This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the IEEE Globecom 2011 proceedings.
QoS Oriented Cross-Layer Design for Improving Multimedia Transmissions over Cooperative Relaying Networks Dan Chen, Student Member, IEEE, and Hong Ji, Senior Member, IEEE
Key Laboratory of Universal Wireless Communications, Ministry of Education Beijing University of Posts and Telecommunications, Beijing, 100876, P.R. China Email:
[email protected], and
[email protected] Abstract—We propose in this paper, a distributed optimal relay selection scheme for cooperative wireless networks to improve the performance of multimedia transmissions, while taking into account application layer quality of service (QoS), i.e., multimedia distortion. We formulate the cooperative relaying network as a stochastic bandit system. Moreover, the adaptive modulation and coding (AMC) strategy at the physical layer and the intra-refreshing rate at the application layer are jointly considered from a cross-layer design perspective. The objective is to minimize multimedia distortion, increase spectral efficiency, as well as prolong the average network lifetime. The optimal relay selection policy has an indexability property that dramatically reduces the on-line computation and implementation complexity. Simulation results are presented to show the effectiveness of the proposed scheme.
I. Introduction Cooperative relaying has been recently incorporated in the 802.16j standard for wireless mobile multi-hop relay systems [1], and has been regarded as a promising technology to combat channel fading and improve system performance, e.g., by saving transmit power, increasing capacity and extending coverage [2]. The basic idea behind cooperative communication rests on the observation that intermediate relay nodes are assigned to help a source node forward information to the destination node, hence forming a virtual distributed antenna array, by which the limitation of installing multiple antennas on small mobile terminals can be overcome and the spatial diversity can be achieved. There are mainly three relaying protocols, i.e., decode-and-forward (DF), amplify-and-forward (AF) and compressed-and-forward (CF). Appropriate relay selection is crucial in improving the performance of cooperative diversity. The authors in [3] presented a distributed best-relay selection approach based on local measurements of the instantaneous channel state information (CSI) without topology information. A semi-distributed user relaying algorithm that jointly optimizes relay selection and resource allocation is proposed in [4] for cooperative wireless networks. In [5], a cross-layer MAC protocol with effective relay selection is devised to improve link utilization and boost network throughput by exploiting beneficial cooperation. In [6], the authors developed a joint relay selection and power minimization algorithm for incremental redundancybased cooperative diversity with code combining and spacetime coded protocol with diversity combining. Although much This paper is jointly sponsored by the Beijing Municipal Natural Science Foundation under Grand 4102044, the National Natural Science Foundation for Distinguished Young Scholar under Grand 61001115, and the National Nature Science Foundation under Grant 60832009.
work has been done for relay selection in cooperative wireless networks, most of the previous work selects the best relay according to the current observed CSI, assuming that the channel states remain unchanged from the current frame to the next. However, this memoryless assumption is often unreasonable given the time-varying nature of wireless environments. On the other hand, multimedia applications such as video surveillance, conference and video telephony, have been promoted to utilize broadband communications over the nextgeneration mobile network. In [7], a cross-layer optimization approach is proposed to achieve the best video quality. The authors in [8] showed that adaptively adjusting intra-refreshing rate, an application layer parameter, can improve the error resilience capability of the coded video data. It is well known that considering QoS at the application layer is more important than at other layers from users’ point of view. However, to the best of our knowledge, previous literature on multimedia transmissions over cooperative relaying networks mainly takes physical layer QoS, e.g., throughput and achievable date rate, as the design criteria. In this paper, we propose a distributed optimal relay selection scheme considering application layer QoS to improve multimedia transmissions over cooperative relaying networks. To minimize multimedia distortion and increase spectral efficiency, we take a cross-layer approach to jointly consider AMC at the physical layer and intra-refreshing rate at the application layer in the process of relay selection optimization. Moreover, the residual energy state of relay nodes is taken into account to prolong the average network lifetime. We formulate the cooperative relaying network as a stochastic bandit system [9], [10]. The finite-state Markov chain (FSMC) model, which has been widely applied to model fading channels [11], is used to predict the upcoming channel condition for the subsequent packets transmission. II. System Description As shown in Fig. 1, we consider a wireless cooperative relay network consisting of one source node S, one destination node D and L intermediate relay nodes, denoted by R = {Rl | l = 1, 2, · · · , L}, each of which is equipped with only one antenna. Assume that the application layer multimedia packets are organized into frames with the same time duration T f at the data-link layer and stored in the transmit buffer. These frames are then divided into bit-streams to be transmitted from S to D with the help of the best relay node chosen from the candidate relay set Rc = Rn | n ∈ N = {1, 2, · · · , N} . In
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This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the IEEE Globecom 2011 proceedings.
