Uplink Random Access Scheme with Prioritized ... - IEEE Xplore

Uplink Random Access Scheme with Prioritized Orthogonal Layers for OFDMA CSI Feedback Megumi Kaneko∗ , Kazunori Hayashi∗ , Petar Popovski# , Hiroyuki Yomo# and Hideaki Sakai∗

Graduate School of Informatics, Kyoto University Yoshida Honmachi Sakyo–ku, Kyoto, 606-8501, Japan Department of Electronic Systems, Aalborg University Niels Jernes Vej 12, DK-9220 Aalborg, Denmark Email: [email protected], [email protected], [email protected], [email protected], [email protected] ∗

#

Abstract— The optimization of the Downlink (DL) performance in wireless systems that utilize Orthogonal Frequency Division Multiple Access (OFDMA) requires knowledge of the Channel State Information (CSI) for each user over each subchannel at the Base Station (BS), which requires a high amount of Uplink (UL) radio resources. In this work, we focus on the problem of CSI feedback by UL Random Access (RA). We introduce the concept of variable collision protection, where the probability that a feedback information experiences a collision depends on its importance. By partitioning the CSI into orthogonal layers of priority, and by allocating different numbers of RA slots to each layer, this scheme ensures that the feedback success probability is higher for the CSI with better quality, as it is more likely to be used by the scheduler. Analytical and simulation results show that our proposed scheme provides an excellent trade-off between system performance and the amount of feedback overhead.

I. I NTRODUCTION Recently, there has been a growing interest in the design of radio resource allocation algorithms for Downlink (DL) Orthogonal Frequency Division Multiple Access (OFDMA) system. OFDMA offers the possibility to exploit the MultiUser Diversity (MUD) effect [1] with a fine per-subcarrier granularity in order to maximize cell throughput. To do so, the knowledge of the Channel State Information (CSI) per user is required at the Base Station (BS). However, as the number of users and subcarriers grow, the amount of CSI sent in the Uplink (UL) becomes prohibitively high. Such an overhead takes radio resource portions from the DL transmission, directly affecting its throughput. Many works have tackled on the problem of reducing the amount of UL CSI feedback. Usually, in order to limit the amount of feedback, modulation levels are fed back instead of SINR values, or per-subchannel CSI rather than per-subcarrier as in [2], where several subcarriers are grouped into a subchannel. However, these reduction techniques are not sufficient. In principle, there are two approaches for providing CSI feedback in the UL. The first is to dedicate a fixed UL control channel. The second is the use of a Random Access (RA) channel. A lot of previous works have considered the first issue. Thus, [3] showed that not This work was supported by the Grant-in-Aid for JSPS Fellow no. 204205 from the Ministry of Education, Science, Sports, and Culture of Japan, and by the KMRC R&D Grant for Mobile Wireless from Kinki Mobile Radio Center, Foundation.

all the feedback is required to keep the MUD gain in scheduling. That is, the higher the channel quality of a subchannel, the higher its chances to be allocated. Thus, CSI should be reported only if it is higher than a predefined threshold. In [4], a simplified opportunistic feedback scheme is proposed for an OFDM system. In [5], we have proposed an adaptive feedback encoding method which can optimize the amount of feedback according to the variable amount of CSI requested by the BS. This scheme can achieve a significant feedback reduction while keeping a good scheduling performance. The advantage of CSI feedback by RA over the fixed control channel is that the amount of UL channel resources can be further limited. This issue has been studied in [6] [7] which propose different protocols for a Single Carrier (SC) system. However, to the best of our knowledge, it has not been investigated in the context of an OFDMA system. In this paper, we propose a new method of CSI feedback by UL RA. We introduce the concept of variable collision protection, where the probability that a certain feedback information experiences a collision depends on the importance of that CSI. Here we propose orthogonal allocation of RA slots among the CSI with different qualities. That is, the amount of CSI is first reduced by only considering the subchannels with good quality, then, depending on their channel quality, their CSIs are fed back with varying collision protection, depending on the number of RA slots. As the quality of the CSI reduces, the level of protection diminishes since they have a lower chance to be used by the BS scheduler. II. S YSTEM M ODEL We focus on the single cell DL scheduling in an OFDMA system, where users feed back to the BS the CSI containing their per-subchannel modulation level every time frame. We adopt a discrete Adaptive Modulation (AM) model where the Signal-to-Noise-Ratio (SNR) of each user in each subchannel is quantized by the SNR thresholds σm of Table I for uncoded Quadrature Amplitude Modulation (QAM) symbols [8]. We define the AM level of a subchannel as the level m among M corresponding to the largest SNR threshold that is not larger than that subchannel’s SNR. The Full CSI of a user is defined as the group of the N AM levels of the N subchannels, for one scheduling time frame. Furthermore, we assume that the average user SNR over the whole bandwidth (or the

