coverage at relatively few RSs. and N F is the receiver noise figure in dB. OFDM system D. Two-Hop Throughput Classes link performance parameters are adopted from [9] giving the Two-hop throughput can be calculated from the link capacSN R minimum requirements for modulation classes as 6.4, 9.4, 16.4, and 22.7 dB. The lowest SN R threshold is sufficient ities of individual single-hop links simply as [10]  −1 for BPSK and the highest for 64-QAM. Corresponding channel 1 1 C2-hop = + (6) coding rates are 1/2 for all other modulation schemes except Chop1 Chop2 for 64-QAM that has the rate 2/3. where Chop1 and Chop2 are the BS-RS hop and RS-MS hop capacities, respectively. The resulting throughput combinations are collected into the matrix of Table I, yielding ten throughput C. Two-Hop Scenarios for Throughput Evaluation classes altogether. Case 1: Fixed relay stations are located at fixed distance (alIII. N UMERICAL R ESULTS ways within the radius of single-hop coverage). For increasing the number of relay stations the angles between BS and RS are Some numerical examples are shown next to illustrate determined according to an algorithm where the overlapping the downlink throughput performance and statistics of relayRS coverage is minimized. Equation (5) illustrates how the enhanced links. Additional parameters for numerical evaluaproposed angle picking and splitting algorithm works as the tions are presented in Table II.

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TABLE II K EY PARAMETERS IN THE NUMERICAL EXAMPLES Parameter BS antenna height hBS RS antenna height hRS MS antenna height hMS BS transmit power PtBS RS transmit power PtRS MS transmit power PtMS RS receiver noise figure N FRS MS receiver noise figure N FMS Number of relay stations NRS Carrier frequency f Signal bandwidth Thermal noise N0

TABLE IV T HROUGHPUT / MODULATION CLASS BREAK DISTANCES

Value 25 m 1.5 m (mobile), 10 m (fixed) 1.5 m 37 dBm 24 dBm (mobile), 30 dBm (fixed) 24 dBm 9 dB (mobile), 7 dB (fixed) 9 dB 1, 2, 4, 8, 16, 32, 64, 128 5.0 GHz 100 MHz -93.9794 dBm

Path Loss Model WINNER, BS-MS WINNER, BS-RS WINNER, RS-MS WINNER, MS-MS IEEE, BS-MS IEEE, BS-RS IEEE, RS-MS IEEE, MS-MS

64-QAM 38.50 m 43.79 m 22.68 m 14.49 m 58.80 m 99.21 m 37.10 m 25.00 m

16-QAM 57.77 m 65.71 m 33.11 m 20.19 m 89.00 m 150.16 m 56.16 m 37.84 m

QPSK 90.69 m 103.16 m 50.40 m 29.18 m 141.06 m 237.99 m 89.00 m 59.98 m

BPSK 110.02 m 125.15 m 60.35 m 34.17 m 171.84 m 289.91 m 108.42 m 73.06 m

0

10

TABLE III S HARES OF SINGLE - HOP THROUGHPUT CLASSES

−1

10

BPSK 0.3206 0.3204 0.3261 0.3263

QPSK 0.4037 0.4029 0.4056 0.4054

16-QAM 0.1533 0.1534 0.1512 0.1508

Outage probability

PLW, dRS = 49.7 m

Path Loss Model WINNER, theor. WINNER, sim. IEEE, theor. IEEE, sim.

64-QAM 0.1224 0.1232 0.1171 0.1175

PL , d W

RS

= 43.8 m

PLW, dRS = 65.7 m −2

10

PL , d I

RS

= 63.4 m

PLI, dRS = 99.2 m PLI, dRS = 150 m PLW, dRS < 110 m −3

10

Table III shows theoretical and simulated percentages of throughput classes over the circular plane. The theoretical results can be derived directly from spatial coverage areas once the distances r1 , r2 , r3 , and r4 are known and fixed (e.g., solved from (3) or (4)). Service area probability density function (PDF) for different single-hop throughput classes thereby becomes  πr2 r2 1  = r12 , for 64-QAM,  πr42  4    π(r2 −r2 1 )2 = (r2 −r2 1 )2 , for 16-QAM, πr4 r4 p1-hop (A) = (7) π(r3 −r2 )2 (r3 −r2 )2  = , for QPSK,  2 2 πr r  4 4    π(r4 −r3 )2 = (r4 −r3 )2 , for BPSK. 2 πr r2 4