order to maximize the application layer QoS (i.e., minimize distortion) for multimedia transmissions, we jointly consider different layer design parameters, i.e., AMC at the physical layer and intra-refreshing rate at the application layer, in the process of optimal relay selection. Totally L relay nodes
Candidate relay set R.c R1 Broadcast
S
Rn
ĂĂ
Buffer
hSR n
hR n D
MRC
hSD
D
1) Channel Model: To the best of our knowledge, the FSMC model has been widely accepted as an effective approach to capture the correlation structure of fading process [11]. In the following, we adopt this model to characterize the time-varying behavior of the Rayleigh block-fading channel by partitioning the range of average received SNR into L discrete levels, and each level corresponds to a state in the Markov chain. More specifically, for the considered links S-D, S-Rn and Rn -D, the average received SNR can be modeled as a random variable γ¯ ij (t) evolving according to a FSMC, which is characterized by a set of states, Γ = [Γ0 , Γ1 , · · · , ΓL−1 ]. Let φgn hn (t) be the probability that γ¯ ij (t) transits from state gn to state hn at epoch t. Therefore, the channel state transition probability matrix can be expressed as
RN Candidate relay node Non-coop. relay node
Fig. 1.
Φn (t) = φgn hn (t) L×L ,
time slot t S to R & D
first time-phase
R to D
second time-phase
Multimedia Transmission Scenario in Cooperative Relay Networks
In the following, we assume that N out of L relay nodes con stitute the candidate relay set, i.e., Rc = Rn | n ∈ N = {1, 2, · · · , N} , and Rn (n ∈ N ) satisfies the following criteria: • Rn can decode both RTS and CTS packets successfully; • The estimated average channel gain in direct link S-D is less than the minimum of average channel gains in the two-hop relaying links S-Rn and Rn -D, i.e., σ¯ SD < min{σ¯ SRn , σ¯ Rn D }. A. System Models We consider block-Rayleigh fading channels, i.e., the channel condition remains unchanged during the transmission of one data block. Besides, we conduct an investigation into DF relaying strategy with two-time-phase implementation. In the first phase, S broadcasts its signal to all relay nodes and D, and then Rl ∈ R attempts to decode it. In the second phase, the bestrelay node chosen from Rc forwards the re-encoded signal to D. Finally, D combines the two copies of the received signals using the maximum-ratio-combining (MRC) method. Assume full CSI is available at S and D. Let hSD , hSRl and hRl D denote the channel coefficients associated with link S-D, S-Rl and Rl D, respectively. For notational convenience, let σ¯ SD = E[|hSD |2 ], σ ¯ SRl = E[|hSRl |2 ] and σ ¯ Rl D = E[|hRl D |2 ] be the corresponding average channel gains. E[·] represents the expectation. The receiver noise is assumed to be Additive white Gaussian noise (AWGN) with zero mean and power spectral density N0 . The system transmission duration is assumed to be partitioned into T time slots with equal length, i.e., T = {0, 1, · · · , T − 1}. Denote the action of each relay node Rn (n ∈ N ) in time slot t ∈ T as an (t), an (t) ∈ A = {0, 1}, in which an (t) = 0 means Rn is passive in time time slot t, and an (t) = 1 means active. Throughout this paper, we assume that a single relay node is selected from Rc to assist multimedia transmissions, i.e., N n=1 an (t) = 1. Besides, S and Rn transmit signals with fixed power PS and PRn , respectively.
