Channel Feedback Reduction for Wireless Multimedia Broadcast ...

IEEE ICC 2015 - Communication Theory Symposium

Channel Feedback Reduction for Wireless Multimedia Broadcast Multicast Service Systems Yu-Yun Chang, Wei-Shun Liao, Jin-Hao Li and Hsuan-Jung Su Graduate Institute of Communication Engineering, Department of Electrical Engineering National Taiwan University, Taipei, Taiwan Email: [email protected], [email protected], [email protected], [email protected]

Abstract—With the increasing demand of wireless multimedia services, the multimedia broadcast multicast service (MBMS) is an emerging technology which is adopted in new wireless communication standards to enhance multimedia data transmission. In an MBMS system, all the users subscribing to the service receive multimedia data via the broadcast channel from the base station (BS). To ensure the quality of the broadcast, the MBMS users feedback their channel state information (CSI) to the BS. The BS then selects the best transmission mode according to the users’ feedbacks to achieve the optimal result. This CSI feedback operation results in increasing feedback load with the number of users and hence reduces the spectrum efficiency. In this paper, a novel method is proposed to reduce the feedback load of the MBMS systems. The proposed method let the users determine individually whether feeding back their CSI will be critical for the BS to select the transmission mode. If not, a user does not feedback. Different decision rules at the users incur different degrees of MBMS rate loss, which is mathematically analyzed. Through simulations, we show that the proposed method can significantly reduce the CSI feedback load with only a slight impact on the MBMS rate.

I. I NTRODUCTION Because of the increasing demand of digital multimedia services, the multimedia contents over cellular networks, such as mobile TV broadcasting services, are foreseen to become a popular and important business for mobile operators. Therefore, a new point-to-multipoint technology for multimedia data transmission called multimedia broadcast multicast service (MBMS) is becoming an emerging topic in the development of new wireless communication systems, such as IEEE 802.16 [1], the 3rd Generation Partnership Project (3GPP) Long Term Evolution (LTE) [2], etc. MBMS possesses some outstanding properties which are suitable for multimedia data transmission. In an MBMS system, all the users receive data on the same radio resource blocks (RBs) transmitted from the base station (BS, or in the 3GPP terminology, eNodeB). Therefore the transmission bandwidth required is significantly reduced. However, distributing multimedia data to multiple users is a challenging task. With users having different channel This work was supported by the Ministry of Science and Technology, Taiwan, under grants 103-2918-I-002-001, 103-2221-E-002-080, the Ministry of Economic Affairs (MOEA), Taiwan, under grant 103-EC-17-A-03-S1214, and the Advanced Wireless Broadband System and Inter-networking Application Technology Development Project of the Institute for Information Industry which was subsidized by the MOEA.

978-1-4673-6432-4/15/$31.00 ©2015 IEEE

conditions, it is necessary for the BS to decide a transmission mode to achieve the best quality at all users. In order to do this, all MBMS users are required to periodically feedback their channel state information (CSI) to the BS. This feedback operation results in a feedback load increasing linearly with the number of MBMS users which is usually quite large. Therefore, reducing the feedback load while maintaining good system performance is an important topic for MBMS systems. Channel feedback reduction for wireless multiuser systems has been a popular research topic, especially for the general multiuser broadcast channel in which individual users receive different data from the BS. In [3][4], the quantized channel direction information (CDI) is utilized to investigate the sum rate loss of the multiuser broadcast channel when zero-forcing (ZF) beamforming is considered. It is shown that the number of feedback bits of each user needs to be increased linearly with the transmission power when the system sum rate loss is kept as a constant. In [5], a low-feedback scheme with orthogonal random beamforming (ORB) was proposed. For the ORB scheme, each user feeds back only the CSI and the beam index of its favorite beam to the BS. The total feedback load can be reduced significantly with negligible rate loss [6]. With an effort to further reduce the feedback load, a threshold based scheme was proposed in [7], where a user does not need to feedback when its CSI is lower than the threshold. In [8], a multi-threshold scheme was proposed to reduce feedback more effectively. In this multi-threshold scheme, multiple thresholds were derived according to the order statistics of the signal-tointerference-plus-noise ratio (SINR) of each user. Each user then decides the amount of feedback according its CSI and the thresholds so the feedback load of the whole system can be reduced with a limited rate loss. For the MBMS, users receive the same data from the BS. Therefore the aforementioned feedback reduction schemes for the general broadcast channel are not directly applicable to the MBMS system. The key difference between MBMS and the general multiuser broadcast channel is in their performance metrics. For the latter, the users receive different data. In order to maximize the sum rate of the system, usually the users with the best channels are selected by the BS to transmit data to. For an MBMS system, all the users need to receive the same data on the same RBs. In order to make sure

