Sounding Method for Proportional Fair Scheduling ... - Semantic Scholar
Sounding Method for Proportional Fair Scheduling in OFDMA/FDD Uplink Jung Min Choi1, Hyojin Lee2, Hyun Kyu Chung2, and Jae Hong Lee1 1
2
School of Electrical Engineering, Seoul National University
Mobile Telecommunication Research Lab.
Shillim-dong, Gwanak-gu, Seoul 151-742, Korea
Electronics and Telecommunications Research Institute (ETRI)
e-mail: [email protected]
Daejeon 305-700, Korea
Abstract - Sounding provides a BS with knowledge of the channel state information of a user in an orthogonal frequency division multiple access (OFDMA) full duplex division (FDD) uplink. In this paper, we propose a novel sounding subband allocation algorithm for the proportional fair (PF) scheduler. Simulation results show that our proposed sounding method enables the PF scheduler to achieve the throughput gain and guarantee fairness at the same time.
signals on it in the preceding frame. Therefore, the UL Dsubband allocation in the current frame is dependent on the sounding subband (S-subband) allocation in the preceding frame. This means that the algorithm for the S-subband allocation needs to be developed in relation to that for the UL D-subband allocation. In this paper, we consider the proportional fair scheduling for UL data transmission and propose an S-subband allocation algorithm for it. The paper is organized as follows. In Section II, the system model of the OFDMA/FDD uplink with sounding are described. We introduce the optimal PF scheduler for OFDMA and one of the suboptimal PF schedulers in Section III. Section IV presents the proposed S-subband allocation algorithm for the PF scheduler. Then, in Section V, the simulation results are presented to show the performance of our proposed method in terms of throughput and fairness. Finally, the conclusion is drawn in Section VI.
I. INTRODUCTION Orthogonal frequency division multiple access (OFDMA) is an attractive multiple access technique for packet-based broadband wireless access. Radio resource allocation in OFDMA can exploit both multiuser diversity and frequency diversity to increase the system throughput. To achieve the throughput gain and guarantee fairness at the same time, we can utilize the proportional fair (PF) scheduler for OFDMA. There are some researches [4-6] on the PF scheduler for OFDMA with the assumption that a base station (BS) has the perfect knowledge of every user’s channel state information as per-subband (or per-subcarrier) signal-to-noise-ratio (SNR). However, the assumption is not valid any more in practical systems. In general, there are two methodologies for providing a BS with knowledge of the channel between the BS and user [1]: feedback and sounding. Since the uplink (UL) and downlink (DL) channel responses are usually independent in OFDMA full duplex division (FDD) systems, feedback and sounding can be utilized for DL and UL scheduling respectively. In this paper, we focus on the OFDMA/FDD uplink. Only if a user transmits a sounding signal on a subband, a BS can obtain his instantaneous channel gain of that subband in the OFDMA/FDD uplink. Since the number of OFDMA symbols for sounding cannot be large due to the data rate loss and the number of sounding signals transmitted simultaneously in one subband is limited, the BS obtains the instantaneous channel gains of only a portion of all the users on each subband. Based on the scheduling algorithm at the BS, each subband for UL data transmission (UL D-subband) will be allocated to one of the users who transmitted sounding This work was supported in part by the ITRC Program and the Brain Korea 21 Project.