4

All simulation results have been generated by running 100000 realizations per random RS location and extracting the desired statistics from them. The theoretical and simulated results are in close agreement. The service area employing QPSK modulation is the dominant one (over 40% of the total singlehop coverage area for both path loss models). Furthermore, switching the path loss model barely alters the occurrence probability of the classes although the break distances in these models deviate significantly. Table IV depicts the edge distances for switching between achievable throughput classes at different link types and channel models (i.e., solved from (3) and (4) with BS, RS and MS specific parameters from Table II). Fig. 2 shows the outage probability curves at various twohop link geometries. An outage event is experienced if SNR of either of the links BS-RS or RS-MS is below 6.4 dB. The key variables are the placement and the number of relay stations over the cell area. In all cases, increasing the density of relay stations reduces clearly the outage probability. However, some link geometries end up in saturated Pout levels where further

PLW, dRS < 49.7 m PLI, dRS < 172 m PLI, dRS < 63.4 m PLW, MS relay

−4

10

1

PLI, MS relay 2

4

8 16 Number of relay stations

32

64

128

Fig. 2. Two-hop link outage probabilities at various path loss models and relay station geometries.

increase in the number of RSs does not pay off. Figs. 3 and 4 collect the first and second moment statistics of throughput performance with the same set-up as in Fig. 2. Additionally, single-hop mean throughput and standard deviation are plotted as a reference. In all set-ups the mean throughput increases steadily as the RS density increases. Yet, only one 2-hop geometry can reach the average performance of the respective 1-hop link. Due to highest attenuation the BSMS-MS links have the lowest throughput. Throughput variance of all two-hop links is less than in their 1-hop reference cases. Variations are not very strongly dependent on the the number of RSs. A histogram of the throughput class occurrences with WINNER path loss model having dRS = 43.8 m is presented in Fig. 5. It is noteworthy that only a fraction of the possible throughput classes are realized. The most drastic throughput increase is experienced at the first incremental steps in RS density. Higher the RS density the better the probability to find high quality links. This trend is best seen at the extremes where the outages decrease and the occurrences in the highest throughput class increase. A similar plot for the IEEE path loss model with dRS = 99.2 m is presented in Fig. 6. Now the outage probability and the lowest throughput class are experienced only at small number of RSs. The average throughput outperforms the previous case due to more favorable link

358

0.7

25 PLW, dRS = 49.7 m PL , d W

RS

= 43.8 m

PLW, dRS = 65.7 m = 63.4 m

PL , d

= 99.2 m

I

RS

I

RS

PL , d

Mean throughput [Mbps]

I

RS

< 110 m

PL , d

< 49.7 m

RS

W

15

= 150 m

PL , d W

RS

PL , d I

RS

0.6

0.5

from left to right NRS = 1, 2, 4, 8, 16, 32, 64, 128

< 172 m

PLI, dRS < 63.4 m

Probability

20

PL , d

PL , MS relay W

PLI, MS relay PL , 1−hop W

10

PLI, 1−hop

0.4

0.3

0.2

5 0.1

0 1

2

4

8 16 Number of relay stations

32

64

0

128

0

18.4333

27.6500

Fig. 5. Distribution of two-hop throughput classes for WINNER path loss model with dRS = 43.8 m. 0.7

16

from left to right NRS = 1, 2, 4, 8, 16, 32, 64, 128

PLW, dRS = 49.7 m PL , d W

RS

= 43.8 m

0.6

PLW, dRS = 65.7 m

14

PL , d

=63.4 m

PL , d

= 99.2 m

I

RS

I

RS

PL , d I

12

RS

= 150 m

0.5

PL , d S < 110 m W

R

PL , d W

RS

PL , d I

RS

< 49.7 m

< 172 m

Probability

Throughput standard deviation [Mbps]

11.0568

Throughput [Mbps]

Fig. 3. Mean throughputs at various path loss models and relay station geometries.