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corresponding average AM level), which varies independently among users, is known at the BS. This is reasonable since the average AM level is slowly varying and needs to be updated only few times in several frames, using a very small number of feedback bits. In our scheme, when there is no CSI available for a subchannel at the BS, a random user is scheduled. III. C ONVENTIONAL UL CSI F EEDBACK S CHEME BY RA We adopt the following collision model: if two users or more select the same slot for RA, there is collision, and the CSI for all the involved users is lost. Packet errors due to channel fading and noise are not considered in the RA channel. In the reference Full CSI-RA scheme, all users try to feedback their Full CSI. Given S slots for random access, each user selects one slot among S. If user k picked slot s, his full CSI is successfully transmitted to the BS if no other user selected the same slot. If several users select the same slot, then all their CSIs are lost. CSI is sent through the RA channel using the lowest AM level, which is the most robust. A CSI is composed of the user ID, the AM level per subchannel, and Cyclic Redundancy Check (CRC) bits. As S slots for RA are reserved, the total number of bits BFRA for feedback is thus BFRA = S × (bID + dlog2 M e × N + bCRC ),

(1)

where bID denotes the number of bits used for user ID, log2 M the number of bits required for encoding the M AM levels, d.e the ceil function, and bCRC the number of bits for CRC. A second reference scheme is defined, denoted ThresholdRA scheme, where only users having subchannel SNRs higher than a certain threshold feedback. If the threshold is set to AM level 4, users with subchannels with level 4 or 5 choose a slot for random access. This is equivalent to say that the L-best AM levels are requested by the BS, with L = 2. For each subchannel, we need to specify the AM level among the ones above the threshold, or if it has a lower level, thus the number of bits for feedback BThresh becomes BThresh = S × (bID + dlog2 (L + 1)e × N + bCRC ).

(2)

IV. P ROPOSED UL CSI F EEDBACK S CHEME BY RA WITH O RTHOGONAL S LOTS A. For Maximum CSI (Max CSI) Algorithm The Max CSI algorithm allocates in each subchannel the user with the highest instantaneous SNR γk,n . In our proposed scheme, we extend the idea of [5] where the subchannels with the same AM level are grouped together. For example, if we consider all the subchannels of all the users that support AM TABLE I D ISCRETE ADAPTIVE MODULATION M ODEL Modulation Rate r [b/symbol] AM Level m SNR Threshold σm [dB]

BPSK 1

QPSK 2

16-QAM 4

64-QAM 6

256-QAM 8

1 −∞

2 13.6

3 20.6

4 26.8

5 32.9

level 5 with rate r5 (256-QAM), they constitute a group of subchannels with the highest reporting priority. We refer to this group as layer 1. Then, the subchannels in layer 2 are those that support AM level 4 with rate r4 . In our scheme, we consider a random access channel composed of S slots and address the problem of RA slots distribution among the different layers, in the case of orthogonal division. For example, if the 2-best AM levels are requested by the BS, how many slots S4 should be reserved for r4 and how many slots S5 for r5 ? This RA channel is illustrated in Fig. 1.

slot

t

S5

S4=S-S5 S

Fig. 1.

Proposed RA channel, example with S = 10, L = 2.

This scheme is referred as the Orthogonal-RA scheme. The per user CSI is composed of the user ID, one AM level (that can be shared by several subchannels), and CRC bits. Thus, since only one AM level is fed back per slot, instead of coding the AM level for each subchannel as in the conventional scheme, the AM level is first coded, followed by N bits with 0 or 1. A value 1 at the n-th bit position marks that the n-th subchannel has the AM level in question. The total number of bits reserved for feedback BORA is BORA = S × (bID + dlog2 M e + N + bCRC ).

