Joint Source-Channel Optimization over Wireless Relay Networks

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Joint Source-Channel Optimization over Wireless Relay Networks Ubolthip Sethakaset, Member, IEEE, Tony Q.S. Quek, Member, IEEE, and Sumei Sun, Member, IEEE

Abstract—Cooperative communications have received considerable attention for wireless multimedia applications as a technique to improve reliability and service coverage. To apply such cooperation over slow fading channels, we consider exploiting the spatial diversity in multiple relay networks. In this paper, we focus on amplify-and-forward relaying schemes, namely, orthogonal amplify-and-forward, selective relaying, and distributed beamforming, for the cooperative wireless multimedia transmission. Furthermore, the successive refinement source coding is exploited such that the multimedia signal is encoded into multiple layers and the quality of its reconstruction at the receiver is improved when more layers are received correctly. We study two strategies for the layered source transmission, namely, progressive transmission and superposition coding. With our developed framework, we propose suboptimal resource allocation algorithms to efficiently assign rate, power, and channel uses to different layers so as to maximize the quality of the multimedia signal reconstructed at the receiver. The proposed optimization methodology is simple and only requires the knowledge of the channel statistics compared to the existing algorithms. As a result, the receiver only requires to feedback the determined rate, power, and channel uses to the transmitter whenever the channel statistics or the layered source transmission strategy changes. Index Terms—Cooperative communications, amplify-andforward, joint source-channel coding, progressive transmission, superposition coding, successive refinement.

R

I. I NTRODUCTION

ECENTLY, the demand on multimedia applications such as video streaming and IPTV (Internet Protocol Television) over wireless communications has dramatically increased [1]–[3]. However, the fluctuating wireless channel condition is worse than the wired link and a fixed multimedia base rate leads to an unacceptable low perceptive quality due to service outages. This undesirable effect of fading can be mitigated by diversity techniques such as antenna diversity and cooperative diversity. Unlike an antenna diversity system, which employs multiple antennas at the receiver and/or the transmitter, a cooperative diversity system utilizes multiple relays without requiring multiple antennas at each terminal [4]–[6]. Hence, cooperative diversity has received considerable attention even for multimedia applications as a technique to enable efficient and robust wireless multimedia transmissions [2]. With the cooperative diversity technique, not only the transmission reliability but also the quality of the multimedia signal reconstructed at the destination can be improved if the source Paper approved by Z. Xiong, the Editor for Distributed Coding and Processing of the IEEE Communications Society. Manuscript received October 8, 2009; revised June 26, 2010, September 15, 2010, and November 18, 2010. The authors are with the Institute for Infocomm Research, A∗ STAR, 1 Fusionopolis Way, #21-01 Connexis(South Tower), 138632 Singapore (e-mail: {usethakaset, qsquek, sunsm}@i2r.a-star.edu.sg). Digital Object Identifier 10.1109/TCOMM.2011.012711.090614

signal is encoded into multiple layers. In general, two common scalability techniques for layered multimedia codec known as multiple description coding (MDC) and successive refinement coding (SRC) are used. In MDC, the source signal is encoded into multiple descriptions at different source coding rates, where each description is decoded independently [7]. In this way, better quality can be achieved when more descriptions are received correctly. On the other hand, with SRC, the source signal is encoded into multiple layers at different source coding rates, i.e., base and several enhancement layers [8]. At the receiver, an enhancement layer is decoded and successively refines the description in the previous enhancement or base layers as long as the previous layers are received correctly. In general, SRC has higher compression efficiency than MDC, i.e., it has better quality of the reconstructed source signal compared to MDC at the same coding rate [9]. Furthermore, the SRC was adopted in multimedia standards such as JPEG2000[10] and H.264/SVC [11]. Therefore, this paper focuses on the transmission of SRC-encoded layered source signals. Under the assumption that the channel state information (CSI) is available at the receiver but not at the transmitter, the layered source transmission over a slow fading channel has been extensively studied for different system models where the performance is measured in terms of expected distortion [8], [12]–[14]. Closely related to our work are [15]–[17], where the authors proposed cooperative source and channel coding for a three-node relay network with both amplify-and-forward (AF) and decode-and-forward (DF) protocols. Its extension to multiple relay networks with however only DF protocol was studied in [18]. In this paper, we propose a framework of cooperative wireless multimedia transmission in a relay network with multiple AF relays. The benefit of the multiple relay networks is to exploit its spatial diversity to increase the coverage range and to enhance the quality of received source signal. Considering the stringent latency requirement in most multimedia application, we focus on AF relaying schemes. We assume that perfect instantaneous backward and forward CSI is not available at the source node, but only at the destination node. Depending on the type of CSI available at the relays, we consider orthogonal amplify-and-forward (OAF), selective relaying (SEL), and distributed beamforming (DBF) for the relay transmissions. Furthermore, we employ the successive refinement coding for the source codec. As we showed in [19], [20], the significant layering gain can be achieved when the source is encoded into two layers and it decreases when the number of

c 2011 IEEE 0090-6778/11$25.00 ⃝

SETHAKASET et al.: JOINT SOURCE-CHANNEL OPTIMIZATION OVER WIRELESS RELAY NETWORKS

r1 h1

r2

f2

h2 s

h3

hM

f1

r3 .. . .. . .. .

backward link

f3

d

fM

forward link rM

Fig. 1.

