s

2

noise

sI

, in turn, denotes the

received nominal signal power per antenna while

and are the covariance matrices of the received

(spatial) noise and interference vectors. The superscript

(.)H denotes conjugate transpose. The noise covariance is

assumed diagonal () and independent of

the user index i. The interference modeling, on the other

hand, takes into account the interference from neighbor-

ing cells. Assuming a total of Lint interference sources,

with corresponding path gain vectors

Coverage – the experienced data rate per UE at the

95% coverage probability (5% UE throughput CDF

level).

noise

Σ

,int i

Σ

noise =Σ

,,lic

g

, the overall

interference covariance at receiving UE i is given by

Jain’s fairness index [19].

In addition to Jain’s index, also the coverage and slope

of the throughput CDF reflect the fairness of the sched-

uling algorithms.

With the proposed modified PF scheduler, different

example values for the power coefficients s1 and s2 are

used as shown in Table 2. To focus mostly on the role of

the channel quality reporting, s2 is fixed here to 1 and the

effects of using different values for s1 are then demon-

strated. This way the impact of the different CQI report-

ing schemes is seen more clearly. For the cases of

Best–m and Threshold based CQI reporting schemes, we

fix the value of m equal to 10 and threshold to 5 dB, re-

spectively. Similar example values have also been used

by other authors in the literature earlier, see e.g. [11].

Complete performance statistics are gathered for both

dual antenna MRC and dual antenna IRC UE receiver

cases.

S2

,,,,,

1

int

L

H

intiintli lic lic

l

gg

,,

(12)

where , denotes the received nominal interferer

power per antenna and per interference source (l).

2,,int l i

s

Concerning the actual UE receiver topologies (spatial

filters), both maximum ratio combining (MRC) and in-

terference rejection combining (IRC) receivers are de-

ployed in the simulations. These are given by (see, e.g.,

[6] and the references therein)

Table 2. Different power coefficient combinations used to

evaluate the performance of the proposed scheduler.

,

,2

,

ic

MRC

ic

ic

=h

w

h

(13) Coefficient Value

s1 1 2 4 6 8 10 20

s2 1 1 1 1 1 1 1

and

S. NONCHEV ET AL.

614

Figure 4. Left column: Average sector throughput and coverage for different scheduling schemes and assuming dual-antenna

MRC UE receiver type with full CQI feedback (a, b), Best -m CQI feedback (c, d) and Threshold based CQI feedback (e, f).

M1-M7 refer to the modified PF scheduler with power coefficient values as given in Table 2 (M1: s1=1, s2=1, etc.). Right col-

umn: CDF’s of individual UE throughputs for different scheduling schemes and assuming dual-antenna MRC UE receiver

type with full CQI feedback (a), Best -m CQI feedback (b) and Threshold based CQI feedback (c).

5.1. Dual Antenna MRC UE Receiver Case

Figure 4 (left column) illustrates the average sector

throughput and coverage for the different schedulers,

assuming dual antenna maximum ratio combining (MRC)

UE receiver type. The power coefficient values from

Table 2 are presented as index M, where M1 represents

the first couple (s1=1, s2=1), etc, for the metric calcula-

Copyright © 2009 SciRes. IJCNS

S. NONCHEV ET AL. 615

tion of the modified PF scheduler. The used reference

scheduler is the ordinary proportional fair approach. In

the first coefficient case (M1), in combination with full

CQI reporting scheme, we achieve coverage gain in the order

of 50% at the expense of only 15% throughput loss as shown

in Figure 4 (a) and (b). This sets the basic reference for com-

parisons in the other cases. In the case of best-m and thresh-

old based reporting schemes presented in and (d), and Figure

4 (e) and (f), we have coverage increases by 57% and 63%

with throughput losses of 16% and 19%, correspondingly.

Figure 5. Left column: MCS distributions [%] for different scheduling principles with (a) Full CQI reporting, (b) Best-m CQI

reporting, and (c) Threshold based CQI reporting assuming dual-antenna MRC UE receiver. Right column: CDF’s of sched-

uled PRB’s per user for different schedulers with (a) Full CQI reporting, (b) Best-m CQI reporting, and (c) Threshold based

CQI reporting assuming dual-antenna MRC UE receiver.