(3)

Compared to the Threshold-RA scheme, Orthogonal-RA has a higher collision probability since a slot is chosen per layer (e.g., if a user has subchannels with r5 and r4 , he will use 2 slots) versus only one slot per user having subchannels above the threshold, in the reference scheme. However, by adjusting the orthogonal slot distribution in our scheme, we can vary the collision probability among each layer, in order to maximize the overall throughput. Thus, a variable collision protection can be achieved, where the higher quality CSI experiences lower collision probability compared to the lower quality CSI, as subchannels with higher AM levels have a higher probability to be scheduled than those with lower ones. B. For Proportional Fair Scheduler (PFS) Algorithm The feedback of L-absolute levels significantly reduces the number of collisions, while ensuring a high throughput for a large number of users thanks to the MUD effect. However, it may result in poor fairness, as users with lower channel qualities would hardly be scheduled. To avoid this, we introduce the feedback of relative-best levels, which is more adequate for PFS, where subchannel n is allocated to the user r with the best peak ρk,n = Rk,n 0 , with rk,n the instantaneous k subchannel rate and R0k the past average rate of user k over a time window T . In this case, a user reports his L-best levels,

978-1-4244-4148-8/09/$25.00 ©2009 This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the IEEE "GLOBECOM" 2009 proceedings.

relatively to his average channel condition, so that reported AM levels vary among users, enabling users with lower AM levels to be scheduled. To reduce collisions, we introduce additional thresholds which define the layers of priority for the channel peaks. For example, if β and α are two thresholds with β < α, there will be 2 layers, one with Sα slots and the other with Sβ slots, and Sα + Sβ = S. If the 2-relative best levels are requested, each user identifies his subchannels with the 2-relative best peaks. Then, for the subchannels which peaks are in [β, α[ the user selects one slot among Sβ , and if the peaks are in [α, ∞[, he selects one slot among Sα . Note that again, one slot is chosen per peak value (which can be shared by several subchannels due to the discrete AM model), which corresponds to one AM level since the user’s past average rate is constant over subchannels. Thus, the AM level is fed back, so the number of bits for feedback remains BORA . In the reference Threshold-RA scheme for PFS, users with subchannels which peaks are above the basic threshold β are allowed to feedback. In one slot, all the AM levels of subchannels with peaks larger than β are encoded. Since all AM levels are possible per subchannel, the number of bits is in this case equal to BFRA . The benefit of our proposed layered scheme is analyzed using the total cell throughput for Max CSI algorithm. To facilitate the analysis, we consider a simplified cell model. We consider a circular cell of radius R where users are generated uniformly. The distance of a user location to the cell center is denoted xk . We denote γk,n the instantaneous SNR of a subchannel for this user. Thus, the joint probability distribution of γk,n and x is p(γk,n , xk ) = p(γk,n /xk ) × p(xk ), where p(γk,n /xk ) is the conditional probability of the instantaneous SNR given the user location and p(xk ) is the probability to have this user location. Assuming Rayleigh fading environments, the instantaneous SNR γk,n follows an exponential distribution, 1 − γγk,n e ¯k , γ¯k

with σm expressed in linear and σM+1 = +∞. Q5,i is the probability that at least one subchannel among N supports AM level 5, for user i, Q5,i = 1 − (1 − p5,i )N .

(4)

where γ¯k denotes the average SNR of this user. Fixing ³ the´SNR αexp , to be 0 dB at the edge of the cell, we assume γ¯k = xRk where αexp is the path loss exponent chosen equal to 3. Under the assumption of uniform user distribution, we obtain 2xk . (5) R2 A. Analysis for Proposed CSI Feedback with Orthogonal RA p(xk ) =

In the analysis, we focus on a subchannel n, since the cell throughput is defined as the sum of the each subchannel throughput divided by the total number of subchannels N, which have independent instantaneous SNRs. Thus the subscript n is dropped in the sequel. However, the analysis is still multi-carrier specific since the allocation of subchannel n depends on the other subchannels. First, we determine the probability that the best AM level r5 is allocated on

(7)

There is successful report if there is no collision with the other K − 1 users that have at least one subchannel among N with r5 , and since there are S5 slots for RA in this layer, µ ¶ K Y Q5,i Pk (SR, r5 ) = p5,k × 1− . (8) S5 i=1,i6=k

As users have different positions, we take the average joint distribution P k (SR, r5 ) over all positions xi ∈ [0, R], Z R Z R P k (SR, r5 ) = ··· Pk (SR, r5 ) × x1 =0

V. P ERFORMANCE A NALYSIS

p(γk,n /xk ) =

subchannel n. For a user k, we determine the joint probability of supporting the AM level 5 on subchannel n and of reporting successfully, Pk (SR, r5 ). We define pm,k , the probability mass function (pmf) that subchannel n supports AM level m Z σm+1 σ 1 − γγ¯ − σm − m+1 e k dγ = e γ¯k − e γ¯k . (6) pm,k = γ¯k σm

xK =0

(9)

p(x1 ) · · · · · · p(xK )dx1 · · · dxK .