1550-2252/$25.00 ©2007 IEEE
2732
II. SYSTEM MODEL In an OFDMA/FDD uplink with K users, we denote the number of subbands as N sb . A subband consists of N sc consecutive subcarriers in which the channel gains are highly correlated. A user transmits his sounding signal in a predetermined subband and the BS obtains his channel gain on that subband. To exploit multiuser diversity in the UL scheduling, the BS needs the channel gains of multiple users in each subband. Fig. 1 shows two methods for separating multiple sounding signals in one subband within one OFDMA symbol [1]. The decimation-based method is to separate some multiple users based on the decimation. If the decimation-based method is used, the user must be told which subcarrier offset to use and the users who are assigned to the same S-subband have the different decimated subcarrier sets. In the sequence-based method, the multiple users have different sequences with low cross correlation and occupy all the subcarriers in the Ssubband. Fig. 2 shows the sounding instruction and data channel allocation with minimum latency in the OFDMA/FDD system. In the sounding zone of the current UL frame, a user transmits
III. PROPORTIONAL FAIR (PF) SCHEDULER FOR OFDMA A. OPTIMAL PF SCHEDULER FOR OFDMA Let us review the optimal condition for the PF scheduler for OFDMA, which is introduced in [4]. It is well known that a proportionally fair allocation maximizes the sum of logarithmic average user rates Rk . From this fact, it is shown that a scheduler is proportionally fair for OFDMA if and only if it maximizes the PF metric G defined as ∑ rk ,n n∈Ck G = ∏1 + (T − 1) Rk k∈U
(1)
where U is the user set, Ck is the set of D-subbands allocated to user k in the current frame by a scheduler, and T is the average window size. R k is the average rate of user k at the preceding frame and rk ,n is the instantaneous transmittable rate of the n-th D-subband. However, it is not possible to implement the optimal PF scheduler due to the computational complexity and we consider the suboptimal PF algorithm of [6], named Best Proportional Fair Scheduling (Best-PFS) algorithm.
Fig. 1. Two methods for separating multiple sounding transmissions.
B. BEST-PFS ALGORITHM The Best-PFS algorithm selects, at each iteration, the best PFS user who has the maximum user PFS metric. The user PFS metric of the user k on the n th subband at the l th iteration is defined as
ηk ,n =
rk ,n ( t ) Rkl −1 ( t )
(2)
where Rkl −1 ( t ) is the average rate of the user k at the (l − 1)th iteration in the t th frame. Here, Rk0 ( t ) is set to (1 − 1/ T ) R k , where R k is equal to RkNsb ( t − 1) . At the l th iteration, the best PFS user is selected as follows:
Fig. 2. Sounding instruction and data channel allocation with minimum latency in the OFDMA/FDD system.
( k , n ) = arg max η ∗
sounding signals only on the S-subbands allocated to him, which are predetermined in the UL MAP of the current DL frame. Note that UL sounding is independent of UL data allocation in the same frame. After receiving sounding signals from users, the BS allocates the UL D-subbands based on the proportional fair scheduling algorithm. Then, it also determines the S-subband allocation based on a specific algorithm. In this paper, we consider only low mobility users for simplicity. Then, we can assume that the channel of a user is quasi-static during one frame and the channel gains obtained from sounding signals are almost same to the channel gains during the UL data transmission at the next frame. Since each user’s average channel gain over all the subbands changes much more slowly than a channel gain on a subband, it is a reasonable assumption that the average channel gains of all the users are known at the base station by updating them periodically.
∗
k , n∈N l −1
k ,n
(3)
where Nl −1 is the set of the remaining D-subbands after the (l − 1)th iteration. After the D-subband n∗ is allocated to the user k ∗ , the average rate of each user is partially updated as l −1 ∗ R ( t ) + rk ,n ( t ) , if k = k Rkl ( t ) = kl −1 (4) otherwise. Rk ( t ) , After all the subbands are allocated, the users’ average rates are given by 1 RkNsb ( t ) = 1 − RkNsb ( t − 1) + ∑ rk ,n ( t ). T n∈Ck
(5)
IV. SOUNDING METHOD FOR PF SCHEDULER In this section, we will describe our proposed S-subband allocation algorithm for the PF scheduler. If the number of D-
2733
subbands allocated to user k is mk , we can approximate the data rate of user k at the current frame as
∑r
k ,n
≈ mk r k .