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Fig. 1. The MBMS system model. There are Nt beams each transmitting the signal for an MBMS service. For the MBMS service in consideration, there are K users in a multicast group.

take advantage of the multiplexing gain provided by multiple transmit antennas. In addition, each beam serves a different group of users, and has different data. Since the users have single antenna, each of them can subscribe to only one beam. We assume that, without loss of generality, all the K users in consideration subscribe to the jth beam. The reason for using ORB is its simplicity. Furthermore, since the same signal will be received by all users with different channels, it is not possible to form user specific beams. The BS keeps an ORB precoding matrix W = [w1 w2 · · · wNt ], where wi ∈ CNt ×1 , i = 1, 2, · · · , Nt , are random orthogonal beamforming vectors generated from isotropic distribution. The received signal yjk of MBMS user k which is served on beam j can be expressed as Nt

†

yjk = {hk wj }xj +

†

{hk wl }xl + nk ,

(1)

l=1,l=j

that the data is successfully received by all the users, the transmission rate of the BS is limited by the user with the worst channel. There are some previous works considering the feedback issue of the MBMS system. For example, in [9], the authors proposed a feedback schemes based on the pathloss, geometry information, and block error rate (BLER) of users to reduce the feedback load. However, that work did not investigate the rate performance of the MBMS system. In this paper, a novel threshold based feedback scheme is proposed to reduce the feedback load for the MBMS systems. To derive the proposed scheme, we first investigate the characteristics of the MBMS system. Then the MBMS rate performance is analyzed. The threshold values for this feedback scheme are derived based on the order statistics of the MBMS user channels and the tolerable rate loss of the system. II. S YSTEM M ODEL In this paper, we consider an MBMS system which includes a BS with Nt antennas and Nt different multicast groups. The transmission technology adopted here is orthogonal frequencydivision multiplexing (OFDM), and all the MBMS users in the same group receive the same multimedia data via a broadcast channel, i.e., they receive data on the same radio RBs in each OFDM transmission frame. The MBMS users are all equipped with single antenna. Each MBMS user is capable of measuring the channel gain between itself and the BS. It is assumed that, without loss of generality, there are K MBMS users in a group. We also assume that there is an error-free feedback channel with a constant feedback latency between each MBMS user k, k = 1, 2, · · · , K, and the BS. The feedback channel carries the CSI of the MBMS users to the BS which then determines the modulation and coding scheme (MCS) to be used for transmission. The MBMS system equips neither the automatic repeat request (ARQ) protocol nor the hybrid-ARQ (HARQ) mechanisms. The system diagram is shown in Fig. 1. It is assumed that the system adopts ORB to form multiple beams to

where xm is the data for the MBMS service on beam m, hk ∈ CNt ×1 is the channel fading vector between the BS and the MBMS user k, nk is the noise seen by MBMS user k, and the notation † means the Hermitian operator. From (1), the SINR γˆjk of user k served on beam j is †

γˆjk = Nt

|hk wj |2 P †

l=1,l=j

|hk wl |2 P + N0k

(2)

†

= Nt

|hk wj |2 †

l=1,l=j

|hk wl |2 +

N0k P

,

where P is the transmission power which is constant during each transmission, N0k is the noise power seen by MBMS user k, and | · | is the norm function. As mentioned above, the BS will select the MCS according to the worst channel among all users in the same group, so it can ensure that all the users in the same group can receive the MBMS data successfully. In other words, the BS will select the worst user k ∗ (on beam j) according to the following criterion: k ∗ = arg

min

k∈{1,2,...,K}

γˆjk .