Copyright © 2009 SciRes. IJCNS

S. NONCHEV ET AL.

616

Continuing on the evaluation of relative system per-

formance using the modified PF scheduler, we clearly

see a trade-off between average cell throughput and cov-

erage for different power coefficient cases. The remain-

ing power coefficient values shown in Table 2 are used

for tuning the overall system behaviour together with the

choice of the CQI reporting scheme. In the case of full

CQI feedback and coefficient s1 varying between 2 and

10 (M2–M6) the cell throughput loss is decreased to

around 1%, while the coverage gain is reduced to around

6%. Similar behaviour is observed for the other feedback

reporting schemes as well. The exact percentage values

for the coverage gains and throughput losses are stated in

Table 3 in the end.

Further illustrations on the obtainable system per-

formance are presented in Figure 4 (right column) in

terms of the statistics of individual UE data rates for the

applied simulation scenarios. The slope of the CDF re-

flects generally the fairness of the algorithms. Therefore

we aim to achieve steeper slope corresponding to algo-

rithm fairness. This type of slope change behavior can

clearly be established for each simulation scenario.

Clearly, at 5% (coverage) point of the CDF curves, cor-

responding to users typically situated at the cell edges,

we observe significant data rate increases indicated by

shift to the right for all CQI feedback schemes when the

coefficient s1 is changed in the proposed metric. This

indicates improved overall cell coverage at the expense

of slight total throughput loss.

Figure 5 (left column) shows the modulation and cod-

ing scheme (MCS) distributions for different schedulers

and with applied feedback reporting schemes, still as-

suming the case of 2 antenna MRC UE receiver type.

The negligible decrease in higher order modulation usage

(less than 3%) leads to the increase in the lower (more

robust) ones for improving the cell coverage. In all the

simulated cases, the MCS distribution behaviour has a

relatively similar trend following the choice of the power

coefficients in the proposed packet scheduling. In gen-

eral, the use of higher-order modulations is affected

mostly in the most coarse CQI feedback (threshold based)

case while the other two reporting schemes behave fairly

similarly.

Similarly, Figure 5 (right column) illustrates the

CDF’s of scheduled PRB’s per UE for the different

scheduler scenarios and reporting schemes. Clearly, the

modified PF provides better resource allocation in the

full and best-m feedback cases. Considering the 50%

probability point for the resource allocation, and taking

the case of M1, we have about 5% gain, while in case of

M2 the gain is raised to 15% compared to ordinary PF.

The average obtained improvement for the rest of the

cases is about 33%. In the case of threshold-based feed-

back, the resource allocation is not as efficient, and even

a small reduction in the RB allocation is observed with

small power coefficients, compared to the reference PF

scheduler. Starting from M3, the improvement is anyway

noticeable and the achieved gain is about 20%.

Table 3. Obtained performance statistics compared to ordinary PF scheduler with different CQI reporting schemes and

different power coefficients (M1-M7) for the proposed scheduler. Dual-antenna MRC UE receiver case.

Coverage Gain [%] Throughput Loss [%]

full best-m threshold full best-m threshold

M1 54 57 63 16 16 19

M2 40 42 51 10 10 12

M3 23 26 33 6 6 7

M4 16 18 25 3 4 5

M5 11 14 11 2 3 3

M6 6 7 8 1 2 2

M7 -2 0 -4 0 0 0

Table 4. Obtained performance statistics compared to ordinary PF scheduler with different CQI reporting schemes and

different power coefficients (M1-M7) for the proposed scheduler. Dual-antenna IRC UE receiver case.

Coverage Gain [%] Throughput Loss [%]

full best-m threshold full best-m threshold

M1 56 58 64 15 15 18

M2 43 46 48 9 9 11

M3 26 30 32 6 6 8

M4 17 20 24 4 4 5

M5 10 12 13 2 3 3

M6 8 10 8 2 2 2

M7 -1 1 1 0 1 0

Copyright © 2009 SciRes. IJCNS

S. NONCHEV ET AL. 617

5.2. Dual Antenna IRC UE Receiver Case

Next similar performance statistics are obtained for dual

antenna interference rejection combining (IRC) UE re-

ceiver case. Starting from the primary case M1, with full

CQI, we obtain a 13% loss in throughput and 57% cov-

erage improvement. For the reduced feedback reporting

schemes – best-m and threshold based – we have 13%

and 15% throughput losses and 58% and 62% coverage

gains, respectively. Furthermore, resource allocation

gains for full CQI feedback and best-m are 7% for M1

and 17% for M2 correspondingly. The average obtained

improvement for the rest of the cases is about 34%.