Multiple relay networks.

layers increases further; eventually becomes marginal as the number of layers tends to infinity. Moreover, large number of layers can cause high computational complexity at the codec. Therefore, in this paper, we consider only the two-layer case, i.e., a base layer and an enhancement layer. Then, these two layers are transmitted at different rates and channel uses if progressive transmission strategy is used; if superposition coding strategy is used, they are transmitted with different power and rates. With our developed framework, we propose suboptimal resource allocation algorithms to efficiently assign rate, power, and channel uses to different layers so as to maximize the quality of the reconstructed multimedia. The proposed optimization methodology is simple and only requires knowledge of the channel statistics to compute the parameters. Numerical results verify the effectiveness of our proposed optimization algorithms and show that their performances are comparable to those proposed in [8], [13], [14], while requiring a much lower computational complexity. The paper is organized as follows: Section II introduces the system model and the relaying schemes. Section III describes the layered source transmission strategies and presents their associated distortion exponent with various cooperative relaying schemes. The proposed resource allocation algorithms are described in Section IV. Numerical results are provided in Section V. Finally, the conclusion is given in Section VI. II. M ULTIPLE -R ELAY N ETWORKS The multiple relay networks comprise of 𝑀 + 2 singleantenna nodes, i.e., one source (s), one destination (d), and 𝑀 AF half-duplex relay nodes (r). The relay nodes are used to assist in transmitting the layered source information from the source node to the destination node as illustrated in Fig. 1. We denote the channel gain vectors of the backward link (from the source node to the relay nodes) as h = [ℎ1 , ℎ2 , . . . , ℎ𝑀 ]𝑇 and the forward link (from the relay nodes to the destination node) as f = [𝑓1 , 𝑓2 , . . . , 𝑓𝑀 ]𝑇 , where ℎ𝑚 and 𝑓𝑚 are i.i.d. zero-mean complex circularly symmetric Gaussian distribution with variance 𝜎ℎ2 𝑚 and 𝜎𝑓2𝑚 , respectively. We assume a block fading channel where the channel fading coefficients remain constant within 𝐿 channel uses.

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Under the assumption that the direct link between source and destination nodes is unavailable, the signal transmission from the source to the destination nodes is implemented with a two-phase protocol where the first phase requires only one time slot while one or more time slots are used in the second phase depending on the adopted AF scheme. In the first phase, the source node broadcasts the transmitted signal 𝑥s ∈ ℂ where 𝔼(𝑥s ) = 1 to all relay nodes under total transmit power constraint 𝐸s . Thus, the received signal at the 𝑚th relay node can be written as √ 𝑦𝑚 = ℎ𝑚 𝐸s 𝑥s + 𝑣𝑚 , (1) where 𝑣𝑚 ∼ 𝒞𝒩 (0, 1) denotes the additive white Gaussian noise (AWGN) at the 𝑚th relay node. For AF relaying protocol, the relay nodes simply transmit scaled versions of their received signals while ∑ satisfying the total relay transmit power constraint 𝐸r , i.e., 𝑀 𝑚=1 𝐸𝑚 ≤ 𝐸r where 𝐸𝑚 is the transmit power at the 𝑚th relay node. Let 𝑔𝑚 denote the scaling factor at the 𝑚th relay node. The transmitted signal from the 𝑚th relay to the destination node is given as 𝑥𝑚 = 𝑔𝑚 𝑦𝑚 .