(6)
n∈Ck
Here, r k is the average transmittable rate per D-subband of user k , which is calculated from the average channel gain as follows: p g r k = log 2 1 + 2 k k (7) σ AWGN Γ 2 where pk is the transmission power of the user k , σ AWGN is the power of the additive white Gaussian noise (AWGN), and g k is his average channel gain over all the subbands. The SNR gap Γ is the function of the target BER [3], which is defined as Γ=
− log ( 5BER target )
. (8) 1.5 From (1) and (6), we can obtain the following approximation
∑ rk ,n n∈Ck 1 + ∏ (T − 1) Rk k∈U
mk r k ≈ ∏ 1 + T − 1 R ) k k∈U (
.
(9)
where the sum of the mk 's is equal to the total number of subbands N sb . Now let us define the approximated PF metric i as G mk r k i= G (10) 1 + . ∏ (T − 1) R k k∈U If we find the values of mk 's which maximize the metric i , m can be thought as the estimated number of DG k subbands required for user k . Let us define the multiplexing coefficient as the number of OFDMA symbols in sounding zone, multiplied by the maximum number of sounding signals which can be separated in one S-subband. When the multiplexing coefficient is M , one of the M users is selected to transmit data in that subband with probability 1 / M roughly. Therefore, we determine the number of Ssubbands for user k to mk M . We can find mk 's using the greedy descent algorithm. Algorithm 1 describes the detailed process of the proposed greedy descent S-subband allocation (GDSA) algorithm for the PF scheduler.
We employ the Best-PFS scheduler for the UL data transmission and compare the proposed GDSA algorithm with the round-robin S-subband allocation (RRSA) algorithm. We assume all the users receive sounding instructions from the base station without error and the base station obtains exact channel gains from sounding signals. The system under consideration has parameters given in table I. Path loss model for urban areas and ITU pedestrian channel model-A are employed. We consider a single cell with uniformly distributed users.
V. SIMULATION RESULTS In this section, we present the performance of the proposed sounding algorithm for the PF scheduler, in terms of throughput and proportional fairness. We use as the PF metric of a scheduler the General Proportional Fairness (GPF) metric l as [3], G l ( t ) = logR Nsb ( t ) . G ∑ k
Table I. System Parameters
(11)
k∈U
2734
Bandwidth (only UL)
1.25 MHz
Total number of subcarriers
128
Number of used subcarriers
108
Subcarriers per subband N sc
18
Number of subbands N sb
6
3.00
42
2.95
Averaging window size T
5 frames
2.90
Target BER (uncoded)
10
Cell throughput (bps/Hz)
OFDMA symbols per frame
−3
Fig. 3 shows the GPF performance as a function of time when the number of users K = 20 and the multiplexing coefficient M = 3. We simulated 1000 sets of channel realization and averaged the GPF metrics. The proposed GDSA algorithm outperforms the RRSA algorithm except only the first five frames after the data transmission started.
GDS K=5 GDS K=10 GDS K=15 GDS K=20 RRS K=5 RRS K=10 RRS K=15 RRS K=20
2.85 2.80 2.75 2.70 2.65 2.60 2.55
2
3
4
Multiplexing coefficient M
Fig. 4. Cell throughput according to the multiplexing coefficient M. 48
3.10
46
3.05
44
3.00
42
2.95
Cell throughput (bps/Hz)
GPF
50
40 38 36 34 GDS RRS
32 30
5
10
15 20 Frame Index
25
GDS M=2 GDS M=3 GDS M=4 GDS M=6 RRS M=2 RRS M=3 RRS M=4 RRS M=6
2.90 2.85 2.80 2.75 2.70 2.65
30
2.60 5
10
15
20
Number of users K
Fig. 3. GPF performances of the proposed GDS and the RRS, K =20 and
Fig. 5. Cell throughput according to the number of users K.
M =3.
Fig. 4 shows the throughput performance according to the multiplexing coefficient and Fig. 5 depicts the throughput performance according to the number of users. In Fig. 4, we can see that the throughputs of both the sounding methods increase as the multiplexing coefficient does. In Fig. 5, however, the throughput of the RRSA decreases as the number of the users increases while that of the proposed GDSA increases. The proposed GDSA outperforms the RRSA except that the number of users is 5. This means that the proposed GDSA supports the PF scheduler better than the RRSA. Moreover, we can see that the increase of multiplexing coefficient enables us to exploit multiuser diversity rather than that of the number of users does.