Threshold based reporting scheme leads to decrease of

12% for M1 and 7% for M2, and roughly 14% increase

for the rest of simulated cases. The exact percentage

Figure 6. Jain’s fairness index per feedback reporting

scheme for dual-antenna MRC UE receiver case (up) and

dual-antenna IRC UE receiver case (down). Scheduler type

1 means ordinary PF, while 2-8 means proposed modified

PF with power coefficients as described in Table 2.

read from the figures are again stated in table format in

Table 4 in the end.

5.3. Fairness Index

Figure 6 illustrates the Jain’s fairness index per scheduler

for the applied feedback reporting schemes, calculated

over all the ITOT = 20 UE’s using the truly realized UE

throughputs at each TTI and over all the simulation runs.

The value on the x-axis corresponds to the used sched-

uler type, where 1 refers to the reference PF scheduler

and 2-8 refer to the proposed modified PF schedulers

with different power coefficients. The Jain’s fairness

index defined in [19] is generally in the range of [0…1],

where the value of 1 corresponds to all users having the

same amount of resources (maximum fairness). Clearly,

the fairness distribution with the proposed modified PF

scheduler outperforms the used reference PF scheduler

for both UE receiver types. The received fairness gains

are in range of 2%-17% for the MRC receiver case, and

1%-14% for the IRC receiver case, respectively.

6. Conclusions

In this article, we have studied the potential of advanced

packet scheduling principles in OFDMA type radio sys-

tem context, using UTRAN long term evolution (LTE) as

a practical example system scenario. A modified propor-

tional fair scheduler taking both the instantaneous chan-

nel qualities (CQI’s) as well as resource allocation fair-

ness into account was proposed. Also different practical

CQI reporting schemes were discussed, and used in the

system level performance evaluations of the proposed

scheduler. All the performance evaluations were carried

out with a comprehensive quasi-static system level simu-

lator, conforming fully to the current LTE working as-

sumptions. Also different UE receiver types were dem-

onstrated in the performance assessments. In general, the

achieved throughput and coverage gains were assessed

against more traditional ordinary proportional fair sched-

uling. In the case of fixed coverage requirements and

based on the optimal parameter choice for CQI reporting

schemes, the proposed scheduling metric calculations

based on UE channel feedback offers better control over

the ratio between the achievable cell/UE throughput and

coverage increase. As a practical example, even with

limited CQI feedback, the cell coverage can be increased

significantly (more than 30%) by allowing a small de-

crease (in the order of only 5-10%) in the cell throughput.

This is seen to give great flexibility to the overall RRM

process and optimization.

7. Acknowledgments

Fruitful discussions with Markku Kuusela, Nokia De-

vices, Helsinki, Finland, and Dr. Toni Huovinen, Tam-

Copyright © 2009 SciRes. IJCNS

S. NONCHEV ET AL.

Copyright © 2009 SciRes. IJCNS

618

pere University of Technology, Tampere, Finland, are

greatly acknowledged.

8. References

[1] 3GPP RAN Technical Specification Group, “E-UTRA/

E-UTRAN Overall description, stage 2,” Technical Re-

port TR 36.300, ver. 9.0.0, June 2009.

[2] 3GPP RAN Technical Specification Group, “E-UTRA/

LTE physical layer—General description,” Technical

Report TR 36.201, ver. 8.3.0, March 2009.

[3] 3GPP RAN Technical Specification Group, “Physical

layer aspects for evolved UTRA,” Technical Report TR

25.814, ver. 7.1.0, Oct. 2006.

[4] N. D. Tripathi, et al., “Radio resource management in

cellular systems,” Springer, 2001.

[5] H. Holma and A. Toskala, Eds., “HSDPA/HSUPA for

UMTS–High speed radio access for mobile communica-

tions,” Wiley, 2006.

[6] E. Dahlman, et al., “3G evolution: HSPA and LTE for

mobile broadband,” Academic Press, 2007.

[7] S. Yoon, C. Suh, Y. Cho, and D. Park, “Orthogonal fre-

quency division multiple access with an aggregated sub-

channel structure and statistical channel quality meas-

urements,” in Proc. IEEE Vehicular Technology Confer-

ence (VTC’04 Fall), Los Angeles, CA, September 2004.