(2)

After processing the received signals, the relay nodes transmit the processed signal to the destination node in the subsequent time slots while the source node remains silent. In the following, we consider three different AF relaying schemes depending on the CSI knowledge available at the relay nodes where perfect synchronization among the relay nodes is assumed. A. Orthogonal Amplify-and-Forward First, we consider the OAF scheme where the relay nodes transmit their own scaled signals to the destination node at different time slots [21]. As a result, the total number of time slots needed to transmit the source signal from the source node to the destination node is 𝑀 + 1. The received signal at the destination node from the 𝑚th relay can be written as √ (3) 𝑦d = 𝑓𝑚 𝑔𝑚 ℎ𝑚 𝐸s 𝑥s + 𝑓𝑚 𝑔𝑚 𝑣𝑚 + 𝑤, where 𝑤 ∼ 𝒞𝒩 (0, 1) denotes the additive noise at the destination node and the scaling factor at the 𝑚th relay is given by √ 𝐸𝑚 . (4) 𝑔𝑚 = 𝐸s ∣ℎ𝑚 ∣2 + 1 To minimize the outage probability, the optimal relay power allocation is obtained by using a water-filling solution and thus the transmit power at the 𝑚th relay is given by [21] [ √ ] 𝐸s2 ∣ℎ𝑚 ∣4 + 𝐸s ∣ℎ𝑚 ∣2 𝐸s ∣ℎ𝑚 ∣2 + 1 𝐸𝑚 = max 0, 𝜆− (5) ∣𝑓𝑚 ∣2 ∣𝑓𝑚 ∣2 ∑𝑀 where 𝜆 is chosen such that 𝑚=1 𝐸𝑚 = 𝐸r . To compute the scaling factor in (4), each relay node thus requires the knowledge of its own backward and forward CSI.

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B. Distributed beamforming

Es

In the DBF scheme, all relay nodes simultaneously transmit their own scaled signals to the destination node in the second time slot with the scaling factor [22], [23] √ 𝑔𝑚 =

∗ ℎ∗𝑚 𝑓𝑚 𝐸𝑚 , 2 𝐸s ∣ℎ𝑚 ∣ + 1 ∣ℎ𝑚 ∣ ∣𝑓𝑚 ∣

𝐸𝑟 𝑐

(

∣ℎ𝑚 𝑓𝑚 ∣2 (1 + ∣ℎ𝑚 ∣2 𝐸s ) (∣ℎ𝑚 ∣2 𝐸s + ∣𝑓𝑚 ∣2 𝐸r + 1)2

(1 − α)L

(a) Progressive transmission (PT)

(6) αEs

RB

(1 − α)Es

RE

) ,

L

(7)

(b) Superposition coding (SC)

where

Fig. 2.

𝑐=

RE

αL

and thus only two time slots are required per transmission frame. From [22], the optimal relay power allocation that minimizes the outage probability is given by 𝐸𝑚 =

RB

𝑀 ∑

∣ℎ𝑚 𝑓𝑚 ∣2 (1 + ∣ℎ𝑚 ∣2 𝐸s ) . (∣ℎ𝑚 ∣2 𝐸s + ∣𝑓𝑚 ∣2 𝐸r + 1)2 𝑚=1

(8)

In (7), the term in the parenthesis is a function of the local bidirectional CSI, whereas the constant 𝑐 is the same for all relay nodes. Therefore, with their local bidirectional CSI knowledge, relay nodes can calculate their own transmit power when the constant 𝑐 is broadcasted from the destination node. Let G be the 𝑀 × 𝑀 diagonal matrix representing relay gains and v = [𝑣1 , 𝑣2 , . . . , 𝑣𝑚 ]𝑇 be the noise vector at the relay nodes. The received signal at the destination node can be written as √ (9) 𝑦d = f 𝑇 Gh 𝐸s 𝑥s + f 𝑇 Gv + 𝑤.

Expected distortion for different cooperation schemes.

III. L AYERED S OURCE T RANSMISSION S TRATEGIES The quality of the received multimedia signal at the destination node is commonly measured by the mean squarederror distortion between the original multimedia signal vector s = [𝑠1 , 𝑠2 , . . . , 𝑠𝐾 ]𝑇 ∈ ℂ𝐾 and its reconstruction ˆs = [ˆ 𝑠1 , 𝑠ˆ1 , . . . , 𝑠ˆ𝐾 ]𝑇 ∈ ℂ𝐾 , which is given by 𝐾 1 ∑ 𝒟(s, ˆs) = (𝑠𝑘 − 𝑠ˆ𝑘 )2 , 𝐾

where 𝐾 is the source block length. Let each source sample be encoded into 𝑅𝑠 bits, the distortion-rate function can be simply modeled as [26]–[28] 𝐷(𝑅𝑠 ) = 𝑐1 2−𝑐2 𝑅𝑠 ,

C. Selective relaying Unlike OAF and DBF schemes, only one relay node is selected to actively forward the source signal to the destination in the SEL scheme and thus the transmission occurs only within two time slots [21]. Therefore, the scaling factors at the relay nodes are given by {√ 𝐸r 𝑚=𝑚 ˆ 𝐸s ∣ℎ𝑚 ∣2 +1 , (10) 𝑔𝑚 = 0, otherwise, where 𝑚 ˆ denotes the selected relay node and the received signal at the destination node can be written as 𝑦d = 𝑓 𝑚 ˆ 𝑔𝑚 ˆ ℎ𝑚 ˆ

√ 𝐸s 𝑥s + 𝑓𝑚 ˆ 𝑔𝑚 ˆ 𝑣𝑚 ˆ + 𝑤.