REFERENCES [1] IEEE C802.16e-04/103r2, “Signaling methodologies to support closed-loop transmit processing in TDD-OFDMA,” 7/07/2004. [2] IEEE 802.16e/D12 - Draft IEEE Standard for Local and Metropolitan area Networks
– Part 16: Air Interface for Fixed and Mobile
Broadband Wireless Access Systems – Amendment for Physical and Medium Access Control Layers for Combined Fixed and Mobile Operation in Licensed Bands, IEEE, New York, NY, USA, Oct. 2005. [3] P. S. Chow, “Bandwidth optimized digital transmission techniques for spectrally shaped channels with impulse noise,” Ph. D. Thesis, Standford University, 1993. [4] H. Kim and Y. Han, “A proportional fair scheduling for multicarrier transmission systems,” IEEE Commun. Lett., vol. 9, pp. 210-212, Mar.
VI. CONCLUSIONS
2005.
In the uplink of the OFDMA/FDD system, sounding enables the PF scheduler to exploit the instantaneous channel gains of multiple users. In the process of scheduling UL data of multiple users, the D-subband allocation is related to the Ssubband allocation. To improve the proportional fairness of the considered system, we proposed the GDSA algorithm for the PF scheduler. Simulations indicate that our proposed GDSA outperforms the RRSA in terms of the throughput as well as the GPF metric.
[5] W. Anchum, X. Liang, Z. Xibin, and Y. Yan, “Dynamic resource management in the fourth generation wireless systems,” in Proc. IEEE ICCT 2003, pp. 1095-1098. [6] M. Kaneko, P. Popovski, and J. Dahl, “Proportional fairness in multicarrier system: upper bound and approximation algorithms,” IEEE Commun. Lett., vol. 10, pp. 462-464, June 2006. [7] D. Kivanc, G. Li, and H. Liu, “Computationally efficient bandwidth allocation and power control for OFDMA,” IEEE Trans. Wireless Commun., vol. 2, pp. 1150-1158, Nov. 2003.
2735
2
School of Electrical Engineering, Seoul National University
Mobile Telecommunication Research Lab.
Shillim-dong, Gwanak-gu, Seoul 151-742, Korea
Electronics and Telecommunications Research Institute (ETRI)
e-mail: [email protected]
Daejeon 305-700, Korea
Abstract - Sounding provides a BS with knowledge of the channel state information of a user in an orthogonal frequency division multiple access (OFDMA) full duplex division (FDD) uplink. In this paper, we propose a novel sounding subband allocation algorithm for the proportional fair (PF) scheduler. Simulation results show that our proposed sounding method enables the PF scheduler to achieve the throughput gain and guarantee fairness at the same time.
signals on it in the preceding frame. Therefore, the UL Dsubband allocation in the current frame is dependent on the sounding subband (S-subband) allocation in the preceding frame. This means that the algorithm for the S-subband allocation needs to be developed in relation to that for the UL D-subband allocation. In this paper, we consider the proportional fair scheduling for UL data transmission and propose an S-subband allocation algorithm for it. The paper is organized as follows. In Section II, the system model of the OFDMA/FDD uplink with sounding are described. We introduce the optimal PF scheduler for OFDMA and one of the suboptimal PF schedulers in Section III. Section IV presents the proposed S-subband allocation algorithm for the PF scheduler. Then, in Section V, the simulation results are presented to show the performance of our proposed method in terms of throughput and fairness. Finally, the conclusion is drawn in Section VI.