(3)

To select k ∗ , it is necessary that all MBMS users subscribing to the jth beam feedback their CSI to the BS, and then the BS can select a proper MCS according to the criterion in (3). The ergodic rate of the MBMS service on beam j can be expressed as ¯ = E log2 (1 + γˆjk∗ ) , R (4) where E{X} means the expectation function of X. However, this feedback operation needs radio resource which increases with the number of MBMS users. This results in great system inefficiency when the number of users K is large. Therefore, it is necessary to reduce the feedback load to save the system resource.

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III. F EEDBACK R EDUCTION FOR MBMS S YSTEMS To improve the efficiency of the MBMS system, we propose a threshold-based feedback scheme to reduce the system feedback load. To introduce the proposed feedback scheme, firstly we brief the basic concept, and investigate the order statistics of the SINR of MBMS users in Sec. III-A. Then the ergodic rate in the MBMS system and the rate loss will be investigated in Sec. III-B.

users γˆj1 , γˆj2 , · · · , γˆjK , all with PDF (6). In addition, we denote a feedback threshold set which consists of K + 1 thresholds as T = {ξth,0 , ξth,1 , · · · , ξth,K−1 , ξth,K } where ξth,0 = ∞, ξth,K = 0, and ξth,0 > ξth,1 > · · · > ξth,K−1 > ξth,K . Then the probability of the event that the SINR γˆjk of user k is ranked p-th in the group given that its value (i.e., realization) is γ is Pr{ˆ γjk = γ(p) |ˆ γjk = γ} (8) (K − 1)! K−p p−1 = [F (γ)] , [1 − F (γ)] (K − p)!(p − 1)!

A. Threshold Based Feedback Scheme To guarantee successful reception of the MBMS service by all users in the same group, the BS needs to know the worst user’s SINR, as shown in (3). Therefore, if an MBMS user knew the ranking of its SINR in the group, it could decide not to feedback when its SINR was relatively higher in the group. Although it is not possible for a user to exactly know the ranking of its SINR, it is possible to provide the users certain information to assist them to infer their possible rankings. We propose in this paper a threshold based feedback scheme in which a proper threshold is derived for each user so that the user can decide whether to feedback by comparing its SINR to the threshold. With this scheme, most of the users do not need to feedback, thus the feedback load can be reduced significantly. For simplicity, we assume that all the channel fading vectors hk are drawn from identical independently distributed (i.i.d.) Rayleigh distributions, and the precoding matrix W which consists of wj ’s is unitary. In practice, the channels of the users also depend on the locations of the users, and may not be i.i.d. This issue can be handled by methods similar to that used in [10]. † From (2), we denote the signal part |hk wj |2 as Zjk , the Nt † interference part l=1,l=j |hk wl |2 as Wjk , and the noise part N0k P

as ρkj . Specifically, the terms Zjk and Wjk are random variables with independent chi-square (χ2 ) distribution, i.e., Zjk ∼ χ2 (2) and Wjk ∼ χ2 (2Nt − 2), respectively [5]. Then the SINR γˆjk of MBMS user k served on the jth beam can be rewritten as γˆjk =

ρkj

Zjk

+ Wjk

.