(11)

Depending on the overhead and implementation constraints, we can adopt different selective criteria [21], [24], [25]. For simplicity, we assume that the destination node selects the relay node based on the highest product of backward and forward link channel gain, i.e., ∣ℎ𝑚 𝑓𝑚 ∣2 , and broadcasts the chosen relay index to all relay nodes. This SEL scheme requires only backward CSI availability at the selected relay node and thus it requires less computational complexity than the OAF and DBF schemes.

(12)

𝑘=1

(13)

where 𝑐1 and 𝑐2 are constants and depend on the distribution of the source samples. The delay constraint is imposed such that a sequence of 𝐾 source samples are to be transmitted within a fading block corresponding to 𝐿 channel uses. As a result, the channel code rate equals to 𝑅𝑠 /𝑏 bits per channel use where 𝑏 is a bandwidth expansion ratio, defined as [ ] 𝐿 channel uses 𝑏= . (14) 𝐾 source symbol sample As in [16], we assume that 𝐿 and 𝐾 are sufficiently large to approach the instantaneous capacity and Gaussian ratedistortion bound. Note that the bandwidth expansion factor is limited, especially for the real-time multimedia streaming where the delay constraint is strict. Adopting a layering transmission approach, the source sequence is encoded into two layers, i.e., base and enhancement layers [8]. In the following, we consider two different layered source transmission strategies, i.e., progressive transmission (PT) and superposition coding (SC), together with the cooperative relaying schemes discussed in the previous section. To obtain sufficient insight into the design of the cooperative joint source-channel coding schemes, we assume that the source signal is a memoryless, zero mean, unit variance complex Gaussian source and thus we have 𝑐1 = 𝑐2 = 1 in (13) so as to make the analysis tractable as in [15]–[18].

SETHAKASET et al.: JOINT SOURCE-CHANNEL OPTIMIZATION OVER WIRELESS RELAY NETWORKS

TABLE I C ONSTANTS 𝜇 AND 𝜂 IN (15) FOR PT AND (22)-(23) FOR SC. Cooperative scheme OAF SEL DBF

𝜇 ( ) −2 + 𝜎𝑓−2 𝜎 𝑚=1 ℎ 𝑚 𝑚 ) ∏𝑀 ( −2 −2 𝑚=1 𝜎ℎ𝑚 + 𝜎𝑓𝑚 ( ) ∏ −2 −2 𝑀 −𝑀/2 𝑀 𝑚=1 𝜎ℎ𝑚 + 𝜎𝑓𝑚 ∏𝑀

(16) can be rewritten as

𝑀 +1 2 2

As shown in Fig. 2(a), the source node transmits the layered source information within 𝐿 channel uses, where the symbols associated with the base layer are transmitted within the first 𝛼𝐿 channel uses at rate 𝑅B and the rest of channel uses is for transmitting the enhancement layer at rate 𝑅E where 𝛼 ∈ (0, 1]. At the destination node, the source signals are reconstructed by first decoding the base layer followed by the enhancement layer from the associated channel uses. Therefore, the probabilities of correctly decoding only the base layer and both layers are (𝑃𝑅E − 𝑃𝑅B ) and (1 − 𝑃𝑅E ), where 𝑃𝑅B and 𝑃𝑅E denote the outage probabilities associated with the base and enhancement layers, respectively. In the following, we provide a lemma that approximates 𝑃𝑅B and 𝑃𝑅E in the high SNR regime. Lemma 1: When PT is adopted, the outage probabilities associated with the base and enhancement layers at high SNR can be approximated as ( 𝜂𝑅 )𝑀 2 −1 , (15) 𝑃𝑅 ≈ 𝜇 SNR

where 𝑅 = 𝑅B and 𝑅 = 𝑅E , respectively, SNR = 𝐸s = 𝐸r is the transmit SNR and the constants 𝜇 and 𝜂 depend on the adopted cooperative relaying scheme as shown in Table I. Proof: See Appendix A. When both layers are not successfully decoded, the receiver simply outputs the average value of the source distribution and thus the distortion in this case is the variance of the Gaussian source samples, i.e., 𝑐1 = 1. Therefore, the overall expected distortion for PT can be written as [8] (16)

Our objective is to determine the rate and channel allocation such that the overall expected distortion in (16) is minimized. Since the enhancement layer will be useless once the base layer is in outage, the constraint 𝑅B < 𝑅E is introduced and the optimization problem can be cast as min

ℰD (𝛼, 𝑅B , 𝑅E )

s.t.