(1)
where φgn hn = Pr γ¯ ij (t + 1) = hn | γ¯ ij (t) = gn , for gn , hn ∈ Γ. 2) Energy Model: Most wireless mobile devices are battery-powered with limited energy. In order to prolong the network lifetime, the energy consumption and residual energy should be taken as important factors when selecting the active relay node. However, due to the dynamic operations of such devices caused by multimedia applications and wireless transmissions, the energy consumption changes dynamically over time. Therefore, the residual energy is modeled as a random variable en . For simplification, we divide the continuous range of residual battery energy en into discrete levels, E = {E1 , E2 , · · · , EV }, where V denotes the number of total available energy states. Let En (t) be the residual energy state of Rn in time slot t. As discussed in [12], the transition of residual energy levels can be modeled as a Markov chain. We define the energy state transition probability matrix as Ψan (t) = ψaζn ηn (t) V×V ,
(2)
where ψaζn ηn (t) = Pr En (t + 1) = ηn | En (t) = ζn , an (t) = a , for ζn , ηn ∈ E . After each data transmission action, the residual energy state will remain unchanged or transits to a lower state. 3) Adaptive Modulation and Coding Model: The M -ary quadrature amplitude modulation ( M -QAM) using R=1/2 and R=3/4 Turbo code is employed. Under assumption that the average received signal-to-noise ratio (SNR) is divided into K regions, we assign constellation size Mk to the k-th region, k ∈ K = {0, 1, · · · , K − 1} and Mk = 2k . Given knowledge of target BER (i.e., BER0 ), the decoding SNR thresholds for different region boundaries can be calculated by [13] γk∗
⎧ 2 ⎪ ⎪ ⎪ ⎪ − ln(5BER0 ) · (2k − 1); k = 0, 1, 2, · · · , K − 1 ⎨ 3 =⎪ . ⎪ ⎪ ⎪ ⎩ +∞; k=K
(3)
Since we consider two-hop DF relaying strategy, the AMC mode will be determined by the minimum of combined average SNRs over two hops, i.e., γt = min{¯γSRn , γ¯ SD + γ¯ Rn D }, where P σ ¯ P σ ¯ γ¯ SRn = SN0SRn , γ¯ SD = PSNσ¯0SD and γ¯ Rn D = RnN0Rn D . If γt is in the range of ∗ ), it will belong to k-th region. [γk∗ , γk+1
This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the IEEE Globecom 2011 proceedings.
B. Rate-Distortion (R-D) Model for Multimedia Applications With the increasing demand for bandwidth in the nextgeneration mobile network, video signals have to be highly compressed by efficient coding algorithms, e.g., MPEG-4 and H.263. However, under the time-varying error-prone wireless environments, the highly compressed video data becomes extremely vulnerable. A single bit error could cause sever degradation in video quality. As a consequence, it is necessary for the video encoder to provide adequate error resilience features for channel error protection. Intra-refreshing, also called intra update of macroblocks (MBs), is taken as an efficient approach to mitigate error propagation for DCT-based video coding [8]. To the best of our knowledge, the intra-coded MB usually requires more bits than inter-coded MB, since the motion compensation of the latter can largely remove the temporal redundancy between two neighboring video frames. However, the intercoded MB enables channel errors introduced in previous frames to propagate along the motion-compensation path, which has significant impact on the video quality. Thus, a tradeoff needs to be made when selecting the coding mode of MBs. Let ξ denote the intra-refreshing rate, i.e., the percentage of MBs coded with intra mode. Given the transmission channel conditions, the overall video quality at the receiver end (i.e., D) can be maximized by determining the optimal ξ. According to [8], the source distortion is given by DS (HS , ξ) = DS (HS , 0) + ξ(1 − ρ + ρξ) · [DS (HS , 1) − DS (HS , 0)],
(4)
where ρ is a constant based on the video sequence, and HS denotes the source coding bit rate. Besides, DS (HS , 0) and DS (HS , 1) represent the distortion values for all frames, when all the MBs are inter and intra coded, respectively. On the other hand, the average channel distortion is p ε · E[Fd (k, k − 1)], DC (p, ξ) = 1 − b + bξ 1 − p
(5)
where p is the packet-loss ratio, ε is the energy loss ratio of the encoder filter, and b is a constant based on the motion randomness of the video scene. Besides, E[Fd (k, k − 1)] denotes the average value of the frame difference Fd (k, k − 1) over the whole time slots. We assume that DS (HS , ξ) and DC (p, ξ) are uncorrelated with each other. Therefore, the total average distortion is D(HS , p, ξ) = DS (HS , ξ) + DC (p, ξ).