(5)

In (5), the probability density function (PDF) f (ˆ γjk ) and k cumulative density function (CDF) F (ˆ γj ) of the SINR γˆjk of the MBMS user k (on beam j), ∀k, can be expressed as k

f (ˆ γjk ) =

e−ρˆγj ρ(1 + γˆjk ) + Nt − 1 k N (1 + γˆj ) t

(6)

and k

F (ˆ γjk )

e−ρˆγj =1− (1 + γˆjk )Nt −1

(7)

respectively. To derive the thresholds for CSI feedback, we denote γ(1) > γ(2) > · · · > γ(K) as the order statistics of the SINR of MBMS

where Pr{X} denotes the probability of event X, and this conditional probability satisfies K

Pr{ˆ γjk = γ(p) |ˆ γjk = γ} = 1.

(9)

p=1

With the conditional probability in (8), when a user’s received SINR is γ, it can infer its most likely rank among all users as Rank(γ) = arg

max

p∈{1,...,K}

Pr{ˆ γjk = γ(p) |ˆ γjk = γ}.

(10)

Based on this observation, we propose to set the thresholds for CSI feedback such that if a user’s received SINR falls in the interval [ξth,l , ξth,l−1 ), it will infer its rank as being the lth. It is worth noting that, given that for all p, the conditional probability in (8) is a unimodal function in γ. Since we hope that a user can infer its rank simply by comparing its SINR to the designed thresholds, the thresholds can be determined according to Pr{ˆ γjk = γ(l) |ˆ γjk = ξth,l } = Pr{ˆ γjk = γ(l+1) |ˆ γjk = ξth,l }. (11) Substituting the condition γˆjk = ξth,l into (8), from (11), each element ξth,l of the threshold set T can be solved by the following expression: l , l = 1, 2, · · · , K, (12) K where F (x) is the CDF in (7). Because of the assumption of i.i.d. Rayleigh fading and ORB for all users, the threshold set T calculated by the method mentioned above can be applied for all MBMS users. Besides, the threshold set T can be computed by (12) at the BS offline. In addition, for the heterogeneous case, i.e., the channels of the users are not i.i.d., the same procedure still can be applied becasue of the fact that every CDF is non-decreasing. After the threshold set is determined, a threshold is selected from the set and then broadcasted to the MBMS users so that each user can decide whether to feedback by comparing its received SINR with this threshold. That is, for a selected and broadcasted threshold ξth,l ∈ T, for the MBMS user k, k ∈ {1, 2, · · · , K}, only when its received SINR falls in the region [0, ξth,l ) will the user feedback its CSI to the BS. Otherwise, the user does not feedback anything. The BS then select the transmission MCS according to the lowest SINR among the users who

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F (ξth,l ) = 1 −


1

In (15) and (16), f (x) and F (x) are the CDF and PDF of the SINR of each MBMS user, respectively. Hence, the probability of the event that at least one user feeds back to the BS is ∗ ∗ Pr γˆjk ≤ ξth,l = 1 − Pr γˆjk > ξth,l (17) K l . =1− K

p=1 p=2 p=3 p=5 p=7 p = 20

0.9 0.8 Pr{ˆ γjk = γ(p) | γˆjk = γ}

0.7 0.6 0.5 0.4 0.3

Therefore, from the criterion (3) and the definition of the rate (4) in Sec. II, together with (14), we can calculate the MBMS rate as

0.2 0.1 0 0

0.5

1

1.5

2

2.5 SINR γ

3

3.5

4

4.5

5

Fig. 2. The conditional probabilities in (8). In this case, Nt = 4, K = 20, and ρ = 10.

have fed back their CSI. If there is no user with its received SINR falling in [0, ξth,l ), the BS adopts ξth,l as the system CSI to transmit data which is guaranteed to be successfully received by all users since γˆjk > ξth,l , ∀k. Apparently the system performance will depend on the broadcasted threshold. This will be analyzed in the next section. B. System Rate Analysis For a selected and broadcasted threshold ξth,l , from (12), the probability of the event that MBMS user k does not feedback anything is γjk ≤ ξth,l } Pr{ˆ γjk > ξth,l } = 1 − Pr{ˆ

(13)