0 ≤ 𝛼 ≤ 1, 𝑅B ≤ 𝑅E .

𝛼,𝑅B ,𝑅E

(17)

In the high-SNR regime, the expected distortion decays as

SNR−Δ , where Δ is the distortion exponent and is defined as

[12]

Δ=−

log ℰD . SNR→∞ log SNR lim

ℰD = SNR−(𝛼𝑏𝑟𝐵 +(1−𝛼)𝑏𝑟𝐸 ) + SNR𝑀(𝜂𝑟𝐸 −1)−𝛼𝑏𝑟𝐵 +SNR𝑀(𝜂𝑟𝐵 −1) . (19)

𝜂

A. Progressive transmission

ℰD = (1 − 𝑃𝑅E )𝐷(𝑏(𝛼𝑅B + (1 − 𝛼)𝑅E )) +(𝑃𝑅E − 𝑃𝑅B )𝐷(𝑏𝛼𝑅B ) + 𝑐1 𝑃𝑅B .

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The optimal distortion exponent can be obtained by setting all three exponents to be equal [8]. Therefore, the optimal distortion exponent for PT is given by ( ( )2 ) 𝜂𝑀 PT Δ =𝑀 1− . (20) 𝜂𝑀 + 𝑏/2 B. Superposition coding When SC is exploited, the base and enhancement layers are transmitted at rate 𝑅B and 𝑅E , respectively, simultaneously over the whole transmission block by superimposing enhancement layer on top of the base layer as illustrated in Fig. 2(b) [8]. The transmit power 𝛼𝐸s and (1 − 𝛼)𝐸s denote the power levels allocated to the base and enhancement layers, respectively, where 𝛼 ∈ (0, 1]. At the destination node, the successive decoding is performed with perfect knowledge of CSI. The decoding order is fixed such that the destination node will always decode the base layer first by taking the enhancement layer as noise. After that, the enhancement layer is decoded by first removing the base layer from the received signal. The overall expected distortion is given by [8] ℰD = (1 − 𝑃𝑅E )𝐷(𝑏(𝑅B + 𝑅E )) +(𝑃𝑅E − 𝑃𝑅B )𝐷(𝑏𝑅B ) + 𝑐1 𝑃𝑅B .

Similar to PT, we approximate the outage probabilities 𝑃𝑅B and 𝑃𝑅E in the high SNR regime using the following lemma. Lemma 2: When SC is adopted, the outage probabilities associated with the base and enhancement layers at high SNR can be approximated as ( )𝑀 2𝜂𝑅B − 1 , (22) 𝑃𝑅B ≈ 𝜇 [𝛼 − (1 − 𝛼)(2𝜂𝑅B − 1)]SNR and

( 𝑃𝑅E ≈ 𝜇

By letting the base layer and enhancement layer rates scale as 𝑅B = 𝑟𝐵 log2 (SNR) and 𝑅E = 𝑟𝐸 log2 (SNR), respectively,

2𝜂𝑅E − 1 (1 − 𝛼)SNR

)𝑀 ,

(23)

respectively. Proof: Since the base layer is decoded by treating the enhancement layer as noise, Γ𝑚 in (32) is now equal to 𝛼𝐸s 𝐸r ∣ℎ𝑚 𝑓𝑚 ∣2 1+𝐸s ∣ℎ𝑚 ∣2 +𝐸r ∣𝑓𝑚 ∣2 +(1−𝛼)𝐸s 𝐸r ∣ℎ𝑚 𝑓𝑚 ∣2 . Following the proof in Appendix A, we obtain the desired result in (22). With the similar approach, it is easy to proof (23) where now (1−𝛼)𝐸s 𝐸r ∣ℎ𝑚 𝑓𝑚 ∣2 Γ𝑚 = 1+𝐸 2 2. s ∣ℎ𝑚 ∣ +𝐸r ∣𝑓𝑚 ∣ To minimize the expected distortion in (21), we need to determine the rate and power allocation for the two layers. Since the enhancement layer will be in outage if the base layer is in outage, the constraint 𝑃𝑅B ≤ 𝑃𝑅E is introduced and the optimization problem can be cast as min

ℰD (𝛼, 𝑅B , 𝑅E )

s.t.

0 ≤ 𝛼 ≤ 1, 0 ≤ 𝑃𝑅B ≤ 𝑃𝑅E ≤ 1.

𝛼,𝑅B ,𝑅E

(18)

(21)

(24)

In high SNR regime, we let the base layer and enhancement layer rates scale as 𝑅B = 𝑟𝐵 log2 (SNR) and 𝑅E =

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SIMO is upperbounded by the smaller number between the diversity order and the bandwidth expansion ratio [12], we can see that the distortion exponent ΔPT and ΔSC are also upperbounded by the diversity order 𝑀 when 𝑏 → ∞.

