>
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.