I. INTRODUCTION Orthogonal frequency division multiple access (OFDMA) is an attractive multiple access technique for packet-based broadband wireless access. Radio resource allocation in OFDMA can exploit both multiuser diversity and frequency diversity to increase the system throughput. To achieve the throughput gain and guarantee fairness at the same time, we can utilize the proportional fair (PF) scheduler for OFDMA. There are some researches [4-6] on the PF scheduler for OFDMA with the assumption that a base station (BS) has the perfect knowledge of every user’s channel state information as per-subband (or per-subcarrier) signal-to-noise-ratio (SNR). However, the assumption is not valid any more in practical systems. In general, there are two methodologies for providing a BS with knowledge of the channel between the BS and user [1]: feedback and sounding. Since the uplink (UL) and downlink (DL) channel responses are usually independent in OFDMA full duplex division (FDD) systems, feedback and sounding can be utilized for DL and UL scheduling respectively. In this paper, we focus on the OFDMA/FDD uplink. Only if a user transmits a sounding signal on a subband, a BS can obtain his instantaneous channel gain of that subband in the OFDMA/FDD uplink. Since the number of OFDMA symbols for sounding cannot be large due to the data rate loss and the number of sounding signals transmitted simultaneously in one subband is limited, the BS obtains the instantaneous channel gains of only a portion of all the users on each subband. Based on the scheduling algorithm at the BS, each subband for UL data transmission (UL D-subband) will be allocated to one of the users who transmitted sounding This work was supported in part by the ITRC Program and the Brain Korea 21 Project.
1550-2252/$25.00 ©2007 IEEE
2732
II. SYSTEM MODEL In an OFDMA/FDD uplink with K users, we denote the number of subbands as N sb . A subband consists of N sc consecutive subcarriers in which the channel gains are highly correlated. A user transmits his sounding signal in a predetermined subband and the BS obtains his channel gain on that subband. To exploit multiuser diversity in the UL scheduling, the BS needs the channel gains of multiple users in each subband. Fig. 1 shows two methods for separating multiple sounding signals in one subband within one OFDMA symbol [1]. The decimation-based method is to separate some multiple users based on the decimation. If the decimation-based method is used, the user must be told which subcarrier offset to use and the users who are assigned to the same S-subband have the different decimated subcarrier sets. In the sequence-based method, the multiple users have different sequences with low cross correlation and occupy all the subcarriers in the Ssubband. Fig. 2 shows the sounding instruction and data channel allocation with minimum latency in the OFDMA/FDD system. In the sounding zone of the current UL frame, a user transmits
III. PROPORTIONAL FAIR (PF) SCHEDULER FOR OFDMA A. OPTIMAL PF SCHEDULER FOR OFDMA Let us review the optimal condition for the PF scheduler for OFDMA, which is introduced in [4]. It is well known that a proportionally fair allocation maximizes the sum of logarithmic average user rates Rk . From this fact, it is shown that a scheduler is proportionally fair for OFDMA if and only if it maximizes the PF metric G defined as ∑ rk ,n n∈Ck G = ∏1 + (T − 1) Rk k∈U
(1)
where U is the user set, Ck is the set of D-subbands allocated to user k in the current frame by a scheduler, and T is the average window size. R k is the average rate of user k at the preceding frame and rk ,n is the instantaneous transmittable rate of the n-th D-subband. However, it is not possible to implement the optimal PF scheduler due to the computational complexity and we consider the suboptimal PF algorithm of [6], named Best Proportional Fair Scheduling (Best-PFS) algorithm.
Fig. 1. Two methods for separating multiple sounding transmissions.
B. BEST-PFS ALGORITHM The Best-PFS algorithm selects, at each iteration, the best PFS user who has the maximum user PFS metric. The user PFS metric of the user k on the n th subband at the l th iteration is defined as
ηk ,n =
rk ,n ( t ) Rkl −1 ( t )
(2)
where Rkl −1 ( t ) is the average rate of the user k at the (l − 1)th iteration in the t th frame. Here, Rk0 ( t ) is set to (1 − 1/ T ) R k , where R k is equal to RkNsb ( t − 1) . At the l th iteration, the best PFS user is selected as follows:
Fig. 2. Sounding instruction and data channel allocation with minimum latency in the OFDMA/FDD system.