4

Distortion exponent (Δ)

DBF/SEL 3

IV. O PTIMIZATION F RAMEWORK 2 OAF 1

1 layer PT (2 layers) SC (2 layers) upperbound

No Cooperation 0 0

Fig. 3.

5

10 15 20 Bandwidth expansion ratio (b)

25

30

Distortion exponent versus bandwidth expansion ratio.

𝑟𝐸 log2 (SNR), respectively. Since the probability value cannot be negative, the denominator in (22) must be positive, i.e., 𝛼 − (1 − 𝛼)(2𝜂𝑅B − 1) > 0. Then, we have 1 − 𝛼 < 2−𝜂𝑅B and thus the expected distortion in (21) can be rewritten as ℰD = SNR−𝑏(𝑟𝐵 +𝑟𝐸 ) + SNR𝑀(𝜂𝑟𝐵 +𝜂𝑟𝐸 −1)−𝑏𝑟𝐵 +SNR𝑀(𝜂𝑟𝐵 −1) .

(25)

Similar to PT, we set all three exponents to be equal in (25) and the optimal distortion exponent for SC can be obtained as ⎞ ⎛ ⎜ ΔSC = 𝑀 ⎝1 −

1 1+

𝑏 𝜂𝑀

+

(

𝑏 𝜂𝑀

⎟ )2 ⎠ .

(26)

C. Distortion-exponent comparison For any bandwidth expansion ratio 𝑏, the distortion exponents for the PT and SC with various cooperative relaying schemes are plotted in Fig. 3. At low 𝑏, SC achieves slightly better performance than PT which has the same distortion exponent as if without layering.1 As 𝑏 increases, the gains of using the layering strategies significantly increase especially for the SC strategy. We can see that the distortion exponent of OAF increases slower than those of SEL and DBF as 𝑏 increases and the cooperation schemes offer higher distortion exponent than no cooperation only when 𝑏 ≥ 𝑀 +1 for OAF and 𝑏 ≥ 2 for SEL and DBF schemes. In other words, they achieve a significant improvement on the quality of the source signal reconstructed at the destination node compared to the no cooperation if the delay constraint is not too stringent. Otherwise, no cooperation outperforms the cooperation schemes since the transmit rate has more influence on the quality of the reconstructed signal than the transmission reliability. According to the Cut-Set Theorem in [26] where the relay and destination nodes are combined as a virtual antenna array destination node, the network functions as if it were a singleinput multiple-output (SIMO). As the distortion exponent of 1 In case of without layering, the source signal is encoded by using single coding rate.

The optimization problems in (17) and (24) are non-convex and hence generally difficult to solve. As a result, a basic approach for finding the rate, power, and channel allocation so as to minimize the expected distortion is an exhaustive search over all possible values [8]. In this case, its complexity is 𝒪(∣𝒜∣∣ℛ∣2 ) where 𝒜 = [0, 𝛿𝒜 , 2𝛿𝒜 , . . . , 1] and ℛ = [ℛmin , ℛmin + 𝛿ℛ , ℛmin + 2𝛿ℛ , . . . , ℛmax ] are the set of possible 𝛼, 𝑅B , and 𝑅E , respectively, such that 𝛿𝒜 and 𝛿ℛ are fixed step size and ∣𝒳 ∣ denotes the cardinality of set 𝒳 . To reduce the complexity, two iterative algorithms were proposed in [13] and [14] for the PT and SC strategies, respectively. In the case of PT, the rate search over the 2-dimensional grid search is replaced with 2 single-dimensional searches and the 𝛼 in (16) can be calculated from a closed-form function for given 𝑅B and 𝑅E [13]. Then, the combination of the rate allocation in [13] and a binary search for a Lagrange multiplier 𝜆 ∈ (0, 𝜆max ) to obtain the power allocation was proposed in [14] for the SC strategy. Thus, the complexity can be reduced to 𝒪(2∣ℛ∣) for PT and 𝒪(2∣ℛ∣ log(𝜆max /𝜖)) for SC, where 𝜖 is the desired accuracy of the 𝜆. In this section, we propose two algorithms that can further reduce the computational complexity at the destination node to 𝒪(∣ℛ∣) for both transmission strategies. The main idea is to preset the outage probability of the enhancement layer at a certain value 𝛾𝑡ℎ and then determine the rate, power, and channel allocation based on this value.2 The performance of our proposed algorithms is however close to that of exhaustive search as demonstrated by numerical results in the next Section. A. Progressive transmission For the PT strategy, the enhancement layer rate that satisfies the outage probability 𝛾𝑡ℎ can be calculated from the inverse function of (15) as follows: ] [( ) 1/𝑀 𝛾th 1 +1 . (27) 𝑅E = log2 𝜂 𝜇 For given 𝑅B and 𝑅E , we can determine the 𝛼 such that the expected distortion in (16) is minimized from a closed-form expression given by [13] 𝛼=1−