Since x1 ,...,xK are independent random variables, where K is the number of users in the cell, we can factorize the integrals, where

P k (SR, r5 ) = I1 × · · · × Ik × · · · × IK ,

Ii

=

Ik

=

Z Z

µ ¶ Q5,i 2xi 1− × 2 dxi S5 R xi =0

(10)

R

R

xk =0

p5,k ×

2xk dxk . R2

for i 6= k (11)

σ5 x3 RR k k − R3 First, let us determine Ik = xk =0 2x e dxk . With a 2 R change of variables y = x3k , Z R3 2 −1/3 − σ53y y e R dy. (12) Ik = 2 y=0 3R

Using Eq. (3.381-1) in [9] we can show that ³ σ ´−2/3 2 5 Ik = × × Γ(2/3) × γinc (σ5 , 2/3), (13) 3R2 R3 where denotes the gamma function defined as Γ(z) = R ∞ −tΓz−1 dt, and γRinc the incomplete gamma function, de0 e t u fined as γinc (z, u) = 0 e−t tz−1 dt [9]. Next, we calculate Ii , 5 which can be written Ii = 1 − Q S5 , where µ ¶N Z R σ5 x3 i 2xi − R 3 Q5 = 1 − dxi . (14) 1−e 2 xi =0 R

With the change of variables y = x3k and using Newton’s binomial theorem, the second term becomes Z R3 N σ5 ay 2 −1/3 X a y CN (−1)a e− R3 dy. (15) Σ5 = 2 y=0 3R a=0

978-1-4244-4148-8/09/$25.00 ©2009 This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the IEEE "GLOBECOM" 2009 proceedings.

Using Eq. (3.381-1) in [9], we finally obtain µ ¶K−1 Q5 P (SR, r5 ) = p5 × 1 − , S5

B. Analysis for Full CSI Feedback with Random Access (16)

where the index k was dropped since users are generated uniformly in the cell, and 2 ³ σ5 ´−2/3 p5 = Γ(2/3) × γinc (σ5 , 2/3) 3R2 R3 N X 2 ³ σ5 a ´−2/3 Q5 = 1 − CaN (−1)a 2 Γ(2/3) 3R R3 a=0

(17)

×γinc (σ5 a, 2/3).

Similarly, we can write the joint probability of supporting the AM level 4 on subchannel n and of reporting successfully P (SR, r4 ). In this case, a user with AM level 4 has to compete with K −1 competitors who have at least one subchannel with AM level 4 among N. Therefore we have µ ¶K−1 Q4 P (SR, r4 ) = p4 × 1 − , (18) S − S5 with S5 < S where 2 ³ σ4 ´−2/3 p4 = Γ(2/3) × γinc (σ4 , 2/3) − p5 3R2 R3 N a X X Q4 = 1 − CaN (−1)a Cba (−1)(a−b) a=0

b=0

µ ¶−2/3 2 σ5 b + σ4 (a − b) 3R2 R3 ×Γ(2/3) × γinc (σ5 b + σ4 (a − b), 2/3).

(19)

Finally, the overall throughput given by analysis can be written (20)

where POMax (ri ) expresses that there is at least one user with the joint probability P (SR, ri ), i = 4, 5, ¡ ¢K POMax (ri ) = 1 − 1 − P (SR, ri ) . (21) The outage cases, e.g., when there are no reports of r5 nor r4 , occur with probability Pout = 1 − POMax (r5 ) − POMax (r4 ) × (1 − POMax (r5 )), and a random user is allocated on that subchannel with the AM level corresponding to his average SNR level γ r . Thus, the throughput τr is τr

=

M X

m=1

"

rm P (σm ≤ γ r < σm+1 )

¶2/αexp # µ ¶2/αexp 1 1 = r1 1 − + rM σ2 σL "µ ¶2/αexp µ ¶2/αexp # M−1 X 1 1 + rm − (22) σm σm+1 m=2 µ

with σ1 = 0 and σM+1 = +∞.