( k , n ) = arg max η ∗
sounding signals only on the S-subbands allocated to him, which are predetermined in the UL MAP of the current DL frame. Note that UL sounding is independent of UL data allocation in the same frame. After receiving sounding signals from users, the BS allocates the UL D-subbands based on the proportional fair scheduling algorithm. Then, it also determines the S-subband allocation based on a specific algorithm. In this paper, we consider only low mobility users for simplicity. Then, we can assume that the channel of a user is quasi-static during one frame and the channel gains obtained from sounding signals are almost same to the channel gains during the UL data transmission at the next frame. Since each user’s average channel gain over all the subbands changes much more slowly than a channel gain on a subband, it is a reasonable assumption that the average channel gains of all the users are known at the base station by updating them periodically.
∗
k , n∈N l −1
k ,n
(3)
where Nl −1 is the set of the remaining D-subbands after the (l − 1)th iteration. After the D-subband n∗ is allocated to the user k ∗ , the average rate of each user is partially updated as l −1 ∗ R ( t ) + rk ,n ( t ) , if k = k Rkl ( t ) = kl −1 (4) otherwise. Rk ( t ) , After all the subbands are allocated, the users’ average rates are given by 1 RkNsb ( t ) = 1 − RkNsb ( t − 1) + ∑ rk ,n ( t ). T n∈Ck
(5)
IV. SOUNDING METHOD FOR PF SCHEDULER In this section, we will describe our proposed S-subband allocation algorithm for the PF scheduler. If the number of D-
2733
subbands allocated to user k is mk , we can approximate the data rate of user k at the current frame as
∑r
k ,n
≈ mk r k .
(6)
n∈Ck
Here, r k is the average transmittable rate per D-subband of user k , which is calculated from the average channel gain as follows: p g r k = log 2 1 + 2 k k (7) σ AWGN Γ 2 where pk is the transmission power of the user k , σ AWGN is the power of the additive white Gaussian noise (AWGN), and g k is his average channel gain over all the subbands. The SNR gap Γ is the function of the target BER [3], which is defined as Γ=
− log ( 5BER target )
. (8) 1.5 From (1) and (6), we can obtain the following approximation
∑ rk ,n n∈Ck 1 + ∏ (T − 1) Rk k∈U
mk r k ≈ ∏ 1 + T − 1 R ) k k∈U (
.
(9)
where the sum of the mk 's is equal to the total number of subbands N sb . Now let us define the approximated PF metric i as G mk r k i= G (10) 1 + . ∏ (T − 1) R k k∈U If we find the values of mk 's which maximize the metric i , m can be thought as the estimated number of DG k subbands required for user k . Let us define the multiplexing coefficient as the number of OFDMA symbols in sounding zone, multiplied by the maximum number of sounding signals which can be separated in one S-subband. When the multiplexing coefficient is M , one of the M users is selected to transmit data in that subband with probability 1 / M roughly. Therefore, we determine the number of Ssubbands for user k to mk M . We can find mk 's using the greedy descent algorithm. Algorithm 1 describes the detailed process of the proposed greedy descent S-subband allocation (GDSA) algorithm for the PF scheduler.
We employ the Best-PFS scheduler for the UL data transmission and compare the proposed GDSA algorithm with the round-robin S-subband allocation (RRSA) algorithm. We assume all the users receive sounding instructions from the base station without error and the base station obtains exact channel gains from sounding signals. The system under consideration has parameters given in table I. Path loss model for urban areas and ITU pedestrian channel model-A are employed. We consider a single cell with uniformly distributed users.
V. SIMULATION RESULTS In this section, we present the performance of the proposed sounding algorithm for the PF scheduler, in terms of throughput and proportional fairness. We use as the PF metric of a scheduler the General Proportional Fairness (GPF) metric l as [3], G l ( t ) = logR Nsb ( t ) . G ∑ k
Table I. System Parameters
(11)
k∈U
2734
Bandwidth (only UL)
1.25 MHz
Total number of subcarriers
128
Number of used subcarriers
108
Subcarriers per subband N sc
18
Number of subbands N sb
6
3.00
42
2.95
Averaging window size T
5 frames
2.90
Target BER (uncoded)
10
Cell throughput (bps/Hz)
OFDMA symbols per frame
−3
Fig. 3 shows the GPF performance as a function of time when the number of users K = 20 and the multiplexing coefficient M = 3. We simulated 1000 sets of channel realization and averaged the GPF metrics. The proposed GDSA algorithm outperforms the RRSA algorithm except only the first five frames after the data transmission started.