(1 − 𝑃𝑅E )(𝑅E − 𝑅B ) 1 log2 . 𝑏𝑐2 𝑅E (𝑃𝑅E − 𝑃𝑅B )𝑅B

(28)

Our algorithm is summarized in Algorithm 1. The process starts by setting 𝑅B = ℛmin and repeats by increasing base layer rate to 𝑅B + 𝛿ℛ until 𝑅B = ℛmax . Due to the constraint on the rate allocation such that 𝑅B ≤ 𝑅E , the 𝑅E is set equal to 𝑅B if 𝑅E calculated from (27) is less than the given 𝑅B . ∗ ∗ The 𝑅B , 𝑅E , and 𝛼∗ which minimizes the expected distortion in (16) are attained. 2 Note that the value 𝛾 𝑡ℎ depends on the transmitted multimedia content and the transmission strategy.

SETHAKASET et al.: JOINT SOURCE-CHANNEL OPTIMIZATION OVER WIRELESS RELAY NETWORKS

(1−𝑃

)(𝑅 −𝑅 )

𝛼 = 1 − 𝑏𝑐21𝑅E log2 (𝑃𝑅𝑅E−𝑃𝑅E )𝑅BB E B Calculate ℰD from (16) ∗ then if ℰD < ℰD ∗ ∗ ∗ ℰD = ℰD , 𝛼∗ = 𝛼, 𝑅B = 𝑅B , and 𝑅E = 𝑅E end if 𝑅B = 𝑅B + 𝛿𝑅 end while

0

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Algorithm 1 Resource allocation algorithm for PT ∗ initial ℰD = 𝑐1 and 𝑅B = 𝑅min while 𝑅B ≤ 𝑅max { do ]} [( ) 1/𝑀 𝑅E = max 𝑅B , 𝜂1 log2 𝛾𝜇th +1

For the SC strategy, the outage probability of the enhancement layer depends on both its setting rate and allocated power. By giving an arbitrary 𝑅E and the outage probability 𝛾𝑡ℎ , the power allocated to the base layer can be calculated from the inverse function of (23) as follows: ( 𝜂𝑅E ) ( )1/𝑀 2 𝜇 −1 𝛼=1− . (29) SNR 𝛾th However, this may result that most of the power is allocated to the enhancement layer and then 𝑃𝑅E ≤ 𝑃𝑅B which violates the constraint in (24). To prevent this event, we apply the (𝑅E , 𝛾𝑡ℎ )), where 𝛼 ˆ is constraint 𝛼 ≥ 𝛼 ˆ , i.e., 𝛼 = max(ˆ 𝛼, 𝑃𝑅−1 E the minimum power level for base layer such that 𝑃𝑅B ≤ 𝑃𝑅E . Given 𝑅E and 𝛼, we can then determine the rate 𝑅B that minimizes ℰD in (21) by solving the following equation: { } 𝑅B = arg min (1 − 2−𝑏𝑐2 𝑅B )𝑃𝑅B + 𝑡2−𝑏𝑐2 𝑅B , (30) 𝑅B

where 𝑡 = (1 − 2−𝑏𝑐2𝑅E )𝑃𝑅E + 2−𝑏𝑐2 𝑅E . Due to its convexity, the rate 𝑅B can be easily obtained by a convex optimization method with much less computational complexity than exhaustive search. Similarly, we have summarized our algorithm in Algorithm 2 where the process starts by setting 𝑅E = ℛmin and repeats by increasing enhancement layer rate to 𝑅E + 𝛿ℛ ∗ ∗ until 𝑅E = ℛmax . The 𝑅B , 𝑅E , and 𝛼∗ which minimizes the expected distortion ℰD in (21) are obtained. V. N UMERICAL R ESULTS We consider 𝑀 = 4 relay nodes randomly located between the source and destination nodes. The distance between

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Algorithm 2 Resource allocation algorithm for SC ∗ initial ℰD = 𝑐1 and 𝑅E = 𝑅min while 𝑅E ≤ 𝑅 {max do ( ) ( )1/𝑀 } 𝜇 2𝜂𝑅E −1 𝛼 = max 𝛼, ˆ 1− SNR 𝛾th 𝑅B is the solution of (30). Calculate ℰD from (21) ∗ then if ℰD < ℰD ∗ ∗ ∗ ℰD = ℰD , 𝛼∗ = 𝛼, 𝑅B = 𝑅B , and 𝑅E = 𝑅E end if 𝑅E = 𝑅E + 𝛿𝑅 end while