b=1

(23)

where pm and P (r < rm ) are the probability for a subchannel to support AM level m, and the probability for a subchannel to support a AM level strictly smaller than m, respectively, averaged over all possible user positions. Eq. (23) expresses that j out of K users have no collision with the other K − 1 users, and b out of these j users support rm while the other j − b users achieve a lower rate. We can determine pm by < 5, where fm = observing that pm = fm − fRm+1 for m RR ∞ 1 − γγ¯ − σγ¯m k k dγ = e . Using 0 fm,k p(x)dx and fm,k = σm γ¯k e Eq. (3.381-1) in [9], 2 ³ σm ´−2/3 Γ(2/3) × γinc (σm , 2/3). (24) fm = 3R2 R3 For m = 5, p5 = f5 . In the same way, we observe that P (r < rm ) = 1 − fm . The overall throughput given by analysis is ANA τFRA

M X

=

m=1

×

ANA τOMax = r5 POMax (r5 ) +r4 POMax (r4 )(1 − POMax (r5 )) + τr Pout ,

For this scheme, the joint probability of supporting a AM level m and reporting success PF (SR, rm ), can be written µ ¶(K−1)×j K X 1 j PF (SR, rm ) = CK 1 − S j=1 Ã µ ¶(K−1) !(K−j) X j 1 × 1− 1− Cbj pbm P (r < rm )(j−b) S

where Pout = 1 −

rm × PF (SR, rm ) + τr × Pout ,

PM

m=1 PF (SR, rm )

(25)

and τr defined in (22).

C. Analysis for Threshold CSI Feedback with Random Access For the threshold based reference scheme, a user will feedback if at least one of his subchannels supports r5 or r4 , expressed by probability Q4,5 Q4,5

= 1−

N X

CaN (−1)a

a=0

2 ³ σ4 a ´−2/3 3R2 R3

×Γ(2/3) × γinc (σ4 a, 2/3).

(26)

Thus, the throughput can be written ANA τThr = r5 PThr (r5 ) + r4 PThr (r4 )(1 − PThr (r5 )) + τr Pout , (27) where PThr (ri ) expresses that there is at least one user with the joint probability P (SR, ri ), i = 4 or 5, equal to à !K−1 Q4,5 P (SR, ri ) = pi × 1 − . (28) S

VI. N UMERICAL R ESULTS First, using the formulas obtained by analysis, we compare the performance of the different schemes. As mentioned previously, we simply model one cell as a circle with radius R = 0.5 km, where users are uniformly distributed. The Max CSI algorithm is performed over 8 subchannels or subcarriers,

978-1-4244-4148-8/09/$25.00 ©2009 This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the IEEE "GLOBECOM" 2009 proceedings.

5

Cell Throughput [b/s/Hz]

4.5

Cell Throughput, [b/s/Hz]

5 4.5 4

ANA S5=10 SIMU S5=10 ANA S5=18 SIMU S5=18 ANA FRA SIMU FRA Full CSI ANA Thresh SIMU Thresh

3.5 3 2.5 2 1.5 1 10

Fig. 3.

20

30

40 50 Number of users

60

70

Cell throughput for Max CSI algorithm

2 1.8 1.6

OMax S5=10 OMax S5=18 FRA Max Full Max Thresh Max

1.4 1.2 1 0.8 0.6

0.2 10

3.5

Fig. 4.

3

2.5

Fig. 2.

5.5

0.4

4

2 0

6

Net Cell Throughput, [b/s/Hz]

for different numbers of users. Note that as the number of subchannels grows, the gap between the overheads BThresh and BORA increases (for N = 8, BThresh /BORA ' 1.2 but for N = 32, BThresh /BORA ' 1.6), so the performance gain of the proposed scheme will increase. There are S = 20 slots for RA and L is fixed to 2, bID = 10 bits and bCRC = 8 bits. Fig. 2 shows the throughput given by analysis for the proposed scheme, OMax algorithm, for all slot distributions and different number of users. We can first observe that the curves are rather flat, and that there is not a distinct optimal point, even if the maximum occurs at S5 = 9 in all three cases. That is, by an equal distribution of slots among the two layers, a near optimal throughput is achieved. As the number of users grows, the flatness of the curve diminishes, but very slowly. Note that, equal slot distribution means unequal collision protection since the probability of occurrence of AM level 5 is smaller than that of AM level 4, since γ follows an exponential distribution. Thus, in this setting, a lower collision probability is achieved for the feedback of the CSI with highest quality, hence providing a higher protection.