= 1 − F (ξth,l ) l l = . =1− 1− K K When the SINRs of all MBMS users served on beam j are larger than the selected ξth,l , i.e., γˆjk > ξth,l , ∀k, a rate-loss event occurs because the transmission rate may be lower than the minimum rate the worst user can receive successfully. From (13) and the assumption of i.i.d. channels for all users, the probability that a rate-loss event occurs, or in other words, the probability of the event that no user feeds back to the BS, is K ∗

Pr γˆjk > ξth,l = Pr{ˆ γjk > ξth,l } k=1

=

l K

(14)

K ,

∗ where γˆjk = min γˆj1 , γˆj2 , · · · , γˆjK . Besides, the CDF ∗ Fγˆ k∗ (x) and PDF fγˆ k∗ (x) of the random variable γˆjk can j j be expressed as Fγˆ k∗ (x) = 1 − (1 − F (x))

K

(15)

j

and fγˆ k∗ (x) = Kf (x) (1 − F (x)) j

K−1

.

(16)

¯ th,l ) R(ξ (18) ∗ ∗ = E log2 (1 + min γˆjk ) | γˆjk ≤ ξth,l Pr γˆjk ≤ ξth,l k∈Sf (ξth,l ) ∗ ∗ + E log2 (1 + ξth,l ) | γˆjk > ξth,l Pr γˆjk > ξth,l , where Sf (ξth,l ) is the set of users who have fed back their CSI. From (4) and (18), the rate loss for a selected threshold ξth,l can be expressed as ¯ th,l ) ΔR(ξ l K ∗ ∗ = E log2 (1 + γˆjk ) − log2 (1 + ξth,l ) | γˆjk > ξth,l K (19) K

∗ ∗ l (20) γjk − ξth,l ) | γˆjk > ξth,l ≤ E log2 1 + (ˆ K

∗ l K ∗ . (21) ≤ log2 1 + E γˆjk − ξth,l | γˆjk > ξth,l K The derivation from (19) to (20) is due to the fact that the function log2 (1 + x) is a concave and strictly increasing function. The inequality from (20) to (21) comes from Jensen’s inequality for the concave case. In order to evaluate the performance quickly and simply in ¯ u (ξth,l ) advance, we define the upper bound of rate loss ΔR under a specific selected threshold ξth,l as

∗ l K k k∗ ¯ . ΔRu (ξth,l ) log2 1 + E γˆj − ξth,l | γˆj > ξth,l K (22) Given a rate loss requirement, we can select a threshold from the feedback threshold set T by using the upper bound (22) to reduce the feedback load and meet the rate loss requirement. From the analysis above, it can be seen that, given a system tolerable rate loss, the threshold to be broadcasted can be analytically derived. IV. S IMULATION R ESULTS To validate the performance of the proposed feedback scheme for MBMS systems, some simulations are set up to investigate the system performance. In the simulations, there is one BS with 4 antennas, i.e., Nt = 4, in the MBMS system. Each MBMS user is equipped single antenna. The given tolerable rate loss is set to be 0.01 bps/sec, and a largest

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0.35

30 Full CSI feedback Proposed scheme

Full CSI feedback Proposed scheme

0.3

25

20 Feedback load

MBMS rate (bps/Hz)

0.25

0.2

0.15

15

10 0.1 5

0.05

0

5

10

15 20 Number of users

25

0

30

Fig. 3. Rate loss of the MBMS systems.

5

10

15 20 Number of users

25

30

Fig. 4. Feedback load of the MBMS systems.