(6)
According to (4) and (5), there is a tradeoff between source and channel distortion in selecting the intra-refreshing rate. Consequently, we should determine the optimal ξ∗ such that the overall distortion is minimized, i.e., ξ∗ = arg min D(HS , p, ξ) ξ
(7)
III. Problem Formulation In this section, we formulate the multimedia transmission optimization problem over cooperative relay networks as a stochastic bandit problem [9]. The wireless fading channel and residual energy states change in a Markov fashion according to
their transition probability matrices. We select the best relay over time under a policy u ∈ U , where U is the set of all Markovian policies. A. State Space and Transition Probability In time slot t ∈ {0, 1, · · · , T − 1}, the state of candidate relay node Rn , denoted as in (t), is characterized by S-D channel state γ¯ SD (t), S-Rn channel state γ¯ SRn (t), Rn -D channel state γ¯ Rn D (t) and residual energy state En (t). Consequently, the relay state in (t) can be expressed as the combination of them, that is in (t) = γ¯ SD , γ¯ SRn , γ¯ Rn D , En (t) .
(8)
In practice, γ¯ SD (t), γ¯ SRn (t), γ¯ Rn D (t) and En (t) are independent with each other. Thus, in (t) will change in a Markov fashion, and the corresponding finite-state space is denoted as In , in (t) ∈ In , with the transition probability matrix
Pan (t) = φgn hn (t), φun vn (t), φ xn yn (t), ψaζn ηn (t)
H×H
,
(9)
where φ(t) and ψa (t) are defined in (1) and (2), respectively. gn , hn , un , vn , xn , yn ∈ Γ, ζ(n), η(n) ∈ E and H = |L|3 · V . The element of Pan (t) is pain jn (t), denoting the probability that the state of Rn changes from in to jn under action a, where in , jn ∈ In . B. System Reward In the stochastic bandit problem, the optimization objective is expressed as the system reward. Since the goal is to maximize application layer QoS (i.e., minimize distortion), increase spectral efficiency and maximize the average network lifetime, we define the immediate reward of Rn as (t) Rainn(t) = an (t)R c1 D rth , p in (t), MCn (t) , ξ(t) ; c2 η in (t), MCn (t) ; c3 Jn PRn , L, CRn D ; c4 En (t) ,
(10)
where |c1 |+|c2 |+|c3 |+|c4 |=1, c1 and c3 are negative weights, c2 and c4 are positive weights. The first term D rth , p in (t), MCn (t) , ξ(t) represents the multimedia distortion, in which rth is the target bit rate, p in (t), MCn (t) is the packet loss ratio determined by channel state in (t) and the corresponding modulation-coding scheme (i.e., MCn (t)), and ξ(t) is the intra refreshing rate in time slot t. The second term η in (t), MCn (t) denotes the spectral efficiency for transmitting multimedia data packets from the source to destination, the expression of which is given by η=
k · ϕk 2 k∈K
(11)
where ϕk is the probability that 2k -QAM is used, i.e., ϕk = Pr[γk∗ ≤ ∗ ]. 12 is necessary due to the half-duplex min{¯γSRn , γ¯ SD + γ¯ Rn D } < γk+1 nature of DF relaying. Besides, the third term Jn PRn , L, CRn D is a energy consumption function of transmit power PRn , packet length L and data rate CRn D in link Rn -D. The immediate reward Rainn(t)(t) is earned when relay node Rn with state in (t) takes action an (t) in time slot t. For a stochastic process, a maximum immediate value is not equivalent to the maximum expected long-term accumulated value. Denote by u∗ ∈U and β (0< β