[8] Y. Sun, et al., “Multi-user scheduling for OFDMA

downlink with limited feedback for evolved UTRA,” in

Proc. IEEE Vehicular Technology Conference (VTC’06

Fall), Montreal, Canada, September 2006.

[9] I. Toufik and H. Kim, “MIMO-OFDMA opportunistic

beamforming with partial channel state information,” in

Proc. IEEE International Conference on Communications,

Instanbul, Turkey, pp. 5389–5394, June 2006.

[10] T. E. Kolding, F. Frederiksen, and A. Pokhariyal, “Low-

bandwidth channel quality indication for OFDMA fre-

quency domain packet scheduling,” in Proc. ISWCS’06,

Spain, September 2006.

[11] K. I. Pedersen, G. Monghal, I. Z. Kovacs, T. E. Kolding,

A. Pokhariyal, F. Frederiksen, and P. Mogensen, “Fre-

quency domain scheduling for OFDMA with limited and

noisy channel feedback,” in Proc. IEEE Vehicular Tech-

nology Conference (VTC’07 Fall), Baltimore, MD, pp.

1792–1796, Sept. 2007.

[12] P. Svedman, D. Hammarwall, and B. Ottersten, “Sub-

carrier SNR estimation at the transmitter for reduced

feedback OFDMA,” in Proc. European Signal Processing

Conf., Florence, Italy, September 2006.

[13] C. Wengerter, J. Ohlhorst, and A. G. E Von Elbwert,”

Fairness and throughput analysis for generalized propor-

tional fair frequency scheduling in OFDMA,” in Proc.

IEEE Vehicular Technology Conference (VTC’ 05

Spring), Stockholm, Sweden, May 2005.

[14] S. Nonchev, J. Venäläinen, and M. Valkama, “New fre-

quency domain packet scheduling schemes for UTRAN

LTE Downlink,” in Proc. ICT Mobile Summit, Stock-

holm, Sweden, June 2008.

[15] S. Nonchev and M. Valkama, “Efficient packet schedul-

ing schemes for multiantenna packet radio downlink,” in

Proc. Fifth Advanced Int. Conf. Telecommunications

(AICT’09), Venice, Italy, May 2009.

[16] T. E. Kolding, “Link and system performance aspects of

proportional fair scheduling in WCDMA/HSDPA,” in

Proc. IEEE Vehicular Technology Conference (VTC’03

Fall), Orlando, FL, pp. 1717–1723, Oct. 2003.

[17] A. Pokhariyal, K. I. Pedersen, G. Monghal, I. Z. Kovacs,

C. Rosa, T. E. Kolding, and P. E. Mogensen, “HARQ

aware frequency domain packet scheduler with different

degrees of fairness for the UTRAN long term evolution,”

in Proc. IEEE Vehicular Technology Conference (VTC’

07 Spring), Dublin, Ireland, April 2007, pp. 2761–2765.

[18] A. Pokhariyal, T. E. Kolding, and P. E. Mogensen, “Per-

formance of downlink frequency domain packet schedul-

ing for the UTRAN long term evolution,” in Proc. IEEE

Personal, Indoor and Mobile Radio Communications

Conference (PIMRC’06), Helsinki, Finland, Sept. 2006.

[19] D. Chui and R. Jain, “Analysis of the increase and de-

crease algorithms for congestion avoidance in computer

networks,” Computer Networks and ISDN Systems,

1989.

[20] P. Svedman, S. K. Wilson, L. J. Cimini, and B. Ottersten,

“A simplified opportunistic feedback and scheduling

scheme for OFDMA,” in Proc. IEEE Vehicular Technol-

ogy Conference (VTC’04 Spring), pp. 1878–1882, May

2004.

[21] P. Svedman, L. J. Cimini, and B. Ottersten, “Using un-

claimed sub-carriers in opportunistic OFDMA systems,”

in Proc. IEEE Vehicular Technology Conference (VTC’

06 Fall), Montreal, Canada, September 2006.

[22] S. Sanayei, A. Nosratinia, and N. Aldhahir, “Opportunis-

tic dynamic sub-channel allocation in multiuser OFDM

networks with limited feedback,” in IEEE Proc. Inform.

Theory Workshop, San Antonio, TX, pp. 182–186, Oc-

tober 2004.

[23] P. Morgensen, et al., “LTE capacity compared to the

Shannon bound,” in Proc. IEEE Vehicular Technology

Conference (VTC’07 Spring), Dublin, Ireland, April

2007.