V. C ONCLUSION threshold is selected to satisfy the rate loss requirement (i.e., ¯ u (ξth,l ) ≤ 0.01) using the above derivations and minimize ΔR the feedback load. The simulation results are shown in Fig. 3 and 4. In both figures, the solid curve with diamond mark is the result of the system with full CSI feedback, while the dashed curve with circle mark is the result with the proposed method. In Fig. 3, it can be seen that the MBMS system rate decreases with the number of users. It is because, when the number of users increases, the probability of occurrence of deep-fading users also increases. Because of the inherent requirement of MBMS system that all the users need to successfully receive data, the user with the worst channel condition limits the system rate. As a result, the system rate decreases with the increase of the number of users. From Fig. 3, it can be seen that the rate loss of the proposed method compared to the full-CSI case is indeed within the setup value 0.01 bps/sec. Besides, from Fig. 4, it can be seen that the feedback load of the proposed method is nearly constant, while for the full-CSI case, the feedback load increases linearly with the number of users. The reason why the proposed method keeps the system feedback load nearly constant is that, from (14), it can be shown that the probability that a user feeds back its CSI under the threshold ξth,l is 1 − Kl . Hence, the expected number of users who feedback is K(1 − Kl ) = K − l. With a given rate loss requirement, it was observed that the selected threshold value decreases with the number of users K, or, the threshold index l increases with K. As a result, K − l is kept almost constant. This phenomenon can also be explained by considering the rate loss upper bound (22) when the number of users K is large. When K is large, the rate loss upper bound is roughly proportional to ( Kl )K which converges to el−K . With a given (fixed) rate loss requirement, when K is large, el−K should be a constant, which means that K − l should be a constant, and K − l is proportional to the feedback load of the system.

In this paper, we investigated the channel feedback issue of MBMS systems. A feedback load reduction method based on thresholds derived from order statistics of the users’ channels was proposed. In addition, the ergodic rate of the MBMS system and the rate loss caused by the proposed feedback reduction method were derived. Through simulations, we showed that the proposed method can significantly reduce the feedback load of MBMS systems while keeping the rate loss within the required level. Therefore, the proposed method can save the feedback bandwidth and well utilize the transmission resource to improve the system efficiency. R EFERENCES [1] The Draft IEEE 802.16m System Description Document, October 2008, available: http://wirelessman.org/tgm/docs/80216m-08 003r7.zip. [2] Multimedia Broadcast/Multicast Service (MBMS); Stage 1 (Release 11). 3GPP TS 22.146 Version 11.1.0, May 2013. [3] T. Yoo, N. Jindal, and A. Goldsmith, “Multi-antenna downlink channels with limited feedback and user selection,” IEEE J. Sel. Areas Commun., vol. 25, no. 7, pp. 1478–1491, Sep. 2007. [4] N. Jindal, “Mimo broadcast channels with finite-rate feedback,” IEEE Trans. Inf. Theory, vol. 52, no. 11, pp. 5045–5060, Nov. 2006. [5] M. Sharif and B. Hassibi, “On the capacity of MIMO broadcast channel with partial side information,” IEEE Trans. Inf. Theory, vol. 51, no. 2, pp. 506–522, Feb. 2005. [6] M. Pugh and B. D. Rao, “Reduced feedback schemes using random beamforming in MIMO broadcast channels,” IEEE Trans. Signal Process., vol. 58, no. 3, pp. 1821–1832, Mar. 2010. [7] D. Gesbert and M. S. Alouini, “How much feedback is multi-user diversity really worth?” in IEEE Int. Conf. on Commun.(ICC), vol. 1, Paris, France, June 20-24 2004, pp. 234–238. [8] J.-H. Li and H.-J. Su, “Opportunistic feedback reduction for multiuser MIMO broadcast channel with orthogonal beamforming,” IEEE Trans. Wireless Commun., vol. 13, no. 3, pp. 1321–1333, Mar. 2014. [9] Y. Cai, S. Lu, C. Wang, P. Skov, Z. He, and K. Niu, “Reduced feedback scheme for LTE MBMS,” in IEEE Vehiclar Technology Conference (VTC Spring), Barcelona, Spain, April 26-29 2009, pp. 1–5. [10] J.-H. Li and H.-J. Su, “Feedback reduction for MIMO broadcast channel with heterogeneous fading,” in IEEE Symposium on Computers and Communications (ISCC), Kerkyra (Corfu), Greece, June 28-July 1 2011, pp. 573–578.

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