GDS K=5 GDS K=10 GDS K=15 GDS K=20 RRS K=5 RRS K=10 RRS K=15 RRS K=20
2.85 2.80 2.75 2.70 2.65 2.60 2.55
2
3
4
Multiplexing coefficient M
Fig. 4. Cell throughput according to the multiplexing coefficient M. 48
3.10
46
3.05
44
3.00
42
2.95
Cell throughput (bps/Hz)
GPF
50
40 38 36 34 GDS RRS
32 30
5
10
15 20 Frame Index
25
GDS M=2 GDS M=3 GDS M=4 GDS M=6 RRS M=2 RRS M=3 RRS M=4 RRS M=6
2.90 2.85 2.80 2.75 2.70 2.65
30
2.60 5
10
15
20
Number of users K
Fig. 3. GPF performances of the proposed GDS and the RRS, K =20 and
Fig. 5. Cell throughput according to the number of users K.
M =3.
Fig. 4 shows the throughput performance according to the multiplexing coefficient and Fig. 5 depicts the throughput performance according to the number of users. In Fig. 4, we can see that the throughputs of both the sounding methods increase as the multiplexing coefficient does. In Fig. 5, however, the throughput of the RRSA decreases as the number of the users increases while that of the proposed GDSA increases. The proposed GDSA outperforms the RRSA except that the number of users is 5. This means that the proposed GDSA supports the PF scheduler better than the RRSA. Moreover, we can see that the increase of multiplexing coefficient enables us to exploit multiuser diversity rather than that of the number of users does.
REFERENCES [1] IEEE C802.16e-04/103r2, “Signaling methodologies to support closed-loop transmit processing in TDD-OFDMA,” 7/07/2004. [2] IEEE 802.16e/D12 - Draft IEEE Standard for Local and Metropolitan area Networks
– Part 16: Air Interface for Fixed and Mobile
Broadband Wireless Access Systems – Amendment for Physical and Medium Access Control Layers for Combined Fixed and Mobile Operation in Licensed Bands, IEEE, New York, NY, USA, Oct. 2005. [3] P. S. Chow, “Bandwidth optimized digital transmission techniques for spectrally shaped channels with impulse noise,” Ph. D. Thesis, Standford University, 1993. [4] H. Kim and Y. Han, “A proportional fair scheduling for multicarrier transmission systems,” IEEE Commun. Lett., vol. 9, pp. 210-212, Mar.
VI. CONCLUSIONS
2005.
In the uplink of the OFDMA/FDD system, sounding enables the PF scheduler to exploit the instantaneous channel gains of multiple users. In the process of scheduling UL data of multiple users, the D-subband allocation is related to the Ssubband allocation. To improve the proportional fairness of the considered system, we proposed the GDSA algorithm for the PF scheduler. Simulations indicate that our proposed GDSA outperforms the RRSA in terms of the throughput as well as the GPF metric.
[5] W. Anchum, X. Liang, Z. Xibin, and Y. Yan, “Dynamic resource management in the fourth generation wireless systems,” in Proc. IEEE ICCT 2003, pp. 1095-1098. [6] M. Kaneko, P. Popovski, and J. Dahl, “Proportional fairness in multicarrier system: upper bound and approximation algorithms,” IEEE Commun. Lett., vol. 10, pp. 462-464, June 2006. [7] D. Kivanc, G. Li, and H. Liu, “Computationally efficient bandwidth allocation and power control for OFDMA,” IEEE Trans. Wireless Commun., vol. 2, pp. 1150-1158, Nov. 2003.
2735