ANA OMax K=30 ANA OMax K=50 ANA OMax K=70

5

10 S5

15

20

Max CSI algorithm with orthogonal RA slots (OMax), analysis.

In Fig. 3, the throughput curves obtained by analysis and simulations are compared. In all cases, simulations validate the analysis very well. In addition to the reference scheme described in section III, we introduce the Full CSI-Fixed scheme where all users feedback their full CSI in a reserved control channel. This scheme, which achieves the throughput upper-bound, uses BFix feedback bits, BFix = (bID + log2 (M ) × N + bCRC ) × K.

(29)

For a low number of users, the Full CSI-RA scheme achieves a higher throughput than the proposed scheme, but is outperformed as the number of users increases, due to the increasing number of collisions. In terms of throughput, we can see that the proposed OMax algorithm with a near-optimal slot distribution (S5 = S4 = 10) achieves a similar performance as the Threshold-RA scheme, even with the increased number of collisions due to layering, as explained in Section IV. That is, the drawback due to the higher number of collisions is canceled out by the variable collision protection effect, e.g.,

20

30

40 50 Number of users

60

70

Net Cell throughput for Max CSI algorithm

the feedback of a whole information using one slot is in this case similar to the feedback of parts of that information using multiple slots but with a higher protection of the important parts. Thus, for K = 50 and S5 = 10, the probability of feedback success for a user having subchannels in layer 1 is (1 − Q5 /S5 )K−1 = 0.94, and for layer 2, (1 − Q4 /S4 )K−1 = 0.86, whereas it is (1 − Q4,5 /S)K−1 = 0.92 for a user having subchannels with r5 or r4 in the Threshold-RA scheme. Then, the difference between both schemes comes from the overhead, as observed in Fig. 4. The performance metric used is the net cell throughput τ˜, which is the achieved cell throughput given the amount of overhead used for UL CSI, bdata , (30) bdata + bOH where τ is the cell throughput, bdata the number of bits carrying data and bOH , the number of overhead bits for CSI. It can be seen in Fig. 4 that the proposed scheme outperforms all reference schemes, for S5 = S4 = 10. With a different slot distribution, namely S5 = 18, the performance degrades notably when K = 70. The net throughput for Full CSI-Fixed is tremendously decreased by the amount of overhead, and by the number of collisions for Full CSI-RA. Finally, PFS algorithm is evaluated with the time window T = 1000. The 2 relative-best AM levels are required and τ˜ = τ ×

978-1-4244-4148-8/09/$25.00 ©2009 This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the IEEE "GLOBECOM" 2009 proceedings.

where Rk is the amount of resource allocated to user k. J is comprised between 1 and 1/K, where 1 indicates absolute fairness and 1/K indicates unfairness. Figs. 5 and 6 show the net cell throughput and fairness performances, respectively. The proposed scheme, the PFS algorithm with Orthogonal-RA scheme (OPFS) is evaluated with different slot distributions among the 2 layers, (Sα = 5, Sβ = 15), (Sα = 10, Sβ = 10) and (Sα = 15, Sβ = 5). In terms of net cell throughput, the reference algorithms, PFS with Full CSI-Fixed, Full CSI-RA and Threshold-RA schemes are outperformed by all 3 cases of the proposed feedback scheme. But in terms of fairness, the case (Sα = 5, Sβ = 15) is not adequate as it achieves the lowest Jain’s index. However, with (Sα = 10, Sβ = 10) and (Sα = 15, Sβ = 5), a good fairness level is achieved, the latter case even improving the fairness of Full CSI-RA and Threshold-RA schemes. Note that when K is small, these schemes experience a low number of collisions, so the scheduler can make use of most of the users’ CSI for Full CSI-RA, or the CSIs strictly larger than 1 for Threshold-RA. When K is large, these reference schemes suffer from collisions so that more subchannels are in outage and a random user is scheduled, which increases Jain’s index as users are given equal opportunity. In contrast, by considering only the L-best peaks among the ones strictly larger than 1 (L = 2 here), we significantly reduce the number of collisions. Furthermore, by adapting the slot distribution between the 2 layers, i.e., peaks in ]1, 2[ or [2, ∞[, the levels of throughput/fairness can be varied. If the focus is on improving the net throughput, then (Sα = 5, Sβ = 15) should be chosen, whereas (Sα = 15, Sβ = 5) gives the best fairness performance while at the same time outperforming net throughput compared to reference algorithms. 1 0.9

OPFS Sα=5 OPFS Sα=10

Net Cell Throughput, [b\s\Hz]

OPFS Sα=15

0.8 0.7

FRA PFS Full PFS Thresh PFS

0.6 0.5 0.4 0.3 0.2 0.1 10

Fig. 5.