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the source and destination nodes is normalized to one. The backward and forward links are distributed according to 𝒞𝒩 (0, 𝑑1𝜈 ), where 𝑑 is the distance between two nodes and 𝜈 = 2.5 is the path-loss exponent. 1) Gaussian sequence: Let assume that the source samples are complex Gaussian variable with zero-mean and unitvariance. Therefore, 𝑐1 and 𝑐2 in (13) are equal to one. In this case, we show the achieved expected distortion for different cooperative relaying schemes in Fig. 4, where the rate, power, and channel allocations are obtained by exhaustive search. These figures show that the expected distortion decays at the exponential rate as calculated from (20) and (26) in the high SNR regime. Due to lower distortion exponent, all cooperative relaying schemes are expected to perform worse than the no cooperation when 𝑏 = 1. However, this applies only in the high SNR regime but not in the finite SNR regime. Our result shows that SEL and DBF still perform better and can yield up to 3-7 dB gain compared to no cooperation for the SNR range shown in Fig. 4(a). When 𝑏 = 2, the quality of the reconstructed signal can be greatly enhanced when SEL or DBF is adopted and up to 10 dB gain can be achieved compared to no cooperation as shown in Fig. 4(b). From these

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IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 59, NO. 4, APRIL 2011

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Fig. 5. Expected distortion for the transmission of a Gaussian source sequence.

Fig. 6. Expected PSNR for the transmission of the ‘Akiyo’ video sequence.

expected peak signal-to-noise ratio (PSNR), defined as figures, we can conclude that SEL is the most preferable since it achieves comparable performance to DBF but requires much less computational complexities at the relay and destination nodes. Furthermore, we compare the performance of our proposed resource allocation algorithms with the exhaustive search when the SEL relaying scheme is adopted in Fig. 5 for 𝑏 = 2 and 𝑏 = 5.3 Clearly, we can see that our proposed algorithms are comparable to the exhaustive search while requiring much lower computational complexity. 2) Video sequence: We also verify the effectiveness of our proposed algorithms when the transmitted source is a video sequence. Let ‘Akiyo’ video sequence encoded by the MPEG4 FGS codec be the transmitted source sequence and the channel bandwidth be 1 MHz. In this case, the parameters 𝑐1 and 𝑐2 in (13) are 70 and 4, respectively [27]. In general, the common measure used to evaluate the quality of the video signal is

3 Note

that 𝛼 ˆ in Algorithm 2 is set to 0.7.

PSNR = 10 log10

(2B − 1)2 , ℰD

(31)

where B is the number of bits per pixel. The performance of our algorithms for the video transmission is therefore examined in terms of expected PSNR as shown in Fig. 6. Again, we can see that they can achieve nearly same performance as the exhaustive search and the layering provides better performance, especially when PSNR is greater than 40 dB which is the practical range for high quality medical video applications. Moreover, due to the source-channel rate optimization, the expected PSNR can be linearly increased as SNR (in dB) increases in the high-SNR regime. VI. C ONCLUSIONS A framework of the wireless layered multimedia transmission over multiple relay networks with delay constraint has been proposed to increase the coverage range and to enhance the quality of its reconstruction at the destination node. We proposed to use amplify-and-forward cooperation for relaying

SETHAKASET et al.: JOINT SOURCE-CHANNEL OPTIMIZATION OVER WIRELESS RELAY NETWORKS

and the expected-distortion performances of various AF relaying schemes with progressive transmission and superposition coding have been investigated. Low complexity resource allocation algorithms have been proposed in order to minimize the overall expected distortion. The numerical results showed that our proposed algorithms perform comparably to those in the literature while requiring much lower computational complexity. Among the studied relaying schemes, the selective relaying scheme achieves good performance with very low computational complexity at the relay and destination nodes, hence the most favorable for practical adoption. Our proposed framework can be applied to any future wireless systems incorporated with relays for transmission of multiple classes of layered signals, e.g., LTE-Advanced or 4G systems providing IPTV services and multimedia broadcast multicast services (MBMS).

First, we consider the SEL scheme where the transmission occurs over two time slots and the total relay power is allocated to the relay node which results the largest mutual information. Thus, its outage probability at transmit rate 𝑅 is given by } { [ ] 1 SEL−PT log2 1 + max Γ𝑚 < 𝑅 =ℙ 𝑃𝑅 𝑚 2 { } 𝑀 ∏ 𝐸r ∣ℎ𝑚 𝑓𝑚 ∣2 = ℙ