PLI, dRS < 63.4 m

10

PL , MS relay W

PLI, MS relay PL , 1−hop W

8

0.4

0.3

PLI, 1−hop

6

0.2

4

0.1

2 1

6.1425

0

2

4

8 16 Number of relay stations

32

64

128

0

6.1425

11.0568

18.4333

27.6500

Throughput [Mbps]

Fig. 4. Throughput standard deviations at various path loss models and relay station geometries.

geometries and thereby altered performance merits. Histograms of Fig. 7 express the distributions of throughput classes while the RS positions are uniformly distributed around the BS inside a disk of radius 49.7 m. By increasing the the number of relays located in the coverage area the outages decrease steadily and the concentration of throughput classes moves towards the higher end. Fig. 8 illustrates the throughput shares of the case where other mobile stations are utilized as relays. This means that the propagation models are not as favorable as in the case of fixed RSs. Thus, the low throughput classes are registered more frequently than in the previously shown cases. Because all communicating nodes are randomly dropped over the coverage area all link quality (throughput) classes are conceivable. As NRS increases the occurrences in throughput classes 6.14, 11.06, 18.43, and 27.65 Mbps

Fig. 6. Distribution of two-hop throughput classes for IEEE path loss model with dRS = 99.2 m.

become more frequent. The other throughput classes have their maximum likelihoods at medium NRS values. IV. C ONCLUSION Single-hop and relay-extended two-hop link throughput performances were evaluated in various link geometries and two propagation models. A novel algorithm was proposed to jointly minimize the number of required relay stations and maximize the RS coverage area. The proposed scheme was compared, in terms of throughput statistics and link outage probabilities, to random RS placement schemes and a reference single-hop scenario. Four level modulation was assumed with two NLOS path loss models. The results showed that the proposed RS placement scheme clearly achieves the same mean throughput as the random setting with significantly less RSs. However, the results depend also strongly on the BS-RS distance that

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0.8

should be carefully balanced in order to satisfy both the desired outage and throughput criteria.

from left to right NRS = 1, 2, 4, 8, 16, 32, 64, 128 Probability

0.6 0.4

ACKNOWLEDGMENT

0.2

The author would like to thank the Finnish Funding Agency for Technology and Innovation (Tekes), Nokia, Nokia Siemens Networks, and Elektrobit (EB) for the project funding.

0

0

5.5284 6.1425 Throughput [Mbps]

9.2144

R EFERENCES

0.8

Probability

0.6

[1] R. Babst, B. H. Walke, D. C. Schultz, P. Herhold, H. Yanikomeroglu, S. Mukherjee, H. Viswanathan, M. Lott, W. Zirwas, M. Dohler, H. Aghvami, D. D. Falconer, and G. P. Fettweis, “Relay-based deployment concepts for wireless and mobile broadband radio,” IEEE Commun. Mag., vol. 42, pp. 80–89, Sept. 2004. [2] IEEE 802.16’s Relay Task Group. [Online]. Available: http://ieee802. org/16/relay/index.html [3] WINNER - Wireless World Initiative New Radio. [Online]. Available: http://www.ist-winner.org/

0.4 0.2 0

11.0568

13.8250 18.4333 Throughput [Mbps]

27.6500

Fig. 7. Distribution of two-hop throughput classes at WINNER path loss model with dRS ∈ [0, 49.7] m.

Probability

0.8

from left to right NRS = 1, 2, 4, 8, 16, 32, 64, 128

0.6 0.4 0.2 0

0

3.4550

4.6067

5.5284

6.1425

6.9100

Throughput [Mbps]

Probability

0.8 0.6 0.4 0.2 0

9.2144

11.0568

13.8250

18.4333

27.6500

Throughput [Mbps]

Fig. 8. Distribution of two-hop throughput classes at IEEE path loss model with MS relay.

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