20

30

40 50 Number of users

60

70

Net cell throughput for PFS algorithm

0.74 0.72 0.7 Jain fairness, [b/s/Hz]

the threshold α and β are set to 2 and 1, where each user feedbacks if peaks are strictly larger than 1, i.e., only if the subchannel instantaneous rate is strictly larger than its average value (corresponding to the average user’s SNR). To measure fairness, Jain’s index J is introduced, defined as [10] PK ( k=1 Rk )2 , (31) J= P 2 K× K k=1 Rk

0.68 0.66 0.64 0.62

OPFS Sα=5 OPFS Sα=10 OPFS S =15 α

0.6 0.58

10

Fig. 6.

FRA PFS Full PFS Thresh PFS

20

30

40 50 Number of users

60

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Jain’s fairness index for PFS algorithm

VII. C ONCLUSION We have investigated the problem of CSI feedback in a cellular OFDMA system. We have proposed a method for CSI feedback using UL RA, with orthogonal partition among CSI levels of different quality. The scheme provides a variable collision protection depending on the importance of the CSI, while reducing the amount of feedback overhead. The analysis and simulation results have shown that, with adequate slot distributions, the proposed scheme achieved the best net throughput/fairness performance for Max CSI and PFS algorithms, compared to conventional reporting schemes, thanks to its ability to prioritize the best quality CSI and reducing collisions, thereby maximizing MUD gain at the scheduler. In the future work, we intend to study analytically the proposed scheme for PFS to determine the optimal thresholds. Moreover, different user priorities coming from the higher layers may be considered. R EFERENCES [1] R. Knopp and P. Humblet, “Information capacity and power control in single cell multiuser communications,” in Proc. IEEE ICC, vol. 1, Seattle, WA, June 1995, pp. 331–335. [2] M. Sternad, T. Ottosson, A. Ahlen and A. Svensson, “Attaining both coverage and high spectral efficiency with adaptive OFDM downlinks,” in Proc. IEEE VTC–Fall, vol. 4, October 2003, pp. 2486–2490. [3] D. Gesbert and M.S. Alouini, “How Much Feedback is Multi-User Diversity Really Worth,” in Proc. ICC, vol. 1, June 2004, pp. 234–238. [4] P. Svedman, S.K. Wilson, L.J. Cimini Jr., B. Ottersten, “A simplified opportunistic feedback and scheduling scheme for OFDM,” in Proc. IEEE VTC–Spring, vol. 4, Milan, Italy, May 2004, pp. 1878–1882. [5] M. Kaneko, P. Popovski and H. Yomo, “Adaptive Provision of CSI Feedback in OFDMA Systems,” in Proc. IEEE PIMRC, Helsinki, Finland, September 2006, pp. 1–5. [6] T. Tang and R.W. Heath, “Opportunistic feedback for downlink multiuser diversity,” IEEE Commun. Letters, vol. 9, no. 10, pp. 948–950, October 2005. [7] S. Patil and G. de Veciana, “Reducing Feedback for Opportunistic Scheduling in Wireless Systems,” IEEE Trans. Wireless Comm., vol. 6, no. 12, pp. 4227–4232, December 2007. [8] S. T. Chung and A. J. Goldsmith, “Degrees of Freedom in Adaptive Modulation: A Unified View,” IEEE Trans. Comm., vol. 49, no. 9, pp. 1561–1571, September 2001. [9] I. Gradshteyn and I. Ryzhik, Table of Integrals, Series and Products. San Diego, CA: Academic Press, 2000. [10] R. Jain, The art of computer systems performance analysis. John Wiley and Sons, 1991.

978-1-4244-4148-8/09/$25.00 ©2009 This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the IEEE "GLOBECOM" 2009 proceedings.